Ee2203 electronic-devices-and-circuits-lecture-notes

Einstein College of Engineering
UNIT I
PN DIODE AND ITS APPLICATIONS
INTRODUCTION
The current-voltage characteristics is of prime concern in the study of semiconductor devices
with light entering as a third variable in optoelectronics devices.The external characteristics of
the device is determined by the interplay of the following internal variables:
1. Electron and hole currents
2. Potential
3. Electron and hole density
4. Doping
5. Temperature
Semiconductor equations
The semiconductor equations relating these variables are given below:
Carrier density:
where is the electron quasi Fermi level and is the hole quasi Fermi level. These two
equations lead to
In equilibrium = = Constant
Current:
There are two components of current; electron current density and hole current density .
There are several mechanisms of current flow:
(i) Drift
(ii) Diffusion
(iii) thermionic emission
(iv) tunneling
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The last two mechanisms are important often only at the interface of two different materials such
as a metal-semiconductor junction or a semiconductor-semiconductor junction where the two
semiconductors are of different materials. Tunneling is also important in the case of PN junctions
where both sides are heavily doped.
In the bulk of semiconductor , the dominant conduction mechanisms involve drift and diffusion.
The current densities due to these two mechanisms can be written as
where are electron and hole mobilities respectively and are their diffusion
constants.
Potential:
The potential and electric field within a semiconductor can be defined in the following ways:
All these definitions are equivalent and one or the other may be chosen on the basis of
convenience.The potential is related to the carrier densities by the Poisson equation: -
where the last two terms represent the ionized donor and acceptor density.
Continuity equations
These equations are basically particle conservation equations:

Where G and R represent carrier generation and recombination rates.Equations (1-8) will form
the basis of most of the device analysis that shall be discussed later on. These equations require
models for mobility and recombination along with models of contacts and boundaries.
Analysis Flow
Like most subjects, the analysis of semiconductor devices is also carried out by starting from
simpler problems and gradually progressing to more complex ones as described below:
(i) Analysis under zero excitation i.e. equilibrium.
(ii) Analysis under constant excitation: in other words dc or static characteristics.
(iii) Analysis under time varying excitation but with quasi-static approximation dynamic
characteristics.
(iv) Analysis under time varying excitation: non quasi-static dynamic characteristics.
Even though there is zero external current and voltage in equilibrium, the situation inside the
device is not so trivial. In general, voltages, charges and drift-diffusion current components at
any given point within the semiconductor may not be zero.

Equilibrium in semiconductors implies the following:
(i) steady state:
Where Z is any physical quantity such as charge, voltage electric field etc
(ii) no net electrical current and thermal currents:
Since current can be carried by both electrons and holes, equilibrium implies zero values for both
net electron current and net hole current. The drift and diffusion components of electron and hole
currents need not be zero.
(iii) Constant Fermi energy:
The only equations that are relevant (others being zero!) for analysis in equilibrium are:
Poisson Eq:
In equilibrium, there is only one independent variable out of the three variables :
If one of them is known, all the rest can be computed from the equations listed above. We shall
take this independent variable to be potential.
The analysis problem in equilibrium is therefore determination of potential or equivalently,
energy band diagram of the semiconductor device.
This is the reason why we begin discussions of all semiconductor devices with a sketch of its
energy band diagram in equilibrium.

Energy Band Diagram
This diagram in qualitative form is sketched by following the following procedure:
1. The semiconductor device is imagined to be formed by bringing together the various
distinct semiconductor layers, metals or insulators of which it is composed. The starting
point is therefore the energy band diagram of all the constituent layers.
2. The band diagram of the composite device is sketched using the fact that after
equilibrium, the Fermi energy is the same everywhere in the system. The equalization of
the Fermi energy is accompanied with transfer of electrons from regions of higher Fermi
energy to region of lower Fermi energy and viceversa for holes.
3. The redistribution of charges results in electric field and creation of potential barriers in
the system. These effects however are confined only close to the interface between the
layers. The regions which are far from the interface remain as they were before the
equilibrium
Analysis in equilibrium: Solution of Poisson‘s Equation with appropriate boundary conditions -
Non-equilibrium analysis:
 The electron and hole densities are no longer related together by the inverse relationship
of Eq. (5) but through complex relationships involving all three variables Y , , p
 The three variables are in general independent of each other in the sense that a knowledge
of two of them does not lead automatically to a knowledge of the third.
 The concept of Fermi energy is no longer valid but new quantities called the quasi-Fermi
levels are used and these are not in general constant.
 For static or dc analysis, the continuity equation becomes time independent so that only
ordinary differential equations need to be solved.
 For dynamic analysis however, the partial differential equations have to be solved
increasing the complexity of the analysis.
Analysis of Semiconductor Devices
There are two complementary ways of studying semiconductor devices:
(i) Through numerical simulation of the semiconductor equations.
(ii) Through analytical solution of semiconductor equations.
 There are a variety of techniques used for device simulation with some of them starting
from the drift diffusion formalism outlined earlier, while others take a more fundamental
approach starting from the Boltzmann transport equation instead.
 In general, the numerical approach gives highly accurate results but requires heavy
computational effort also.

 The output of device simulation in the form of numerical values for all internal variables
requires relatively larger effort to understand and extract important relationships among
the device characteristics.
The electrons in the valence band are not capable of gaining energy from external electric field
and hence do not contribute to the current. This band is never empty but may be partially or
completely with electrons. On the contrary in the conduction band, electrons are rarely present.
But it is possible for electrons to gain energy from external field and so the electrons in these
bands contribute to the electric current. The forbidden energy gap is devoid of any electrons and
this much energy is required by electrons to jump from valence band to the conduction band.
In other words, in the case of conductors and semiconductors, as the temperature increases, the
valence electrons in the valence energy move from the valence band to conductance band. As the
electron (negatively charged) jumps from valence band to conductance band, in the valence band
there is a left out deficiency of electron that is called Hole (positively charged).
Depending on the value of Egap, i.e., energy gap solids can be classified as metals (conductors),
insulators and semi conductors.
Semiconductors
 Conductivity in between those of metals and insulators.
 Conductivity can be varied over orders of magnitude by changes in temperature, optical
excitation, and impurity content (doping).
 Generally found in column IV and neighboring columns of the periodic table.
 Elemental semiconductors: Si, Ge.
 Compound semiconductors:
Binary :
GaAs, AlAs, GaP,
etc. (III-V).
ZnS, ZnTe, CdSe (II-
VI).
SiC, SiGe (IV
compounds).
 Ternary : GaAsP.
Quaternary : InGaAsP.
 Si widely used for rectifiers, transistors, and ICs.
 III-V compounds widely used in optoelectronic and high-speed applications.

Applications
 Integrated circuits (ICs) SSI, MSI, LSI, and VLSI.
 Fluorescent materials used in TV screens II-VI (ZnS).
 Light detectors InSb, CdSe, PbTe, HgCdTe.
 Infrared and nuclear radiation detectors Si and Ge.
 Gunn diode (microwave device) GaAs, InP.
 Semiconductor LEDs GaAs, GaP.
 Semiconductor LASERs GaAs, AlGaAs.
Energy Gap
 Distinguishing feature among metals, insulators, and semiconductors.
 Determines the absorption/emission spectra, the leakage current, and the intrinsic
conductivity.
 Unique value for each semiconductor (e.g. 1.12 eV for Si, 1.42 eV for GaAs) function of
temperature.
Impurities
 Can be added in precisely controlled amounts.
 Can change the electronic and optical properties.
 Used to vary conductivity over wide ranges.
 Can even change conduction process from conduction by negative charge carriers to
positive charge carriers and vice versa.
 Controlled addition of impurities doping.
Energy Bands and Charge Carriers in Semiconductors
Bonding Forces and Energy Bands in Solids
 Electrons are restricted to sets of discrete energy levels within atoms, with large gaps
among them where no energy state is available for the electron to occupy.
 Electrons in solids also are restricted to certain energies and are not allowed at other
energies.
 Difference in the solid, the electron has a range (or band) of available energies.
 The discrete energy levels of the isolated atom spread into bands of energies in the solid
because
i) in the solid, the wave functions of electrons in neighboring atoms overlap, thus, it
affects the potential energy term and the boundary conditions in the
equation, and different energies are obtained in the solution, and
ii) an electron is not necessarily localized at a particular atom.
 The influence of neighboring atoms on the energy levels of a particular atom can be
treated as a small perturbation, giving rise to shifting and splitting of energy states into
energy bands.

Bonding Forces in Solids
Ionic Bonding
 Example: NaCl.
 Na (Z = 11) gives up its outermost shell electron to Cl (Z=17) atom, thus the crystal is
made up of ions with the electronic structures of the inert atoms Ne and Ar.
 Note: the ions have net electric charges after the electron exchange ion has a net
positive charge, having lost an electron, and ion has a net negative charge, having
acquired an electron.
 Thus, an electrostatic attractive force is established, and the balance is reached when this
equals the net repulsive force.
 Note: all the electrons are tightly bound to the atom.
 Since there are no loosely bound electrons to participate in current flow NaCl is a good
insulator.
Metallic Bonding
 In metals, the outer shell is filled by no more than three electrons (loosely bound and
given up easily) great chemical activity and high electrical conductivity.
 Outer electron(s) contributed to the crystal as a whole solid made up of ions with
closed shells immersed in a sea of free electrons, which are free to move about the crystal
under the influence of an electric field.
 Coulomb attraction force between the ions and the electrons hold the lattice together.
Covalent Bonding
 Exhibited by the diamond lattice semiconductors.
 Each atom surrounded by four nearest neighbors, each having four electrons in the
outermost orbit.
 Each atom shares its valence electrons with its four nearest neighbors.
 Bonding forces arise from a quantum mechanical interaction between the shared
electrons.
 Both electrons belong to each bond, are indistinguishable, and have opposite spins.
 No free electrons available at 0 K, however, by thermal or optical excitation, electrons
can be excited out of a covalent bond and can participate in current conduction
important feature of semiconductors.
Mixed Bonding
 Shown by III-V compounds bonding partly ionic and partly covalent.
 Ionic character of bonding becomes more prominent as the constituent atoms move
further away in the periodic table, e.g., II-VI compounds.

Energy Bands
 As isolated atoms are brought together to form a solid, the electron wave functions begin
to overlap.
 Various interactions occur, and, at the proper interatomic spacing for the crystal, the
forces of attraction and repulsion find a balance.
 Due to Pauli exclusion principle, the discrete energy levels of individual atoms split into
bands belonging to the pair instead of to individual atoms.
 In a solid, due to large number of atoms, the split energy levels for essentially continuous
bands of energy.
Fig.2.1 Splitting of individual energy levels to energy bands as atoms are brought closer
together.
 Imaginary formation of a diamond crystal from isolated carbon atoms .
 Each atom has two 1s states, two 2s states, six 2p states, and higher states.
 For N atoms, the numbers of states are 2N, 2N, and 6N of type 1s, 2s, and 2p
respectively.
 With a reduction in the interatomic spacing, these energy levels split into bands, and the
2s and 2p bands merge into a single band having 8N available states.
 As the interatomic spacing approaches the equilibrium spacing of diamond crystal, this
band splits into two bands separated by an energy gap , where no allowed energy
states for electrons exist forbidden gap.
 The upper band (called the conduction band) and the lower band (called the valence
band) contain 4N states each.
 The lower 1s band is filled with 2N electrons, however, the 4N electrons residing in the
original n = 2 state will now occupy states either in the valence band or in the conduction
band.
 At 0 K, the electrons will occupy the lowest energy states available to them thus, the
4N states in the valence band will be completely filled, and the 4N states in the
conduction band will be completely empty.

Metals, Semiconductors, and Insulators
 For electrons to move under an applied electric field, there must be states available to
them.
 A completely filled band cannot contribute to current transport; neither can a completely
empty band.
 Thus, semiconductors at 0 K are perfect insulators.
 With thermal or optical excitation, some of these electrons can be excited from the
valence band to the conduction band, and then they can contribute to the current transport
process.
 At temperatures other than 0 K, the magnitude of the band gap separates an insulator
from a semiconductor, e.g., at 300 K, (diamond) = 5 eV (insulator), and (Silicon) =
1.12 eV (semiconductor).
 Number of electrons available for conduction can be increased greatly in semiconductors
by reasonable amount of thermal or optical energy.
 In metals, the bands are either partially filled or they overlap thus, electrons and
empty states coexist great electrical conductivity.
Direct and Indirect Semiconductors
 In a typical quantitative calculation of band structures, the wave function of a single
electron traveling through a perfectly periodic lattice is assumed to be in the form of a
plane wave moving in the x-direction (say) with propagation constant k, also called a
wave vector.
 In quantum mechanics, the electron momentum can be given by
 The space dependent wave function for the electron is
(2.1)
where the function modulates the wave function according to the periodicity of the
lattice.
 Allowed values of energy, while plotted as a function of k, gives the E-k diagram.
 Since the periodicity of most lattices is different in various directions, the E-k diagram is
a complex surface, which is to be visualized in three dimensions.

Fig.2.2 Direct and indirect transition of electrons from the conduction band to the valence band:
(a) direct - with accompanying photon emission, (b) indirect via defect level.
 Direct band gap semiconductor: the minima of the conduction band and the maxima of
the valence band occur at the same value of k an electron making the smallest energy
transition from the conduction band to the valence band can do so without a change in k
(and, the momentum).
 Indirect band gap semiconductor: the minima of the conduction band and the maxima of
the valence band occur for different values of k, thus, the smallest energy transition for an
electron requires a change in momentum.
 Electron falling from conduction band to an empty state in valence band
recombination.
 Recombination probability for direct band gap semiconductors is much higher than that
for indirect band gap semiconductors.
 Direct band gap semiconductors give up the energy released during this transition (= )
in the form of light used for optoelectronic applications (e.g., LEDs and LASERs).
 Recombination in indirect band gap semiconductors occurs through some defect states
within the band gap, and the energy is released in the form of heat given to the lattice.
Variation of Energy Bands with Alloy Composition
 The band structures of III-V ternary and quaternary compounds change as their
composition is varied.
 There are three valleys in the conduction band: (at k = 0), L, and X.
 In GaAs, the valley has the minimum energy (direct with = 1.43 eV) with very few
electrons residing in L and X valleys (except for high field excitations).
 In AlAs, the X valley has minimum energy (indirect with = 2.16 eV).

Fig.2.3 The E-k diagram of (a) GaAs and (b) AlAs, showing the three valleys (L, , and X) in
the conduction band.
Charge Carriers in Semiconductors
 In a metal, the atoms are imbedded in a "sea" of free electrons, and these electrons can
move as a group under the influence of an applied electric field.
 In semiconductors at 0 K, all states in the valence band are full, and all states in the
conduction band are empty.
 At T > 0 K, electrons get thermally excited from the valence band to the conduction band,
and contribute to the conduction process in the conduction band.
 The empty states left in the valence band can also contribute to current conduction.
 Also, introduction of impurities has an important effect on the availability of the charge
carriers.
 Considerable flexibility in controlling the electrical properties of semiconductors.
Electrons and Holes
 For T> 0 K, there would be some electrons in the otherwise empty conduction band, and
some empty states in the otherwise filled valence band.
 The empty states in the valence band are referred to as holes.
 If the conduction band electron and the valence band hole are created by thermal
excitation of a valence band electron to the conduction band, then they are called
electron-hole pair (EHP).

 After excitation to the conduction band, an electron is surrounded by a large number of
empty states, e.g., the equilibrium number of EHPs at 300 K in Si is , whereas
the Si atom density is .
 Thus, the electrons in the conduction band are free to move about via the many available
empty states.
 Corresponding problem of charge transport in the valence band is slightly more complex.
 Current transport in the valence band can be accounted for by keeping track of the holes
themselves.
 In a filled band, all available energy states are occupied.
 For every electron moving with a given velocity, there is an equal and opposite electron
motion somewhere else in the band.
 Under an applied electric field, the net current is zero, since for every electron j moving
with a velocity , there is a corresponding electron moving with a velocity - .
 In a unit volume, the current density J can be given by
(filled band) (2.2)
where N is the number of in the band, and q is the electronic charge.
 Now, if the electron is removed and a hole is created in the valence band, then the net
current density
 Thus, the current contribution of the empty state (hole), obtained by removing the jth
electron, is equivalent to that of a positively charged particle with velocity .
 Note that actually this transport is accounted for by the motion of the uncompensated
electron having a charge of q and moving with a velocity .
 Its current contribution (- q)(- ) is equivalent to that of a positively charged particle
with velocity + .
 For simplicity, therefore, the empty states in the valence band are called holes, and they
are assigned positive charge and positive mass.
 The electron energy increases as one moves up the conduction band, and electrons
gravitate downward towards the bottom of the conduction band.
 On the other hand, hole energy increases as one moves down the valence band (since
holes have positive charges), and holes gravitate upwards towards the top of the valence
band.

Effective Mass
 The "wave-particle" motion of electrons in a lattice is not the same as that for a free
electron, because of the interaction with the periodic potential of the lattice.
 To still be able to treat these particles as "free", the rest mass has to be altered to take into
account the influence of the lattice.
 The calculation of effective mass takes into account the shape of the energy bands in
three-dimensional k-space, taking appropriate averages over the various energy bands.
 The effective mass of an electron in a band with a given (E,k) relation is given by
(2.4)
EXAMPLE 2.1: Find the dispersion relation for a free electron, and, thus, observe the relation
between its rest mass and effective mass.
SOLUTION: For a free electron, the electron momentum is . Thus,
. Therefore, the dispersion relation, i.e., the E-k relation is
parabolic. Hence, . This is a very interesting relation, which states that for
a free electron, the rest mass and the effective mass are one and the same, which is due to the
parabolic band structure. Most materials have non-parabolic E-k relation, and, thus, they have
quite different rest mass and effective mass for electrons.
Note: for severely non-parabolic band structures, the effective mass may become a function of
energy, however, near the minima of the conduction band and towards the maxima of the
valence band, the band structure can be taken to be parabolic, and, thus, an effective mass, which
is independent of energy, may be obtained.
 Thus, the effective mass is an inverse function of the curvature of the E-k diagram: weak
curvature gives large mass, and strong curvature gives small mass.
 Note that in general, the effective mass is a tensor quantity, however, for parabolic bands,
it is a constant.
 Another interesting feature is that the curvature is positive at the conduction band
minima, however, it is negative at the valence band maxima.
 Thus, the electrons near the top of the valence band have negative effective mass.
 Valence band electrons with negative charge and negative mass move in an electric field
in the same direction as holes with positive charge and positive mass.
 Thus, the charge transport in the valence band can be fully accounted for by considering
hole motion alone.
 The electron and hole effective masses are denoted by and respectively.

Intrinsic Material
 A perfect semiconductor crystal with no impurities or lattice defects.
 No carriers at 0 K, since the valence band is completely full and the conduction band is
completely empty.
 For T > 0 K, electrons are thermally excited from the valence band to the conduction
band (EHP generation).
 EHP generation takes place due to breaking of covalent bonds required energy = .
 The excited electron becomes free and leaves behind an empty state (hole).
 Since these carriers are created in pairs, the electron concentration ( ) is always
equal to the hole concentration ( ), and each of these is commonly referred to as the
intrinsic carrier concentration ( ).
 Thus, for intrinsic material n = p = .
 These carriers are not localized in the lattice; instead they spread out over several lattice
spacings, and are given by quantum mechanical probability distributions.
 Note: ni = f(T).
 To maintain a steady-state carrier concentration, the carriers must also recombine at the
same rate at which they are generated.
 Recombination occurs when an electron from the conduction band makes a transition
(direct or indirect) to an empty state in the valence band, thus annihilating the pair.
 At equilibrium, = , where and are the generation and recombination rates
respectively, and both of these are temperature dependent.
 (T) increases with temperature, and a new carrier concentration ni is established, such
that the higher recombination rate (T) just balances generation.
 At any temperature, the rate of recombination is proportional to the equilibrium
concentration of electrons and holes, and can be given by (2.5)
where is a constant of proportionality (depends on the mechanism by which
recombination takes place).
Extrinsic Material
 In addition to thermally generated carriers, it is possible to create carriers in the
semiconductor by purposely introducing impurities into the crystal doping.
 Most common technique for varying the conductivity of semiconductors.
 By doping, the crystal can be made to have predominantly electrons (n-type) or holes (p-
type).

 When a crystal is doped such that the equilibrium concentrations of electrons (n0) and
holes (p0) are different from the intrinsic carrier concentration (ni), the material is said to
be extrinsic.
 Doping creates additional levels within the band gap.
 In Si, column V elements of the periodic table (e.g., P, As, Sb) introduce energy levels
very near (typically 0.03-0.06 eV) the conduction band.
 At 0 K, these levels are filled with electrons, and very little thermal energy (50 K to 100
K) is required for these electrons to get excited to the conduction band.
 Since these levels donate electrons to the conduction band, they are referred to as the
donor levels.
 Thus, Si doped with donor impurities can have a significant number of electrons in the
conduction band even when the temperature is not sufficiently high enough for the
intrinsic carriers to dominate, i.e., >> , n-type material, with electrons as
majority carriers and holes as minority carriers.
 In Si, column III elements of the periodic table (e.g., B, Al, Ga, In) introduce energy
levels very near (typically 0.03-0.06 eV) the valence band.
 At 0 K, these levels are empty, and very little thermal energy (50 K to 100 K) is required
for electrons in the valence band to get excited to these levels, and leave behind holes in
the valence band.
 Since these levels accept electrons from the valence band, they are referred to as the
acceptor levels.
 Thus, Si doped with acceptor impurities can have a significant number of holes in the
valence band even at a very low temperature, i.e., >> , p-type material, with
holes as majority carriers and electrons as minority carriers.
 The extra electron for column V elements is loosely bound and it can be liberated very
easily ionization; thus, it is free to participate in current conduction.
 Similarly, column III elements create holes in the valence band, and they can also
participate in current conduction.
 Rough calculation of the ionization energy can be made based on the Bohr's model for
atoms, considering the loosely bound electron orbiting around the tightly bound core
electrons. Thus,
(2.6)where is the relative permittivity of Si.
EXAMPLE2.2: Calculate the approximate donor binding energy for Si ( r = 11.7, = 1.18
).
SOLUTION: From Eq.(2.6), we have
= 1.867 x J = 0.117 eV.
Note: The effective mass used here is an average of the effective mass in different

crystallographic directions, and is called the "conductivity effective mass" with values of 1.28
(at 600 K), 1.18 (at 300 K), 1.08 (at 77 K), and 1.026 (at 4.2 K).
 In III-V compounds, column VI impurities (e.g., S, Se, Te) occupying column V sites act
as donors. Similarly, column II impurities (e.g., Be, Zn, Cd) occupying column III sites
act as acceptors.
 When a column IV material (e.g., Si, Ge) is used to dope III-V compounds, then they
may substitute column III elements (and act as donors), or substitute column V elements
(and act as acceptors) amphoteric dopants.
 Doping creates a large change in the electrical conductivity, e.g., with a doping of
, the resistivity of Si changes from 2 x -cm to 5 -cm.
Carrier Concentrations
 For the calculation of semiconductor electrical properties and analyzing device behavior,
it is necessary to know the number of charge carriers/cm3 in the material.
 The majority carrier concentration in a heavily doped material is obvious, since for each
impurity atom, one majority carrier is obtained.
 However, the minority carrier concentration and the dependence of carrier concentrations
on temperature are not obvious.
 To obtain the carrier concentrations, their distribution over the available energy states is
required.
 These distributions are calculated using statistical methods.
The Fermi Level
 Electrons in solids obey Fermi-Dirac (FD) statistics.
 This statistics accounts for the indistinguishability of the electrons, their wave nature, and
the Pauli exclusion principle.
 The Fermi-Dirac distribution function f(E) of electrons over a range of allowed energy
levels at thermal equilibrium can be given by
(2.7)where k is Boltzmann's constant (= 8.62 x eV/K = 1.38 x
J/K).
 This gives the probability that an available energy state at E will be occupied by an
electron at an absolute temperature T.
 is called the Fermi level and is a measure of the average energy of the electrons in the
lattice an extremely important quantity for analysis of device behavior.
 Note: for (E - ) > 3kT (known as Boltzmann approximation), f(E) exp[- (E- )/kT]
this is referred to as the Maxwell-Boltzmann (MB) distribution (followed by gas
atoms).

 The probability that an energy state at will be occupied by an electron is 1/2 at all
temperatures.
 At 0 K, the distribution takes a simple rectangular form, with all states below
occupied, and all states above empty.
 At T > 0 K, there is a finite probability of states above to be occupied and states
below to be empty.
 The F-D distribution function is highly symmetric, i.e., the probability f( + ) that a
state E above is filled is the same as the probability [1- f( - )] that a state E
below is empty.
 This symmetry about EF makes the Fermi level a natural reference point for the
calculation of electron and hole concentrations in the semiconductor.
 Note: f(E) is the probability of occupancy of an available state at energy E, thus, if there
is no available state at E (e.g., within the band gap of a semiconductor), there is no
possibility of finding an electron there.
 For intrinsic materials, the Fermi level lies close to the middle of the band gap (the
difference between the effective masses of electrons and holes accounts for this small
deviation from the mid gap).
 In n-type material, the electrons in the conduction band outnumber the holes in the
valence band, thus, the Fermi level lies closer to the conduction band.
 Similarly, in p-type material, the holes in the valence band outnumber the electrons in the
conduction band, thus, the Fermi level lies closer to the valence band.
 The probability of occupation f(E) in the conduction band and the probability of vacancy
[1- f(E)] in the valence band are quite small, however, the densities of available states in
these bands are very large, thus a small change in f(E) can cause large changes in the
carrier concentrations.

Fig.2.4 The density of states N(E), the Fermi-Dirac distribution function f(E), and the carrier
concentration as functions of energy for (a) intrinsic, (b) n-type, and (c) p-type semiconductors at
thermal equilibrium.
 Note: since the function f(E) is symmetrical about , a large electron concentration
implies a small hole concentration, and vice versa.
 In n-type material, the electron concentration in the conduction band increases as
moves closer to ; thus, ( - ) gives a measure of n.
 Similarly, in p-type material, the hole concentration in the valence band increases as
moves closer to ; thus, ( - ) gives a measure of p.
Electron and Hole Concentrations at Equilibrium
 The F-D distribution function can be used to calculate the electron and hole
concentrations in semiconductors, if the densities of available states in the conduction
and valence bands are known.
 In equilibrium, the concentration of electrons in the conduction band can be given by
(2.8)
where N(E)dE is the density of available states/cm3 in the energy range dE.
 Note: the upper limit of is theoretically not proper, since the conduction band does not
extend to infinite energies; however, since f(E) decreases rapidly with increasing E, the
contribution to this integral for higher energies is negligible.
 Using the solution of 's wave equation under periodic boundary conditions, it
can be shown that
(2.9)

 Thus, N(E) increases with E, however, f(E) decreases rapidly with E, thus, the product
f(E)N(E) decreases rapidly with E, and very few electrons occupy states far above the
conduction band edge, i.e., most electrons occupy a narrow energy band near the
conduction band edge.
 Similarly, the probability of finding an empty state in the valence band [1 - f(E)]
decreases rapidly below , and most holes occupy states near the top of the valence
band.
 Thus, a mathematical simplification can be made assuming that all available states in the
conduction band can be represented by an effective density of states NC located at the
conduction band edge and using Boltzmann approximation.
Thus, (2.10)
where .
 Note: as ( - ) decreases, i.e., the Fermi level moves closer to the conduction band,
the electron concentration increases.
 By similar arguments,
(2.11)
where is the effective density of states located at the valence band edge .
 Note: the only terms separating the expressions for and are the effective masses of
electrons ( ) and holes ( ) respectively, and since , hence, .
 Thus, as ( - ) decreases, i.e., the Fermi level moves closer to the valence band
edge, and the hole concentration increases.
 These equations for and are valid in equilibrium, irrespective of the material being
intrinsic or doped.
 For intrinsic material lies at an intrinsic level (very near the middle of the band
gap), and the intrinsic electron and hole concentrations are given by
and (2.12)
 Note: At equilibrium, the product is a constant for a particular material and
temperature, even though the doping is varied,
i.e., (2.13)
 This equation gives an expression for the intrinsic carrier concentration ni as a function of
, , and temperature:
(2.14)

 These relations are extremely important, and are frequently used for calculations.
 Note: if were to be equal to , then would have been exactly at mid gap (i.e., -
= - = /2).
 However, since , is displaced slightly from mid gap (more for GaAs than that
for Si).
 Alternate expressions for and :
and (2.15)
 Note: the electron concentration is equal to ni when is at , and n0 increases
exponentially as moves away from towards the conduction band.
 Similarly, the hole concentration varies from to larger values as moves from
towards the valence band.
EXAMPLE 2.3: A Si sample is doped with B . What is the equilibrium electron
concentration n0 at 300 K? Where is relative to ? Assume for Si at 300 K = 1.5 x
SOLUTION: Since B (trivalent) is a p-type dopant in Si, hence, the material will be
predominantly p-type, and since >> , therefore, will be approximately equal to , and
= . Also,
. The resulting band diagram is:
Temperature Dependence of Carrier Concentrations
 The intrinsic carrier concentration has a strong temperature dependence, given by
(2.16)
 Thus, explicitly, ni is proportional to T3/2 and to e 1/T, however, Eg also has a
temperature dependence (decreasing with increasing temperature, since the interatomic
spacing changes with temperature).

Fig.2.5 The intrinsic carrier concentration as a function of inverse temperature for Si, Ge,
and GaAs.
 As changes with temperature, so do and .
 With and T given, the unknowns are the carrier concentrations and the Fermi level
position with respect to one of these quantities must be given in order to calculate the
other.
 Example: Si doped with donors ( ).
 At very low temperature, negligible intrinsic EHPs exist, and all the donor electrons are
bound to the donor atoms.
 As temperature is raised, these electrons are gradually donated to the conduction band,
and at about 100 K (1000/T = 10), almost all these electrons are donated this
temperature range is called the ionization region.
Once all the donor atoms are ionized, the electron concentration , since for each donor
atom, one electron is obtained.

Fig.2.6 Variation of carrier concentration with inverse temperature clearly showing the three
regions: ionization, extrinsic, and intrinsic.
 Thus, remains virtually constant with temperature for a wide range of temperature
(called the extrinsic region), until the intrinsic carrier concentration ni starts to become
comparable to .
 For high temperatures, >> , and the material loses its extrinsic property (called the
intrinsic region).
 Note: in the intrinsic region, the device loses its usefulness => determines the maximum
operable temperature range.
Compensation and Space Charge Neutrality
 Semiconductors can be doped with both donors ( ) and acceptors ( ) simultaneously.
 Assume a material doped with > predominantly n-type lies above
acceptor level Ea completely full, however, with above , the hole concentration
cannot be equal to .
 Mechanism:
o Electrons are donated to the conduction band from the donor level
o An acceptor state gets filled by a valence band electron, thus creating a hole in the
valence band.
o An electron from the conduction band recombines with this hole.
o Extending this logic, it is expected that the resultant concentration of electrons in
the conduction band would be instead of .
o This process is called compensation.
 By compensation, an n-type material can be made intrinsic (by making = ) or even
p-type (for > ).
Note: a semiconductor is neutral to start with, and, even after doping, it remains neutral

(since for all donated electrons, there are positively charged ions ( ); and for all
accepted electrons (or holes in the valence band), there are negatively charged ions ( ).
 Therefore, the sum of positive charges must equal the sum of negative charges, and this
governing relation,
given by (2.17) is referred to as the equation for space charge neutrality.
 This equation, solved simultaneously with the law of mass action (given by )
gives the information about the carrier concentrations.
Note: for ,
Drift of Carriers in Electric and Magnetic Fields
 In addition to the knowledge of carrier concentrations, the collisions of the charge
carriers with the lattice and with the impurity atoms (or ions) under electric and/or
magnetic fields must be accounted for, in order to compute the current flow through the
device.
 These processes will affect the ease (mobility) with which carriers move within a lattice.
 These collision and scattering processes depend on temperature, which affects the
thermal motion of the lattice atoms and the velocity of the carriers.
Conductivity and Mobility
 Even at thermal equilibrium, the carriers are in a constant motion within the lattice.
 At room temperature, the thermal motion of an individual electron may be visualized as
random scattering from lattice atoms, impurities, other electrons, and defects.
 There is no net motion of the group of n electrons/cm3 over any period of
time, since the scattering is random, and there is no preferred direction of motion for the
group of electrons and no net current flow.
 However, for an individual electron, this is not true the probability of an electron
returning to its starting point after time t is negligibly small.
 Now, if an electric field is applied in the x-direction, each electron experiences a net
force q from the field.
 This will create a net motion of group in the x-direction, even though the force may be
insufficient to appreciably alter the random path of an individual electron.
 If is the x-component of the total momentum of the group, then the force of the field on
the n is
(2.18)
Note: this expression indicates a constant acceleration in the x-direction, which
realistically cannot happen.
 In steady state, this acceleration is just balanced by the deceleration due to the collisions.
 Thus, while the steady field does produce a net momentum , for steady state
current flow, the net rate of change of momentum must be zero when collisions are
included.

 Note: the collision processes are totally random, thus, there is a constant probability of
collision at any time for each electron.
 Consider a group of electrons at time t = 0, and define N(t) as the number of electrons
that have not undergone a collision by time t
Fig.2.7 The random thermal motion of an individual electron, undergoing random
scattering.
 The rate of decrease of N(t) at any time t is proportional to the number left unscattered at
t, i.e.
(2.19)
where is the constant of proportionality.
 The solution is an exponential function
(2.20)
and represents the mean time between scattering events, called the mean free time.
 The probability that any electron has a collision in time interval dt is dt/ , thus, the
differential change in due to collisions in time dt is
(2.21)
 Thus, the rate of change of due to the decelerating effect of collisions is
(2.22)
 For steady state, the sum of acceleration and deceleration effects must be zero, thus,
(2.23)
 The average momentum per electron (averaged over the entire group of electrons) is
(2.24)

 Thus, as expected for steady state, the electrons would have on the average a constant net
velocity in the -x-direction
(2.25)
 This speed is referred to as the drift speed, and, in general, it is usually much smaller than
the random speed due to thermal motion .
 The current density resulting from this drift
(2.26)
 This is the familiar Ohm's law with being the conductivity of the sample, which
can also be written as , with is defined as the electron mobility
(in ), and it describes the ease with which electrons drift in the material.
 The mobility can also be expressed as the average drift velocity per unit electric field,
thus with the negative sign denoting a positive value for mobility since
electrons drift opposite to the direction of the electric field.
 The total current density can be given by (2.27) when both electrons
and holes contribute to the current conduction; on the other hand, for predominantly n-
type or p-type samples, respectively the first or the second term of the above equation
dominates.
Note: both electron and hole drift currents are in the same direction, since holes (with
positive charges) move along the direction of the electric field, and electrons (with
negative charges) drift opposite to the direction of the electric field.
 Since GaAs has a strong curvature of the E-k diagram at the bottom of the conduction
band, the electron effective mass in GaAs is very small the electron mobility in GaAs
is very high since is inversely proportional to .
 The other parameter in the mobility expression, i.e., (the mean free time between
collisions) is a function of temperature and the impurity concentration in the
semiconductor.
 For a uniformly doped semiconductor bar of length L, width w, and thickness t, the
resistance R of the bar can be given by where is the resistivity.

Effects of Temperature and Doping on Mobility
 The two main scattering events that influence electron and hole motion (and, thus,
mobility) are the lattice scattering and the impurity scattering.
 All lattice atoms vibrate due to temperature and can scatter carriers due to collisions.
 These collective vibrations are called phonons, thus lattice scattering is also known as
phonon scattering.
 With increasing temperature, lattice vibrations increase, and the mean free time between
collisions decreases mobility decreases (typical dependence ).
 Scattering from crystal defects and ionized impurities dominate at low temperatures.
 Since carriers moving with low velocity (at low temperature) can get scattered more
easily by ionized impurities, this kind of scattering causes a decrease in carrier mobility
with decreasing temperature (typical dependence ).
 Note: the scattering probability is inversely proportional to the mean free time (and to
mobility), hence, the mobilities due to two or more scattering events add inversely:
(2.28)
 Thus, the mechanism causing the lowest mobility value dominates.
 Mobility also decreases with increasing doping, since the ionized impurities scatter
carriers more (e.g., for intrinsic Si is 1350 at 300 K, whereas with a donor
doping of , n drops to 700 ).
High Field Effects
 For small electric fields, the drift current increases linearly with the electric field, since
is a constant.
 However, for large electric fields (typically > ), the current starts to show a
sublinear dependence on the electric field and eventually saturates for very high fields.
 Thus, becomes a function of the electric field, and this is known as the hot carrier effect,
when the carrier drift velocity becomes comparable to its thermal velocity.
 The maximum carrier drift velocity is limited to its mean thermal velocity (typically
), beyond which the added energy imparted by the electric field is absorbed by
the lattice (thus generating heat) instead of a corresponding increase in the drift velocity.
2.4.4 The Hall Effect
 An extremely important measurement procedure for determining the majority carrier
concentration and mobility.

Fig.2.8 The experimental setup for the Hall Effect measurement.
 If a magnetic field is applied perpendicular to the direction of carrier flow, the path of the
carriers get deflected due to the Lorentz force experienced by the carriers, which can be
given by
F = q(E + v x B) (2.29)
 Thus, the holes will get deflected towards the -y-direction, and establish an electric field
along the y-direction, such that in steady state
 The establishment of this electric field is known as the Hall effect, and the resulting
voltage is called the Hall voltage.
 Using the expression for the drift current, is called the
Hall coefficient.
 A measurement of the Hall voltage along with the information for magnetic field and
current density gives the majority carrier concentration
 Also, the majority carrier mobility can be obtained from a measurement of
the resistivity
 This experiment can be performed to obtain the variation of majority carrier
concentration and mobility as a function of temperature.
 For n-type samples, the Hall voltage and the Hall coefficient are negative a common
diagnostic tool for obtaining the sample type.
 Note: caution should be exercised for near intrinsic samples.
EXAMPLE 2.4: A sample of Si is doped with In . What will be the measured
value of its resistivity? What is the expected Hall voltage in a 150 m thick sample if
?

SOLUTION:
Equilibrium Condition
 In equilibrium, there is no external excitation except a constant temperature, no net
transfer of energy, no net carrier motion, and no net current transport.
 An important condition for equilibrium is that no discontinuity or gradient can arise in the
equilibrium Fermi level EF.
 Assume two materials 1 and 2 (e.g., n- and p-type regions, dissimilar semiconductors,
metal and semiconductor, two adjacent regions in a nonuniformly doped semiconductor)
in intimate contact such that electron can move between them.
 Assume materials 1 and 2 have densities of state N1(E) and N2(E), and F-D distribution
functions f1(E) and f2(E) respectively at any energy E.
 The rate of electron motion from 1 to 2 can be given byrate from 1 to 2 N1(E)f1(E) .
N2(E)[1 f2(E)] (2.30)and the rate of electron motion from 2 to 1 can be given byrate from
2 to 1 N2(E)f2(E) . N1(E)[1 f1(E)] (2.31)" At equilibrium, these two rates must be equal,
which gives f1(E) = f2(E) => EF1 = EF2 => dEF/dx = 0; thus, the Fermi level is constant
at equilibrium, or, in other words, there cannot be any discontinuity or gradient in the
Fermi level at equilibrium.
Practice Problems
2.1 Electrons move in a crystal as wave packets with a group velocity where
is the angular frequency. Show that in a given electric field, these wave packets obey

Newton's second law of motion, i.e., the force F = m*a, where m* is the effective mass
and a is the acceleration.
2.2 Some semiconductors of interest have the dependence of its energy E with respect to
the wave vector k, given by is the effective mass for E =
0, k is the wave vector, and is a constant. Calculate the dependence of the effective
mass on energy.
2.3 Determine the equilibrium recombination constant r for Si and GaAs, having
equilibrium thermal generation rates of
respectively, and intrinsic carrier concentrations of
respectively. Comment on the answers. Will change with doping at equilibrium?
2.4 The relative dielectric constant for GaP is 10.2 and the electron effective mass is
Calculate the approximate ionization energy of a donor atom in GaP.
2.5 Show that the probability that a state above the Fermi level is occupied is the
same as the probability that a state below is empty.
2.6 Derive an expression relating the intrinsic level to the center of the band gap
and compute the magnitude of this displacement for Si and GaAs at 300 K. Assume
respectively.
2.7 Show that in order to obtain maximum resistivity in a GaAs sample
it has to be
doped slightly p-type. Determine this doping concentration. Also, determine the ratio of
the maximum resistivity to the intrinsic resistivity.
2.8 A GaAs sample (use the date given in Problem 2.7) is doped uniformly with
out of which 70% occupy Ga sites, and the rest 30% occupy As sites.
Assume 100% ionization and T = 300 K.
a) Calculate the equilibrium electron and hole concentrations
b) Clearly draw the equilibrium band diagram, showing the position of the Fermi level
with respect to the intrinsic level , assuming that lies exactly at midgap.
c) Calculate the percentage change in conductivity after doping as compared to the
intrinsic case.
2.9 A Si sample is doped with donor atoms. Determine the minimum
temperature at which the sample becomes intrinsic. Assume that at this minimum
temperature, the free electron concentration does not exceed by more than 1% of the
donor concentration (beyond its extrinsic value). For

2.10 Since the event of collision of an electron in a lattice is a truly random process, thus
having a constant probability of collision at any given time, the number of particles left
unscattered at time t,
Hence, show that if there are a total of i number of scattering events, each with a mean
free time of then the net electron mobility can be given by where
is the mobility due to the ith scattering event.
2.11 A Ge sample is oriented in a magnetic field (refer to
Fig.2.8). The current is 4 mA, and the sample dimensions are w = 0.25 mm,
t = 50 m, and L = 2.5 mm. The following data are taken:
Find the type and concentration of the majority
carrier, and its mobility. Hence, compute the net relaxation time for the various scattering
events, assuming
2.12 In the Hall effect experiment, there is a chance that the Hall Probes A and B (refer to
Fig.2.8) are not perfectly aligned, which may give erroneous Hall voltage readings. Show
that the true Hall voltage can be obtained from two measurements of with the
magnetic field first in the +z-direction, and then in the z-direction.
Metals
or

In metals, either the conduction band is partially filled or overlaps with valence band. There is no
forbidden energy gap in between. Even if a small electric field is applied, free electrons start
moving in a direction opposite to field and hence a good conductor of electricity.
Insulators
Here the valency bands are completely filled and conduction band is empty and the forbidden
gap is quite large. For example in diamond Egap is 6eV. Even if an electric field is applied, no
electron is able to go from valence band to conduction band.
Semiconductors
The valence band is completely filled and conduction band is empty. The Egap is also less i.e., of
the order of few eV. At zero kelvin, electrons are not able to cross this forbidden gap and so
behave like insulators. But as temperature is increased, electrons in valence band (VB) gain
thermal energy and jump to conduction band (CB) and acquire small conductivity at room
temperature and so behave like conductors. Hence they are called semiconductors.
Charge carriers in semiconductors
At high temperature, electrons move from valance band to conduction band and as a result a
vacancy is created in the valence band at a place where an electron was present before shifting to
conduction band. The valency is a hole and is seat of positive charge having the same value of
electron. Therefore the electrical conduction in semiconductors is due to motion of electrons in
conduction band and also due to motion of holes in valence band.

Semiconductor Basics
If Resistors are the most basic passive component in electrical or electronic circuits, then we
have to consider the Signal Diode as being the most basic "Active" component. However, unlike
a resistor, a diode does not behave linearly with respect to the applied voltage as it has an
exponential I-V relationship and therefore can not be described simply by using Ohm's law as we
do for resistors. Diodes are unidirectional semiconductor devices that will only allow current to
flow through them in one direction only, acting more like a one way electrical valve, (Forward
Biased Condition). But, before we have a look at how signal or power diodes work we first need
to understand their basic construction and concept.
Diodes are made from a single piece of Semiconductor material which has a positive "P-region"
at one end and a negative "N-region" at the other, and which has a resistivity value somewhere
between that of a conductor and an insulator. But what is a "Semiconductor" material?, firstly
let's look at what makes something either a Conductor or an Insulator.
Resistivity
The electrical Resistance of an electrical or electronic component or device is generally defined
as being the ratio of the voltage difference across it to the current flowing through it, basic
Ohm´s Law principals. The problem with using resistance as a measurement is that it depends
very much on the physical size of the material being measured as well as the material out of
which it is made. For example, If we were to increase the length of the material (making it
longer) its resistance would also increase. Likewise, if we increased its diameter (making it
fatter) its resistance would then decrease. So we want to be able to define the material in such a
way as to indicate its ability to either conduct or oppose the flow of electrical current through it
no matter what its size or shape happens to be. The quantity that is used to indicate this specific
resistance is called Resistivity and is given the Greek symbol of ρ, (Rho). Resistivity is
measured in Ohm-metres, ( Ω-m ) and is the inverse to conductivity.
If the resistivity of various materials is compared, they can be classified into three main groups,
Conductors, Insulators and Semi-conductors as shown below.

Resistivity Chart
Notice also that there is a very small
margin between the resistivity of the
conductors such as silver and gold,
compared to a much larger margin for
the resistivity of the insulators
between glass and quartz. The
resistivity of all the materials at any
one time also depends upon their
temperature.
Conductors
From above we now know that Conductors are materials that have a low value of resistivity
allowing them to easily pass an electrical current due to there being plenty of free electrons
floating about within their basic atom structure. When a positive voltage potential is applied to
the material these "free electrons" leave their parent atom and travel together through the
material forming an electron drift. Examples of good conductors are generally metals such as
Copper, Aluminium, Silver or non metals such as Carbon because these materials have very few
electrons in their outer "Valence Shell" or ring, resulting in them being easily knocked out of the
atom's orbit. This allows them to flow freely through the material until they join up with other
atoms, producing a "Domino Effect" through the material thereby creating an electrical current.
Generally speaking, most metals are good conductors of electricity, as they have very small
resistance values, usually in the region of micro-ohms per metre with the resistivity of

conductors increasing with temperature because metals are also generally good conductors of
heat.
Insulators
Insulators on the other hand are the exact opposite of conductors. They are made of materials,
generally non-metals, that have very few or no "free electrons" floating about within their basic
atom structure because the electrons in the outer valence shell are strongly attracted by the
positively charged inner nucleus. So if a potential voltage is applied to the material no current
will flow as there are no electrons to move and which gives these materials their insulating
properties. Insulators also have very high resistances, millions of ohms per metre, and are
generally not affected by normal temperature changes (although at very high temperatures wood
becomes charcoal and changes from an insulator to a conductor). Examples of good insulators
are marble, fused quartz, p.v.c. plastics, rubber etc.
Insulators play a very important role within electrical and electronic circuits, because without
them electrical circuits would short together and not work. For example, insulators made of glass
or porcelain are used for insulating and supporting overhead transmission cables while epoxy-
glass resin materials are used to make printed circuit boards, PCB's etc.
Semiconductor Basics
Semiconductors materials such as silicon (Si), germanium (Ge) and gallium arsenide (GaAs),
have electrical properties somewhere in the middle, between those of a "conductor" and an
"insulator". They are not good conductors nor good insulators (hence their name "semi"-
conductors). They have very few "fee electrons" because their atoms are closely grouped
together in a crystalline pattern called a "crystal lattice". However, their ability to conduct
electricity can be greatly improved by adding certain "impurities" to this crystalline structure
thereby, producing more free electrons than holes or vice versa. By controlling the amount of
impurities added to the semiconductor material it is possible to control its conductivity. These
impurities are called donors or acceptors depending on whether they produce electrons or holes.
This process of adding impurity atoms to semiconductor atoms (the order of 1 impurity atom per
10 million (or more) atoms of the semiconductor) is called Doping.
The most commonly used semiconductor material by far is silicon. It has four valence electrons
in its outer most shell which it shares with its adjacent atoms in forming covalent bonds. The
structure of the bond between two silicon atoms is such that each atom shares one electron with
its neighbour making the bond very stable. As there are very few free electrons available to move
from place to place producing an electrical current, crystals of pure silicon (or germanium) are

therefore good insulators, or at the very least very high value resistors. Silicon atoms are
arranged in a definite symmetrical pattern making them a crystalline solid structure. A crystal of
pure silicon (silicon dioxide or glass) is generally said to be an intrinsic crystal (it has no
impurities).
The diagram above shows the structure and lattice of a 'normal' pure crystal
of Silicon.
N-type Semiconductor Basics
In order for our silicon crystal to conduct electricity, we need to introduce an impurity atom such
as Arsenic, Antimony or Phosphorus into the crystalline structure making it extrinsic (impurities
are added). These atoms have five outer electrons in their outermost co-valent bond to share with
other atoms and are commonly called "Pentavalent" impurities. This allows four of the five
electrons to bond with its neighbouring silicon atoms leaving one "free electron" to move about
when an electrical voltage is applied (electron flow). As each impurity atom "donates" one
electron, pentavalent atoms are generally known as "donors".
Antimony (symbol Sb) is frequently used as a pentavalent additive as it has 51 electrons
arranged in 5 shells around the nucleus. The resulting semiconductor material has an excess of
current-carrying electrons, each with a negative charge, and is therefore referred to as "N-type"
material with the electrons called "Majority Carriers" and the resultant holes "Minority Carriers".
Then a semiconductor material is N-type when its donor density is greater than its acceptor
density. Therefore, a N-type semiconductor has more electrons than holes.

The diagram above shows the structure and lattice of the donor impurity atom
Antimony.
P-Type Semiconductor Basics
If we go the other way, and introduce a "Trivalent" (3-electron) impurity into the crystal
structure, such as Aluminium, Boron or Indium, only three valence electrons are available in the
outermost covalent bond meaning that the fourth bond cannot be formed. Therefore, a complete
connection is not possible, giving the semiconductor material an abundance of positively charged
carriers known as "holes" in the structure of the crystal. As there is a hole an adjoining free
electron is attracted to it and will try to move into the hole to fill it. However, the electron filling
the hole leaves another hole behind it as it moves. This in turn attracts another electron which in
turn creates another hole behind, and so forth giving the appearance that the holes are moving as
a positive charge through the crystal structure (conventional current flow). As each impurity
atom generates a hole, trivalent impurities are generally known as "Acceptors" as they are
continually "accepting" extra electrons.
Boron (symbol B) is frequently used as a trivalent additive as it has only 5 electrons arranged in
3 shells around the nucleus. Addition of Boron causes conduction to consist mainly of positive
charge carriers results in a "P-type" material and the positive holes are called "Majority Carriers"
while the free electrons are called "Minority Carriers". Then a semiconductors is P-type when its
acceptor density is greater than its donor density. Therefore, a P-type semiconductor has more
holes than electrons.

The diagram above shows the structure and lattice of the acceptor impurity
atom Boron.
Semiconductor Basics Summary
N-type (e.g. add Antimony)
These are materials which have Pentavalent impurity atoms (Donors) added and conduct by
"electron" movement and are called, N-type Semiconductors.
In these types of materials are:
 1. The Donors are positively charged.
 2. There are a large number of free electrons.
 3. A small number of holes in relation to the number of free electrons.
 4. Doping gives:
o positively charged donors.
o negatively charged free electrons.
 5. Supply of energy gives:
o positively charged holes.
P-type (e.g. add Boron)
These are materials which have Trivalent impurity atoms (Acceptors) added and conduct by
"hole" movement and are called, P-type Semiconductors.

In these types of materials are:
 1. The Acceptors are negatively charged.
 2. There are a large number of holes.
 3. A small number of free electrons in relation to the number of holes.
 4. Doping gives:
o negatively charged acceptors.
 5. Supply of energy gives:
and both P and N-types as a whole, are electrically neutral.
In the next tutorial about semiconductors and diodes, we will look at joining the two
semiconductor materials, the P-type and the N-type materials to form a PN Junction which can
be used to produce diodes.
Pn junction
The PN junction
In the previous tutorial we saw how to make an N-type semiconductor material by doping it with
Antimony and also how to make a P-type semiconductor material by doping that with Boron.
This is all well and good, but these semiconductor N and P-type materials do very little on their
own as they are electrically neutral, but when we join (or fuse) them together these two materials
behave in a very different way producing what is generally known as a PN Junction.
When the N and P-type semiconductor materials are first joined together a very large density
gradient exists between both sides of the junction so some of the free electrons from the donor
impurity atoms begin to migrate across this newly formed junction to fill up the holes in the P-
type material producing negative ions. However, because the electrons have moved across the
junction from the N-type silicon to the P-type silicon, they leave behind positively charged donor
ions (ND) on the negative side and now the holes from the acceptor impurity migrate across the
junction in the opposite direction into the region were there are large numbers of free electrons.
As a result, the charge density of the P-type along the junction is filled with negatively charged
acceptor ions (NA), and the charge density of the N-type along the junction becomes positive.
This charge transfer of electrons and holes across the junction is known as diffusion.

This process continues back and forth until the number of electrons which have crossed the
junction have a large enough electrical charge to repel or prevent any more carriers from
crossing the junction. The regions on both sides of the junction become depleted of any free
carriers in comparison to the N and P type materials away from the junction. Eventually a state
of equilibrium (electrically neutral situation) will occur producing a "potential barrier" zone
around the area of the junction as the donor atoms repel the holes and the acceptor atoms repel
the electrons. Since no free charge carriers can rest in a position where there is a potential barrier
the regions on both sides of the junction become depleted of any more free carriers in
comparison to the N and P type materials away from the junction. This area around the junction
is now called the Depletion Layer.
The PN junction
The total charge on each side of the junction must be equal and opposite to maintain a neutral
charge condition around the junction. If the depletion layer region has a distance D, it therefore
must therefore penetrate into the silicon by a distance of Dp for the positive side, and a distance
of Dn for the negative side giving a relationship between the two of Dp.NA = Dn.ND in order to
maintain charge neutrality also called equilibrium.

PN junction Distance
As the N-type material has lost electrons and the P-type has lost holes, the N-type material has
become positive with respect to the P-type. Then the presence of impurity ions on both sides of
the junction cause an electric field to be established across this region with the N-side at a
positive voltage relative to the P-side. The problem now is that a free charge requires some extra
energy to overcome the barrier that now exists for it to be able to cross the depletion region
junction.
This electric field created by the diffusion process has created a "built-in potential difference"
across the junction with an open-circuit (zero bias) potential of:
Where: Eo is the zero bias junction voltage, VT the thermal voltage of 26mV at room
temperature, ND and NA are the impurity concentrations and ni is the intrinsic concentration.
A suitable positive voltage (forward bias) applied between the two ends of the PN junction can
supply the free electrons and holes with the extra energy. The external voltage required to
overcome this potential barrier that now exists is very much dependent upon the type of
semiconductor material used and its actual temperature. Typically at room temperature the
voltage across the depletion layer for silicon is about 0.6 - 0.7 volts and for germanium is about
0.3 - 0.35 volts. This potential barrier will always exist even if the device is not connected to any
external power source.

The significance of this built-in potential across the junction, is that it opposes both the flow of
holes and electrons across the junction and is why it is called the potential barrier. In practice, a
PN junction is formed within a single crystal of material rather than just simply joining or fusing
together two separate pieces. Electrical contacts are also fused onto either side of the crystal to
enable an electrical connection to be made to an external circuit. Then the resulting device that
has been made is called a PN junction Diode or Signal Diode.
In the next tutorial about the PN junction, we will look at one of the most interesting aspects of
the PN junction is its use in circuits as a diode. By adding connections to each end of the P-type
and the N-type materials we can produce a two terminal device called a PN Junction Diode
which can be biased by an external voltage to either block or allow the flow of current through it.
Introduction to depletion layer pn junction:
If one side of crystal pure semiconductor Si(silicon) or Ge(Germanium) is doped with acceptor
impurity atoms and the other side is doped with donor impurity atoms , a PN junction is formed
as shown in figure.P region has high concentration of holes and N region contains large number
of electrons.
What is Depletion Layer of Pn Junction?
As soon as the junction is formed, free electrons and holes cross through the junction by the
process of diffusion.During this process , the electrons crossing the junction from N- region into
P-region , recombine with holes in the P-region very close to the junction.Similarly holes
crossing the junction from the P-region into the N-region, recombine with electrons in the N-
region very close to the junction. Thus a region is formed, which does not have any mobile
charge very close to the junction. This region is called the depletion layer of pn junction.

In this region, on the left side of the junction, the acceptor atoms become negative ions and on
the right side of the junction, the donor atoms become positive ions as shown in figure.
Function of Depletion Layer of Pn Junction :
An electric field is set up, between the donor and acceptor ions in the depletion layer of the pn
junction .The potential at the N-side is higher than the potential at P-side.Therefore electrons in
the N- side are prevented to go to the lower potential of P-side. Similarly, holes in the P-side find
themselves at a lower potential and are prevented to cross to the N-side. Thus, there is a barrier at
the junction which opposes the movement of the majority charge carriers. The difference of
potential from one side of the barrier to the other side of the barrier is called potential
barrier.The potential barrier is approximately 0.7V for a silicon PN junction and 0.3V for
germanium PN junction. The distance from one side of the barrier to the other side is called the
width of the barrier, which depends on the nature of the material.
Introduction to Diodes and Transistors:
Diodes are known as p-n junction in the physics or in most of the basic sciences but in the
electronics and engineering sciences a p-n junction has the abbreviated name i.e. diode. Diodes
are the electrical component of any electric circuit which prevents the circuit from the high
electric current because diodes are get break i.e. they get burn when a large current is flowing
through them and hence prevents the electrical circuits.
Transistors are the electrical device which mainly consists of two junctions thus they are called
as the junction transistors. The transistors have three terminals instead of the two terminals and
each terminal has its specific characteristics. In electronic circuits two transistors namely n-p-n
and p-n-p are most preferably used.
More about Diodes and Transistors:
When a p-type semiconductor is brought into a close contact with an n-type semiconductor, then
the resultant arrangement is called a p-n junction or a junction diode or simply a diode.
A junction transistor is obtained by growing a thin layer of one semiconductor in between two
thick layers of other similar type semiconductor. Thus a junction transistor is a semiconductor
device having two junctions and three terminals.
Example of Diodes and Transistors:
Junction diodes are of many types. Important among them are:

(a) Zener diode: A zener diode is specially designed junction diode which can operate
continuously without being damaged in the region of reverse break down voltage shown in Fig.1.
(b) Photo diode: Its working is based on the electric conduction from light shown in Fig.2.
(c) Light emitting diode (LED): Its working is based on the production of light from electric
current shown in Fig.3.
Fig.1 Zener Diode Fig.2 Photo Diode Fig.3 LED
The transistors are also of several types but most important among them are listed below:
(a) Junction Transistors: These are of two kind p-n-p and n-p-n and they are basic transistors
which are used in the electronic circuitry and other electronic equipment very rapidly because of
there low cost and high reliability.
(b) Field effect transistors: In present days most of the electronic integrated circuits are using
these kinds of transistors because they are highly conductive and easy to prepare then the
junction transistor.
The Junction Diode
The Junction Diode
The effect described in the previous tutorial is achieved without any external voltage being
applied to the actual PN junction resulting in the junction being in a state of equilibrium.
However, if we were to make electrical connections at the ends of both the N-type and the P-type
materials and then connect them to a battery source, an additional energy source now exists to
overcome the barrier resulting in free charges being able to cross the depletion region from one
side to the other. The behaviour of the PN junction with regards to the potential barrier width
produces an asymmetrical conducting two terminal device, better known as the Junction Diode.
A diode is one of the simplest semiconductor devices, which has the characteristic of passing
current in one direction only. However, unlike a resistor, a diode does not behave linearly with

respect to the applied voltage as the diode has an exponential I-V relationship and therefore we
can not described its operation by simply using an equation such as Ohm's law.
If a suitable positive voltage (forward bias) is applied between the two ends of the PN junction, it
can supply free electrons and holes with the extra energy they require to cross the junction as the
width of the depletion layer around the PN junction is decreased. By applying a negative voltage
(reverse bias) results in the free charges being pulled away from the junction resulting in the
depletion layer width being increased. This has the effect of increasing or decreasing the
effective resistance of the junction itself allowing or blocking current flow through the diode.
Then the depletion layer widens with an increase in the application of a reverse voltage and
narrows with an increase in the application of a forward voltage. This is due to the differences in
the electrical properties on the two sides of the PN junction resulting in physical changes taking
place. One of the results produces rectification as seen in the PN junction diodes static I-V
(current-voltage) characteristics. Rectification is shown by an asymmetrical current flow when
the polarity of bias voltage is altered as shown below.
Junction Diode Symbol and Static I-V Characteristics.

But before we can use the PN junction as a practical device or as a rectifying device we need to
firstly bias the junction, ie connect a voltage potential across it. On the voltage axis above,
"Reverse Bias" refers to an external voltage potential which increases the potential barrier. An
external voltage which decreases the potential barrier is said to act in the "Forward Bias"
direction.
There are two operating regions and three possible "biasing" conditions for the standard
Junction Diode and these are:
 1. Zero Bias - No external voltage potential is applied to the PN-junction.

2. Reverse Bias - The voltage potential is connected negative, (-ve) to the P-type material and
positive, (+ve) to the N-type material across the diode which has the effect of Increasing the
PN-junction width.

3. Forward Bias - The voltage potential is connected positive, (+ve) to the P-type material and
negative, (-ve) to the N-type material across the diode which has the effect of Decreasing the
PN-junction width.
Zero Biased Junction Diode
When a diode is connected in a Zero Bias condition, no external potential energy is applied to
the PN junction. However if the diodes terminals are shorted together, a few holes (majority
carriers) in the P-type material with enough energy to overcome the potential barrier will move
across the junction against this barrier potential. This is known as the "Forward Current" and is
referenced as IF
Likewise, holes generated in the N-type material (minority carriers), find this situation
favourable and move across the junction in the opposite direction. This is known as the "Reverse
Current" and is referenced as IR. This transfer of electrons and holes back and forth across the
PN junction is known as diffusion, as shown below.

Zero Biased Junction Diode
The potential barrier that now exists discourages the diffusion of any more majority carriers
across the junction. However, the potential barrier helps minority carriers (few free electrons in
the P-region and few holes in the N-region) to drift across the junction. Then an "Equilibrium" or
balance will be established when the majority carriers are equal and both moving in opposite
directions, so that the net result is zero current flowing in the circuit. When this occurs the
junction is said to be in a state of "Dynamic Equilibrium".
The minority carriers are constantly generated due to thermal energy so this state of equilibrium
can be broken by raising the temperature of the PN junction causing an increase in the generation
of minority carriers, thereby resulting in an increase in leakage current but an electric current
cannot flow since no circuit has been connected to the PN junction.
Reverse Biased Junction Diode
When a diode is connected in a Reverse Bias condition, a positive voltage is applied to the N-
type material and a negative voltage is applied to the P-type material. The positive voltage
applied to the N-type material attracts electrons towards the positive electrode and away from the
junction, while the holes in the P-type end are also attracted away from the junction towards the
negative electrode. The net result is that the depletion layer grows wider due to a lack of
electrons and holes and presents a high impedance path, almost an insulator. The result is that a

high potential barrier is created thus preventing current from flowing through the semiconductor
material.
Reverse Biased Junction Diode showing an Increase in the Depletion Layer
This condition represents a high resistance value to the PN junction and practically zero current
flows through the junction diode with an increase in bias voltage. However, a very small leakage
current does flow through the junction which can be measured in microamperes, (μA). One final
point, if the reverse bias voltage Vr applied to the diode is increased to a sufficiently high enough
value, it will cause the PN junction to overheat and fail due to the avalanche effect around the
junction. This may cause the diode to become shorted and will result in the flow of maximum
circuit current, and this shown as a step downward slope in the reverse static characteristics
curve below.
Reverse Characteristics Curve for a Junction Diode

Sometimes this avalanche effect has practical applications in voltage stabilising circuits where a
series limiting resistor is used with the diode to limit this reverse breakdown current to a preset
maximum value thereby producing a fixed voltage output across the diode. These types of diodes
are commonly known as Zener Diodes and are discussed in a later tutorial.
Forward Biased Junction Diode
When a diode is connected in a Forward Bias condition, a negative voltage is applied to the N-
type material and a positive voltage is applied to the P-type material. If this external voltage
becomes greater than the value of the potential barrier, approx. 0.7 volts for silicon and 0.3 volts
for germanium, the potential barriers opposition will be overcome and current will start to flow.
This is because the negative voltage pushes or repels electrons towards the junction giving them
the energy to cross over and combine with the holes being pushed in the opposite direction
towards the junction by the positive voltage. This results in a characteristics curve of zero current
flowing up to this voltage point, called the "knee" on the static curves and then a high current
flow through the diode with little increase in the external voltage as shown below.
Forward Characteristics Curve for a Junction Diode

The application of a forward biasing voltage on the junction diode results in the depletion layer
becoming very thin and narrow which represents a low impedance path through the junction
thereby allowing high currents to flow. The point at which this sudden increase in current takes
place is represented on the static I-V characteristics curve above as the "knee" point.
Forward Biased Junction Diode showing a Reduction in the Depletion Layer
This condition represents the low resistance path through the PN junction allowing very large
currents to flow through the diode with only a small increase in bias voltage. The actual potential
difference across the junction or diode is kept constant by the action of the depletion layer at
approximately 0.3v for germanium and approximately 0.7v for silicon junction diodes. Since the
diode can conduct "infinite" current above this knee point as it effectively becomes a short
circuit, therefore resistors are used in series with the diode to limit its current flow. Exceeding its

maximum forward current specification causes the device to dissipate more power in the form of
heat than it was designed for resulting in a very quick failure of the device.
Junction Diode Summary
The PN junction region of a Junction Diode has the following important characteristics:
 1). Semiconductors contain two types of mobile charge carriers, Holes and Electrons.

 2). The holes are positively charged while the electrons negatively charged.

 3). A semiconductor may be doped with donor impurities such as Antimony (N-type doping), so
that it contains mobile charges which are primarily electrons.

 4). A semiconductor may be doped with acceptor impurities such as Boron (P-type doping), so
that it contains mobile charges which are mainly holes.

 5). The junction region itself has no charge carriers and is known as the depletion region.

 6). The junction (depletion) region has a physical thickness that varies with the applied voltage.

 7).When a diode is Zero Biased no external energy source is applied and a natural Potential
Barrier is developed across a depletion layer which is approximately 0.5 to 0.7v for silicon
diodes and approximately 0.3 of a volt for germanium diodes.

 8). When a junction diode is Forward Biased the thickness of the depletion region reduces and
the diode acts like a short circuit allowing full current to flow.

 9). When a junction diode is Reverse Biased the thickness of the depletion region increases and
the diode acts like an open circuit blocking any current flow, (only a very small leakage current).
In the next tutorial about diodes, we will look at the small signal diode sometimes called a
switching diode that are used in general electronic circuits. A signal diode is designed for low-
voltage or high frequency signal applications such as in radio or digital switching circuits as
opposed to the high-current mains rectification diodes in which silicon diodes are usually used,
and examine the Signal Diode static current-voltage characteristics curve and parameters.

Signal Diode
The Signal Diode
The semiconductor Signal Diode is a small non-linear semiconductor devices generally used in
electronic circuits, where small currents or high frequencies are involved such as in radio,
television and digital logic circuits. The signal diode which is also sometimes known by its older
name of the Point Contact Diode or the Glass Passivated Diode, are physically very small in
size compared to their larger Power Diode cousins.
Generally, the PN junction of a small signal diode is encapsulated in glass to protect the PN
junction, and usually have a red or black band at one end of their body to help identify which end
is the cathode terminal. The most widely used of all the glass encapsulated signal diodes is the
very common 1N4148 and its equivalent 1N914 signal diode. Small signal and switching diodes
have much lower power and current ratings, around 150mA, 500mW maximum compared to
rectifier diodes, but they can function better in high frequency applications or in clipping and
switching applications that deal with short-duration pulse waveforms.
The characteristics of a signal point contact diode are different for both germanium and silicon
types and are given as:
 Germanium Signal Diodes - These have a low reverse resistance value giving a lower forward
volt drop across the junction, typically only about 0.2-0.3v, but have a higher forward resistance
value because of their small junction area.

 Silicon Signal Diodes - These have a very high value of reverse resistance and give a forward
volt drop of about 0.6-0.7v across the junction. They have fairly low values of forward resistance
giving them high peak values of forward current and reverse voltage.
The electronic symbol given for any type of diode is that of an arrow with a bar or line at its end
and this is illustrated below along with the Steady State V-I Characteristics Curve.

Silicon Diode V-I Characteristic Curve
The arrow points in the direction of conventional current flow through the diode meaning that
the diode will only conduct if a positive supply is connected to the Anode (a) terminal and a
negative supply is connected to the Cathode (k) terminal thus only allowing current to flow
through it in one direction only, acting more like a one way electrical valve, (Forward Biased
Condition). However, we know from the previous tutorial that if we connect the external energy
source in the other direction the diode will block any current flowing through it and instead will
act like an open switch, (Reversed Biased Condition) as shown below.
Forward and Reversed Biased Diode
Then we can say that an ideal small signal diode conducts current in one direction (forward-
conducting) and blocks current in the other direction (reverse-blocking). Signal Diodes are used

in a wide variety of applications such as a switch in rectifiers, limiters, snubbers or in wave-
shaping circuits.
Signal Diode Parameters
Signal Diodes are manufactured in a range of voltage and current ratings and care must be taken
when choosing a diode for a certain application. There are a bewildering array of static
characteristics associated with the humble signal diode but the more important ones are.
1. Maximum Forward Current
The Maximum Forward Current (IF(max)) is as its name implies the maximum forward current
allowed to flow through the device. When the diode is conducting in the forward bias condition,
it has a very small "ON" resistance across the PN junction and therefore, power is dissipated
across this junction (Ohm´s Law) in the form of heat. Then, exceeding its (IF(max)) value will
cause more heat to be generated across the junction and the diode will fail due to thermal
overload, usually with destructive consequences. When operating diodes around their maximum
current ratings it is always best to provide additional cooling to dissipate the heat produced by
the diode.
For example, our small 1N4148 signal diode has a maximum current rating of about 150mA with
a power dissipation of 500mW at 25o
C. Then a resistor must be used in series with the diode to
limit the forward current, (IF(max)) through it to below this value.
2. Peak Inverse Voltage
The Peak Inverse Voltage (PIV) or Maximum Reverse Voltage (VR(max)), is the maximum
allowable Reverse operating voltage that can be applied across the diode without reverse
breakdown and damage occurring to the device. This rating therefore, is usually less than the
"avalanche breakdown" level on the reverse bias characteristic curve. Typical values of VR(max)
range from a few volts to thousands of volts and must be considered when replacing a diode.
The peak inverse voltage is an important parameter and is mainly used for rectifying diodes in
AC rectifier circuits with reference to the amplitude of the voltage were the sinusoidal waveform
changes from a positive to a negative value on each and every cycle.
3. Forward Power Dissipation
Signal diodes have a Forward Power Dissipation, (PD(max)) rating. This rating is the maximum
possible power dissipation of the diode when it is forward biased (conducting). When current

flows through the signal diode the biasing of the PN junction is not perfect and offers some
resistance to the flow of current resulting in power being dissipated (lost) in the diode in the form
of heat. As small signal diodes are nonlinear devices the resistance of the PN junction is not
constant, it is a dynamic property then we cannot use Ohms Law to define the power in terms of
current and resistance or voltage and resistance as we can for resistors. Then to find the power
that will be dissipated by the diode we must multiply the voltage drop across it times the current
flowing through it: PD = VxI
4. Maximum Operating Temperature
The Maximum Operating Temperature actually relates to the Junction Temperature (TJ) of
the diode and is related to maximum power dissipation. It is the maximum temperature allowable
before the structure of the diode deteriorates and is expressed in units of degrees centigrade per
Watt, ( o
C/W ). This value is linked closely to the maximum forward current of the device so that
at this value the temperature of the junction is not exceeded. However, the maximum forward
current will also depend upon the ambient temperature in which the device is operating so the
maximum forward current is usually quoted for two or more ambient temperature values such as
25o
C or 70o
C.
Then there are three main parameters that must be considered when either selecting or replacing
a signal diode and these are:
 The Reverse Voltage Rating
 The Forward Current Rating
 The Forward Power Dissipation Rating
Signal Diode Arrays
When space is limited, or matching pairs of switching signal diodes are required, diode arrays
can be very useful. They generally consist of low capacitance high speed silicon diodes such as
the 1N4148 connected together in multiple diode packages called an array for use in switching
and clamping in digital circuits. They are encased in single inline packages (SIP) containing 4 or
more diodes connected internally to give either an individual isolated array, common cathode,
(CC), or a common anode, (CA) configuration as shown.

Signal Diode Arrays
Signal diode arrays can also be used in digital and computer circuits to protect high speed data
lines or other input/output parallel ports against electrostatic discharge, (ESD) and voltage
transients. By connecting two diodes in series across the supply rails with the data line connected
to their junction as shown, any unwanted transients are quickly dissipated and as the signal
diodes are available in 8-fold arrays they can protect eight data lines in a single package.

CPU Data Line Protection
Signal diode arrays can also be used to connect together diodes in either series or parallel
combinations to form voltage regulator or voltage reducing type circuits or to produce a known
fixed voltage. We know that the forward volt drop across a silicon diode is about 0.7v and by
connecting together a number of diodes in series the total voltage drop will be the sum of the
individual voltage drops of each diode. However, when signal diodes are connected together in
series, the current will be the same for each diode so the maximum forward current must not be
exceeded.
Connecting Signal Diodes in Series
Another application for the small signal diode is to create a regulated voltage supply. Diodes are
connected together in series to provide a constant DC voltage across the diode combination. The
output voltage across the diodes remains constant in spite of changes in the load current drawn
from the series combination or changes in the DC power supply voltage that feeds them.
Consider the circuit below.
Signal Diodes in Series
As the forward voltage drop across a silicon diode is almost constant at about 0.7v, while the
current through it varies by relatively large amounts, a forward-biased signal diode can make a
simple voltage regulating circuit. The individual voltage drops across each diode are subtracted
from the supply voltage to leave a certain voltage potential across the load resistor, and in our
simple example above this is given as 10v - (3 x 0.7v) = 7.9v. This is because each diode has a

junction resistance relating to the small signal current flowing through it and the three signal
diodes in series will have three times the value of this resistance, along with the load resistance
R, forms a voltage divider across the supply.
By adding more diodes in series a greater voltage reduction will occur. Also series connected
diodes can be placed in parallel with the load resistor to act as a voltage regulating circuit. Here
the voltage applied to the load resistor will be 3 x 0.7v = 2.1v. We can of course produce the
same constant voltage source using a single Zener Diode. Resistor, RD is used to prevent
excessive current flowing through the diodes if the load is removed.
Freewheel Diodes
Signal diodes can also be used in a variety of clamping, protection and wave shaping circuits
with the most common form of clamping diode circuit being one which uses a diode connected
in parallel with a coil or inductive load to prevent damage to the delicate switching circuit by
suppressing the voltage spikes and/or transients that are generated when the load is suddenly
turned "OFF". This type of diode is generally known as a "Free-wheeling Diode" or Freewheel
diode as it is more commonly called.
The Freewheel diode is used to protect solid state switches such as power transistors and
MOSFET's from damage by reverse battery protection as well as protection from highly
inductive loads such as relay coils or motors, and an example of its connection is shown below.
Use of the Freewheel Diode
Modern fast switching, power semiconductor devices require fast switching diodes such as free
wheeling diodes to protect them form inductive loads such as motor coils or relay windings.
Every time the switching device above is turned "ON", the freewheel diode changes from a
conducting state to a blocking state as it becomes reversed biased. However, when the device

rapidly turns "OFF", the diode becomes forward biased and the collapse of the energy stored in
the coil causes a current to flow through the freewheel diode. Without the protection of the
freewheel diode high di/dt currents would occur causing a high voltage spike or transient to flow
around the circuit possibly damaging the switching device.
Previously, the operating speed of the semiconductor switching device, either transistor,
MOSFET, IGBT or digital has been impaired by the addition of a freewheel diode across the
inductive load with Schottky and Zener diodes being used instead in some applications. But
during the past few years however, freewheel diodes had regained importance due mainly to
their improved reverse-recovery characteristics and the use of super fast semiconductor materials
capable at operating at high switching frequencies.
Other types of specialized diodes not included here are Photo-Diodes, PIN Diodes, Tunnel
Diodes and Schottky Barrier Diodes. By adding more PN junctions to the basic two layer diode
structure other types of semiconductor devices can be made. For example a three layer
semiconductor device becomes a Transistor, a four layer semiconductor device becomes a
Thyristor or Silicon Controlled Rectifier and five layer devices known as Triacs are also
available.
In the next tutorial about diodes, we will look at the large signal diode sometimes called the
Power Diode. Power diodes are silicon diodes designed for use in high-voltage, high-current
mains rectification circuits.
Power Diodes and Rectifiers
The Power Diode
In the previous tutorials we saw that a semiconductor signal diode will only conduct current in
one direction from its anode to its cathode (forward direction), but not in the reverse direction
acting a bit like an electrical one way valve. A widely used application of this feature is in the
conversion of an alternating voltage (AC) into a continuous voltage (DC). In other words,
Rectification. Small signal diodes can be used as rectifiers in low-power, low current (less than
1-amp) rectifiers or applications, but were larger forward bias currents or higher reverse bias
blocking voltages are involved the PN junction of a small signal diode would eventually overheat
and melt so larger more robust Power Diodes are used instead.
The power semiconductor diode, known simply as the Power Diode, has a much larger PN
junction area compared to its smaller signal diode cousin, resulting in a high forward current

capability of up to several hundred amps (KA) and a reverse blocking voltage of up to several
thousand volts (KV). Since the power diode has a large PN junction, it is not suitable for high
frequency applications above 1MHz, but special and expensive high frequency, high current
diodes are available. For high frequency rectifier applications Schottky Diodes are generally
used because of their short reverse recovery time and low voltage drop in their forward bias
condition.
Power diodes provide uncontrolled rectification of power and are used in applications such as
battery charging and DC power supplies as well as AC rectifiers and inverters. Due to their high
current and voltage characteristics they can also be used as freewheeling diodes and snubber
networks. Power diodes are designed to have a forward "ON" resistance of fractions of an Ohm
while their reverse blocking resistance is in the mega-Ohms range. Some of the larger value
power diodes are designed to be "stud mounted" onto heatsinks reducing their thermal resistance
to between 0.1 to 1o
C/Watt.
If an alternating voltage is applied across a power diode, during the positive half cycle the diode
will conduct passing current and during the negative half cycle the diode will not conduct
blocking the flow of current. Then conduction through the power diode only occurs during the
positive half cycle and is therefore unidirectional i.e. DC as shown.
Power Diode Rectifier
Power diodes can be used individually as above or connected together to produce a variety of
rectifier circuits such as "Half-Wave", "Full-Wave" or as "Bridge Rectifiers". Each type of
rectifier circuit can be classed as either uncontrolled, half-controlled or fully controlled were an
uncontrolled rectifier uses only power diodes, a fully controlled rectifier uses thyristors (SCRs)
and a half controlled rectifier is a mixture of both diodes and thyristors. The most commonly
used individual power diode for basic electronics applications is the general purpose 1N400x
Series Glass Passivated type rectifying diode with standard ratings of continuous forward
rectified current of 1.0 amp and reverse blocking voltage ratings from 50v for the 1N4001 up to

1000v for the 1N4007, with the small 1N4007GP being the most popular for general purpose
mains voltage rectification.
Half Wave Rectification
A rectifier is a circuit which converts the Alternating Current (AC) input power into a Direct
Current (DC) output power. The input power supply may be either a single-phase or a multi-
phase supply with the simplest of all the rectifier circuits being that of the Half Wave Rectifier.
The power diode in a half wave rectifier circuit passes just one half of each complete sine wave
of the AC supply in order to convert it into a DC supply. Then this type of circuit is called a
"half-wave" rectifier because it passes only half of the incoming AC power supply as shown
below.
Half Wave Rectifier Circuit
During each "positive" half cycle of the AC sine wave, the diode is forward biased as the anode
is positive with respect to the cathode resulting in current flowing through the diode. Since the
DC load is resistive (resistor, R), the current flowing in the load resistor is therefore proportional
to the voltage (Ohm´s Law), and the voltage across the load resistor will therefore be the same
as the supply voltage, Vs (minus Vf), that is the "DC" voltage across the load is sinusoidal for
the first half cycle only so Vout = Vs.
During each "negative" half cycle of the AC sine wave, the diode is reverse biased as the anode
is negative with respect to the cathode therefore, No current flows through the diode or circuit.
Then in the negative half cycle of the supply, no current flows in the load resistor as no voltage
appears across it so Vout = 0.

The current on the DC side of the circuit flows in one direction only making the circuit
Unidirectional and the value of the DC voltage VDC across the load resistor is calculated as
follows.
Where Vmax is the maximum voltage value of the AC supply, and VS is the r.m.s. value of the
supply.
Example No1.
Calculate the current, ( IDC ) flowing through a 100Ω resistor connected to a 240v single phase
half-wave rectifier as shown above. Also calculate the power consumed by the load.
During the rectification process the resultant output DC voltage and current are therefore both
"ON" and "OFF" during every cycle. As the voltage across the load resistor is only present
during the positive half of the cycle (50% of the input waveform), this results in a low average
DC value being supplied to the load. The variation of the rectified output waveform between this
ON and OFF condition produces a waveform which has large amounts of "ripple" which is an
undesirable feature. The resultant DC ripple has a frequency that is equal to that of the AC
supply frequency.
Very often when rectifying an alternating voltage we wish to produce a "steady" and continuous
DC voltage free from any voltage variations or ripple. One way of doing this is to connect a large
value Capacitor across the output voltage terminals in parallel with the load resistor as shown
below. This type of capacitor is known commonly as a "Reservoir" or Smoothing Capacitor.

Half-wave Rectifier with Smoothing Capacitor
When rectification is used to provide a direct voltage power supply from an alternating source,
the amount of ripple can be further reduced by using larger value capacitors but there are limits
both on cost and size. For a given capacitor value, a greater load current (smaller load resistor)
will discharge the capacitor more quickly (RC Time Constant) and so increases the ripple
obtained. Then for single phase, half-wave rectifier circuits it is not very practical to try and
reduce the ripple voltage by capacitor smoothing alone, it is more practical to use "Full-wave
Rectification" instead.
In practice, the half-wave rectifier is used most often in low-power applications because of their
major disadvantages being. The output amplitude is less than the input amplitude, there is no
output during the negative half cycle so half the power is wasted and the output is pulsed DC
resulting in excessive ripple. To overcome these disadvantages a number of Power Diodes are
connected together to produce a Full Wave Rectifier as discussed in the next tutorial.
Full Wave Rectifier
In the previous Power Diodes tutorial we discussed ways of reducing the ripple or voltage
variations on a direct DC voltage by connecting capacitors across the load resistance. While this
method may be suitable for low power applications it is unsuitable to applications which need a
"steady and smooth" DC supply voltage. One method to improve on this is to use every half-
cycle of the input voltage instead of every other half-cycle. The circuit which allows us to do this
is called a Full Wave Rectifier.

Like the half wave circuit, a full wave rectifier circuit produces an output voltage or current
which is purely DC or has some specified DC component. Full wave rectifiers have some
fundamental advantages over their half wave rectifier counterparts. The average (DC) output
voltage is higher than for half wave, the output of the full wave rectifier has much less ripple
than that of the half wave rectifier producing a smoother output waveform.
In a Full Wave Rectifier circuit two diodes are now used, one for each half of the cycle. A
transformer is used whose secondary winding is split equally into two halves with a common
centre tapped connection, (C). This configuration results in each diode conducting in turn when
its anode terminal is positive with respect to the transformer centre point C producing an output
during both half-cycles, twice that for the half wave rectifier so it is 100% efficient as shown
below.
Full Wave Rectifier Circuit
The full wave rectifier circuit consists of two power diodes connected to a single load resistance
(RL) with each diode taking it in turn to supply current to the load. When point A of the
transformer is positive with respect to point B, diode D1 conducts in the forward direction as
indicated by the arrows. When point B is positive (in the negative half of the cycle) with respect
to point A, diode D2 conducts in the forward direction and the current flowing through resistor R
is in the same direction for both circuits. As the output voltage across the resistor R is the phasor

sum of the two waveforms combined, this type of full wave rectifier circuit is also known as a
"bi-phase" circuit.
As the spaces between each half-wave developed by each diode is now being filled in by the
other diode the average DC output voltage across the load resistor is now double that of the
single half-wave rectifier circuit and is about 0.637Vmax of the peak voltage, assuming no
losses. However in reality, during each half cycle the current flows through two diodes instead of
just one so the amplitude of the output voltage is two voltage drops ( 2 x 0.7 = 1.4V ) less than
the input VMAX amplitude.
The peak voltage of the output waveform is the same as before for the half-wave rectifier
provided each half of the transformer windings have the same rms voltage value. To obtain a
different DC voltage output different transformer ratios can be used. The main disadvantage of
this type of full wave rectifier circuit is that a larger transformer for a given power output is
required with two separate but identical secondary windings making this type of full wave
rectifying circuit costly compared to the "Full Wave Bridge Rectifier" circuit equivalent.
The Full Wave Bridge Rectifier
Another type of circuit that produces the same output waveform as the full wave rectifier circuit
above, is that of the Full Wave Bridge Rectifier. This type of single phase rectifier uses four
individual rectifying diodes connected in a closed loop "bridge" configuration to produce the
desired output. The main advantage of this bridge circuit is that it does not require a special
centre tapped transformer, thereby reducing its size and cost. The single secondary winding is
connected to one side of the diode bridge network and the load to the other side as shown below.
The Diode Bridge Rectifier

The four diodes labelled D1 to D4 are arranged in "series pairs" with only two diodes conducting
current during each half cycle. During the positive half cycle of the supply, diodes D1 and D2
conduct in series while diodes D3 and D4 are reverse biased and the current flows through the
load as shown below.
The Positive Half-cycle
During the negative half cycle of the supply, diodes D3 and D4 conduct in series, but diodes D1
and D2 switch of as they are now reverse biased. The current flowing through the load is the
same direction as before.

The Negative Half-cycle
As the current flowing through the load is unidirectional, so the voltage developed across the
load is also unidirectional the same as for the previous two diode full-wave rectifier, therefore
the average DC voltage across the load is 0.637Vmax and the ripple frequency is now twice the
supply frequency (e.g. 100Hz for a 50Hz supply).
Typical Bridge Rectifier
Although we can use four individual power diodes to make a full wave bridge rectifier, pre-made
bridge rectifier components are available "off-the-shelf" in a range of different voltage and
current sizes that can be soldered directly into a PCB circuit board or be connected by spade
connectors. The image to the right shows a typical single phase bridge rectifier with one corner
cut off. This cut-off corner indicates that the terminal nearest to the corner is the positive or +ve
output terminal or lead with the opposite (diagonal) lead being the negative or -ve output lead.
The other two connecting leads are for the input alternating voltage from a transformer
secondary winding.

The Smoothing Capacitor
We saw in the previous section that the single phase half-wave rectifier produces an output wave
every half cycle and that it was not practical to use this type of circuit to produce a steady DC
supply. The full-wave bridge rectifier however, gives us a greater mean DC value (0.637 Vmax)
with less superimposed ripple while the output waveform is twice that of the frequency of the
input supply frequency. We can therefore increase its average DC output level even higher by
connecting a suitable smoothing capacitor across the output of the bridge circuit as shown below.
Full-wave Rectifier with Smoothing Capacitor
The smoothing capacitor converts the full-wave rippled output of the rectifier into a smooth DC
output voltage. Generally for DC power supply circuits the smoothing capacitor is an Aluminium
Electrolytic type that has a capacitance value of 100uF or more with repeated DC voltage pulses
from the rectifier charging up the capacitor to peak voltage. However, their are two important
parameters to consider when choosing a suitable smoothing capacitor and these are its Working
Voltage, which must be higher than the no-load output value of the rectifier and its Capacitance
Value, which determines the amount of ripple that will appear superimposed on top of the DC
voltage. Too low a value and the capacitor has little effect but if the smoothing capacitor is large
enough (parallel capacitors can be used) and the load current is not too large, the output voltage
will be almost as smooth as pure DC. As a general rule of thumb, we are looking to have a ripple
voltage of less than 100mV peak to peak.

The maximum ripple voltage present for a Full Wave Rectifier circuit is not only determined by
the value of the smoothing capacitor but by the frequency and load current, and is calculated as:
Bridge Rectifier Ripple Voltage
Where: I is the DC load current in amps, ƒ is the frequency of the ripple or twice the input
frequency in Hertz, and C is the capacitance in Farads.
The main advantages of a full-wave bridge rectifier is that it has a smaller AC ripple value for a
given load and a smaller reservoir or smoothing capacitor than an equivalent half-wave rectifier.
Therefore, the fundamental frequency of the ripple voltage is twice that of the AC supply
frequency (100Hz) where for the half-wave rectifier it is exactly equal to the supply frequency
(50Hz).
The amount of ripple voltage that is superimposed on top of the DC supply voltage by the diodes
can be virtually eliminated by adding a much improved π-filter (pi-filter) to the output terminals
of the bridge rectifier. This type of low-pass filter consists of two smoothing capacitors, usually
of the same value and a choke or inductance across them to introduce a high impedance path to
the alternating ripple component. Another more practical and cheaper alternative is to use a 3-
terminal voltage regulator IC, such as a LM78xx for a positive output voltage or the LM79xx for
a negative output voltage which can reduce the ripple by more than 70dB (Datasheet) while
delivering a constant output current of over 1 amp.
In the next tutorial about diodes, we will look at the Zener Diode which takes advantage of its
reverse breakdown voltage characteristic to produce a constant and fixed output voltage across
itself.
Zener Diodes
The Zener Diode
In the previous Signal Diode tutorial, we saw that a "reverse biased" diode blocks current in the
reverse direction, but will suffer from premature breakdown or damage if the reverse voltage
applied across it is too high. However, the Zener Diode or "Breakdown Diode" as they are
sometimes called, are basically the same as the standard PN junction diode but are specially
designed to have a low pre-determined Reverse Breakdown Voltage that takes advantage of

this high reverse voltage. The point at which a zener diode breaks down or conducts is called the
"Zener Voltage" (Vz).
The Zener diode is like a general-purpose signal diode consisting of a silicon PN junction.
When biased in the forward direction it behaves just like a normal signal diode passing the rated
current, but when a reverse voltage is applied to it the reverse saturation current remains fairly
constant over a wide range of voltages. The reverse voltage increases until the diodes breakdown
voltage VB is reached at which point a process called Avalanche Breakdown occurs in the
depletion layer and the current flowing through the zener diode increases dramatically to the
maximum circuit value (which is usually limited by a series resistor). This breakdown voltage
point is called the "zener voltage" for zener diodes.
The point at which current flows can be very accurately controlled (to less than 1% tolerance) in
the doping stage of the diodes construction giving the diode a specific zener breakdown voltage,
(Vz) ranging from a few volts up to a few hundred volts. This zener breakdown voltage on the I-
V curve is almost a vertical straight line.
Zener Diode I-V Characteristics
The Zener Diode is used in its "reverse bias" or reverse breakdown mode, i.e. the diodes anode

connects to the negative supply. From the I-V characteristics curve above, we can see that the
zener diode has a region in its reverse bias characteristics of almost a constant negative voltage
regardless of the value of the current flowing through the diode and remains nearly constant even
with large changes in current as long as the zener diodes current remains between the breakdown
current IZ(min) and the maximum current rating IZ(max).
This ability to control itself can be used to great effect to regulate or stabilise a voltage source
against supply or load variations. The fact that the voltage across the diode in the breakdown
region is almost constant turns out to be an important application of the zener diode as a voltage
regulator. The function of a regulator is to provide a constant output voltage to a load connected
in parallel with it in spite of the ripples in the supply voltage or the variation in the load current
and the zener diode will continue to regulate the voltage until the diodes current falls below the
minimum IZ(min) value in the reverse breakdown region.
The Zener Diode Regulator
Zener Diodes can be used to produce a stabilised voltage output with low ripple under varying
load current conditions. By passing a small current through the diode from a voltage source, via a
suitable current limiting resistor (RS), the zener diode will conduct sufficient current to maintain
a voltage drop of Vout. We remember from the previous tutorials that the DC output voltage
from the half or full-wave rectifiers contains ripple superimposed onto the DC voltage and that
as the load value changes so to does the average output voltage. By connecting a simple zener
stabiliser circuit as shown below across the output of the rectifier, a more stable output voltage
can be produced.
Zener Diode Regulator

The resistor, RS is connected in series with the zener diode to limit the current flow through the
diode with the voltage source, VS being connected across the combination. The stabilised output
voltage Vout is taken from across the zener diode. The zener diode is connected with its cathode
terminal connected to the positive rail of the DC supply so it is reverse biased and will be
operating in its breakdown condition. Resistor RS is selected so to limit the maximum current
flowing in the circuit.
With no load connected to the circuit, the load current will be zero, ( IL = 0 ), and all the circuit
current passes through the zener diode which inturn dissipates its maximum power. Also a small
value of the series resistor RS will result in a greater diode current when the load resistance RL is
connected and large as this will increase the power dissipation requirement of the diode so care
must be taken when selecting the appropriate value of series resistance so that the zeners
maximum power rating is not exceeded under this no-load or high-impedance condition.
The load is connected in parallel with the zener diode, so the voltage across RL is always the
same as the zener voltage, ( VR = VZ ). There is a minimum zener current for which the
stabilization of the voltage is effective and the zener current must stay above this value operating
under load within its breakdown region at all times. The upper limit of current is of course
dependant upon the power rating of the device. The supply voltage VS must be greater than VZ.
One small problem with zener diode stabiliser circuits is that the diode can sometimes generate
electrical noise on top of the DC supply as it tries to stabilise the voltage. Normally this is not a
problem for most applications but the addition of a large value decoupling capacitor across the
zeners output may be required to give additional smoothing.
Then to summarise a little. A zener diode is always operated in its reverse biased condition. A
voltage regulator circuit can be designed using a zener diode to maintain a constant DC output
voltage across the load in spite of variations in the input voltage or changes in the load current.
The zener voltage regulator consists of a current limiting resistor RS connected in series with the
input voltage VS with the zener diode connected in parallel with the load RL in this reverse
biased condition. The stabilized output voltage is always selected to be the same as the
breakdown voltage VZ of the diode.
Example No1
A 5.0V stabilised power supply is required to be produced from a 12V DC power supply
input source. The maximum power rating PZ of the zener diode is 2W. Using the zener
regulator circuit above calculate:

a) The maximum current flowing through the zener diode.
b) The value of the series resistor, RS
c) The load current IL if a load resistor of 1kΩ is connected across the Zener diode.
d) The total supply current IS
Zener Diode Voltages
As well as producing a single stabilised voltage output, zener diodes can also be connected
together in series along with normal silicon signal diodes to produce a variety of different
reference voltage output values as shown below.
Zener Diodes Connected in Series

The values of the individual Zener diodes can be chosen to suit the application while the silicon
diode will always drop about 0.6 - 0.7V in the forward bias condition. The supply voltage, Vin
must of course be higher than the largest output reference voltage and in our example above this
is 19v.
A typical zener diode for general electronic circuits is the 500mW, BZX55 series or the larger
1.3W, BZX85 series were the zener voltage is given as, for example, C7V5 for a 7.5V diode
giving a diode reference number of BZX55C7V5. The 500mW series of zener diodes are
available from about 2.4 up to about 100 volts and typically have the same sequence of values as
used for the 5% (E24) resistor series with the individual voltage ratings for these small but very
useful diodes are given in the table below.
Zener Diode Standard Voltages
BZX55 Zener Diode Power Rating 500mW
2.4V 2.7V 3.0V 3.3V 3.6V 3.9V 4.3V 4.7V
5.1V 5.6V 6.2V 6.8V 7.5V 8.2V 9.1V 10V
11V 12V 13V 15V 16V 18V 20V 22V
24V 27V 30V 33V 36V 39V 43V 47V
BZX85 Zener Diode Power Rating 1.3W
3.3V 3.6V 3.9V 4.3V 4.7V 5.1V 5.6 6.2V
6.8V 7.5V 8.2V 9.1V 10V 11V 12V 13V
15V 16V 18V 20V 22V 24V 27V 30V
33V 36V 39V 43V 47V 51V 56V 62V

Zener Diode Clipping Circuits
Thus far we have looked at how a zener diode can be used to regulate a constant DC source but
what if the input signal was not steady state DC but an alternating AC waveform how would the
zener diode react to a constantly changing signal.
Diode clipping and clamping circuits are circuits that are used to shape or modify an input AC
waveform (or any sinusoid) producing a differently shape output waveform depending on the
circuit arrangement. Diode clipper circuits are also called limiters because they limit or clip-off
the positive (or negative) part of an input AC signal. As zener clipper circuits limit or cut-off part
of the waveform across them, they are mainly used for circuit protection or in waveform shaping
circuits. For example, if we wanted to clip an output waveform at +7.5V, we would use a 7.5V
zener diode. If the output waveform tries to exceed the 7.5V limit, the zener diode will "clip-off"
the excess voltage from the input producing a waveform with a flat top still keeping the output
constant at +7.5V. Note that in the forward bias condition a zener diode is still a diode and when
the AC waveform output goes negative below -0.7V, the zener diode turns "ON" like any normal
silicon diode would and clips the output at -0.7V as shown below.
Square Wave Signal
The back to back connected zener diodes can be used as an AC regulator producing what is
jokingly called a "poor man's square wave generator". Using this arrangement we can clip the
waveform between a positive value of +7.5V and a negative value of -7.5V. If we wanted to clip

an output waveform between different minimum and maximum values for example, +8V and -
6V, use would simply use two differently rated zener diodes.
Note that the output will actually clip the AC waveform between +8.7V and -6.7V due to the
addition of the forward biasing diode voltage, which adds another 0.7V voltage drop to it. This
type of clipper configuration is fairly common for protecting an electronic circuit from over
voltage. The two zeners are generally placed across the power supply input terminals and during
normal operation, one of the zener diodes is "OFF" and the diodes have little or no affect.
However, if the input voltage waveform exceeds its limit, then the zeners turn "ON" and clip the
input to protect the circuit.
In the next tutorial about diodes, we will look at using the forward biased PN junction of a diode
to produce light. We know from the previous tutorials that when charge carriers move across the
junction, electrons combine with holes and energy is lost in the form of heat, but also some of
this energy is dissipated as photons but we can not see them. If we place a translucent lens
around the junction, visible light will be produced and the diode becomes a light source. This
effect produces another type of diode known commonly as the Light Emitting Diode which
takes advantage of this light producing characteristic to emit light (photons) in a variety of
colours and wavelengths.
Light Emitting Diodes
Light Emitting Diodes or LED´s, are among the most widely used of all the different types of
semiconductor diodes available today. They are the most visible type of diode, that emit a fairly
narrow bandwidth of either visible light at different coloured wavelengths, invisible infra-red
light for remote controls or laser type light when a forward current is passed through them. A
"Light Emitting Diode" or LED as it is more commonly called, is basically just a specialised
type of PN junction diode, made from a very thin layer of fairly heavily doped semiconductor
material. When the diode is forward biased, electrons from the semiconductors conduction band
recombine with holes from the valence band releasing sufficient energy to produce photons
which emit a monochromatic (single colour) of light. Because of this thin layer a reasonable
number of these photons can leave the junction and radiate away producing a coloured light
output. Then we can say that when operated in a forward biased direction Light Emitting
Diodes are semiconductor devices that convert electrical energy into light energy.

The construction of a light emitting diode is very different from that of a normal signal diode.
The PN junction of an LED is surrounded by a transparent, hard plastic epoxy resign
hemispherical shaped shell or body which protects the LED from both vibration and shock.
Surprisingly, an LED junction does not actually emit that much light so the epoxy resin body is
constructed in such a way that the photons of light emitted by the junction are reflected away
from the surrounding substrate base to which the diode is attached and are focused upwards
through the domed top of the LED, which itself acts like a lens concentrating the amount of light.
This is why the emitted light appears to be brightest at the top of the LED.
However, not all LEDs are made with a hemispherical shaped dome for their epoxy shell. Some
LEDs have a rectangular or cylindrical shaped construction that has a flat surface on top. Also,
nearly all LEDs have their cathode, (K) terminal identified by either a notch or flat spot on the
body, or by one of the leads being shorter than the other, (the Anode, A).
Unlike normal incandescent lamps and bulbs which generate large amounts of heat when
illuminated, the light emitting diode produces a "cold" generation of light which leads to high
efficiencies than the normal "light bulb" because most of the generated energy radiates away
within the visible spectrum. Because LEDs are solid-state devices, they can be extremely small
and durable and provide much longer lamp life than normal light sources.
Light Emitting Diode Colours
So how does a light emitting diode get its colour. Unlike normal signal diodes which are made
for detection or power rectification, and which are made from either Germanium or Silicon
semiconductor materials, Light Emitting Diodes are made from exotic semiconductor
compounds such as Gallium Arsenide (GaAs), Gallium Phosphide (GaP), Gallium Arsenide
Phosphide (GaAsP), Silicon Carbide (SiC) or Gallium Indium Nitride (GaInN) all mixed
together at different ratios to produce a distinct wavelength of colour. Different LED compounds
emit light in specific regions of the visible light spectrum and therefore produce different

intensity levels. The exact choice of the semiconductor material used will determine the overall
wavelength of the photon light emissions and therefore the resulting colour of the light emitted.
Thus, the actual colour of a light
emitting diode is determined by the
wavelength of the light emitted, which
inturn is determined by the actual
semiconductor compound used in
forming the PN junction during
manufacture and NOT by the colouring
of the LEDs plastic body although these
are slightly coloured to both enhance
the light and indicate its colour when its
not be used. Light emitting diodes are
available in a wide range of colours with the most common being RED, AMBER, YELLOW
and GREEN and are thus widely used as visual indicators and as moving light displays.
Recently developed blue and white coloured LEDs are also available but these tend to be much
more expensive than the normal standard colours due to the production costs of mixing together
two or more complementary colours at an exact ratio within the semiconductor compound and
also by injecting nitrogen atoms into the crystal structure during the doping process.
From the table above we can see that the main P-type dopant used in the manufacture of Light
Emitting Diodes is Gallium (Ga, atomic number 31) and that the main N-type dopant used is
Arsenic (As, atomic number 31) giving the resulting compound of Gallium Arsenide (GaAs)
crystal structure. The problem with using Gallium Arsenide on its own as the semiconductor
compound is that it radiates large amounts of low brightness infra-red radiation (850nm-940nm
approx.) from its junction when a forward current is flowing through it. This infra-red light is ok
for television remote controls but not very useful if we want to use the LED as an indicating
light. But by adding Phosphorus (P, atomic number 15), as a third dopant the overall wavelength
of the emitted radiation is reduced to below 680nm giving visible red light to the human eye.
Further refinements in the doping process of the PN junction have resulted in a range of colours
spanning the spectrum of visible light as we have seen above as well as infra-red and ultra-violet
wavelengths.
By mixing together a variety of semiconductor, metal and gas compounds the following list of
LEDs can be produced.
 Gallium Arsenide (GaAs) - infra-red
Typical LED Characteristics
Semiconductor
Material
Wavelength Colour VF @ 20mA
GaAs 850-940nm Infra-Red 1.2v
GaAsP 630-660nm Red 1.8v
GaAsP 605-620nm Amber 2.0v
GaAsP:N 585-595nm Yellow 2.2v
AlGaP 550-570nm Green 3.5v
SiC 430-505nm Blue 3.6v
GaInN 450nm White 4.0v

 Gallium Arsenide Phosphide (GaAsP) - red to infra-red, orange
 Aluminium Gallium Arsenide Phosphide (AlGaAsP) - high-brightness red, orange-red, orange,
and yellow
 Gallium Phosphide (GaP) - red, yellow and green
 Aluminium Gallium Phosphide (AlGaP) - green
 Gallium Nitride (GaN) - green, emerald green
 Gallium Indium Nitride (GaInN) - near ultraviolet, bluish-green and blue
 Silicon Carbide (SiC) - blue as a substrate
 Zinc Selenide (ZnSe) - blue
 Aluminium Gallium Nitride (AlGaN) - ultraviolet
Like conventional PN junction diodes, LEDs are current-dependent devices with its forward
voltage drop VF, depending on the semiconductor compound (its light colour) and on the forward
biased LED current. The point where conduction begins and light is produced is about 1.2V for a
standard red LED to about 3.6V for a blue LED. The exact voltage drop will of course depend on
the manufacturer because of the different dopant materials and wavelengths used. The voltage
drop across the LED at a particular current value, for example 20mA, will also depend on the
initial conduction VF point. As an LED is effectively a diode, its forward current to voltage
characteristics curves can be plotted for each diode colour as shown below.
Light Emitting Diodes I-V Characteristics.

Light Emitting Diode (LED) Schematic symbol and its I-V Characteristics Curves showing
the different colours available.
Before a light emitting diode can "emit" any form of light it needs a current to flow through it, as
it is a current dependant device with their light output intensity being directly proportional to the
forward current flowing through the LED. As the LED is to be connected in a forward bias
condition across a power supply it should be current limited using a series resistor to protect it
from excessive current flow. Never connect an LED directly to a battery or power supply as it
will be destroyed almost instantly because too much current will pass through and burn it out.
From the table above we can see that each LED has its own forward voltage drop across the PN
junction and this parameter which is determined by the semiconductor material used, is the
forward voltage drop for a specified amount of forward conduction current, typically for a
forward current of 20mA. In most cases LEDs are operated from a low voltage DC supply, with
a series resistor, RS used to limit the forward current to a safe value from say 5mA for a simple
LED indicator to 30mA or more where a high brightness light output is needed.
LED Series Resistance.
The series resistor value RS is calculated by simply using Ohm´s Law, by knowing the required
forward current IF of the LED, the supply voltage VS across the combination and the expected

forward voltage drop of the LED, VF at the required current level, the current limiting resistor is
calculated as:
LED Series Resistor Circuit
Example No1
An amber coloured LED with a forward volt drop of 2 volts is to be connected to a 5.0v
stabilised DC power supply. Using the circuit above calculate the value of the series resistor
required to limit the forward current to less than 10mA. Also calculate the current flowing
through the diode if a 100Ω series resistor is used instead of the calculated first.
1). series resistor value at 10mA.
2). with a 100Ω series resistor.

We remember from the Resistors tutorials, that resistors come in standard preferred values. Our
first calculation above shows to limit the current flowing through the LED to 10mA exactly, we
would require a 300Ω resistor. In the E12 series of resistors there is no 300Ω resistor so we
would need to choose the next highest value, which is 330Ω. A quick re-calculation shows the
new forward current value is now 9.1mA, and this is ok.
LED Driver Circuits
Now that we know what is an LED, we need some way of controlling it by switching it "ON"
and "OFF". The output stages of both TTL and CMOS logic gates can both source and sink
useful amounts of current therefore can be used to drive an LED. Normal integrated circuits
(ICs) have an output drive current of up to 50mA in the sink mode configuration, but have an
internally limited output current of about 30mA in the source mode configuration. Either way the
LED current must be limited to a safe value using a series resistor as we have already seen.
Below are some examples of driving light emitting diodes using inverting ICs but the idea is the
same for any type of integrated circuit output whether combinational or sequential.
IC Driver Circuit
If more than one LED requires driving at the same time, such as in large LED arrays, or the load
current is to high for the integrated circuit or we may just want to use discrete components
instead of ICs, then an alternative way of driving the LEDs using either bipolar NPN or PNP
transistors as switches is given below. Again as before, a series resistor, RS is required to limit
the LED current.

Transistor Driver Circuit
The brightness of a light emitting diode cannot be controlled by simply varying the current
flowing through it. Allowing more current to flow through the LED will make it glow brighter
but will also cause it to dissipate more heat. LEDs are designed to produce a set amount of light
operating at a specific forward current ranging from about 10 to 20mA. In situations were power
savings are important, less current may be possible. However, reducing the current to below say
5mA may dim its light output too much or even turn the LED "OFF" completely. A much better
way to control the brightness of LEDs is to use a control process known as "Pulse Width
Modulation" or PWM, in which the LED is repeatedly turned "ON" and "OFF" at varying
frequencies depending upon the required light intensity.
LED Light Intensity using PWM

When higher light outputs are required, a pulse width modulated current with a fairly short duty
cycle ("ON-OFF" Ratio) allows the diode current and therefore the output light intensity to be
increased significantly during the actual pulses, while still keeping the LEDs "average current
level" and power dissipation within safe limits. This "ON-OFF" flashing condition does not
affect what is seen as the human eyes fills in the gaps between the "ON" and "OFF" light pulses,
providing the pulse frequency is high enough, making it appear as a continuous light output. So
pulses at a frequency of 100Hz or more actually appear brighter to the eye than a continuous
light of the same average intensity.
Multi-coloured Light Emitting Diode
LEDs are available in a wide range of shapes, colours and various sizes with different light
output intensities available, with the most common (and cheapest to produce) being the standard
5mm Red Gallium Arsenide Phosphide (GaAsP) LED. LED's are also available in various
"packages" arranged to produce both letters and numbers with the most common being that of
the "seven segment display" arrangement. Nowadays, full colour flat screen LED displays are
available with a large number of dedicated ICs available for driving the displays directly. Most
light emitting diodes produce just a single output of coloured light however, multi-coloured
LEDs are now available that can produce a range of different colours from within a single
device. Most of these are actually two or three LEDs fabricated within a single package.
Bicolour Light Emitting Diodes
A bicolour light emitting diode has two LEDs chips connected together in "inverse parallel" (one
forwards, one backwards) combined in one single package. Bicolour LEDs can produce any one
of three colours for example, a red colour is emitted when the device is connected with current
flowing in one direction and a green colour is emitted when it is biased in the other direction.
This type of bi-directional arrangement is useful for giving polarity indication, for example, the

correct connection of batteries or power supplies etc. Also, a bi-directional current produces both
colours mixed together as the two LEDs would take it in turn to illuminate if the device was
connected (via a suitable resistor) to a low voltage, low frequency AC supply.
A Bicolour LED
LED
Selected
Terminal A
AC
+ -
LED 1 ON OFF ON
LED 2 OFF ON ON
Colour Green Red Yellow
Tricolour Light Emitting Diodes
The most popular type of tricolour LED comprises of a single Red and a Green LED combined
in one package with their cathode terminals connected together producing a three terminal
device. They are called tricolour LEDs because they can give out a single red or a green colour
by turning "ON" only one LED at a time. They can also generate additional shades of colours
(the third colour) such as Orange or Yellow by turning "ON" the two LEDs in different ratios of
forward current as shown in the table thereby generating 4 different colours from just two diode
junctions.
A Multi or Tricolour LED
Output
Colour
Red Orange Yellow Green
LED 1
Current
0 5mA 9.5mA 15mA
LED 2
Current
10mA 6.5mA 3.5mA 0
LED Displays
As well as individual colour or multi-colour LEDs, several light emitting diodes can be
combined together within a single package to produce displays such as bargraphs, strips, arrays

and seven segment displays. A seven segment LED display provides a very convenient way
when decoded properly of displaying information or digital data in the form of numbers, letters
or even alpha-numerical characters and as their name suggests, they consist of seven individual
LEDs (the segments), within one single display package.
In order to produce the required numbers or characters from 0 to 9 and A to F respectively, on
the display the correct combination of LED segments need to be illuminated. A standard seven
segment LED display generally has eight input connections, one for each LED segment and one
that acts as a common terminal or connection for all the internal segments.
 The Common Cathode Display (CCD) - In the common cathode display, all the cathode
connections of the LEDs are joined together and the individual segments are illuminated by
application of a HIGH, logic "1" signal.

 The Common Anode Display (CAD) - In the common anode display, all the anode connections
of the LEDs are joined together and the individual segments are illuminated by connecting the
terminals to a LOW, logic "0" signal.
A Typical Seven Segment LED Display
Opto-coupler
Finally, another useful application of light emitting diodes is Opto-coupling. An opto-coupler or
opto-isolator as it is also called, is a single electronic device that consists of a light emitting
diode combined with either a photo-diode, photo-transistor or photo-triac to provide an optical
signal path between an input connection and an output connection while maintaining electrical
isolation between two circuits. An opto-isolator consists of a light proof plastic body that has a

typical breakdown voltages between the input (photo-diode) and the output (photo-transistor)
circuit of up to 5000 volts. This electrical isolation is especially useful where the signal from a
low voltage circuit such as a battery powered circuit, computer or microcontroller, is required to
operate or control another external circuit operating at a potentially dangerous mains voltage.
Photo-diode and Photo-transistor Opto-couplers
The two components used in an opto-isolator, an optical transmitter such as an infra-red emitting
Gallium Arsenide LED and an optical receiver such as a photo-transistor are closely optically
coupled and use light to send signals and/or information between its input and output. This
allows information to be transferred between circuits without an electrical connection or
common ground potential. Opto-isolators are digital or switching devices, so they transfer either
"ON-OFF" control signals or digital data. Analogue signals can be transferred by means of
frequency or pulse-width modulation.
Diode
From Wikipedia, the free encyclopedia
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Figure 1: Closeup of a diode, showing the square shaped semiconductor crystal (black object on
left).
Figure 2: Various semiconductor diodes. Bottom: A bridge rectifier. In most diodes, a white or
black painted band identifies the cathode terminal, that is, the terminal which conventional
current flows out of when the diode is conducting.

Figure 3: Structure of a vacuum tube diode. The filament may be bare, or more commonly (as
shown here), embedded within and insulated from an enclosing cathode
In electronics, a diode is a two-terminal electronic component that conducts electric current in
only one direction. The term usually refers to a semiconductor diode, the most common type
today. This is a crystalline piece of semiconductor material connected to two electrical
terminals.[1]
A vacuum tube diode (now little used except in some high-power technologies) is a
vacuum tube with two electrodes; a plate and a cathode.
The most common function of a diode is to allow an electric current to pass in one direction
(called the diode's forward direction) while blocking current in the opposite direction (the
reverse direction). Thus, the diode can be thought of as an electronic version of a check valve.
This unidirectional behavior is called rectification, and is used to convert alternating current to
direct current, and to extract modulation from radio signals in radio receivers.
However, diodes can have more complicated behavior than this simple on-off action, due to their
complex non-linear electrical characteristics, which can be tailored by varying the construction
of their P-N junction. These are exploited in special purpose diodes that perform many different
functions. For example, specialized diodes are used to regulate voltage (Zener diodes), to
electronically tune radio and TV receivers (varactor diodes), to generate radio frequency
oscillations (tunnel diodes), and to produce light (light emitting diodes).
Diodes were the first semiconductor electronic devices. The discovery of crystals' rectifying
abilities was made by German physicist Ferdinand Braun in 1874. The first semiconductor
diodes, called cat's whisker diodes were made of crystals of minerals such as galena. Today most
diodes are made of silicon, but other semiconductors such as germanium are sometimes used.[2]
o
Thermionic and gaseous state diodes
Figure 4: The symbol for an indirect heated vacuum tube diode. From top to bottom, the
components are the anode, the cathode, and the heater filament.

Thermionic diodes are thermionic-valve devices (also known as vacuum tubes, tubes, or valves),
which are arrangements of electrodes surrounded by a vacuum within a glass envelope. Early
examples were fairly similar in appearance to incandescent light bulbs.
In thermionic valve diodes, a current through the heater filament indirectly heats the cathode,
another internal electrode treated with a mixture of barium and strontium oxides, which are
oxides of alkaline earth metals; these substances are chosen because they have a small work
function. (Some valves use direct heating, in which a tungsten filament acts as both heater and
cathode.) The heat causes thermionic emission of electrons into the vacuum. In forward
operation, a surrounding metal electrode called the anode is positively charged so that it
electrostatically attracts the emitted electrons. However, electrons are not easily released from
the unheated anode surface when the voltage polarity is reversed. Hence, any reverse flow is
negligible.
For much of the 20th century, thermionic valve diodes were used in analog signal applications,
and as rectifiers in many power supplies. Today, valve diodes are only used in niche applications
such as rectifiers in electric guitar and high-end audio amplifiers as well as specialized high-
voltage equipment.
Semiconductor diodes
A modern semiconductor diode is made of a crystal of semiconductor like silicon that has
impurities added to it to create a region on one side that contains negative charge carriers
(electrons), called n-type semiconductor, and a region on the other side that contains positive
charge carriers (holes), called p-type semiconductor. The diode's terminals are attached to each
of these regions. The boundary within the crystal between these two regions, called a PN
junction, is where the action of the diode takes place. The crystal conducts conventional current
in a direction from the p-type side (called the anode) to the n-type side (called the cathode), but
not in the opposite direction.
Another type of semiconductor diode, the Schottky diode, is formed from the contact between a
metal and a semiconductor rather than by a p-n junction.
Current–voltage characteristic
A semiconductor diode‘s behavior in a circuit is given by its current–voltage characteristic, or I–
V graph (see graph below). The shape of the curve is determined by the transport of charge
carriers through the so-called depletion layer or depletion region that exists at the p-n junction
between differing semiconductors. When a p-n junction is first created, conduction band
(mobile) electrons from the N-doped region diffuse into the P-doped region where there is a
large population of holes (vacant places for electrons) with which the electrons ―recombine‖.
When a mobile electron recombines with a hole, both hole and electron vanish, leaving behind
an immobile positively charged donor (dopant) on the N-side and negatively charged acceptor
(dopant) on the P-side. The region around the p-n junction becomes depleted of charge carriers
and thus behaves as an insulator.

However, the width of the depletion region (called the depletion width) cannot grow without
limit. For each electron-hole pair that recombines, a positively charged dopant ion is left behind
in the N-doped region, and a negatively charged dopant ion is left behind in the P-doped region.
As recombination proceeds more ions are created, an increasing electric field develops through
the depletion zone which acts to slow and then finally stop recombination. At this point, there is
a ―built-in‖ potential across the depletion zone.
If an external voltage is placed across the diode with the same polarity as the built-in potential,
the depletion zone continues to act as an insulator, preventing any significant electric current
flow (unless electron/hole pairs are actively being created in the junction by, for instance, light.
see photodiode). This is the reverse bias phenomenon. However, if the polarity of the external
voltage opposes the built-in potential, recombination can once again proceed, resulting in
substantial electric current through the p-n junction (i.e. substantial numbers of electrons and
holes recombine at the junction). For silicon diodes, the built-in potential is approximately 0.7 V
(0.3 V for Germanium and 0.2 V for Schottky). Thus, if an external current is passed through the
diode, about 0.7 V will be developed across the diode such that the P-doped region is positive
with respect to the N-doped region and the diode is said to be ―turned on‖ as it has a forward
bias.
Figure 5: I–V characteristics of a P-N junction diode (not to scale).
A diode‘s 'I–V characteristic' can be approximated by four regions of operation (see the figure
at right).
At very large reverse bias, beyond the peak inverse voltage or PIV, a process called reverse
breakdown occurs which causes a large increase in current (i.e. a large number of electrons and
holes are created at, and move away from the pn junction) that usually damages the device
permanently. The avalanche diode is deliberately designed for use in the avalanche region. In the
zener diode, the concept of PIV is not applicable. A zener diode contains a heavily doped p-n
junction allowing electrons to tunnel from the valence band of the p-type material to the

conduction band of the n-type material, such that the reverse voltage is ―clamped‖ to a known
value (called the zener voltage), and avalanche does not occur. Both devices, however, do have a
limit to the maximum current and power in the clamped reverse voltage region. Also, following
the end of forward conduction in any diode, there is reverse current for a short time. The device
does not attain its full blocking capability until the reverse current ceases.
The second region, at reverse biases more positive than the PIV, has only a very small reverse
saturation current. In the reverse bias region for a normal P-N rectifier diode, the current through
the device is very low (in the µA range). However, this is temperature dependent, and at
suffiently high temperatures, a substantial amount of reverse current can be observed (mA or
more).
The third region is forward but small bias, where only a small forward current is conducted.
As the potential difference is increased above an arbitrarily defined ―cut-in voltage‖ or ―on-
voltage‖ or ―diode forward voltage drop (Vd)‖, the diode current becomes appreciable (the level
of current considered ―appreciable‖ and the value of cut-in voltage depends on the application),
and the diode presents a very low resistance. The current–voltage curve is exponential. In a
normal silicon diode at rated currents, the arbitrary ―cut-in‖ voltage is defined as 0.6 to 0.7 volts.
The value is different for other diode types — Schottky diodes can be rated as low as 0.2 V,
Germanium diodes 0.25-0.3 V, and red or blue light-emitting diodes (LEDs) can have values of
1.4 V and 4.0 V respectively.
At higher currents the forward voltage drop of the diode increases. A drop of 1 V to 1.5 V is
typical at full rated current for power diodes.
Shockley diode equation
The Shockley ideal diode equation or the diode law (named after transistor co-inventor William
Bradford Shockley, not to be confused with tetrode inventor Walter H. Schottky) gives the I–V
characteristic of an ideal diode in either forward or reverse bias (or no bias). The equation is:
where
I is the diode current,
IS is the reverse bias saturation current (or scale current),
VD is the voltage across the diode,
VT is the thermal voltage, and
n is the ideality factor, also known as the quality factor or sometimes emission
coefficient. The ideality factor n varies from 1 to 2 depending on the fabrication process
and semiconductor material and in many cases is assumed to be approximately equal to 1
(thus the notation n is omitted).

The thermal voltage VT is approximately 25.85 mV at 300 K, a temperature close to ―room
temperature‖ commonly used in device simulation software. At any temperature it is a known
constant defined by:
where k is the Boltzmann constant, T is the absolute temperature of the p-n junction, and q is the
magnitude of charge on an electron (the elementary charge).
The Shockley ideal diode equation or the diode law is derived with the assumption that the only
processes giving rise to the current in the diode are drift (due to electrical field), diffusion, and
thermal recombination-generation. It also assumes that the recombination-generation (R-G)
current in the depletion region is insignificant. This means that the Shockley equation doesn‘t
account for the processes involved in reverse breakdown and photon-assisted R-G. Additionally,
it doesn‘t describe the ―leveling off‖ of the I–V curve at high forward bias due to internal
resistance.
Under reverse bias voltages (see Figure 5) the exponential in the diode equation is negligible,
and the current is a constant (negative) reverse current value of −IS. The reverse breakdown
region is not modeled by the Shockley diode equation.
For even rather small forward bias voltages (see Figure 5) the exponential is very large because
the thermal voltage is very small, so the subtracted ‗1‘ in the diode equation is negligible and the
forward diode current is often approximated as
The use of the diode equation in circuit problems is illustrated in the article on diode modeling.
Small-signal behaviour
For circuit design, a small-signal model of the diode behavior often proves useful. A specific
example of diode modeling is discussed in the article on small-signal circuits.
Types of semiconductor diode
Diode
Zener
diode
Schottky
diode
Tunnel
diode

Light-emitting
diode
Photodiode Varicap Silicon controlled rectifier
Figure 6: Some diode symbols.
Figure 7: Typical diode packages in same alignment as diode symbol. Thin bar depicts the
cathode.
Figure 8: Several types of diodes. The scale is centimeters.
There are several types of junction diodes, which either emphasize a different physical aspect of
a diode often by geometric scaling, doping level, choosing the right electrodes, are just an
application of a diode in a special circuit, or are really different devices like the Gunn and laser
diode and the MOSFET:
Normal (p-n) diodes, which operate as described above, are usually made of doped silicon or,
more rarely, germanium. Before the development of modern silicon power rectifier diodes,
cuprous oxide and later selenium was used; its low efficiency gave it a much higher forward
voltage drop (typically 1.4–1.7 V per ―cell‖, with multiple cells stacked to increase the peak
inverse voltage rating in high voltage rectifiers), and required a large heat sink (often an

extension of the diode‘s metal substrate), much larger than a silicon diode of the same current
ratings would require. The vast majority of all diodes are the p-n diodes found in CMOS
integrated circuits, which include two diodes per pin and many other internal diodes.
Avalanche diodes
Diodes that conduct in the reverse direction when the reverse bias voltage exceeds the
breakdown voltage. These are electrically very similar to Zener diodes, and are often
mistakenly called Zener diodes, but break down by a different mechanism, the avalanche
effect. This occurs when the reverse electric field across the p-n junction causes a wave of
ionization, reminiscent of an avalanche, leading to a large current. Avalanche diodes are
designed to break down at a well-defined reverse voltage without being destroyed. The
difference between the avalanche diode (which has a reverse breakdown above about
6.2 V) and the Zener is that the channel length of the former exceeds the ―mean free
path‖ of the electrons, so there are collisions between them on the way out. The only
practical difference is that the two types have temperature coefficients of opposite
polarities.
Cat‘s whisker or crystal diodes
These are a type of point-contact diode. The cat‘s whisker diode consists of a thin or
sharpened metal wire pressed against a semiconducting crystal, typically galena or a
piece of coal.[9]
The wire forms the anode and the crystal forms the cathode. Cat‘s
whisker diodes were also called crystal diodes and found application in crystal radio
receivers. Cat‘s whisker diodes are generally obsolete, but may be available from a few
manufacturers.[citation needed]
Constant current diodes
These are actually a JFET[10]
with the gate shorted to the source, and function like a two-
terminal current-limiter analog to the Zener diode, which is limiting voltage. They allow
a current through them to rise to a certain value, and then level off at a specific value.
Also called CLDs, constant-current diodes, diode-connected transistors, or current-
regulating diodes.
Esaki or tunnel diodes
These have a region of operation showing negative resistance caused by quantum
tunneling, thus allowing amplification of signals and very simple bistable circuits. These
diodes are also the type most resistant to nuclear radiation.
Gunn diodes
These are similar to tunnel diodes in that they are made of materials such as GaAs or InP
that exhibit a region of negative differential resistance. With appropriate biasing, dipole

domains form and travel across the diode, allowing high frequency microwave oscillators
to be built.
Light-emitting diodes (LEDs)
In a diode formed from a direct band-gap semiconductor, such as gallium arsenide,
carriers that cross the junction emit photons when they recombine with the majority
carrier on the other side. Depending on the material, wavelengths (or colors)[11]
from the
infrared to the near ultraviolet may be produced.[12]
The forward potential of these diodes
depends on the wavelength of the emitted photons: 1.2 V corresponds to red, 2.4 V to
violet. The first LEDs were red and yellow, and higher-frequency diodes have been
developed over time. All LEDs produce incoherent, narrow-spectrum light; ―white‖
LEDs are actually combinations of three LEDs of a different color, or a blue LED with a
yellow scintillator coating. LEDs can also be used as low-efficiency photodiodes in
signal applications. An LED may be paired with a photodiode or phototransistor in the
same package, to form an opto-isolator.
Laser diodes
When an LED-like structure is contained in a resonant cavity formed by polishing the
parallel end faces, a laser can be formed. Laser diodes are commonly used in optical
storage devices and for high speed optical communication.
Peltier diodes
These diodes are used as sensors, heat engines for thermoelectric cooling. Charge carriers
absorb and emit their band gap energies as heat.
Photodiodes
All semiconductors are subject to optical charge carrier generation. This is typically an
undesired effect, so most semiconductors are packaged in light blocking material.
Photodiodes are intended to sense light(photodetector), so they are packaged in materials
that allow light to pass, and are usually PIN (the kind of diode most sensitive to light).[13]
A photodiode can be used in solar cells, in photometry, or in optical communications.
Multiple photodiodes may be packaged in a single device, either as a linear array or as a
two-dimensional array. These arrays should not be confused with charge-coupled
devices.
Point-contact diodes
These work the same as the junction semiconductor diodes described above, but their
construction is simpler. A block of n-type semiconductor is built, and a conducting sharp-
point contact made with some group-3 metal is placed in contact with the semiconductor.
Some metal migrates into the semiconductor to make a small region of p-type

semiconductor near the contact. The long-popular 1N34 germanium version is still used
in radio receivers as a detector and occasionally in specialized analog electronics.
PIN diodes
A PIN diode has a central un-doped, or intrinsic, layer, forming a p-type/intrinsic/n-type
structure.[14]
They are used as radio frequency switches and attenuators. They are also
used as large volume ionizing radiation detectors and as photodetectors. PIN diodes are
also used in power electronics, as their central layer can withstand high voltages.
Furthermore, the PIN structure can be found in many power semiconductor devices, such
as IGBTs, power MOSFETs, and thyristors.
Schottky diodes
Schottky diodes are constructed from a metal to semiconductor contact. They have a
lower forward voltage drop than p-n junction diodes. Their forward voltage drop at
forward currents of about 1 mA is in the range 0.15 V to 0.45 V, which makes them
useful in voltage clamping applications and prevention of transistor saturation. They can
also be used as low loss rectifiers although their reverse leakage current is generally
higher than that of other diodes. Schottky diodes are majority carrier devices and so do
not suffer from minority carrier storage problems that slow down many other diodes —
so they have a faster ―reverse recovery‖ than p-n junction diodes. They also tend to have
much lower junction capacitance than p-n diodes which provides for high switching
speeds and their use in high-speed circuitry and RF devices such as switched-mode
power supply, mixers and detectors.
Super barrier diodes
Super barrier diodes are rectifier diodes that incorporate the low forward voltage drop of
the Schottky diode with the surge-handling capability and low reverse leakage current of
a normal p-n junction diode.
Gold-doped diodes
As a dopant, gold (or platinum) acts as recombination centers, which help a fast
recombination of minority carriers. This allows the diode to operate at signal frequencies,
at the expense of a higher forward voltage drop. Gold doped diodes are faster than other
p-n diodes (but not as fast as Schottky diodes). They also have less reverse-current
leakage than Schottky diodes (but not as good as other p-n diodes).[15][16]
A typical
example is the 1N914.
Snap-off or Step recovery diodes
The term step recovery relates to the form of the reverse recovery characteristic of these
devices. After a forward current has been passing in an SRD and the current is interrupted
or reversed, the reverse conduction will cease very abruptly (as in a step waveform).

SRDs can therefore provide very fast voltage transitions by the very sudden
disappearance of the charge carriers.
Transient voltage suppression diode (TVS)
These are avalanche diodes designed specifically to protect other semiconductor devices
from high-voltage transients.[17]
Their p-n junctions have a much larger cross-sectional
area than those of a normal diode, allowing them to conduct large currents to ground
without sustaining damage.
Varicap or varactor diodes
These are used as voltage-controlled capacitors. These are important in PLL (phase-
locked loop) and FLL (frequency-locked loop) circuits, allowing tuning circuits, such as
those in television receivers, to lock quickly, replacing older designs that took a long time
to warm up and lock. A PLL is faster than an FLL, but prone to integer harmonic locking
(if one attempts to lock to a broadband signal). They also enabled tunable oscillators in
early discrete tuning of radios, where a cheap and stable, but fixed-frequency, crystal
oscillator provided the reference frequency for a voltage-controlled oscillator.
Zener diodes
Diodes that can be made to conduct backwards. This effect, called Zener breakdown,
occurs at a precisely defined voltage, allowing the diode to be used as a precision voltage
reference. In practical voltage reference circuits Zener and switching diodes are
connected in series and opposite directions to balance the temperature coefficient to near
zero. Some devices labeled as high-voltage Zener diodes are actually avalanche diodes
(see above). Two (equivalent) Zeners in series and in reverse order, in the same package,
constitute a transient absorber (or Transorb, a registered trademark). The Zener diode is
named for Dr. Clarence Melvin Zener of Southern Illinois University, inventor of the
device.
Other uses for semiconductor diodes include sensing temperature, and computing analog
logarithms (see Operational amplifier applications#Logarithmic).
Numbering and coding schemes
There are a number of common, standard and manufacturer-driven numbering and coding
schemes for diodes; the two most common being the EIA/JEDEC standard and the European Pro
Electron standard:
EIA/JEDEC
A standardized 1N-series numbering system was introduced in the US by EIA/JEDEC (Joint
Electron Device Engineering Council) about 1960. Among the most popular in this series were:

1N34A/1N270 (Germanium signal), 1N914/1N4148 (Silicon signal), 1N4001-1N4007 (Silicon
1A power rectifier) and 1N54xx (Silicon 3A power rectifier)[18][19][20]
Pro Electron
The European Pro Electron coding system for active components was introduced in 1966 and
comprises two letters followed by the part code. The first letter represents the semiconductor
material used for the component (A = Germanium and B = Silicon) and the second letter
represents the general function of the part (for diodes: A = low-power/signal, B = Variable
capacitance, X = Multiplier, Y = Rectifier and Z = Voltage reference), for example:
 AA-series germanium low-power/signal diodes (e.g.: AA119)
 BA-series silicon low-power/signal diodes (e.g.: BAT18 Silicon RF Switching Diode)
 BY-series silicon rectifier diodes (e.g.: BY127 1250V, 1A rectifier diode)
 BZ-series silicon zener diodes (e.g.: BZY88C4V7 4.7V zener diode)
Other common numbering / coding systems (generally manufacturer-driven) include:
 GD-series germanium diodes (ed: GD9) — this is a very old coding system
 OA-series germanium diodes (e.g.: OA47) — a coding sequence developed by Mullard, a
UK company
As well as these common codes, many manufacturers or organisations have their own systems
too — for example:
 HP diode 1901-0044 = JEDEC 1N4148
 UK military diode CV448 = Mullard type OA81 = GEC type GEX23
Related devices
 Rectifier
 Transistor
 Thyristor or silicon controlled rectifier (SCR)
 TRIAC
 Diac
 Varistor
In optics, an equivalent device for the diode but with laser light would be the Optical isolator,
also known as an Optical Diode, that allows light to only pass in one direction. It uses a Faraday
rotator as the main component.
Applications
Radio demodulation

The first use for the diode was the demodulation of amplitude modulated (AM) radio broadcasts.
The history of this discovery is treated in depth in the radio article. In summary, an AM signal
consists of alternating positive and negative peaks of voltage, whose amplitude or ―envelope‖ is
proportional to the original audio signal. The diode (originally a crystal diode) rectifies the AM
radio frequency signal, leaving an audio signal which is the original audio signal, minus
atmospheric noise. The audio is extracted using a simple filter and fed into an audio amplifier or
transducer, which generates sound waves.
Power conversion
Rectifiers are constructed from diodes, where they are used to convert alternating current (AC)
electricity into direct current (DC). Automotive alternators are a common example, where the
diode, which rectifies the AC into DC, provides better performance than the commutator of
earlier dynamo. Similarly, diodes are also used in Cockcroft–Walton voltage multipliers to
convert AC into higher DC voltages.
Over-voltage protection
Diodes are frequently used to conduct damaging high voltages away from sensitive electronic
devices. They are usually reverse-biased (non-conducting) under normal circumstances. When
the voltage rises above the normal range, the diodes become forward-biased (conducting). For
example, diodes are used in (stepper motor and H-bridge) motor controller and relay circuits to
de-energize coils rapidly without the damaging voltage spikes that would otherwise occur. (Any
diode used in such an application is called a flyback diode). Many integrated circuits also
incorporate diodes on the connection pins to prevent external voltages from damaging their
sensitive transistors. Specialized diodes are used to protect from over-voltages at higher power
(see Diode types above).
Logic gates
Diodes can be combined with other components to construct AND and OR logic gates. This is
referred to as diode logic.
Ionizing radiation detectors
In addition to light, mentioned above, semiconductor diodes are sensitive to more energetic
radiation. In electronics, cosmic rays and other sources of ionizing radiation cause noise pulses
and single and multiple bit errors. This effect is sometimes exploited by particle detectors to
detect radiation. A single particle of radiation, with thousands or millions of electron volts of
energy, generates many charge carrier pairs, as its energy is deposited in the semiconductor
material. If the depletion layer is large enough to catch the whole shower or to stop a heavy
particle, a fairly accurate measurement of the particle‘s energy can be made, simply by
measuring the charge conducted and without the complexity of a magnetic spectrometer or etc.
These semiconductor radiation detectors need efficient and uniform charge collection and low
leakage current. They are often cooled by liquid nitrogen. For longer range (about a centimetre)
particles they need a very large depletion depth and large area. For short range particles, they

need any contact or un-depleted semiconductor on at least one surface to be very thin. The back-
bias voltages are near breakdown (around a thousand volts per centimetre). Germanium and
silicon are common materials. Some of these detectors sense position as well as energy. They
have a finite life, especially when detecting heavy particles, because of radiation damage. Silicon
and germanium are quite different in their ability to convert gamma rays to electron showers.
Semiconductor detectors for high energy particles are used in large numbers. Because of energy
loss fluctuations, accurate measurement of the energy deposited is of less use.
Temperature measurements
A diode can be used as a temperature measuring device, since the forward voltage drop across
the diode depends on temperature, as in a Silicon bandgap temperature sensor. From the
Shockley ideal diode equation given above, it appears the voltage has a positive temperature
coefficient (at a constant current) but depends on doping concentration and operating
temperature (Sze 2007). The temperature coefficient can be negative as in typical thermistors or
positive for temperature sense diodes down to about 20 kelvins. Typically, silicon diodes have
approximately −2 mV/˚C temperature coefficient at room temperature.
Current steering
Diodes will prevent currents in unintended directions. To supply power to an electrical circuit
during a power failure, the circuit can draw current from a battery. An Uninterruptible power
supply may use diodes in this way to ensure that current is only drawn from the battery when
necessary. Similarly, small boats typically have two circuits each with their own
battery/batteries: one used for engine starting; one used for domestics. Normally both are
charged from a single alternator, and a heavy duty split charge diode is used to prevent the higher
charge battery (typically the engine battery) from discharging through the lower charged battery
when the alternator is not running.
Diodes are also used in electronic musical keyboards. To reduce the amount of wiring needed in
electronic musical keyboards, these instruments often use keyboard matrix circuits. The
keyboard controller scans the rows and columns to determine which note the player has pressed.
The problem with matrix circuits is that when several notes are pressed at once, the current can
flow backwards through the circuit and trigger "phantom keys" that cause ―ghost‖ notes to play.
To avoid triggering unwanted notes, most keyboard matrix circuits have diodes soldered with the
switch under each key of the musical keyboard. The same principle is also used for the switch
matrix in solid state pinball machines.
p-n Junction Diode
Diode:
A pure silicon crystal or germanium crystal is known as an intrinsic semiconductor. There are

not enough free electrons and holes in an intrinsic semi-conductor to produce a usable current.
The electrical action of these can be modified by doping means adding impurity atoms to a
crystal to increase either the number of free holes or no of free electrons.
When a crystal has been doped, it is called a extrinsic semi-conductor. They are of two types
• n-type semiconductor having free electrons as majority carriers
• p-type semiconductor having free holes as majority carriers
By themselves, these doped materials are of little use. However, if a junction is made by joining
p-type semiconductor to n-type semiconductor a useful device is produced known as diode. It
will allow current to flow through it only in one direction. The unidirectional properties of a
diode allow current flow when forward biased and disallow current flow when reversed biased.
This is called rectification process and therefore it is also called rectifier.
How is it possible that by properly
joining two semiconductors each of
which, by itself, will freely conduct
the current in any direct refuses to
allow conduction in one direction.
Consider first the condition of p-
type and n-type germanium just
prior to joining fig. 1. The majority
and minority carriers are in constant
motion.
The minority carriers are thermally
produced and they exist only for
short time after which they
recombine and neutralize each
other. In the mean time, other
minority carriers have been
produced and this process goes on
and on.
The number of these electron hole
pair that exist at any one time
depends upon the temperature. The
number of majority carriers is
however, fixed depending on the
number of impurity atoms available.
While the electrons and holes are in
motion but the atoms are fixed in
place and do not move.
Fig.1

As soon as, the junction is formed, the following processes are initiated fig. 2.
Fig.2
 Holes from the p-side diffuse into n-side where
they recombine with free electrons.
 Free electrons from n-side diffuse into p-side
where they recombine with free holes.
 The diffusion of electrons and holes is due to the
fact that large no of electrons are concentrated in
one area and large no of holes are concentrated in
another area.
 When these electrons and holes begin to diffuse
across the junction then they collide each other
and negative charge in the electrons cancels the
positive charge of the hole and both will lose their
charges.
 The diffusion of holes and electrons is an electric
current referred to as a recombination current.
The recombination process decay exponentially
with both time and distance from the junction.
Thus most of the recombination occurs just after
the junction is made and very near to junction.
 A measure of the rate of recombination is
the lifetime defined as the time required for the
density of carriers to decrease to 37% to the
original concentration
The impurity atoms are fixed in their individual places. The atoms itself is a part of the crystal
and so cannot move. When the electrons and hole meet, their individual charge is cancelled and
this leaves the originating impurity atoms with a net charge, the atom that produced the electron
now lack an electronic and so becomes charged positively, whereas the atoms that produced the
hole now lacks a positive charge and becomes negative.
The electrically charged atoms are called ions since they are no longer neutral. These ions
produce an electric field as shown in fig. 3. After several collisions occur, the electric field is
great enough to repel rest of the majority carriers away of the junction. For example, an electron
trying to diffuse from n to p side is repelled by the negative charge of the p-side. Thus diffusion
process does not continue indefinitely but continues as long as the field is developed.

Fig.3
This region is produced immediately surrounding the junction that has no majority carriers. The
majority carriers have been repelled away from the junction and junction is depleted from
carriers. The junction is known as the barrier region or depletion region. The electric field
represents a potential difference across the junction also called space charge potential or barrier
potential . This potential is 0.7v for Si at 25o
celcious and 0.3v for Ge.
The physical width of the depletion region depends on the doping level. If very heavy doping is
used, the depletion region is physically thin because diffusion charge need not travel far across
the junction before recombination takes place (short life time). If doping is light, then depletion
is more wide (long life time).
p-n Junction Diode
The symbol of diode is shown in fig. 4. The terminal connected to p-layer is called anode (A) and the terminal c
n-layer is called cathode (K)

Reverse Bias:
If positive terminal of dc source is connected to cathode and negative terminal is connected to anode, the diode
biased as shown in fig. 5.
Fig.5
When the diode is reverse biased then the depletion region width increases, majority carriers move away from
there is no flow of current due to majority carriers but there are thermally produced electron hole pair also. If th
holes are generated in the vicinity of junction then there is a flow of current. The negative voltage applied to the
attract the holes thus generated and repel the electrons. At the same time, the positive voltage will attract the elec
battery and repel the holes. This will cause current to flow in the circuit. This current is usually very small (inter
to nano amp). Since this current is due to minority carriers and these number of minority carriers are fixed at a g
therefore, the current is almost constant known as reverse saturation current ICO.
In actual diode, the current is not almost constant but increases slightly with voltage. This is due to surface leak
surface of diode follows ohmic law (V=IR). The resistance under reverse bias condition is very high 100k to m
the reverse voltage is increased, then at certain voltage, then breakdown to diode takes place and it conducts he
to avalanche or zener breakdown. The characteristic of the diode is shown in fig. 6.

Fig.6
Forward bias:
When the diode is forward bias, then majority carriers are pushed towards junction, when they collide and rec
place. Number of majority carriers are fixed in semiconductor. Therefore as each electron is eliminated at the
electron must be introduced, this comes from battery. At the same time, one hole must be created in p-layer. T
extracting one electron from p-layer. Therefore, there is a flow of carriers and thus flow of current.
Diode
Space charge capacitance CT of diode:
Reverse bias causes majority carriers to move away from the junction, thereby creating more
ions. Hence the thickness of depletion region increases. This region behaves as the dielectric
material used for making capacitors. The p-type and n-type conducting on each side of dielectric
act as the plate. The incremental capacitance CT is defined by
Since

Therefore, (E-1)
where, dQ is the increase in charge caused by a change dV in voltage. CT is not constant, it
depends upon applied voltage, there fore it is defined as dQ / dV.
When p-n junction is forward biased, then also a capacitance is defined called diffusion
capacitance CD (rate of change of injected charge with voltage) to take into account the time
delay in moving the charges across the junction by the diffusion process. It is considered as a
fictitious element that allow us to predict time delay.
If the amount of charge to be moved across the junction is increased, the time delay is greater, it
follows that diffusion capacitance varies directly with the magnitude of forward current.
(E-2)
Relationship between Diode Current and Diode Voltage
An exponential relationship exists between the carrier density and applied potential of diode
junction as given in equation E-3. This exponential relationship of the current iD and the voltage
vD holds over a range of at least seven orders of magnitudes of current - that is a factor of 107
.
(E-3)
Where,
iD= Current through the diode (dependent variable in this expression)
vD= Potential difference across the diode terminals (independent variable in this expression)
IO= Reverse saturation current (of the order of 10-15
A for small signal diodes, but IO is a strong
function of temperature)
q = Electron charge: 1.60 x 10-19
joules/volt
k = Boltzmann's constant: 1.38 x l0-23
joules /° K
T = Absolute temperature in degrees Kelvin (°K = 273 + temperature in °C)
n = Empirical scaling constant between 0.5 and 2, sometimes referred to as the Exponential
Ideality Factor
The empirical constant, n, is a number that can vary according to the voltage and current levels.
It depends on electron drift, diffusion, and carrier recombination in the depletion region. Among
the quantities affecting the value of n are the diode manufacture, levels of doping and purity of
materials. If n=1, the value of k T/ q is 26 mV at 25°C. When n=2, k T/ q becomes 52 mV.
For germanium diodes, n is usually considered to be close to 1. For silicon diodes, n is in the

range of 1.3 to 1.6. n is assumed 1 for all junctions all throughout unless otherwise noted.
Equation (E-3) can be simplified by defining VT =k T/q, yielding
(E-4)
At room temperature (25°C) with forward-bias voltage only the first term in the parentheses is
dominant and the current is approximately given by
(E-5)
The current-voltage (l-V) characteristic of the diode, as defined by (E-3) is illustrated in fig. 1.
The curve in the figure consists of two exponential curves. However, the exponent values are
such that for voltages and currents experienced in practical circuits, the curve sections are close
to being straight lines. For voltages less than VON, the curve is approximated by a straight line of
slope close to zero. Since the slope is the conductance (i.e., i / v), the conductance is very small
in this region, and the equivalent resistance is very high. For voltages above VON, the curve is
approximated by a straight line with a very large slope. The conductance is therefore very large,
and the diode has a very small equivalent resistance.
Fig.1 - Diode Voltage relationship
The slope of the curves of fig.1 changes as the current and voltage change since the l-V
characteristic follows the exponential relationship of relationship of equation (E-4). Differentiate
the equation (E-4) to find the slope at any arbitrary value of vDor iD,

(E-6)
This slope is the equivalent conductance of the diode at the specified values of vD or iD.
We can approximate the slope as a linear function of the diode current. To eliminate the
exponential function, we substitute equation (E-4) into the exponential of equation (E-7) to
obtain
(E-7)
A realistic assumption is that IO<< iD equation (E-7) then yields,
(E-8)
The approximation applies if the diode is forward biased. The dynamic resistance is the
reciprocal of this expression.
(E-9)
Although rd is a function of id, we can approximate it as a constant if the variation of iD is small.
This corresponds to approximating the exponential function as a straight line within a specific
operating range.
Normally, the term Rf to denote diode forward resistance. Rf is composed of rd and the contact
resistance. The contact resistance is a relatively small resistance composed of the resistance of
the actual connection to the diode and the resistance of the semiconductor prior to the junction.
The reverse-bias resistance is extremely large and is often approximated as infinity.
Diode
Temperature Effects:
Temperature plays an important role in determining the characteristic of diodes. As temperature
increases, the turn-on voltage, vON, decreases. Alternatively, a decrease in temperature results in
an increase in vON. This is illustrated in fig. 2, where VON varies linearly with temperature which
is evidenced by the evenly spaced curves for increasing temperature in 25 °C increments.

The temperature relationship is described by equation
VON(TNew ) – VON(Troom) = kT(TNew – T room) (E-10)
Fig. 2 - Dependence of iD on temperature versus vD for real diode (kT = -2.0 mV /°C)
where,
Troom= room temperature, or 25°C.
TNew= new temperature of diode in °C.
VON(Troom ) = diode voltage at room temperature.
VON (TNew) = diode voltage at new temperature.
kT = temperature coefficient in V/°C.
Although kT varies with changing operating parameters, standard engineering practice permits
approximation as a constant. Values of kT for the various types of diodes at room temperature are
given as follows:
kT= -2.5 mV/°C for germanium diodes
kT = -2.0 mV/°C for silicon diodes
The reverse saturation current, IO also depends on temperature. At room temperature, it increases
approximately 16% per °C for silicon and 10% per °C for germanium diodes. In other words, IO
approximately doubles for every 5 °C increase in temperature for silicon, and for every 7 °C for
germanium. The expression for the reverse saturation current as a function of temperature can be
approximated as
(E-11)

where Ki= 0.15/°C ( for silicon) and T1 and T2 are two arbitrary temperatures.
Applications of Diode
Applications of diode:
Half wave Rectifier:
The single – phase half wave rectifier is shown in fig. 8.
Fig. 8 Fig. 9
In positive half cycle, D is forward biased and conducts. Thus the output voltage is same as the
input voltage. In the negative half cycle, D is reverse biased, and therefore output voltage is zero.
The output voltage waveform is shown in fig. 9.
The average output voltage of the rectifier is given by
The average output current is given by
When the diode is reverse biased, entire transformer voltage appears across the diode. The
maximum voltage across the diode is Vm. The diode must be capable to withstand this voltage.
Therefore PIV half wave rating of diode should be equal to Vm in case of single-phase rectifiers.
The average current rating must be greater than Iavg

Full Wave Rectifier:
A single – phase full wave rectifier using center tap transformer is shown in fig. 10. It supplies
current in both half cycles of the input voltage.
Fig. 10 Fig. 11
In the first half cycle D1 is forward biased and conducts. But D2 is reverse biased and does not
conduct. In the second half cycle D2 is forward biased, and conducts and D1 is reverse biased. It
is also called 2 – pulse midpoint converter because it supplies current in both the half cycles. The
output voltage waveform is shown in fig. 11.
The average output voltage is given by
and the average load current is given by
When D1 conducts, then full secondary voltage appears across D2, therefore PIV rating of the
diode should be 2 Vm.
Bridge Rectifier:
The single – phase full wave bridge rectifier is shown in fig. 1. It is the most widely used
rectifier. It also provides currents in both the half cycle of input supply.

Fig. 1 Fig. 2
In the positive half cycle, D1 & D4 are forward biased and D2 & D3 are reverse biased. In the
negative half cycle, D2 & D3 are forward biased, and D1 & D4 are reverse biased. The output
voltage waveform is shown in fig. 2 and it is same as full wave rectifier but the advantage is that
PIV rating of diodes are V m and only single secondary transformer is required.
The main disadvantage is that it requires four diodes. When low dc voltage is required then
secondary voltage is low and diodes drop (1.4V) becomes significant. For low dc output, 2-pulse
center tap rectifier is used because only one diode drop is there.
The ripple factor is the measure of the purity of dc output of a rectifier and is defined as
Therefore,
Zener Diode:
The diodes designed to work in breakdown region are called zener diode. If the reverse voltage
exceeds the breakdown voltage, the zener diode will normally not be destroyed as long as the
current does not exceed maximum value and the device closes not over load.
When a thermally generated carrier (part of the reverse saturation current) falls down the

junction and acquires energy of the applied potential, the carrier collides with crystal ions and
imparts sufficient energy to disrupt a covalent bond. In addition to the original carrier, a new
electron-hole pair is generated. This pair may pick up sufficient energy from the applied field to
collide with another crystal ion and create still another electron-hole pair. This action continues
and thereby disrupts the covalent bonds. The process is referred to as impact ionization,
avalanche multiplication or avalanche breakdown.
There is a second mechanism that disrupts the covalent bonds. The use of a sufficiently strong
electric field at the junction can cause a direct rupture of the bond. If the electric field exerts a
strong force on a bound electron, the electron can be torn from the covalent bond thus causing
the number of electron-hole pair combinations to multiply. This mechanism is called high field
emission or Zener breakdown. The value of reverse voltage at which this occurs is controlled by
the amount ot doping of the diode. A heavily doped diode has a low Zener breakdown voltage,
while a lightly doped diode has a high Zener breakdown voltage.
At voltages above approximately 8V, the predominant mechanism is the avalanche breakdown.
Since the Zener effect (avalanche) occurs at a predictable point, the diode can be used as a
voltage reference. The reverse voltage at which the avalanche occurs is called the breakdown or
Zener voltage.
A typical Zener diode characteristic is shown in fig. 1. The circuit symbol for the Zener diode is
different from that of a regular diode, and is illustrated in the figure. The maximum reverse
current, IZ(max), which the Zener diode can withstand is dependent on the design and construction
of the diode. A design guideline that the minimum Zener current, where the characteristic curve
remains at VZ (near the knee of the curve), is 0.1/ IZ(max).
Fig. 1 - Zener diode characteristic

The power handling capacity of these diodes is better. The power dissipation of a zener diode
equals the product of its voltage and current.
PZ= VZ IZ
The amount of power which the zener diode can withstand ( VZ.IZ(max) ) is a limiting factor in
power supply design.
Zener Regulator:
When zener diode is forward biased it works as a diode and drop across it is 0.7 V. When it
works in breakdown region the voltage across it is constant (VZ) and the current through diode is
decided by the external resistance. Thus, zener diode can be used as a voltage regulator in the
configuration shown in fig. 2 for regulating the dc voltage. It maintains the output voltage
constant even through the current through it changes.
Fig. 2 Fig. 3
The load line of the circuit is given by Vs= Is Rs + Vz. The load line is plotted along with zener
characteristic in fig. 3. The intersection point of the load line and the zener characteristic gives
the output voltage and zener current.
To operate the zener in breakdown region Vs should always be greater then Vz. Rs is used to limit
the current. If the Vs voltage changes, operating point also changes simultaneously but voltage
across zener is almost constant. The first approximation of zener diode is a voltage source of Vz
magnitude and second approximation includes the resistance also. The two approximate
equivalent circuits are shown in fig. 4.

If second approximation of zener diode is considered, the output voltage varies slightly as shown
in fig. 5. The zener ON state resistance produces more I * R drop as the current increases. As the
voltage varies form V1 to V2 the operating point shifts from Q1 to Q2.
The voltage at Q1 is
V1 = I1 RZ +VZ
and at Q2
V2 = I2 RZ +VZ
Thus, change in voltage is
V2 – V1 = ( I2 – I1 ) RZ
Δ VZ =Δ IZ RZ
Zener Diode
Design of Zener regulator circuit:
A zenere regulator circuit is shown in fig. 6. The varying load current is represented by a
variable load resistance RL.

The zener will work in the breakdown
region only if the Thevenin voltage across
zener is more than VZ .
If zener is operating in breakdown region,
the current through RS is given by
Fig. 6
and load current
Is= Iz + IL
The circuit is designed such that the diode always operates in the breakdown region and the
voltage VZ across it remains fairly constant even though the current IZ through it vary
considerably.
If the load IL should increase, the current IZ should decrease by the same percentage in order to
maintain load current constant Is. This keeps the voltage drop across Rs constant and hence the
output voltage.
If the input voltage should increase, the zener diode passes a larger current, that extra voltage is
dropped across the resistance Rs. If input voltage falls, the current IZ falls such that VZ is
constant.
In the practical application the source voltage, vs, varies and the load current also varies. The
design challenge is to choose a value of Rs which permits the diode to maintain a relatively
constant output voltage, even when the input source voltage varies and the load current also
varies.
We now analyze the circuit to determine the proper choice of Rs. For the circuit shown in figure,
(E-1)
(E-2)
The variable quantities in Equation (E-2) are vZ and iL. In order to assure that the diode remains

in the constant voltage (breakdown) region, we examine the two extremes of input/output
conditions, as follows:
 The current through the diode, iZ, is a minimum (IZ min) when the load current, iL is
maximum (IL max) and the source voltage, vs is minimum (Vs min).
 The current through the diode, iZ, is a maximum (IZ max) when the load current, iL, is
minmum (iL min) and the source voltage vsis minimum(Vs max).
When these characteristics of the two extremes are inserted into Equation (E-1),
we find (E-3)
(E-4)
In a practical problem, we know the range of input voltages, the range of output load currents,
and the desired Zener voltage. Equation (E-4) thus represents one equation in two unknowns, the
maximum and minimum Zener current. A second equation is found from the characteristic of
zener. To avoid the non-constant portion of the characteristic curve, we use an accepted rule of
thumb that the minimum Zener current should be 0.1 times the maximum (i.e., 10%), that is,
(E-5)
Solving the equations E-4 and E-5, we get,
(E-6)
Now that we can solve for the maximum Zener current, the value of Rs, is calculated from
Equation (E-3).
Zener diodes are manufactured with breakdown voltages VZ in the range of a few volts to a few
hundred volts. The manufacturer specifies the maximum power the diode can dissipate. For
example, a 1W, 10 V zener can operate safely at currents up to 100mA.
Special Purpose Diodes
Light Emitting Diode :
In a forward biased diode free electrons cross the junction and enter into p-layer where they

recombine with holes. Each recombination radiates energy as electron falls from higher energy
level to a lower energy level. I n ordinary diodes this energy is in the form of heat. In light
emitting diode, this energy is in the form of light.
The symbol of LED is shown in fig. 2. Ordinary diodes are made of Ge or Si. This material
blocks the passage of light. LEDs are made of different materials such as gallium, arsenic and
phosphorus. LEDs can radiate red, green, yellow, blue, orange or infrared (invisible). The LED's
forward voltage drop is more approximately 1.5V. Typical LED current is between 10 mA to 50
mA.
Fig. 2 Fig. 3
Seven Segment Display :
Seven segment displays are used to display digits and few alphabets. It contains seven
rectangular LEDs. Each LED is called a Segment. External resistors are used to limit the currents
to safe Values. It can display any letters a, b, c, d, e, f, g.as shown in fig. 3.

Fig. 4
The LEDs of seven-segment display are connected in either in common anode configuration or
in common cathode configuration as shown in fig. 4.
Photo diode :
When a diode is reversed biased as shown in fig. 5, a reverse current flows due to minority
carriers. These carriers exist because thermal energy keeps on producing free electrons and
holes. The lifetime of the minority carriers is short, but while they exist they can contribute to the
reverse current. When light energy bombards a p-n junction, it too can produce free electrons.

Fig. 5
In other words, the amount of light striking the junction can control the reverse current in a
diode. A photo diode is made on the same principle. It is sensitive to the light. In this diode,
through a window light falls to the junction. The stronger the light, the greater the minority
carriers and larger the reverse current.
Voltage regulator
A voltage regulator is an electrical regulator designed to automatically maintain a constant
voltage level.
It may use an electromechanical mechanism, or passive or active electronic components.
Depending on the design, it may be used to regulate one or more AC or DC voltages.
With the exception of passive shunt regulators, all modern electronic voltage regulators operate
by comparing the actual output voltage to some internal fixed reference voltage. Any difference
is amplified and used to control the regulation element in such a way as to reduce the voltage
error. This forms a negative feedback control loop; increasing the open-loop gain tends to
increase regulation accuracy but reduce stability (avoidance of oscillation, or ringing during step
changes). There will also be a trade-off between stability and the speed of the response to
changes. If the output voltage is too low (perhaps due to input voltage reducing or load current
increasing), the regulation element is commanded, up to a point, to produce a higher output

voltage - by dropping less of the input voltage (for linear series regulators and buck switching
regulators), or to draw input current for longer periods (boost-type switching regulators); if the
output voltage is too high, the regulation element will normally be commanded to produce a
lower voltage. However, many regulators have over-current protection, so that they will entirely
stop sourcing current (or limit the current in some way) if the output current is too high, and
some regulators may also shut down if the input voltage is outside a given range.
Measures of regulator quality
The output voltage can only be held roughly constant; the regulation is specified by two
measurements:
 load regulation is the change in output voltage for a given change in load current (for
example: "typically 15mV, maximum 100mV for load currents between 5mA and 1.4A,
at some specified temperature and input voltage").
 line regulation or input regulation is the degree to which output voltage changes with
input (supply) voltage changes - as a ratio of output to input change (for example
"typically 13mV/V"), or the output voltage change over the entire specified input voltage
range (for example "plus or minus 2% for input voltages between 90V and 260V, 50-
60Hz").
Other important parameters are:
 Temperature coefficient of the output voltage is the change in output voltage with
temperature (perhaps averaged over a given temperature range), while...
 Initial accuracy of a voltage regulator (or simply "the voltage accuracy") reflects the
error in output voltage for a fixed regulator without taking into account temperature or
aging effects on output accuracy.
 Dropout voltage - the minimum difference between input voltage and output voltage for
which the regulator can still supply the specified current. A Low Drop-Out (LDO)
regulator is designed to work well even with an input supply only a Volt or so above the
output voltage.
 Absolute Maximum Ratings are defined for regulator components, specifying the
continuous and peak output currents that may be used (sometimes internally limited), the
maximum input voltage, maximum power dissipation at a given temperature, etc.
 Output noise (thermal white noise) and output dynamic impedance may be specified as
graphs versus frequency, while output ripple noise (mains "hum" or switch-mode "hash"
noise) may be given as peak-to-peak or RMS voltages, or in terms of their spectra.
 Quiescent current in a regulator circuit is the current drawn internally, not available to
the load, normally measured as the input current while no load is connected (and hence a
source of inefficiency; some linear regulators are, surprisingly, more efficient at very low
current loads than switch-mode designs because of this).

Electromechanical regulators
Circuit design for a simple electromechanical voltage regulator.
Interior of an old electromechanical voltage regulator.
Graph of voltage output on a time scale.
In older electromechanical regulators, voltage regulation is easily accomplished by coiling the
sensing wire to make an electromagnet. The magnetic field produced by the current attracts a
moving ferrous core held back under spring tension or gravitational pull. As voltage increases, so

does the current, strengthening the magnetic field produced by the coil and pulling the core
towards the field. The magnet is physically connected to a mechanical power switch, which
opens as the magnet moves into the field. As voltage decreases, so does the current, releasing
spring tension or the weight of the core and causing it to retract. This closes the switch and
allows the power to flow once more.
If the mechanical regulator design is sensitive to small voltage fluctuations, the motion of the
solenoid core can be used to move a selector switch across a range of resistances or transformer
windings to gradually step the output voltage up or down, or to rotate the position of a moving-
coil AC regulator.
Early automobile generators and alternators had a mechanical voltage regulator using one, two,
or three relays and various resistors to stabilize the generator's output at slightly more than 6 or
12 V, independent of the engine's rpm or the varying load on the vehicle's electrical system.
Essentially, the relay(s) employed pulse width modulation to regulate the output of the generator,
controlling the field current reaching the generator (or alternator) and in this way controlling the
output voltage produced.
The regulators used for generators (but not alternators) also disconnect the generator when it was
not producing electricity, thereby preventing the battery from discharging back into the generator
and attempting to run it as a motor. The rectifier diodes in an alternator automatically perform
this function so that a specific relay is not required; this appreciably simplified the regulator
design.
More modern designs now use solid state technology (transistors) to perform the same function
that the relays perform in electromechanical regulators.
Electromechanical regulators are used for mains voltage stabilisation—see Voltage
regulator#AC voltage stabilizers below.
Coil-rotation AC voltage regulator
Basic design principle and circuit diagram for the rotating-coil AC voltage regulator.
This is an older type of regulator used in the 1920s that uses the principle of a fixed-position
field coil and a second field coil that can be rotated on an axis in parallel with the fixed coil.

When the movable coil is positioned perpendicular to the fixed coil, the magnetic forces acting
on the movable coil balance each other out and voltage output is unchanged. Rotating the coil in
one direction or the other away from the center position will increase or decrease voltage in the
secondary movable coil.
This type of regulator can be automated via a servo control mechanism to advance the movable
coil position in order to provide voltage increase or decrease. A braking mechanism or high ratio
gearing is used to hold the rotating coil in place against the powerful magnetic forces acting on
the moving coil.
AC voltage stabilizers
Magnetic mains regulator
Electromechanical
Electromechanical regulators, usually called voltage stabilizers, have also been used to regulate
the voltage on AC power distribution lines. These regulators operate by using a servomechanism
to select the appropriate tap on an autotransformer with multiple taps, or by moving the wiper on
a continuously variable autotransfomer. If the output voltage is not in the acceptable range, the
servomechanism switches connections or moves the wiper to adjust the voltage into the
acceptable region. The controls provide a deadband wherein the controller will not act,
preventing the controller from constantly adjusting the voltage ("hunting") as it varies by an
acceptably small amount.
Constant-voltage transformer
An alternative method is the use of a type of saturating transformer called a ferro resonant
transformer or constant-voltage transformer. These transformers use a tank circuit composed
of a high-voltage resonant winding and a capacitor to produce a nearly constant average output
with a varying input. The ferroresonant approach is attractive due to its lack of active
components, relying on the square loop saturation characteristics of the tank circuit to absorb
variations in average input voltage. Older designs of ferroresonant transformers had an output
with high harmonic content, leading to a distorted output waveform. Modern devices are used to

construct a perfect sinewave. The ferroresonant action is a flux limiter rather than a voltage
regulator, but with a fixed supply frequency it can maintain an almost constant average output
voltage even as the input voltage varies widely.
The ferroresonant transformers, which are also known as Constant Voltage Transformers (CVTs)
or ferros, are also good surge suppressors, as they provide high isolation and inherent short-
circuit protection.
A ferroresonant transformer can operate with an input voltage range ±40% or more of the
nominal voltage.
Output power factor remains in the range of 0.96 or higher from half to full load.
Because it regenerates an output voltage waveform, output distortion, which is typically less than
4%, is independent of any input voltage distortion, including notching.
Efficiency at full load is typically in the range of 89% to 93%. However, at low loads, efficiency
can drop below 60% and no load losses can be as high as 20%. The current-limiting capability
also becomes a handicap when a CVT is used in an application with moderate to high inrush
current like motors, transformers or magnets. In this case, the CVT has to be sized to
accommodate the peak current, thus forcing it to run at low loads and poor efficiency.
Minimum maintenance is required. Transformers and capacitors can be very reliable. Some units
have included redundant capacitors to allow several capacitors to fail between inspections
without any noticeable effect on the device's performance.
Output voltage varies about 1.2% for every 1% change in supply frequency. For example, a 2-Hz
change in generator frequency, which is very large, results in an output voltage change of only
4%, which has little effect for most loads.
It accepts 100% single-phase switch-mode power supply loading without any requirement for
derating, including all neutral components.
Input current distortion remains less than 8% THD even when supplying nonlinear loads with
more than 100% current THD.
Drawbacks of CVTs (constant voltage transformers) are their larger size, audible humming
sound, and high heat generation.

DC voltage stabilizers
KPEH8A stabilizers
Many simple DC power supplies regulate the voltage using a shunt regulator such as a zener
diode, avalanche breakdown diode, or voltage regulator tube. Each of these devices begins
conducting at a specified voltage and will conduct as much current as required to hold its
terminal voltage to that specified voltage. The power supply is designed to only supply a
maximum amount of current that is within the safe operating capability of the shunt regulating
device (commonly, by using a series resistor). In shunt regulators, the voltage reference is also
the regulating device.
If the stabilizer must provide more power, the shunt regulator output is only used to provide the
standard voltage reference for the electronic device, known as the voltage stabilizer. The voltage
stabilizer is the electronic device, able to deliver much larger currents on demand.
Active regulators
Active regulators employ at least one active (amplifying) component such as a transistor or
operational amplifier. Shunt regulators are often (but not always) passive and simple, but always
inefficient because they (essentially) dump the excess current not needed by the load. When
more power must be supplied, more sophisticated circuits are used. In general, these active
regulators can be divided into several classes:
 Linear series regulators
 Switching regulators
 SCR regulators
Linear regulators
Linear regulators are based on devices that operate in their linear region (in contrast, a switching
regulator is based on a device forced to act as an on/off switch). In the past, one or more vacuum
tubes were commonly used as the variable resistance. Modern designs use one or more
transistors instead, perhaps within an Integrated Circuit. Linear designs have the advantage of

very "clean" output with little noise introduced into their DC output, but are most often much
less efficient and unable to step-up or invert the input voltage like switched supplies. All linear
regulators require a higher input than the output. All linear regulators are subject to the parameter
of dropout voltage.
Entire linear regulators are available as integrated circuits. These chips come in either fixed or
adjustable voltage types.
Switching regulators
Switching regulators rapidly switch a series device on and off. The duty cycle of the switch sets
how much charge is transferred to the load. This is controlled by a similar feedback mechanism
as in a linear regulator. Because the series element is either fully conducting, or switched off, it
dissipates almost no power; this is what gives the switching design its efficiency. Switching
regulators are also able to generate output voltages which are higher than the input, or of
opposite polarity — something not possible with a linear design.
Like linear regulators, nearly-complete switching regulators are also available as integrated
circuits. Unlike linear regulators, these usually require one external component: an inductor that
acts as the energy storage element. (Large-valued inductors tend to be physically large relative to
almost all other kinds of componentry, so they are rarely fabricated within integrated circuits and
IC regulators — with some exceptions.[1]
)
Comparing linear vs. switching regulators
The two types of regulators have their different advantages:
 Linear regulators are best when low output noise (and low RFI radiated noise) is required
 Linear regulators are best when a fast response to input and output disturbances is
required.
 At low levels of power, linear regulators are cheaper and occupy less printed circuit
board space.
 Switching regulators are best when power efficiency is critical (such as in portable
computers), except linear regulators are more efficient in a small number of cases (such
as a 5V microprocessor often in "sleep" mode fed from a 6V battery, if the complexity of
the switching circuit and the junction capacitance charging current means a high
quiescent current in the switching regulator).
 Switching regulators are required when the only power supply is a DC voltage, and a
higher output voltage is required.
 At high levels of power (above a few watts), switching regulators are cheaper (for
example, the cost of removing heat generated is less).
SCR regulators
Regulators powered from AC power circuits can use silicon controlled rectifiers (SCRs) as the
series device. Whenever the output voltage is below the desired value, the SCR is triggered,

allowing electricity to flow into the load until the AC mains voltage passes through zero (ending
the half cycle). SCR regulators have the advantages of being both very efficient and very simple,
but because they can not terminate an on-going half cycle of conduction, they are not capable of
very accurate voltage regulation in response to rapidly-changing loads.
Combination (hybrid) regulators
Many power supplies use more than one regulating method in series. For example, the output
from a switching regulator can be further regulated by a linear regulator. The switching regulator
accepts a wide range of input voltages and efficiently generates a (somewhat noisy) voltage
slightly above the ultimately desired output. That is followed by a linear regulator that generates
exactly the desired voltage and eliminates nearly all the noise generated by the switching
regulator. Other designs may use an SCR regulator as the "pre-regulator", followed by another
type of regulator. An efficient way of creating a variable-voltage, accurate output power supply
is to combine a multi-tapped transformer with an adjustable linear post-regulator.
Voltage stabilizer
A voltage stabilizer is an electronic device able to deliver relatively constant output voltage
while input voltage and load current changes over time.
The voltage stabilizer is the shunt regulator such as a Zener diode or avalanche diode. Each of
these devices begins conducting at a specified voltage and will conduct as much current as
required to hold its terminal voltage to that specified voltage. Hence the shunt regulator can be
viewed as the limited power parallel stabilizer. The shunt regulator output is used as a voltage
reference.
The Zener diode and avalanche diode have opposite threshold voltage dependence on
temperature. By connecting these two devices sequentially, it is possible to construct a voltage
reference with improved thermal stability. Sometimes (mostly for the voltages around 5.6 V)
both effects are combined in the same diode.
Simple voltage stabilizer
In the simplest case emitter follower is used, the base of the regulating transistor is directly
connected to the voltage reference:

The stabilizer uses the power source, having voltage Uin that may vary over time. It delivers the
relatively constant voltage Uout. The output load RL can also vary over time. For such a device to
work properly, the input voltage must be larger than the output voltage and Voltage drop must
not exceed the limits of the transistor used.
The output voltage of the stabilizer is equal to UZ - UBE where UBE is about 0.7v and depends on
the load current. If the output voltage drops below that limit, this increases the voltage difference
between the base and emitter (Ube), opening the transistor and delivering more current.
Delivering more current through the same output resistor RL increases the voltage again.
Voltage stabilizer with an operational amplifier
The stability of the output voltage can be significantly increased by using the operational
amplifier:
In this case, the operational amplifier opens the transistor more if the voltage at its inverting

input drops significantly below the output of the voltage reference at the non-inverting input.
Using the voltage divider (R1, R2 and R3) allows choice of the arbitrary output voltage between
Uz and Uin.
Zener diode
Current-voltage characteristic of a Zener diode with a breakdown voltage of 17 volt. Notice the
change of voltage scale between the forward biased (positive) direction and the reverse biased
(negative) direction.
A Zener diode is a type of diode that permits current not only in the forward direction like a
normal diode, but also in the reverse direction if the voltage is larger than the breakdown voltage
known as "Zener knee voltage" or "Zener voltage". The device was named after Clarence Zener,
who discovered this electrical property.
A conventional solid-state diode will not allow significant current if it is reverse-biased below its
reverse breakdown voltage. When the reverse bias breakdown voltage is exceeded, a
conventional diode is subject to high current due to avalanche breakdown. Unless this current is
limited by circuitry, the diode will be permanently damaged. In case of large forward bias
(current in the direction of the arrow), the diode exhibits a voltage drop due to its junction built-
in voltage and internal resistance. The amount of the voltage drop depends on the semiconductor
material and the doping concentrations.
A Zener diode exhibits almost the same properties, except the device is specially designed so as
to have a greatly reduced breakdown voltage, the so-called Zener voltage. By contrast with the
conventional device, a reverse-biased Zener diode will exhibit a controlled breakdown and allow
the current to keep the voltage across the Zener diode at the Zener voltage. For example, a diode
with a Zener breakdown voltage of 3.2 V will exhibit a voltage drop of 3.2 V if reverse bias
voltage applied across it is more than its Zener voltage. The Zener diode is therefore ideal for
applications such as the generation of a reference voltage (e.g. for an amplifier stage), or as a
voltage stabilizer for low-current applications.
The Zener diode's operation depends on the heavy doping of its p-n junction allowing electrons
to tunnel from the valence band of the p-type material to the conduction band of the n-type
material. In the atomic scale, this tunneling corresponds to the transport of valence band

electrons into the empty conduction band states; as a result of the reduced barrier between these
bands and high electric fields that are induced due to the relatively high levels of dopings on both
sides.[1]
The breakdown voltage can be controlled quite accurately in the doping process. While
tolerances within 0.05% are available, the most widely used tolerances are 5% and 10%.
Breakdown voltage for commonly available zener diodes can vary widely from 1.2 volts to 200
volts.
Another mechanism that produces a similar effect is the avalanche effect as in the avalanche
diode. The two types of diode are in fact constructed the same way and both effects are present
in diodes of this type. In silicon diodes up to about 5.6 volts, the Zener effect is the predominant
effect and shows a marked negative temperature coefficient. Above 5.6 volts, the avalanche
effect becomes predominant and exhibits a positive temperature coefficient[1]
. In a 5.6 V diode,
the two effects occur together and their temperature coefficients neatly cancel each other out,
thus the 5.6 V diode is the component of choice in temperature-critical applications. Modern
manufacturing techniques have produced devices with voltages lower than 5.6 V with negligible
temperature coefficients, but as higher voltage devices are encountered, the temperature
coefficient rises dramatically. A 75 V diode has 10 times the coefficient of a 12 V diode.
All such diodes, regardless of breakdown voltage, are usually marketed under the umbrella term
of "Zener diode".

Uses
Zener diode shown with typical packages. Reverse current − iZ is shown.
Zener diodes are widely used as voltage references and as shunt regulators to regulate the voltage
across small circuits. When connected in parallel with a variable voltage source so that it is
reverse biased, a Zener diode conducts when the voltage reaches the diode's reverse breakdown
voltage. From that point on, the relatively low impedance of the diode keeps the voltage across
the diode at that value.

In this circuit, a typical voltage reference or regulator, an input voltage, UIN, is regulated down to
a stable output voltage UOUT. The intrinsic voltage drop of diode D is stable over a wide current
range and holds UOUT relatively constant even though the input voltage may fluctuate over a
fairly wide range. Because of the low impedance of the diode when operated like this, Resistor R
is used to limit current through the circuit.
In the case of this simple reference, the current flowing in the diode is determined using Ohms
law and the known voltage drop across the resistor R. IDiode = (UIN - UOUT) / RΩ
The value of R must satisfy two conditions:
1. R must be small enough that the current through D keeps D in reverse breakdown. The
value of this current is given in the data sheet for D. For example, the common
BZX79C5V6[2]
device, a 5.6 V 0.5 W Zener diode, has a recommended reverse current of
5 mA. If insufficient current exists through D, then UOUT will be unregulated, and less
than the nominal breakdown voltage (this differs to voltage regulator tubes where the
output voltage will be higher than nominal and could rise as high as UIN). When
calculating R, allowance must be made for any current through the external load, not
shown in this diagram, connected across UOUT.
2. R must be large enough that the current through D does not destroy the device. If the
current through D is ID, its breakdown voltage VB and its maximum power dissipation
PMAX, then IDVB < PMAX.
A load may be placed across the diode in this reference circuit, and as long as the zener stays in
reverse breakdown, the diode will provide a stable voltage source to the load.
A Zener diode used in this way is known as a shunt voltage regulator (shunt, in this context,
meaning connected in parallel, and voltage regulator being a class of circuit that produces a
stable voltage across any load). In a sense, a portion of the current through the resistor is shunted
through the Zener diode, and the rest is through the load. Thus the voltage that the load sees is
controlled by causing some fraction of the current from the power source to bypass it—hence the
name, by analogy with locomotive switching points.
Shunt regulators are simple, but the requirements that the ballast resistor be small enough to
avoid excessive voltage drop during worst-case operation (low input voltage concurrent with
high load current) tends to leave a lot of current flowing in the diode much of the time, making

for a fairly wasteful regulator with high quiescent power dissipation, only suitable for smaller
loads.
Zener diodes in this configuration are often used as stable references for more advanced voltage
regulator circuits.
These devices are also encountered, typically in series with a base-emitter junction, in transistor
stages where selective choice of a device centered around the avalanche/Zener point can be used
to introduce compensating temperature co-efficient balancing of the transistor PN junction. An
example of this kind of use would be a DC error amplifier used in a stabilized power supply
circuit feedback loop system.
Zener diodes are also used in surge protectors to limit transient voltage spikes.
Another notable application of the zener diode is the use of noise caused by its avalanche
breakdown in a random number generator that never repeats.
Voltage Regulators:
An ideal power supply maintains a constant voltage at its output terminals under all operating
conditions. The output voltage of a practical power supply changes with load generally dropping
as load current increases as shown in fig. 1.
Fig. 1
The terminal voltage when full load current is drawn is called full load voltage (VFL). The no
load voltage is the terminal voltage when zero current is drawn from the supply, that is, the open
circuit terminal voltage.
Power supply performance is measured in terms of percent voltage regulation, which indicates its
ability to maintain a constant voltage. It is defined as
The Thevenin's equivalent of a power supply is shown in fig. 2. The Thevenin voltage is the no-

load voltage VNL and the Thevenin resistance is called the output resistance Ro. Let the full load
current be IFL. Therefore, the full load resistance RFL is given by
Fig. 2
From the equivalent circuit, we have
and the voltage regulation is given by
It is clear that the ideal power supply has zero outut resistance.
Example-1
A power supply having output resistance 1.5Ω supplies a full load current of 500mA to a 50Ω
load. Determine:
1. percent voltage regulation of the supply
2. no load output voltage.
Solution:

(a). Full load output voltage VFL = (500mA ) (50Ω) = 25V.
Therefore,
(b). The no load voltage
Voltage Regulators:
An unregulated power supply consists of a transformer (step down), a rectifier and a filter. These
power supplies are not good for some applications where constant voltage is required
irrespective of external disturbances. The main disturbances are:
1. As the load current varies, the output voltage also varies because of its poor regulation.
2. The dc output voltage varies directly with ac input supply. The input voltage may vary
over a wide range thus dc voltage also changes.
3. The dc output voltage varies with the temperature if semiconductor devices are used.
An electronic voltage regulator is essentially a controller used along with unregulated power
supply to stabilize the output dc voltage against three major disturbances
a. Load current (IL)
b. Supply voltage (Vi)
c. Temperature (T)
Fig. 3, shows the basic block diagram of voltage regulator. where
Vi = unregulated dc voltage.
Vo = regulated dc voltage.

Fig. 3
Since the output dc voltage VLo depends on the input unregulated dc voltage Vi, load current IL
and the temperature t, then the change ΔVo in output voltage of a power supply can be expressed
as follows
VO = VO(Vi, IL, T)
Take partial derivative of VO, we get,
SV gives variation in output voltage only due to unregulated dc voltage. RO gives the output
voltage variation only due to load current. ST gives the variation in output voltage only due to
temperature.
The smaller the value of the three coefficients, the better the regulations of power supply. The
input voltage variation is either due to input supply fluctuations or presence of ripples due to
inadequate filtering.
Voltage Regulator:
A voltage regulator is a device designed to maintain the output voltage of power supply nearly
constant. It can be regarded as a closed loop system because it monitors the output voltage and
generates the control signal to increase or decrease the supply voltage as necessary to
compensate for any change in the output voltage. Thus the purpose of voltage regulator is to
eliminate any output voltage variation that might occur because of changes in load, changes in

supply voltage or changes in temperature.
Zener Voltage Regulator:
The regulated power supply may use zener diode as the voltage controlling device as shown in
fig. 4. The output voltage is determined by the reverse breakdown voltage of the zener diode.
This is nearly constant for a wide range of currents. The load voltage can be maintained constant
by controlling the current through zener.
Fig. 4
The zener diode regulator has limitations of range. The load current range for which regulation is
maintained, is the difference between maximum allowable zener current and minimum current
required for the zener to operate in breakdown region. For example, if zener diode requires a
minimum current of 10 mA and is limited to a maximum of 1A (to prevent excessive
dissipation), the range is 1 - 0.01 = 0.99A. If the load current variation exceeds 0.99A, regulation
may be lost.
Emitter Follower Regulator:
To obtain better voltage regulation in shunt regulator, the zener diode can be connected to the
base circuit of a power transistor as shown in fig. 5. This amplifies the zener current range. It is
also known as emitter follower regulation.
Fig. 5
This configuration reduces the current flow in the diode. The power transistor used in this
configuration is known as pass transistor. The purpose of CL is to ensure that the variations in
one of the regulated power supply loads will not be fed to other loads. That is, the capacitor
effectively shorts out high-frequency variations.

Because of the current amplifying property of the transistor, the current in the zenor dioide is
small. Hence there is little voltage drop across the diode resistance, and the zener approximates
an ideal constant voltage source.
Operation of the circuit:
The current through resistor R is the sum of zener current IZ and the transistor base current IB ( =
IL / β ).
IL = IZ + IB
The output voltage across RL resistance is given by
VO = VZ – VBE
Where VBE 0.7 V
Therefore, VO= constant.
The emitter current is same as load current. The current IR is assumed to be constant for a given
supply voltage. Therefore, if IL increases, it needs more base currents, to increase base current Iz
decreases. The difference in this regulator with zener regulator is that in later case the zener
current decreases (increase) by same amount by which the load current increases (decreases).
Thus the current range is less, while in the shunt regulators, if IL increases by ΔIL then IB should
increase by ΔIL / β or IZ should decrease by ΔIL / β. Therefore the current range control is more
for the same rating zener.
The simplified circuit of the shunt regulator is shown in fig. 6.
Fig. 6

In a power supply the power regulation is basically, because of its high internal impedance. In
the circuit discussed, the unregulated supply has resistance RS of the order of 100 ohm. The use
of emitter follower is to reduce the output resistance and it becomes approximately.
RO = ( Rz + hie ) / (1 + hfe)
Where RZ represents the dynamic zener resistance. The voltage stabilization ratio SV is
approximately
SV = ∂ Vo / ∂ VI = Rz / (Rz + R)
SV can be improved by increasing R. This increases VCE and power dissipated in the transistor.
Other disadvantages of the circuit are.
1. No provision for varying the output voltage since it is almost equal to the zener voltage.
2. Change in VBEand Vz due to temperature variations appear at the output since the
transistor is connected in series with load, it is called series regulator and transistor is
allow series pass transistor.
Design of Series Voltage Regulator:
Fig. 1 shows the basic circuit of a series voltage regulator. The operation of this regulator has
been discussed in previous lecture. It consists of series (pass) transistor to control the output
voltage.
Fig. 1
The circuit can be designed taking two extreme operating conditions,
1. VS max, IZ max, I load min / β
2. VS min, IZ min, I load max / β
We calculate R s for both conditions and since R si is constant, we equate these two expressions
as in Equation E-1.

(E-1)
A design guideline that set IZ min = 0.1 I Z max. Then we equate the expressions for Equation (E-1)
to obtain,
(E-2)
Solving for IZ max, we obtain,
(E-3)
We estimate the load resistance by taking the ratio of the minimum source voltage to the
maximum load current. Since R load is large and in parallel, it can be ignored. This is the worst
case since it represents the smallest load and therefore the maximum load current.
(E-4)
The output filter capacitor size can be estimated according to the permissible output voltage
variation and ripple voltage frequency and is given by
(E-5)
Since the voltage gain of an EF amplifier is unity, the output voltage of teh regulated power
supply is,
Vload=VZ - VBE (E-6)
The percent regulation of the power supply is given by
(E-7)
Voltage Regulator
The maximum power dissipated in this type of series regulator is the power dissipated in the

internal pass transistor, which is approximately (VS max - Vout) IL max. Hence, as the load current
increases, the power dissipated in the internal pass transistor increases. If ILoad exceeds 0.75 A,
the IC package should be secured to a heat sink. When this is done, ILoad can increase to about
1.5 A.
We now focus our attention on the 78XX series of regulators. The last two digits of the IC part
number denote the output voltage of the device. Thus, for example, a 7808 IC package produces
an 8V regulated output. These packages, although internally complex, are inexpensive and easy
to use.
There are a number of different voltages that can be obtained from the 78XX series 1C; they are
5, 6, 8, 8.5, 10, 12, 15, 18, and 24 V. In order to design a regulator around one of these ICs, we
need only select a transformer, diodes, and filter. The physical configuration is shown in fig.
3(a). The ground lead and the metal tab are connected together. This permits direct attachment to
a heat sink for cooling purposes. A typical circuit application is shown in fig. 3(c).
(a) (b)
(c)
Fig. 3
The specification sheet for this IC indicates that there must be a common ground between the
input and output, and the minimum voltage at the IC input must be above the regulated output. In
order to assure this last condition, it is necessary to filter the output from the rectifier. The CF in
fig. 3(b) performs this filtering when combined with the input resistance to the IC. We use an n:1
step down transformer, with the secondary winding center-tapped, to drive a full-wave rectifier.

The minimum and maximum input voltages for the 78XX family of regulators are shown in
Table-1.
Type Min Max
7805 7 25
7806 8 25
7808 10.5 25
7885 10.5 25
7810 12.5 28
7812 14.5 30
7815 17.5 30
7818 21 33
7824 27 38
Table - 1
We use Table -1 to select the turns ratio, n, for a 78XX regulator. As a design guide, we will
take the average of Vmax and Vmin of the particular IC regulator to calculate n. For example, using
a 7805 regulator, we obtain
The center tap provides division by 2 so the peak voltage out of the rectifier is 115 √2 / 2n = 16.
Therefore, n = 5. This is a conservative method of selecting the transformer ratio.
The filter capacitor, CF, is chosen to maintain the voltage input range to the regulator as specified
in Table 8.1.
The output capacitor, CLoad, aids in isolating the effect of the transients that may appear on the
regulated supply line. CLoad should be a high quality tantalum capacitor with a capacitance of 1.0
µF. It should be connected close to the 78XX regulator using short leads in order to improve the

stability performance.
This family of regulators can also be used for battery powered systems. Fig. 3(c) shows a battery
powered application. The value of CF is chosen in the same manner as for the standard filter.
The 79XX series regulator is identical to the 78XX series except that it provides negative
regulated voltages instead of positive.
UNIVERSITY QUESTIONS
1. What is mean by depletion region?
2. Define the transition capacitance of a diode.
3. Differentiate a PN junction diode and zener diode.
4. Give the diode current equation.
5. Define cutin voltage.
6. What assumptions are made while analyzing the motion of an electron in an electric field?
7. How do you increase the conductivity of intrinsic semiconductor?
8. What is Hall effect?
9. How do the transition region width and contact potential across a pn junction vary with the
applied bias voltage?
10. Mention the two mechanisms of breakdown in a pn junction.
11. State law of mass action.
12. Why is the mobility of electrons greater than the holes?
13. The reverse saturation current of a silicon PN junction diode is 10 µA.Calculate the diode
current for the forward –bias voltage of 0.6 V at 25 C.
14. Give the equation for diode current under reverse bias.
15. Compare LED and LCD.
16. Define the potential-energy barrier.
17. What is mean by Diffusion capacitance?

18. Name any two material used to manufacture LEDs.
19. What is precision rectifier?
20. Find the ripple factor for a FWR with capacitor filter with the output waveform as shown in
the figure.Assume RL=100Ω with capacitor C=1000µF.
21. Derive the ripple factor for a HWR and FWR .
22. Why a series resistor is necessary when a diode is forward biased?
23. List any four applications of light emitting diode.
BIG QUESTIONS
1. With the volt-ampere characteristics,explain the working principle of the diode and also
explain the static ,dynamic resistance of the diodes? (16)
2. Write a detailed note on:
i) diode switching times (6)
ii)applications of diodes. (4)
iii)capacitance of diodes.(6)
3. Zener diode can be used as a voltage regulator-Justify it.(8)
4. Explain the working of a PN junction diode under various biasing conditions using the
relevant circuit sketch. (16)
5. Explain how a PN junction is formed? (8).
6. Write a note on diode capacitance.(8)
7. Write a detailed note on: LED (8)
8. Describe the conduction of current in an intrinsic semiconductor.(8)
9. Find the conductivity and resistivity of an intrinsic semiconductor at temperature of 300◦k.It is
given that
Ni=2.5*1013/cm3,µn=3800cm2/Sv;
µp=1800 cm2/Sv,q=1.6*10-19 C (8)
10. Derive the continuity equation for a semiconductor. (10)

11.In an N-type semiconductor ,the Fermi-level lies 0.3 Ev below the conduction band at 27 C .If
the temperature is increased to 55 C ,find the new position of the Fermi level.(6)
12. Give the theory of current components of pn junction diode.(10)
13. Determine the ac resistance for a semiconductor diode having a forward bias of 200 mV and
reverse saturation current of 1µA at room temperature.(6)
14. Derive an expression for the diffusion capacitance of a pn junction diode. (8)
15. What is zener effect ?Explain the function of a zener diode and draw its characteristics. (10)
16. Write a note on temperature dependence of breakdown voltages. (6)
17. Derive an expression for total current in a semiconductor due to drift and diffusion
phenomena.
18. What is meant by carrier life time? Discuss. (6)
19. Describe the action of the PN junction diode under forward and reverse biased conditions and
hence draw the volt amp characteristics of the diode . (10)
20. Distinguish between avalanche breakdown and zener breakdown. (8)
21.Explain the switching characteristics of PN junction diode. (8)
22. Derive an expression for the current under forward bias and reverse bias. (10)
23. The diode current is 0.6 Ma,when the applied voltage is 400 Mv 20Ma when the applied
voltage is 500Mv.Determine ƞ .Assume kt/q=25Mv.
24. Explain the effect of temperature on PN junction diodes. (5)
25. Explain the use of zener diode as voltage regulator . (6)
26.With neat diagram explain the operation of LCD.
27. Discuss the V-I characteristics of P-N junction diode and zener diode.
28. Explain the operation of full wave rectifier. Also derive the expression for its average output
voltage.
29. Derive the ripple factor for FWR with capacitor filter. (10)
30.Explain in detailabout the operation of the following type of filters and derive the ripple
factor for all i)C-filter ii) L-filter iii)LC-filter iv)CLC-filter (16)
31. Explain in detail the operation of the electronic voltage regulators.

UNIT 2
Bipolar Junction Transistor And Its Applications
Introduction
A bipolar (junction) transistor (BJT) is a three-terminal electronic device constructed of doped
semiconductor material and may be used in amplifying or switching applications. Bipolar
transistors are so named because their operation involves both electrons and holes. Charge flow
in a BJT is due to bidirectional diffusion of charge carriers across a junction between two regions
of different charge concentrations. This mode of operation is contrasted with unipolar
transistors, such as field-effect transistors, in which only one carrier type is involved in charge
flow due to drift. By design, most of the BJT collector current is due to the flow of charges
injected from a high-concentration emitter into the base where they are minority carriers that
diffuse toward the collector, and so BJTs are classified as minority-carrier devices.
PNP
NPN
Schematic symbols for
PNP- and NPN-type
BJTs.


NPN BJT with forward-biased E–B junction and reverse-biased B–C junction
An NPN transistor can be considered as two diodes with a shared anode. In typical operation, the
base-emitter junction is forward biased and the base–collector junction is reverse biased. In an
NPN transistor, for example, when a positive voltage is applied to the base–emitter junction, the
equilibrium between thermally generated carriers and the repelling electric field of the depletion
region becomes unbalanced, allowing thermally excited electrons to inject into the base region.
These electrons wander (or "diffuse") through the base from the region of high concentration
near the emitter towards the region of low concentration near the collector. The electrons in the
base are called minority carriers because the base is doped p-type which would make holes the
majority carrier in the base.
To minimize the percentage of carriers that recombine before reaching the collector–base
junction, the transistor's base region must be thin enough that carriers can diffuse across it in
much less time than the semiconductor's minority carrier lifetime. In particular, the thickness of
the base must be much less than the diffusion length of the electrons. The collector–base junction
is reverse-biased, and so little electron injection occurs from the collector to the base, but
electrons that diffuse through the base towards the collector are swept into the collector by the
electric field in the depletion region of the collector–base junction. The thin shared base and
asymmetric collector–emitter doping is what differentiates a bipolar transistor from two separate
and oppositely biased diodes connected in series.
Voltage, current, and charge control
The collector–emitter current can be viewed as being controlled by the base–emitter current
(current control), or by the base–emitter voltage (voltage control). These views are related by the
current–voltage relation of the base–emitter junction, which is just the usual exponential current–
voltage curve of a p-n junction (diode).[1]
The physical explanation for collector current is the amount of minority-carrier charge in the
base region.[1][2][3]
Detailed models of transistor action, such as the Gummel–Poon model,

account for the distribution of this charge explicitly to explain transistor behavior more exactly.[4]
The charge-control view easily handles phototransistors, where minority carriers in the base
region are created by the absorption of photons, and handles the dynamics of turn-off, or
recovery time, which depends on charge in the base region recombining. However, because base
charge is not a signal that is visible at the terminals, the current- and voltage-control views are
generally used in circuit design and analysis.
In analog circuit design, the current-control view is sometimes used because it is approximately
linear. That is, the collector current is approximately βF times the base current. Some basic
circuits can be designed by assuming that the emitter–base voltage is approximately constant,
and that collector current is beta times the base current. However, to accurately and reliably
design production BJT circuits, the voltage-control (for example, Ebers–Moll) model is
required[1]
. The voltage-control model requires an exponential function to be taken into account,
but when it is linearized such that the transistor can be modelled as a transconductance, as in the
Ebers–Moll model, design for circuits such as differential amplifiers again becomes a mostly
linear problem, so the voltage-control view is often preferred. For translinear circuits, in which
the exponential I–V curve is key to the operation, the transistors are usually modelled as voltage
controlled with transconductance proportional to collector current. In general, transistor level
circuit design is performed using SPICE or a comparable analogue circuit simulator, so model
complexity is usually not of much concern to the designer.
Turn-on, turn-off, and storage delay
The Bipolar transistor exhibits a few delay characteristics when turning on and off. Most
transistors, and especially power transistors, exhibit long base storage time that limits maximum
frequency of operation in switching applications. One method for reducing this storage time is by
using a Baker clamp.
Transistor 'alpha' and 'beta'
The proportion of electrons able to cross the base and reach the collector is a measure of the BJT
efficiency. The heavy doping of the emitter region and light doping of the base region cause
many more electrons to be injected from the emitter into the base than holes to be injected from
the base into the emitter. The common-emitter current gain is represented by βF or hfe; it is
approximately the ratio of the DC collector current to the DC base current in forward-active
region. It is typically greater than 100 for small-signal transistors but can be smaller in transistors
designed for high-power applications. Another important parameter is the common-base current
gain, αF. The common-base current gain is approximately the gain of current from emitter to
collector in the forward-active region. This ratio usually has a value close to unity; between 0.98
and 0.998. Alpha and beta are more precisely related by the following identities (NPN
transistor):

Structure
Simplified cross section of a planar NPN bipolar junction transistor
Die of a KSY34 high-frequency NPN transistor, base and emitter connected via bonded wires
A BJT consists of three differently doped semiconductor regions, the emitter region, the base
region and the collector region. These regions are, respectively, p type, n type and p type in a
PNP, and n type, p type and n type in a NPN transistor. Each semiconductor region is connected
to a terminal, appropriately labeled: emitter (E), base (B) and collector (C).
The base is physically located between the emitter and the collector and is made from lightly
doped, high resistivity material. The collector surrounds the emitter region, making it almost
impossible for the electrons injected into the base region to escape being collected, thus making
the resulting value of α very close to unity, and so, giving the transistor a large β. A cross section
view of a BJT indicates that the collector–base junction has a much larger area than the emitter–
base junction.

The bipolar junction transistor, unlike other transistors, is usually not a symmetrical device. This
means that interchanging the collector and the emitter makes the transistor leave the forward
active mode and start to operate in reverse mode. Because the transistor's internal structure is
usually optimized for forward-mode operation, interchanging the collector and the emitter makes
the values of α and β in reverse operation much smaller than those in forward operation; often
the α of the reverse mode is lower than 0.5. The lack of symmetry is primarily due to the doping
ratios of the emitter and the collector. The emitter is heavily doped, while the collector is lightly
doped, allowing a large reverse bias voltage to be applied before the collector–base junction
breaks down. The collector–base junction is reverse biased in normal operation. The reason the
emitter is heavily doped is to increase the emitter injection efficiency: the ratio of carriers
injected by the emitter to those injected by the base. For high current gain, most of the carriers
injected into the emitter–base junction must come from the emitter.
The low-performance "lateral" bipolar transistors sometimes used in CMOS processes are
sometimes designed symmetrically, that is, with no difference between forward and backward
operation.
Small changes in the voltage applied across the base–emitter terminals causes the current that
flows between the emitter and the collector to change significantly. This effect can be used to
amplify the input voltage or current. BJTs can be thought of as voltage-controlled current
sources, but are more simply characterized as current-controlled current sources, or current
amplifiers, due to the low impedance at the base.
Early transistors were made from germanium but most modern BJTs are made from silicon. A
significant minority are also now made from gallium arsenide, especially for very high speed
applications (see HBT, below).
NPN
The symbol of an NPN bipolar junction transistor
NPN is one of the two types of bipolar transistors, consisting of a layer of P-doped
semiconductor (the "base") between two N-doped layers. A small current entering the base is
amplified in the collector output. That is, an NPN transistor is "on" when its base is pulled high
relative to the emitter.
Most of the NPN current is carried by electrons, moving from emitter to collector as minority
carriers in the P-type base region. Most bipolar transistors used today are NPN, because electron
mobility is higher than hole mobility in semiconductors, allowing greater currents and faster
operation.

PNP
The symbol of a PNP Bipolar Junction Transistor.
The other type of BJT is the PNP, consisting of a layer of N-doped semiconductor between two
layers of P-doped material. A small current leaving the base is amplified in the collector output.
That is, a PNP transistor is "on" when its base is pulled low relative to the emitter.
The arrows in the NPN and PNP transistor symbols are on the emitter legs and point in the
direction of the conventional current flow when the device is in forward active mode.
A mnemonic device for the NPN / PNP distinction, based on the arrows in their symbols and the
letters in their names, is not pointing in for NPN and pointing in for PNP.[5]
Heterojunction bipolar transistor
Bands in graded heterojunction NPN bipolar transistor. Barriers indicated for electrons to move
from emitter to base, and for holes to be injected backward from base to emitter; Also, grading of
bandgap in base assists electron transport in base region; Light colors indicate depleted regions
The heterojunction bipolar transistor (HBT) is an improvement of the BJT that can handle
signals of very high frequencies up to several hundred GHz. It is common in modern ultrafast
circuits, mostly RF systems.[6][7]
Heterojunction transistors have different semiconductors for the
elements of the transistor. Usually the emitter is composed of a larger bandgap material than the
base. The figure shows that this difference in bandgap allows the barrier for holes to inject

backward into the base, denoted in figure as Δφp, to be made large, while the barrier for electrons
to inject into the base Δφn is made low. This barrier arrangement helps reduce minority carrier
injection from the base when the emitter-base junction is under forward bias, and thus reduces
base current and increases emitter injection efficiency.
The improved injection of carriers into the base allows the base to have a higher doping level,
resulting in lower resistance to access the base electrode. In the more traditional BJT, also
referred to as homojunction BJT, the efficiency of carrier injection from the emitter to the base is
primarily determined by the doping ratio between the emitter and base, which means the base
must be lightly doped to obtain high injection efficiency, making its resistance relatively high. In
addition, higher doping in the base can improve figures of merit like the Early voltage by
lessening base narrowing.
The grading of composition in the base, for example, by progressively increasing the amount of
germanium in a SiGe transistor, causes a gradient in bandgap in the neutral base, denoted in the
figure by ΔφG, providing a "built-in" field that assists electron transport across the base. That
drift component of transport aids the normal diffusive transport, increasing the frequency
response of the transistor by shortening the transit time across the base.
Two commonly used HBTs are silicon–germanium and aluminum gallium arsenide, though a
wide variety of semiconductors may be used for the HBT structure. HBT structures are usually
grown by epitaxy techniques like MOCVD and MBE.
Regions of operation
Applied voltages
B-E Junction
Bias (NPN)
B-C Junction
Bias (NPN)
Mode (NPN)
E < B < C Forward Reverse Forward active
E < B > C Forward Forward Saturation
E > B < C Reverse Reverse Cut-off
E > B > C Reverse Forward Reverse-active
Bipolar transistors have five distinct regions of operation, defined by BJT junction biases.
The modes of operation can be described in terms of the applied voltages (this description
applies to NPN transistors; polarities are reversed for PNP transistors):
Forward active: base higher than emitter, collector higher than base (in this mode the collector
current is proportional to base current by βF).

 Saturation: base higher than emitter, but collector is not higher than base.
 Cut-Off: base lower than emitter, but collector is higher than base. It means the transistor
is not letting conventional current to go through collector to emitter.
 Reverse-action: base lower than emitter, collector lower than base: reverse conventional
current goes through transistor.
Applied voltages
B-E Junction
Bias (PNP)
B-C Junction
Bias (PNP)
Mode (PNP)
E < B < C Reverse Forward Reverse-active
E < B > C Reverse Reverse Cut-off
E > B < C Forward Forward Saturation
E > B > C Forward Reverse Forward active
In terms of junction biasing: ('reverse biased base–collector junction' means Vbc < 0 for NPN,
opposite for PNP)
 Forward-active (or simply, active): The base–emitter junction is forward biased and the base–
collector junction is reverse biased. Most bipolar transistors are designed to afford the greatest
common-emitter current gain, βF, in forward-active mode. If this is the case, the collector–
emitter current is approximately proportional to the base current, but many times larger, for
small base current variations.
 Reverse-active (or inverse-active or inverted): By reversing the biasing conditions of the
forward-active region, a bipolar transistor goes into reverse-active mode. In this mode, the
emitter and collector regions switch roles. Because most BJTs are designed to maximize current
gain in forward-active mode, the βF in inverted mode is several (2–3 for the ordinary
germanium transistor) times smaller. This transistor mode is seldom used, usually being
considered only for failsafe conditions and some types of bipolar logic. The reverse bias
breakdown voltage to the base may be an order of magnitude lower in this region.
 Saturation: With both junctions forward-biased, a BJT is in saturation mode and facilitates high
current conduction from the emitter to the collector. This mode corresponds to a logical "on",
or a closed switch.
 Cut-off: In cut-off, biasing conditions opposite of saturation (both junctions reverse biased) are
present. There is very little current, which corresponds to a logical "off", or an open switch.
 Avalanche breakdown region
Although these regions are well defined for sufficiently large applied voltage, they overlap
somewhat for small (less than a few hundred millivolts) biases. For example, in the typical
grounded-emitter configuration of an NPN BJT used as a pulldown switch in digital logic, the
"off" state never involves a reverse-biased junction because the base voltage never goes below
ground; nevertheless the forward bias is close enough to zero that essentially no current flows, so
this end of the forward active region can be regarded as the cutoff region.

Active-mode NPN transistors in circuits
Structure and use of NPN transistor. Arrow according to schematic.
The diagram opposite is a schematic representation of an NPN transistor connected to two
voltage sources. To make the transistor conduct appreciable current (on the order of 1 mA) from
C to E, VBE must be above a minimum value sometimes referred to as the cut-in voltage. The
cut-in voltage is usually about 600 mV for silicon BJTs at room temperature but can be different
depending on the type of transistor and its biasing. This applied voltage causes the lower P-N
junction to 'turn-on' allowing a flow of electrons from the emitter into the base. In active mode,
the electric field existing between base and collector (caused by VCE) will cause the majority of
these electrons to cross the upper P-N junction into the collector to form the collector current IC.
The remainder of the electrons recombine with holes, the majority carriers in the base, making a
current through the base connection to form the base current, IB. As shown in the diagram, the
emitter current, IE, is the total transistor current, which is the sum of the other terminal currents
(i.e., ).
In the diagram, the arrows representing current point in the direction of conventional current –
the flow of electrons is in the opposite direction of the arrows because electrons carry negative
electric charge. In active mode, the ratio of the collector current to the base current is called the
DC current gain. This gain is usually 100 or more, but robust circuit designs do not depend on

the exact value (for example see op-amp). The value of this gain for DC signals is referred to as
hFE, and the value of this gain for AC signals is referred to as hfe. However, when there is no
particular frequency range of interest, the symbol β is used[citation needed]
.
It should also be noted that the emitter current is related to VBE exponentially. At room
temperature, an increase in VBE by approximately 60 mV increases the emitter current by a
factor of 10. Because the base current is approximately proportional to the collector and emitter
currents, they vary in the same way.
Active-mode PNP transistors in circuits
Structure and use of PNP transistor.
The diagram opposite is a schematic representation of a PNP transistor connected to two voltage
sources. To make the transistor conduct appreciable current (on the order of 1 mA) from E to C,
VEB must be above a minimum value sometimes referred to as the cut-in voltage. The cut-in
voltage is usually about 600 mV for silicon BJTs at room temperature but can be different
depending on the type of transistor and its biasing. This applied voltage causes the upper P-N
junction to 'turn-on' allowing a flow of holes from the emitter into the base. In active mode, the
electric field existing between the emitter and the collector (caused by VCE) causes the majority
of these holes to cross the lower P-N junction into the collector to form the collector current IC.
The remainder of the holes recombine with electrons, the majority carriers in the base, making a
current through the base connection to form the base current, IB. As shown in the diagram, the
emitter current, IE, is the total transistor current, which is the sum of the other terminal currents
(i.e., ).
In the diagram, the arrows representing current point in the direction of conventional current –

the flow of holes is in the same direction of the arrows because holes carry positive electric
charge. In active mode, the ratio of the collector current to the base current is called the DC
current gain. This gain is usually 100 or more, but robust circuit designs do not depend on the
exact value. The value of this gain for DC signals is referred to as hFE, and the value of this gain
for AC signals is referred to as hfe. However, when there is no particular frequency range of
interest, the symbol β is used[citation needed]
.
It should also be noted that the emitter current is related to VEB exponentially. At room
temperature, an increase in VEB by approximately 60 mV increases the emitter current by a
factor of 10. Because the base current is approximately proportional to the collector and emitter
currents, they vary in the same way.
History
The bipolar point-contact transistor was invented in December 1947 at the Bell Telephone
Laboratories by John Bardeen and Walter Brattain under the direction of William Shockley. The
junction version known as the bipolar junction transistor, invented by Shockley in 1948, enjoyed
three decades as the device of choice in the design of discrete and integrated circuits. Nowadays,
the use of the BJT has declined in favor of CMOS technology in the design of digital integrated
circuits.
Germanium transistors
The germanium transistor was more common in the 1950s and 1960s, and while it exhibits a
lower "cut off" voltage, typically around 0.2 V, making it more suitable for some applications, it
also has a greater tendency to exhibit thermal runaway.
Early manufacturing techniques
Various methods of manufacturing bipolar junction transistors were developed[8]
.
 Point-contact transistor – first type to demonstrate transistor action, limited commercial
use due to high cost and noise.
 Grown junction transistor – first type of bipolar junction transistor made[9]
. Invented by
William Shockley at Bell Labs. Invented on June 23, 1948[10]
. Patent filed on June 26,
1948.
 Alloy junction transistor – emitter and collector alloy beads fused to base. Developed at
General Electric and RCA[11]
in 1951.
o Micro alloy transistor – high speed type of alloy junction transistor. Developed at
Philco[12]
.
o Micro alloy diffused transistor – high speed type of alloy junction transistor.
Developed at Philco.
o Post alloy diffused transistor – high speed type of alloy junction transistor.
Developed at Philips.
 Tetrode transistor – high speed variant of grown junction transistor[13]
or alloy junction

transistor[14]
with two connections to base.
 Surface barrier transistor – high speed metal barrier junction transistor. Developed at
Philco[15]
in 1953[16]
.
 Drift-field transistor – high speed bipolar junction transistor. Invented by Herbert
Kroemer[17][18]
at the Central Bureau of Telecommunications Technology of the German
Postal Service, in 1953.
 Diffusion transistor – modern type bipolar junction transistor. Prototypes[19]
developed at
Bell Labs in 1954.
o Diffused base transistor – first implementation of diffusion transistor.
o Mesa transistor – Developed at Texas Instruments in 1957.
o Planar transistor – the bipolar junction transistor that made mass produced
monolithic integrated circuits possible. Developed by Dr. Jean Hoerni[20]
at
Fairchild in 1959.
 Epitaxial transistor – a bipolar junction transistor made using vapor phase deposition. See
epitaxy. Allows very precise control of doping levels and gradients.
Theory and modeling
In the discussion below, focus is on the NPN bipolar transistor. In the NPN transistor in what is
called active mode the base-emitter voltage VBE and collector-base voltage VCB are positive,
forward biasing the emitter-base junction and reverse-biasing the collector-base junction. In
active mode of operation, electrons are injected from the forward biased n-type emitter region
into the p-type base where they diffuse to the reverse biased n-type collector and are swept away
by the electric field in the reverse biased collector-base junction. For a figure describing forward
and reverse bias, see the end of the article semiconductor diodes.
Large-signal models
Ebers–Moll model
Ebers–Moll Model for an NPN transistor.[21]
 IB, IC, IE: base, collector and emitter currents
 ICD, IED: collector and emitter diode currents
 αF, αR: forward and reverse common-base current gains

Ebers–Moll Model for a PNP transistor.
The DC emitter and collector currents in active mode are well modeled by an approximation to the
Ebers–Moll model:
The base internal current is mainly by diffusion (see Fick's law) and
where
 VT is the thermal voltage kT / q (approximately 26 mV at 300 K ≈ room temperature).
 IE is the emitter current
 IC is the collector current
 αT is the common base forward short circuit current gain (0.98 to 0.998)
 IES is the reverse saturation current of the base–emitter diode (on the order of 10−15
to 10−12
amperes)
 VBE is the base–emitter voltage
 Dn is the diffusion constant for electrons in the p-type base
 W is the base width
The α and forward β parameters are as described previously. A reverse β is sometimes included
in the model.

The unapproximated Ebers–Moll equations used to describe the three currents in any operating
region are given below. These equations are based on the transport model for a bipolar junction
transistor.[22]
where
 iC is the collector current
 iB is the base current
 iE is the emitter current
 βF is the forward common emitter current gain (20 to 500)
 βR is the reverse common emitter current gain (0 to 20)
 IS is the reverse saturation current (on the order of 10−15
to 10−12
amperes)
 VT is the thermal voltage (approximately 26 mV at 300 K ≈ room temperature).
 VBE is the base–emitter voltage
 VBC is the base–collector voltage
Base-width modulation

Top: NPN base width for low collector-base reverse bias; Bottom: narrower NPN base width for large
collector-base reverse bias. Hashed regions are depleted regions.
Main article: Early Effect
As the applied collector–base voltage (VCB = VCE − VBE) varies, the collector–base depletion
region varies in size. An increase in the collector–base voltage, for example, causes a greater
reverse bias across the collector–base junction, increasing the collector–base depletion region
width, and decreasing the width of the base. This variation in base width often is called the
"Early effect" after its discoverer James M. Early.
Narrowing of the base width has two consequences:
 There is a lesser chance for recombination within the "smaller" base region.
 The charge gradient is increased across the base, and consequently, the current of minority
carriers injected across the emitter junction increases.
Both factors increase the collector or "output" current of the transistor in response to an increase
in the collector–base voltage.
In the forward-active region, the Early effect modifies the collector current (iC) and the forward
common emitter current gain (βF) as given by:[citation needed]

where:
 VCB is the collector–base voltage
 VA is the Early voltage (15 V to 150 V)
 βF0 is forward common-emitter current gain when VCB = 0 V
 ro is the output impedance
 IC is the collector current
Current–voltage characteristics
The following assumptions are involved when deriving ideal current-voltage characteristics of
the BJT
 Low level injection
 Uniform doping in each region with abrupt junctions
 One-dimensional current
 Negligible recombination-generation in space charge regions
 Negligible electric fields outside of space charge regions.
It is important to characterize the minority diffusion currents induced by injection of carriers.
With regard to pn-junction diode, a key relation is the diffusion equation.
A solution of this equation is below, and two boundary conditions are used to solve and find C1
and C2.
The following equations apply to the emitter and collector region, respectively, and the origins 0,
0', and 0'' apply to the base, collector, and emitter.

A boundary condition of the emitter is below:
The values of the constants A1 and B1 are zero due to the following conditions of the emitter and
collector regions as and .
Because A1 = B1 = 0, the values of ΔnE(0'') and Δnc(0') are A2 and B2, respectively.
Expressions of IEn and ICn can be evaluated.
Because insignificant recombination occurs, the second derivative of ΔpB(x) is zero. There is
therefore a linear relationship between excess hole density and x.
The following are boundary conditions of ΔpB.
Substitute into the above linear relation.

.
With this result, derive value of IEp.
Use the expressions of IEp, IEn, ΔpB(0), and ΔpB(W) to develop an expression of the emitter
current.
Similarly, an expression of the collector current is derived.
An expression of the base current is found with the previous results.
Punchthrough
When the base–collector voltage reaches a certain (device specific) value, the base–collector
depletion region boundary meets the base–emitter depletion region boundary. When in this state
the transistor effectively has no base.The device thus loses all gain when in this state.

Gummel–Poon charge-control model
The Gummel–Poon model is a detailed charge-controlled model of BJT dynamics, which has
been adopted and elaborated by others to explain transistor dynamics in greater detail than the
terminal-based models typically do. This model also includes the dependence of transistor β-
values upon the direct current levels in the transistor, which are assumed current-independent in
the Ebers–Moll model.
Small-signal models
hybrid-pi model
h- parameter model
Generalized h-parameter model of an NPN BJT.
Replace x with e, b or c for CE, CB and CC topologies respectively.
Another model commonly used to analyze BJT circuits is the "h-parameter" model, closely
related to the hybrid-pi model and the y-parameter two-port, but using input current and output
voltage as independent variables, rather than input and output voltages. This two-port network is
particularly suited to BJTs as it lends itself easily to the analysis of circuit behaviour, and may be
used to develop further accurate models. As shown, the term "x" in the model represents a
different BJT lead depending on the topology used. For common-emitter mode the various
symbols take on the specific values as:
 x = 'e' because it is a common-emitter topology
 Terminal 1 = Base
 Terminal 2 = Collector
 Terminal 3 = Emitter
 ii = Base current (ib)
 io = Collector current (ic)
 Vin = Base-to-emitter voltage (VBE)
 Vo = Collector-to-emitter voltage (VCE)
and the h-parameters are given by:

 hix = hie – The input impedance of the transistor (corresponding to the emitter resistance
re).
 hrx = hre – Represents the dependence of the transistor's IB–VBE curve on the value of VCE.
It is usually very small and is often neglected (assumed to be zero).
 hfx = hfe – The current-gain of the transistor. This parameter is often specified as hFE or
the DC current-gain (βDC) in datasheets.
 hox = hoe – The output impedance of transistor. This term is usually specified as an
admittance and has to be inverted to convert it to an impedance.
As shown, the h-parameters have lower-case subscripts and hence signify AC conditions or
analyses. For DC conditions they are specified in upper-case. For the CE topology, an
approximate h-parameter model is commonly used which further simplifies the circuit analysis.
For this the hoe and hre parameters are neglected (that is, they are set to infinity and zero,
respectively). It should also be noted that the h-parameter model as shown is suited to low-
frequency, small-signal analysis. For high-frequency analyses the inter-electrode capacitances
that are important at high frequencies must be added.
Applications
The BJT remains a device that excels in some applications, such as discrete circuit design, due to
the very wide selection of BJT types available, and because of its high transconductance and
output resistance compared to MOSFETs. The BJT is also the choice for demanding analog
circuits, especially for very-high-frequency applications, such as radio-frequency circuits for
wireless systems. Bipolar transistors can be combined with MOSFETs in an integrated circuit by
using a BiCMOS process of wafer fabrication to create circuits that take advantage of the
application strengths of both types of transistor.
Temperature sensors
Main article: Silicon bandgap temperature sensor
Because of the known temperature and current dependence of the forward-biased base–emitter
junction voltage, the BJT can be used to measure temperature by subtracting two voltages at two
different bias currents in a known ratio.
Logarithmic converters
Because base–emitter voltage varies as the log of the base–emitter and collector–emitter
currents, a BJT can also be used to compute logarithms and anti-logarithms. A diode can also
perform these nonlinear functions, but the transistor provides more circuit flexibility.
Vulnerabilities
Exposure of the transistor to ionizing radiation causes radiation damage. Radiation causes a
buildup of 'defects' in the base region that act as recombination centers. The resulting reduction
in minority carrier lifetime causes gradual loss of gain of the transistor.

Power BJTs are subject to a failure mode called secondary breakdown, in which excessive
current and normal imperfections in the silicon die cause portions of the silicon inside the device
to become disproportionately hotter than the others. The doped silicon has a negative
temperature coefficient, meaning that it conducts more current at higher temperatures. Thus, the
hottest part of the die conducts the most current, causing its conductivity to increase, which then
causes it to become progressively hotter again, until the device fails internally. The thermal
runaway process associated with secondary breakdown, once triggered, occurs almost instantly
and may catastrophically damage the transistor package.
If the emitter-base junction is reverse biased into avalanche (zener) mode and current flows for a
short period of time, the current gain of the BJT will be permanently degraded.
Why transistor(BJT) is called a current controlled device and why it is called a nonlinear
device?
A bipolar junction transistor (BJT) is a type of transistor. It is a three-terminal device constructed
of doped semiconductor material and may be used in amplifying or switching applications.
Bipolar transistors are so named because their operation involves both electrons and holes.
Although a small part of the transistor current is due to the flow of majority carriers, most of the
transistor current is due to the flow of minority carriers and so BJTs are classified as 'minority-
carrier' devices.
An NPN transistor can be considered as two diodes with a shared anode region. In typical
operation, the emitter–base junction is forward biased and the base–collector junction is reverse
biased. In an NPN transistor, for example, when a positive voltage is applied to the base–emitter
junction, the equilibrium between thermally generated carriers and the repelling electric field of
the depletion region becomes unbalanced, allowing thermally excited electrons to inject into the
base region. These electrons wander (or "diffuse") through the base from the region of high
concentration near the emitter towards the region of low concentration near the collector. The
electrons in the base are called minority carriers because the base is doped p-type which would
make holes the majority carrier in the base.
The base region of the transistor must be made thin, so that carriers can diffuse across it in much
less time than the semiconductor's minority carrier lifetime, to minimize the percentage of
carriers that recombine before reaching the collector–base junction. The thickness of the base
should be less than the diffusion length of the electrons. The collector–base junction is reverse-
biased, so little electron injection occurs from the collector to the base, but electrons that diffuse
through the base towards the collector are swept into the collector by the electric field in the
depletion region of the collector–base junction.
Voltage, current, and charge control
The collector–emitter current can be viewed as being controlled by the base–emitter current
(current control), or by the base–emitter voltage (voltage control). These views are related by the
current–voltage relation of the base–emitter junction, which is just the usual exponential current–
voltage curve of a p-n junction (diode).

The physical explanation for collector current is the amount of minority-carrier charge in the
base region. Detailed models of transistor action, such as the Gummel–Poon model, account for
the distribution of this charge explicitly to explain transistor behavior more exactly. The charge-
control view easily handles photo-transistors, where minority carriers in the base region are
created by the absorption of photons, and handles the dynamics of turn-off, or recovery time,
which depends on charge in the base region recombining. However, since base charge is not a
signal that is visible at the terminals, the current- and voltage-control views are usually used in
circuit design and analysis.
In analog circuit design, the current-control view is sometimes used since it is approximately
linear. That is, the collector current is approximately βF times the base current. Some basic
circuits can be designed by assuming that the emitter–base voltage is approximately constant,
and that collector current is beta times the base current. However, to accurately and reliably
design production bjt circuits, the voltage-control (for example, Ebers–Moll) model is required
The voltage-control model requires an exponential function to be taken into account, but when it
is linearized such that the transistor can be modelled as a transconductance, as in the Ebers–Moll
model, design for circuits such as differential amplifiers again becomes a mostly linear problem,
so the voltage-control view is often preferred. For translinear circuits, in which the exponential
I–V curve is key to the operation, the transistors are usually modelled as voltage controlled with
transconductance proportional to collector current. In general, transistor level circuit design is
performed using SPICE or a comparable analogue circuit simulator, so model complexity is
usually not of much concern to the designer.
Biploar transistor:
A transistor is basically a Si on Ge
crystal containing three separate
regions. It can be either NPN or
PNP type fig. 1. The middle region
is called the base and the outer two
regions are called emitter and the
collector. The outer layers although
they are of same type but their
functions cannot be changed. They
have different physical and
electrical properties.
In most transistors, emitter is
heavily doped. Its job is to emit or
inject electrons into the base. These
bases are lightly doped and very
thin, it passes most of the emitter-
injected electrons on to the
collector. The doping level of
fig. 1

collector is intermediate between
the heavy doping of emitter and the
light doping of the base.
The collector is so named because
it collects electrons from base. The
collector is the largest of the three
regions; it must dissipate more heat
than the emitter or base. The
transistor has two junctions. One
between emitter and the base and
other between the base and the
collector. Because of this the
transistor is similar to two diodes,
one emitter diode and other
collector base diode.
The depletion layers do not have the same width, because different regions have different doping
levels. The more heavily doped a region is, the greater the concentration of ions near the
junction. This means the depletion layer penetrates more deeply into the base and slightly into
emitter. Similarly, it penetration more into collector. The thickness of collector depletion layer is
large while the base depletion layer is small as shown in fig. 2.
When transistor is made, the diffusion of free electrons across the junction produces two
depletion layers. For each of these depletion layers, the barrier potential is 0.7 V for Si transistor
and 0.3 V for Ge transistor.
fig. 2
If both the junctions are forward biased using two d.c sources, as shown in fig. 3a. free electrons
(majority carriers) enter the emitter and collector of the transistor, joins at the base and come out
of the base. Because both the diodes are forward biased, the emitter and collector currents are
large.

Fig. 3a Fig. 3b
If both the junction are reverse biased as shown in fig. 3b, then small currents flows through both
junctions only due to thermally produced minority carriers and surface leakage. Thermally
produced carriers are temperature dependent it approximately doubles for every 10 degree
celsius rise in ambient temperature. The surface leakage current increases with voltage.
When the emitter diode is forward biased and collector diode is reverse biased as shown in fig. 4
then one expect large emitter current and small collector current but collector current is almost as
large as emitter current.
Fig. 4
When emitter diodes forward biased and the applied voltage is more than 0.7 V (barrier
potential) then larger number of majority carriers (electrons in n-type) diffuse across the
junction.
Once the electrons are injected by the emitter enter into the base, they become minority carriers.
These electrons do not have separate identities from those, which are thermally generated, in the
base region itself. The base is made very thin and is very lightly doped. Because of this only few
electrons traveling from the emitter to base region recombine with holes. This gives rise to
recombination current. The rest of the electrons exist for more time. Since the collector diode is
reverse biased, (n is connected to positive supply) therefore most of the electrons are pushed into
collector layer. These collector elections can then flow into the external collector lead.
Thus, there is a steady stream of electrons leaving the negative source terminal and entering the
emitter region. The VEB forward bias forces these emitter electrons to enter the base region. The

thin and lightly doped base gives almost all those electrons enough lifetime to diffuse into the
depletion layer. The depletion layer field pushes a steady stream of electron into the collector
region. These electrons leave the collector and flow into the positive terminal of the voltage
source. In most transistor, more than 95% of the emitter injected electrons flow to the collector,
less than 5% fall into base holes and flow out the external base lead. But the collector current is
less than emitter current.
Relation between different currents in a transistor:
The total current flowing into the transistor must be equal to the total current flowing out of it.
Hence, the emitter current IE is equal to the sum of the collector (IC ) and base current (IB). That
is,
IE = IC + IB
The currents directions are positive directions. The total collector current IC is made up of two
components.
1. The fraction of emitter (electron) current which reaches the collector ( adc IE )
2. The normal reverse leakage current ICO
dc is known as large signal current gain or dc alpha. It is always positive. Since collector current
is almost equal to the IE therefore αdc IE varies from 0.9 to 0.98. Usually, the reverse leakage
current is very small compared to the total collector current.
NOTE: The forward bias on the emitter diode controls the number of free electrons infected into
the base. The larger (VBE) forward voltage, the greater the number of injected electrons. The
reverse bias on the collector diode has little influence on the number of electrons that enter the
collector. Increasing VCB does not change the number of free electrons arriving at the collector
junction layer.
The symbol of npn and pnp transistors are shown in fig. 5.

Fig. 5
Breakdown Voltages:
Since the two halves of a transistor are diodes, two much reverse voltage on either diode can
cause breakdown. The breakdown voltage depends on the width of the depletion layer and the
doping levels. Because of the heavy doping level, the emitter diode has a low breakdown voltage
approximately 5 to 30 V. The collector diode is less heavily doped so its breakdown voltage is
higher around 20 to 300 V.
Common Base Configuration
If the base is common to the input and output circuits, it is know as common base configuration
as shown in fig. 1.
Fig. 1
For a pnp transistor the largest current components are due to holes. Holes flow from emitter to
collector and few holes flow down towards ground out of the base terminal. The current
directions are shown in fig. 1.
(IE = IC + IB ).
For a forward biased junction, VEB is positive and for a reverse biased junction VCB is negative.
The complete transistor can be described by the following two relations, which give the input

voltage VEB and output current IC in terms of the output voltage (VCB) and input current IE.
VEB = f1(VCB, IE)
IC= f2(VCB, IE)
The output characteristic:
The collector current IC is completely determined by the input current IE and the VCB voltage.
The relationship is given in fig. 2. It is a plot of IC versus VCB, with emitter current IE as
parameter. The curves are known as the output or collector or static characteristics. The transistor
consists of two diodes placed in series back to back (with two cathodes connected together). The
complete characteristic can be divided in three regions.
Figure 7.2
(1). Active region:
In this region the collector diode is reverse biased and the emitter diode is forward biased.
Consider first that the emitter current is zero. Then the collector current is small and equals the
reverse saturation current ICO of the collector junction considered as a diode.
If the forward current IB is increased, then a fraction of IE ie. dcIE will reach the collector. In the
active region, the collector current is essentially independent of collector voltage and depends
only upon the emitter current. Because dc is, less than one but almost equal to unity, the
magnitude of the collector current is slightly less that of emitter current. The collector current is
almost constant and work as a current source.
The collector current slightly increases with voltage. This is due to early effect. At higher voltage
collector gathers in a few more electrons. This reduces the base current. The difference is so
small, that it is usually neglected. If the collector voltage is increased, then space charge width
increases; this decreased the effective base width. Then there is less chance for recombination

within the base region.
(2). Saturation region:
The region to the left of the ordinate VCB = 0, and above the IE = 0, characteristic in which both
emitter and collector junction are forward biased, is called saturation region.
When collector diode is forward biased, there is large change in collector current with small
changes in collector voltage. A forward bias means, that p is made positive with respect to n,
there is a flow of holes from p to n. This changes the collector current direction. If diode is
sufficiently forward biased the current changes rapidly. It does not depend upon emitter current.
(3). Cut off region:
The region below IE = 0 and to the right of VCB for which emitter and collector junctions are both
reversed biased is referred to cutoff region. The characteristics IE = 0, is similar to other
characteristics but not coincident with horizontal axis. The collector current is same as ICO. ICBO
is frequently used for ICO. It means collector to base current with emitter open. This is also
temperature dependent.
Common Base Amplifier
The common base amplifier circuit is
shown in Fig. 1. The VEE source
forward biases the emitter diode and
VCC source reverse biased collector
diode. The ac source vin is connected
to emitter through a coupling
capacitor so that it blocks dc. This ac
voltage produces small fluctuation in
currents and voltages. The load
resistance RL is also connected to
collector through coupling capacitor
so the fluctuation in collector base
voltage will be observed across RL.
The dc equivalent circuit is obtained
by reducing all ac sources to zero
and opening all capacitors. The dc
collector current is same as IE and
Fig. 1

VCB is given by
VCB = VCC - IC RC.
These current and voltage fix the Q point. The ac equivalent circuit is obtained by reducing all dc
sources to zero and shorting all coupling capacitors. r'e represents the ac resistance of the diode
as shown in Fig. 2.
Fig. 2
Fig. 3, shows the diode curve relating IE and VBE. In the absence of ac signal, the transistor
operates at Q point (point of intersection of load line and input characteristic). When the ac
signal is applied, the emitter current and voltage also change. If the signal is small, the operating
point swings sinusoidally about Q point (A to B).

Fig .3
If the ac signal is small, the points A and B are close to Q, and arc A B can be approximated by a
straight line and diode appears to be a resistance given by
If the input signal is small, input voltage and current will be sinusoidal but if the input voltage is
large then current will no longer be sinusoidal because of the non linearity of diode curve. The
emitter current is elongated on the positive half cycle and compressed on negative half cycle.
Therefore the output will also be distorted.
r'e is the ratio of ΔVBE and Δ IE and its value depends upon the location of Q. Higher up the Q
point small will be the value of r' e because the same change in VBE produces large change in IE.
The slope of the curve at Q determines the value of r'e. From calculation it can be proved that.
r'e = 25mV / IE

Proof:
In general, the current through a diode is given by
Where q is he charge on electron, V is the drop across diode, T is the temperature and K is a
constant.
On differentiating w.r.t V, we get,
The value of (q / KT) at 25°C is approximately 40.
Therefore,
or,
To a close approximation the small changes in collector current equal the small changes in
emitter current. In the ac equivalent circuit, the current ‗iC' is shown upward because if ‗ie'
increases, then ‗iC' also increases in the same direction.
Voltage gain:
Since the ac input voltage source is connected across r'e. Therefore, the ac emitter current is
given by
ie = Vin / r'e
or, Vin = ie r'e
The output voltage is given by Vout = ic (RC || RL)

Under open circuit condition vout = ic Rc
Example-1
Find the voltage gain and output of the amplifier shown in fig. 4, if input voltage is 1.5mV.
Fig. 4
Solution:
The emitter dc current I E is given by
Therefore, emitter ac resistance =
or, AV= 56.6

and, Vout = 1.5 x 56.6 = 84.9 mV
Example-2
Repeat example-1 if ac source has resistance R s = 100 W .
Solution:
The ac equivalent circuit with ac source resistance is shown in fig. 5.
Fig. 5
The emitter ac current is given by
or,
Therefore, voltage gain of the amplifier =
and, Vout = 1.5 x 8.71 =13.1 mV
Common Emitter Configuration
Common Emitter Curves:
The common emitter configuration of BJT is shown in fig. 1.

Fig. 1
In C.E. configuration the emitter is made common to the input and output. It is also referred to as
grounded emitter configuration. It is most commonly used configuration. In this, base current
and output voltages are taken as impendent parameters and input voltage and output current as
dependent parameters
VBE = f1 ( IB, VCE )
IC = f2( IB, VCE )
Input Characteristic:
The curve between IB and VBE for different values of VCE are shown in fig. 2. Since the base
emitter junction of a transistor is a diode, therefore the characteristic is similar to diode one. With
higher values of VCE collector gathers slightly more electrons and therefore base current reduces.
Normally this effect is neglected. (Early effect). When collector is shorted with emitter then the
input characteristic is the characteristic of a forward biased diode when VBE is zero and IB is also
zero.

Fig. 2
Output Characteristic:
The output characteristic is the curve between VCE and IC for various values of IB. For fixed
value of IB and is shown in fig. 3. For fixed value of IB, IC is not varying much dependent on VCE
but slopes are greater than CE characteristic. The output characteristics can again be divided into
three parts.
Fig. 3
(1) Active Region:
In this region collector junction is reverse biased and emitter junction is forward biased. It is the

area to the right of VCE = 0.5 V and above IB= 0. In this region transistor current responds most
sensitively to IB. If transistor is to be used as an amplifier, it must operate in this region.
If dc is truly constant then IC would be independent of VCE. But because of early effect, dc
increases by 0.1% (0.001) e.g. from 0.995 to 0.996 as VCE increases from a few volts to 10V.
Thendc increases from 0.995 / (1-0.995) = 200 to 0.996 / (1-0.996) = 250 or about 25%. This
shows that small change in  reflects large change in . Therefore the curves are subjected to
large variations for the same type of transistors.
(2) Cut Off:
Cut off in a transistor is given by IB = 0, IC= ICO. A transistor is not at cut off if the base current is
simply reduced to zero (open circuited) under this condition,
IC = IE= ICO / ( 1-αdc) = ICEO
The actual collector current with base open is designated as ICEO. Since even in the neighborhood
of cut off, dc may be as large as 0.9 for Ge, then IC=10 ICO(approximately), at zero base current.
Accordingly in order to cut off transistor it is not enough to reduce IB to zero, but it is necessary
to reverse bias the emitter junction slightly. It is found that reverse voltage of 0.1 V is sufficient
for cut off a transistor. In Si, thedc is very nearly equal to zero, therefore, IC = ICO. Hence even
with IB= 0, IC= IE= ICO so that transistor is very close to cut off.
In summary, cut off means IE = 0, IC = ICO, IB = -IC = -ICO , and VBE is a reverse voltage whose
magnitude is of the order of 0.1 V for Ge and 0 V for Si.
Reverse Collector Saturation Current ICBO:
When in a physical transistor emitter current is reduced to zero, then the collector current is
known as ICBO (approximately equal to ICO). Reverse collector saturation current ICBO also varies
with temperature, avalanche multiplication and variability from sample to sample. Consider the

circuit shown in fig. 4. VBB is the reverse voltage applied to reduce the emitter current to zero.
IE = 0, IB = -ICBO
If we require, VBE = - 0.1 V
Then - VBB + ICBO RB < - 0.1 V
Fig. 4
If RB = 100 K, ICBO = 100 m A, Then VBB must be 10.1 Volts. Hence transistor must be capable
to withstand this reverse voltage before breakdown voltage exceeds.
(3).Saturation Region:
In this region both the diodes are forward biased by at least cut in voltage. Since the voltage VBE
and VBC across a forward is approximately 0.7 V therefore, VCE = VCB + VBE = - VBC + VBE is
also few tenths of volts. Hence saturation region is very close to zero voltage axis, where all the
current rapidly reduces to zero. In this region the transistor collector current is approximately
given by VCC / R C and independent of base current. Normal transistor action is last and it acts
like a small ohmic resistance.
Large Signal Current Gain βdc :-
The ratio Ic / IB is defined as transfer ratio or large signal current gain bdc

Where IC is the collector current and IB is the base current. The bdc is an indication if how well
the transistor works. The typical value of bdc varies from 50 to 300.
In terms of h parameters, b dc is known as dc current gain and in designated hfE ( b dc = hfE).
Knowing the maximum collector current and bdc the minimum base current can be found which
will be needed to saturate the transistor.
This expression of bdc is defined neglecting reverse leakage current (ICO).
Taking reverse leakage current (ICO) into account, the expression for the bdc can be obtained as
follows:
bdc in terms of adc is given by
Since, ICO = ICBO
Cut off of a transistor means IE = 0, then IC= ICBO and IB = - ICBO. Therefore, the above
expression bdc gives the collector current increment to the base current change form cut off to IB
and hence it represents the large signal current gain of all common emitter transistor.

Biasing Techniques for CE Amplifiers
Biasing Circuit Techniques or Locating the Q - Point:
Fixed Bias or Base Bias:
In order for a transistor to amplify, it has to be properly biased. This means forward biasing the
base emitter junction and reverse biasing collector base junction. For linear amplification, the
transistor should operate in active region ( If IE increases, IC increases, VCE decreases
proportionally).
The source VBB, through a current limit resistor RB forward biases the emitter diode and VCC
through resistor RC (load resistance) reverse biases the collector junction as shown in fig. 1.
Fig. 1
The dc base current through RB is given by
IB = (VBB - VBE) / RB
or VBE = VBB - IB RB
Normally VBE is taken 0.7V or 0.3V. If exact voltage is required, then the input characteristic ( IB
vs VBE) of the transistor should be used to solve the above equation. The load line for the input
circuit is drawn on input characteristic. The two points of the load line can be obtained as given
below
For IB = 0, VBE = VBB.
and For VBE = 0, IB = VBB/ RB.
The intersection of this line with input characteristic gives the operating point Q as shown in
fig. 2. If an ac signal is connected to the base of the transistor, then variation in VBE is about

Q - point. This gives variation in IB and hence IC.
Fig. 2
In the output circuit, the load equation can be written as
VCE = VCC- IC RC
This equation involves two unknown VCE and IC and therefore can not be solved. To solve this
equation output characteristic ( ICvs VCE) is used.
The load equation is the equation of a straight line and given by two points:
IC= 0, VCE = VCC
& VCE = 0, IC= VCC / RC
The intersection of this line which is also called dc load line and the characteristic gives the
operating point Q as shown in fig. 3.

Fig. 3
The point at which the load line intersects with IB = 0 characteristic is known as cut off point. At
this point base current is zero and collector current is almost negligibly small. At cut off the
emitter diode comes out of forward bias and normal transistor action is lost. To a close
approximation.
VCE ( cut off)VCC (approximately).
The intersection of the load line and IB = IB(max) characteristic is known as saturation point . At
this point IB= IB(max), IC= IC(sat). At this point collector diodes comes out of reverse bias and again
transistor action is lost. To a close approximation,
IC(sat) VCC / RC(approximately ).
The IB(sat) is the minimum current required to operate the transistor in saturation region. If the IB
is less than IB (sat), the transistor will operate in active region. If IB > IB (sat) it always operates in
saturation region.
If the transistor operates at saturation or cut off points and no where else then it is operating as a
switch is shown in fig. 4.

Fig. 4
VBB = IB RB+ VBE
IB = (VBB – VBE ) / RB
If IB> IB(sat), then it operates at saturation, If IB = 0, then it operates at cut off.
If a transistor is operating as an amplifier then Q point must be selected carefully. Although we
can select the operating point any where in the active region by choosing different values of RB
& RC but the various transistor ratings such as maximum collector dissipation PC(max) maximum
collector voltage VC(max) and IC(max) & VBE(max) limit the operating range.
Once the Q point is established an ac input is connected. Due to this the ac source the base
current varies. As a result of this collector current and collector voltage also varies and the
amplified output is obtained.
If the Q-point is not selected properly then the output waveform will not be exactly the input
waveform. i.e. It may be clipped from one side or both sides or it may be distorted one.
Example-1
Find the transistor current in the circuit shown in fig. 5, if ICO= 20nA, β =100.

Solution:
For the base circuit, 5 = 200 x IB + 0.7
Therefore,
Since ICO << IB, therefore, IC = β IB = 2.15 mA
From the collector circuit, VCE = 10 - 3 x 2.15 = 3.55 V
Since, VCE = VCB + VBE
Thus, VCB = 3.55 - 0.7 = 2.55 V
Therefore, collector junction is reverse biased and
transistor is operating in its active region.
Fig. 5
Example - 2
If a resistor of 2K is connected in series with emitter in
the circuit as shown in fig. 6, find the currents. Given
ICO= 20 nA, β =100.
Solution:
IE = IB + IC = IB + 100 IB = 101 IB
For the base circuit, 5 = 200 x IB + 0.7 + 2k x 101 IB
Therefore,
Since ICO << IB, therefore, IC = βIB = 1.07 mA
From the collector circuit, VCB = 10 - 3 x 1.07 - 0.7 - 2 x
101 x 0.0107 = 3.93 V
Therefore collector junction is reverse biased and
transistor is operating in its active region.
Fig. 6

Example - 3
Repeat the example-1 if RB is replaced by 50k.
Solution:
The circuit is shown in fig. 7.
Since the base resistance is reduced, the base current must
have increased and there is a possibility that the transistor
has entered into saturation region.
Assuming transistor is operating in its saturation region,
VBE (sat)= 0.8 V and VCE (sat) = 0.2V
Therefore,
and
The minimum base current required for operating the
transistor in saturation region is
Since IB > IB(min), therefore, transistor is operating in its
saturation region.
Fig. 7
Example - 4
Repeat the example-2 if RB is replaced by 50k.
Solution:
The circuit is shown in fig. 8.
Since the base resistance is reduced, the base current must
have increased and there is a possibility that the transistor
has entered into saturation region.
Assuming transistor is operating in its saturation region,
Fig. 8

Solving these equations, we get,
IC = 1.96mA and IB = 0.0035mA
The minimum base current required for operating the
transistor in saturation region is
Since I B < I B(min) , therefore, transistor is operating in
its active region and not in saturation. The base and the
collector currents can be recalculated assuming the
transistor to be in active region.
For the base circuit, 5 = 50 x IB + 0.7 + 2k x 101 IB
Therefore,
IC = 1.71mA
From the collector circuit, VCB = 10 - 3 x 1.71 - 0.7 - 2 x
101 x 0.0171 = 0.716 V
Stability of Operating Point
Let us consider three operating points of transistor operating in common emitter amplifier.
1. Near cut off
2. Near saturation
3. In the middle of active region
If the operating point is selected near the cutoff region, the output is clipped in negative half cycle as shown in fig. 1.

Fig. 1
If the operating point is selected near saturation region, then the output is clipped in positive
cycle as shown in fig. 2.
Fig. 2 Fig. 3
If the operating point is selected in the middle of active region, then there is no clipping and the
output follows input faithfully as shown in fig. 3. If input is large then clipping at both sides will
take place. The first circuit for biasing the transistor is CE configuration is fixed bias.
In biasing circuit shown in fig. 4(a), two different power supplies are required. To avoid the use
of two supplies the base resistance RB is connected to VCC as shown in fig. 4(b).

Fig. 4(a) Fig. 4(b)
Now VCC is still forward biasing emitter diode. In this circuit Q point is very unstable. The base
resistance RB is selected by noting the required base current IB for operating point Q.
IB = (VCC – VBE ) / RB
Voltage across base emitter junction is approximately 0.7 V. Since VCC is usually very high
i.e. IB = VCC/ RB
Since IB is constant therefore it is called fixed bias circuit.
Biasing
Stability of quiescent operating point:
Let us assume that the transistor is replaced by an other transistor of same type. The dc of the
two transistors of same type may not be same. Therefore, ifdc increases then for same IB, output
characteristic shifts upward. If dc decreases, the output characteristic shifts downward. Since IB
is maintained constant, therefore the operating point shifts from Q to Q1 as shown in fig. 5. The
new operating point may be completely unsatisfactory.
Therefore, to maintain operating point stable, IB should be allowed to change so as to maintain
VCE & IC constant as dc changes.

Fig. 5
A second cause for bias instability is a variation in temperature. The reverse saturation current
changes with temperature. Specifically, ICO doubles for every 10o
C rise in temperature. The
collector current IC causes the collector junction temperature to rise, which in turn increases ICO.
As a result of this growth ICO, IC will increase ( dc IB + (1+  dc ) ICO ) and so on. It may be
possible that this process goes on and the ratings of the transistors are exceeded. This increase in
IC changes the characteristic and hence the operating point.
Stability Factor:
The operating point can be made stable by keeping IC and VCE constant. There are two
techniques to make Q point stable.
1. stabilization techniques
2. compensation techniques
In first, resistor biasing circuits are used which allow IB to vary so as to keep IC relatively
constant with variations in dc , ICO and VBE.
In second, temperature sensitive devices such as diodes, transistors are used which provide
compensating voltages and currents to maintain the operating point constant.
To compare different biasing circuits, stability factor S is defined as the rate of change of
collector current with respect to the ICO, keeping dc and VCE constant
S =  IC /  ICO
If S is large, then circuit is thermally instable. S cannot be less than unity. The other stability
factors are, IC /  dc and  IC / VBE. The bias circuit, which provide stability with ICO, also
show stability even if  and VBEchanges.
IC =dcIB + (I + dc ) ICO

Differentiating with respect to IC,
In fixed bias circuit, IB & IC are independent. Therefore and S = 1 + dc. If dc=100, S =
101, which means ICincreases 101 times as fast as ICO. Such a large change definitely operate the
transistor in saturation.
Biasing Techniques
Emitter Feedback Bias:
Fig. 1, shows the emitter feedback bias circuit. In this circuit, the voltage across resistor RE is
used to offset the changes in bdc. If bdc increases, the collector current increases. This increases
the emitter voltage which decrease the voltage across base resistor and reduces base current. The
reduced base current result in less collector current, which partially offsets the original increase
in bdc. The feedback term is used because output current ( IC) produces a change in input current
( IB ). RE is common in input and output circuits.
Fig. 1

In this case
Since IE = IC + IB
Therefore,
In this case, S is less compared to fixed bias circuit. Thus the stability of the Q point is better.
Further,
If IC is to be made insensitive to βdc than
RE cannot be made large enough to swamp out the effects of βdc without saturating the transistor.
Collector Feedback Bias:
In this case, the base resistor is returned back to collector as shown in fig. 2. If temperature
increases. βdc increases. This produces more collectors current. As IC increases, collector emitter
voltage decreases. It means less voltage across RB and causes a decrease in base current this
decreasing IC, and compensating the effect of dc.

Fig. 2
In this circuit, the voltage equation is given by
Circuit is stiff sensitive to changes in βdc. The advantage is only two resistors are used.
Then,
Therefore,
It is better as compared to fixed bias circuit.
Further,
Circuit is still sensitive to changes in βdc. The advantage is only two resistors are used.

Biasing Techniques
Voltage Divider Bias:
If the load resistance RC is very small, e.g. in a transformer coupled circuit, then there is no
improvement in stabilization in the collector to base bias circuit over fixed bias circuit. A circuit
which can be used even if there is no dc resistance in series with the collector, is the voltage
divider bias or self bias. fig. 3.
The current in the resistance RE in the emitter lead causes a voltage drop which is in the direction
to reverse bias the emitter junction. Since this junction must be forward biased, the base voltage
is obtained from the supply through R1, R2 network. If Rb = R1 || R2 equivalent resistance is very
– very small, then VBE voltage is independent of ICO and ¶ IC / ¶ ICO ® 0. For best stability R1 &
R2 must be kept small.
Fig. 3
If IC tends to increase, because of ICO, then the current in RC increases, hence base current is
decreased because of more reverse biasing and it reduces IC .
To analysis this circuit, the base circuit is replaced by its thevenin's equivalent as shown in fig. 4.

Fig. 4
Thevenin's voltage is
Rb is the effective resistance seen back from the base terminal.
If VBE is considered to be independent of IC, then
The smaller the value of Rb, the better is the stabilization but S cannot be reduced be unity.
Hence IC always increases more than ICO. If Rb is reduced, then current drawn from the supply
increases. Also if RE is increased then to operate at same Q-point, the magnitude of VCC must be

increased. In both the cases the power loss increased and reduced h.
In order to avoid the loss of ac signal because of the feedback caused by RE, this resistance is
often by passed by a large capacitance (> 10 m F) so that its reactance at the frequency under
consideration is very small.
Biasing Techniques
Emitter Bias:
Fig. 5, shown the emitter bias circuit. The circuit gets this name because the negative supply VEE
is used to forward bias the emitter junction through resistor RE. VCC still reverse biases collector
junction. This also gives the same stability as voltage divider circuit but it is used only if split
supply is available.
Fig. 5
In this circuit, the voltage equation is given by

Biasing Techniques
Example-1
Determine the Q-point for the CE amplifier given in fig. 1, if R1 = 1.5K  and Rs = 7K  . A
2N3904 transistor is used with β = 180, RE = 100and RC = Rload = 1K  . Also determine the
Pout(ac) and the dc power delivered to the circuit by the source.

Fig. 1
Solution:
We first obtain the Thevenin equivalent.
and
Note that this is not a desirable Q-point location since VBB is very close to VBE. Variation in VBE
therefore significantly change IC.We find Rac = RC || Rload= 500 W and Rdc = RC + RE =1.1K.
The value of VCE representing the quiescent value associated with ICQ is found as follows,
Then
Since the Q-point is on the lower half of the ac load line, the maximum possible symmetrical
output voltage swing is
The ac power output can be calculated as
The power drawn from the dc source is given by
The power loss in the transistor is given by

The Q-point in this example is not in the middle of the load line so that output swing is not as
great as possible. However, if the input signal is small and maximum output is not required, a
small IC can be used to reduce the power dissipated in the circuit.
Biasing Techniques
Moving Ground Around:
Ground is a reference point that can be moved around. e.g. consider a collector feedback bias
circuit. The various stages of moving ground are shown in fig. 2.
Fig. 2
Biasing a pnp Transistor:
The biasing of pnp transistor is done similar to npn transistor except that supply is of opposite
polarity The various biasing circuits of pnp transistor are shown in fig. 3.

Fig. 3
Example 2:
For the circuit shown in fig. 4, calculate IC and VCE
Solution:
Fig. 4

Small Signal CE Amplifiers
Small Signal CE Amplifiers:
CE amplifiers are very popular to amplify the small signal ac. After a transistor has been biased
with a Q point near the middle of a dc load line, ac source can be coupled to the base. This
produces fluctuations in the base current and hence in the collector current of the same shape and
frequency. The output will be enlarged sine wave of same frequency.
The amplifier is called linear if it does not change the wave shape of the signal. As long as the
input signal is small, the transistor will use only a small part of the load line and the operation
will be linear.
On the other hand, if the input signal is too large. The fluctuations along the load line will drive
the transistor into either saturation or cut off. This clips the peaks of the input and the amplifier is
no longer linear.
The CE amplifier configuration is shown in fig. 1.
Fig. 1
The coupling capacitor (CC ) passes an ac signal from one point to another. At the same time it
does not allow the dc to pass through it. Hence it is also called blocking capacitor.

Fig. 2
For example in fig. 2, the ac voltage at point A is transmitted to point B. For this series reactance
XC should be very small compared to series resistance RS. The circuit to the left of A may be a
source and a series resistor or may be the Thevenin equivalent of a complex circuit. Similarly RL
may be the load resistance or equivalent resistance of a complex network. The current in the loop
is given by
As frequency increases, decreases, and current increases until it reaches to its
maximum value vin / R. Therefore the capacitor couples the signal properly from A to B when
XC<< R. The size of the coupling capacitor depends upon the lowest frequency to be coupled.
Normally, for lowest frequency XC 0.1R is taken as design rule.
The coupling capacitor acts like a switch, which is open to dc and shorted for ac.
The bypass capacitor Cb is similar to a coupling capacitor, except that it couples an ungrounded
point to a grounded point. The Cb capacitor looks like a short to an ac signal and therefore
emitter is said ac grounded. A bypass capacitor does not disturb the dc voltage at emitter because
it looks open to dc current. As a design rule XCb  0.1RE at lowest frequency.
Small Signal CE Amplifiers
Analysis of CE amplifier:
In a transistor amplifier, the dc source sets up quiescent current and voltages. The ac source then
produces fluctuations in these current and voltages. The simplest way to analyze this circuit is to
split the analysis in two parts: dc analysis and ac analysis. One can use superposition theorem for

analysis .
AC & DC Equivalent Circuits:
For dc equivalent circuit, reduce all ac voltage sources to zero and open all ac current sources
and open all capacitors. With this reduced circuit shown in fig. 3 dc current and voltages can be
calculated.
Fig. 3
For ac equivalent circuits reduce dc voltage sources to zero and open current sources and short
all capacitors. This circuit is used to calculate ac currents and voltage as shown in fig. 4.
Fig. 4
The total current in any branch is the sum of dc and ac currents through that branch. The total
voltage across any branch is the sum of the dc voltage and ac voltage across that branch.
Phase Inversion:
Because of the fluctuation is base current; collector current and collector voltage also swings

above and below the quiescent voltage. The ac output voltage is inverted with respect to the ac
input voltage, meaning it is 180o
out of phase with input.
During the positive half cycle base current increase, causing the collector current to increase.
This produces a large voltage drop across the collector resistor; therefore, the voltage output
decreases and negative half cycle of output voltage is obtained. Conversely, on the negative half
cycle of input voltage less collector current flows and the voltage drop across the collector
resistor decreases, and hence collector voltage increases we get the positive half cycle of output
voltage as shown in fig. 5.
Fig. 5
Analysis of CE amplifier
AC Load line:
Consider the dc equivalent circuit fig. 1.

Fig. 1
Assuming IC = IC(approx), the output circuit voltage equation can be written as
The slop of the d.c load line is .
When considering the ac equivalent circuit, the output impedance becomes RC || RL which is less
than (RC +RE).
In the absence of ac signal, this load line passes through Q point. Therefore ac load line is a line
of slope (-1 / ( RC || RL) ) passing through Q point. Therefore, the output voltage fluctuations will
now be corresponding to ac load line as shown in fig. 2. Under this condition, Q-point is not in
the middle of load line, therefore Q-point is selected slightly upward, means slightly shifted to
saturation side.

Fig. 2
Analysis of CE amplifier
Voltage gain:
To find the voltage gain, consider an unloaded CE amplifier. The ac equivalent circuit is
shown in fig. 3. The transistor can be replaced by its collector equivalent model i.e. a
current source and emitter diode which offers ac resistance r'e.
Fig. 3
The input voltage appears directly across the emitter diode.
Therefore emitter current ie = Vin / r'e.

Since, collector current approximately equals emitter current and iC = ie and vout = - ie RC (The
minus sign is used here to indicate phase inversion)
Further vout = - (Vin RC) / r'e
Therefore voltage gain A = vout / vin = -RC / r'e
The ac source driving an amplifier has to supply alternating current to the amplifier. The
input impedance of an amplifier determines how much current the amplifier takes from
the ac source.
In a normal frequency range of an amplifier, where all capacitors look like ac shorts and
other reactance are negligible, the ac input impedance is defined as
zin= vin/ iin
Where vin, iin are peak to peak values or rms values
The impedance looking directly into the base is symbolized zin (base) and is given by
Z in(base) = vin / ib ,
Since,v in = ie r'e
» bi b r'e
zin (base) = b r'e.
From the ac equivalent circuit, the input impedance zin is the parallel combination of R1 ,
R2 and b r'e.
Zin = R1 || R2 || b r'e
The Thevenin voltage appearing at the output is
vout = A vin
The Thevenin impedance is the parallel combination of RC and the internal impedance
of the current source. The collector current source is an ideal source, therefore it has an
infinite internal impedance.
zout = RC.
The simplified ac equivalent circuit is shown in fig. 4.

Fig. 4
h-Parameters
Small signal low frequency transistor Models:
All the transistor amplifiers are two port networks having two voltages and two currents. The
positive directions of voltages and currents are shown in fig. 1.
Fig. 1
Out of four quantities two are independent and two are dependent. If the input current i1 and
output voltage v2 are taken independent then other two quantities i2 and v1 can be expressed in
terms of i1 and V2.
The equations can be written as
where h11, h12, h21 and h22 are called h-parameters.

= hi = input impedance with output short circuit to ac.
=hr = fraction of output voltage at input with input open circuited or reverse voltage gain with
input open circuited to ac (dimensions).
= hf = negative of current gain with output short circuited to ac.
The current entering the load is negative of I2. This is also known as forward short circuit current
gain.
= ho = output admittance with input open circuited to ac.
If these parameters are specified for a particular configuration, then suffixes e,b or c are also
included, e.g. hfe ,h ib are h parameters of common emitter and common collector amplifiers
Using two equations the generalized model of the amplifier can be drawn as shown in fig. 2.
Fig. 2

h-Parameters
The hybrid model for a transistor amplifier can be derived as follow:
Let us consider CE configuration as show in fig. 3. The variables, iB, iC ,vC, and vB represent total
instantaneous currents and voltages iB and vC can be taken as independent variables and vB, IC as
dependent variables.
Fig. 3
vB = f1 (iB ,vC )
IC = f2 ( iB , vC ).
Using Taylor 's series expression, and neglecting higher order terms we obtain.
The partial derivatives are taken keeping the collector voltage or base current constant. The Δ vB,
Δ vC, Δ iB, Δ iC represent the small signal (incremental) base and collector current and voltage
and can be represented as vb ,ib ,vC ,iC.

The model for CE configuration is shown in fig. 4.
Fig. 4
h-Parameters
:
To determine the four h-parameters of transister amplifier, input and output characteristic are
used. Input characteristic depicts the relationship between input voltage and input current with
output voltage as parameter. The output characteristic depicts the relationship between output
voltage and output current with input current as parameter. Fig. 5, shows the output
characterisitcs of CE amplifier.

Fig. 5
The current increments are taken around the quiescent point Q which corresponds to iB = IB and
to the collector voltage VCE = VC
The value of hoe at the quiescent operating point is given by the slope of the output characteristic
at the operating point (i.e. slope of tangent AB).
hie is the slope of the appropriate input on fig. 6, at the operating point (slope of tangent EF at Q).

Fig. 6
A vertical line on the input characteristic represents constant base current. The parameter hre can
be obtained from the ratio (VB2– V B1 ) and (VC2– V C1 ) for at Q.
Typical CE h-parametersof transistor 2N1573 are given below:
hie = 1000 ohm.
hre = 2.5 * 10 –4
hfe = 50
hoe = 25 m A / V
h-parameters
Analysis of a transistor amplifier using h-parameters:
To form a transistor amplifier it is only necessary to connect an external load and signal source
as indicated in fig. 1 and to bias the transistor properly.
Fig. 1

Consider the two-port network of CE amplifier. RS is the source resistance and ZL is the load
impedence h-parameters are assumed to be constant over the operating range. The ac equivalent
circuit is shown in fig. 2. (Phasor notations are used assuming sinusoidal voltage input). The
quantities of interest are the current gain, input impedence, voltage gain, and output impedence.
Fig. 2
Current gain:
For the transistor amplifier stage, Ai is defined as the ratio of output to input currents.
Input Impedence:
The impedence looking into the amplifier input terminals ( 1,1' ) is the input impedence Zi

h-parameters
Voltage gain:
The ratio of output voltage to input voltage gives the gain of the transistors.
Output Admittance:
It is defined as

Av is the voltage gain for an ideal voltage source (Rv = 0).
Consider input source to be a current source IS in parallel with a resistance RS as shown in fig. 3.
Fig. 3
In this case, overall current gain AIS is defined as

h-parameters
To analyze multistage amplifier the h-parameters of the transistor used are obtained from
manufacture data sheet. The manufacture data sheet usually provides h-parameter in CE
configuration. These parameters may be converted into CC and CB values. For example fig. 4 hrc
in terms of CE parameter can be obtained as follows.
Fig. 4
For CE transistor configuaration
Vbe = hie Ib + hre Vce
Ic = h fe Ib + hoe Vce
The circuit can be redrawn like CC transistor configuration as shown in fig. 5.
Vbc = hie Ib + hrc Vec
Ic = hfe Ib + hoe Vec

Fig. 5
h-parameters
Example - 1
For the circuits shown in fig. 1. (CE–CC configuration) various h-parameters are given
h ie = 2K, hfe = 50, hre = 6 * 10 -4
, h oc= 25 m A / V.
hic = 2K, hfe = -51, hre = 1, hoc = 25 m A / V.
Fig. 1

The small signal model of the transistor amplifier is shown in fig. 2.
Fig. 2
In the circuit, the collector resistance of first stage is shunted by the input impedence of last
stage. Therefore the analysis is started with last stage. It is convenient; to first compute current
gain, input impedence and voltage gain. Then output impedence is calculated starting from first
stage and moving towards end.

The effective source resistance R'S2 for the second stage is R01 || RC1 . Thus RS2 = R'01 = 4.65K

Frequency response
Overall current gain of the amplifier is Ai and is
given by
The equivalent circuit of the amplifier is shown in
fig. 3. From the circuit it is clear that the current ic1 is
divided into two parts.
Therefore,
and
Fig.3

Overall voltage gain of the amplifier is given by
h-parameters
Simplified common emitter hybrid model:
In most practical cases it is appropriate to obtain approximate values of A V , A i etc rather than
calculating exact values. How the circuit can be modified without greatly reducing the accuracy.
Fig. 4 shows the CE amplifier equivalent circuit in terms of h-parameters Since 1 / hoe in parallel
with RL is approximately equal to RL if 1 / hoe >> RL then hoe may be neglected. Under these
conditions.
Ic = hfe IB .
hre vc = hre Ic RL = hre hfe Ib RL .
Fig. 4
Since h fe.h re  0.01, this voltage may be neglected in comparison with h ic Ib drop across h ie
provided RL is not very large. If load resistance RL is small than hoe and hre can be neglected.

Output impedence seems to be infinite. When Vs = 0, and an external voltage is applied at the
output we fined Ib = 0, I C = 0. True value depends upon RS and lies between 40 K and 80K.
On the same lines, the calculations for CC and CB can be done.
CE amplifier with an emitter resistor:
The voltage gain of a CE stage depends upon hfe. This transistor parameter depends upon
temperature, aging and the operating point. Moreover, hfe may vary widely from device to
device, even for same type of transistor. To stabilize voltage gain A V of each stage, it should be
independent of hfe. A simple and effective way is to connect an emitter resistor Re as shown in
fig. 5. The resistor provides negative feedback and provide stabilization.
Fig. 5
An approximate analysis of the circuit can be made using the simplified model.

Subject to above approximation A V is completely stable. The output resistance is infinite for the
approximate model.
Opto Coupler:
It combines a LED and a photo diode in a single package as shown in fig. 6. LED radiates the light depending on the current
through LED. This light fails on photo diode and this sets up a reverse current. The advantage of an opto coupler is the electrical
isolation between the input and output circuits. The only contact between the input and output is a beam of light. Because of this,
it is possible to have an insulation resistance between the two circuits of the order of thousands of mega ohms. They can be used
to isolate two circuits of different voltage levels.
Fig. 6

TRANSISTOR BIAS STABILITY
BJT: Bipolar Junction Transistors:
Bipolar transistor amplifiers must be properly biased to operate correctly. In circuits made with
individual devices (discrete circuits), biasing networks consisting of resistors are commonly
employed. Much more elaborate biasing arrangements are used in integrated circuits, for
example, bandgap voltage references and current mirrors.
Bias circuit requirements:
For analog circuit operation, the Q-point is placed so the transistor stays in active mode (does not
shift to operation in the saturation region or cut-off region) when input is applied. For digital
operation, the Q-point is placed so the transistor does the contrary - switches from "on" to "off"
state. Often, Q-point is established near the center of active region of transistor characteristic to
allow similar signal swings in positive and negative directions. Q-point should be stable. In
particular, it should be insensitive to variations in transistor parameters (for example, should not
shift if transistor is replaced by another of the same type), variations in temperature, variations in
power supply voltage and so forth. The circuit must be practical: easily implemented and cost-
effective.
Load line:
The concept of load line is very important in understanding the working of a transistor. It is
defined as the locus of operating points on the output characteristics of the transistor. It is the line
on which the operating point moves when ac signal is applied to the transistor.
The dc load line gives the value of Ic and VCE corresponding to zero signal conditions. The ac
load line gives the value of IC and VCE when ac signal is applied. AC load line is steeper than the
dc load line but the two intersect at the Q-point determined by biasing dc voltages and
currents. AC load line takes into account the ac load resistance while dc load line considers only
the dc load resistance.
Q Point:
The operating point of a device, also known as bias point, quiescent point, or Q-point, is the
point on the output characteristics that shows the DC collector–emitter voltage (Vce) and the
collector current (Ic) with no input signal applied. The term is normally used in connection with
devices such as transistors.
For bipolar junction transistors the bias point is chosen to keep the transistor operating in the
active mode, using a variety of circuit techniques, establishing the Q-point DC voltage and
current. A small signal is then applied on top of the Q-point bias voltage, thereby either
modulating or switching the current, depending on the purpose of the circuit.

The quiescent point of operation is typically near the middle of DC load line. The process of
obtaining certain DC collector current at a certain DC collector voltage by setting up operating
point is called biasing.
After establishing the operating point, when input signal is applied, the output signal should not
move the transistor either to saturation or to cut-off. However, this unwanted shift still might
occur, due to the following reasons:
1. Parameters of transistors depend on junction temperature. As junction temperature
increases, leakage current due to minority charge carriers (ICBO) increases. As ICBO
increases, ICEO also increases, causing an increase in collector current IC. This produces
heat at the collector junction. This process repeats, and, finally, Q-point may shift into the
saturation region. Sometimes, the excess heat produced at the junction may even burn the
transistor. This is known as thermal runaway.
2. When a transistor is replaced by another of the same type, the Q-point may shift, due to
changes in parameters of the transistor, such as current gain (β) which varies slightly for
each unique transistor.
To avoid a shift of Q-point, bias-stabilization is necessary. Various biasing circuits can be used
for this purpose.
VARIOUS METHODS FOR TRANSISTOR BIASING
1. Fixed bias
2. Collector-to-base bias
3. Voltage divider bias
4. Emitter bias

1)Fixed bias (base bias):
This form of biasing is also called base bias. In the example image on the right, the single power
source (for example, a battery) is used for both collector and base of transistor, although separate
batteries can also be used.
In the given circuit,
VCC = IBRB + Vbe
Therefore,
IB = (VCC - Vbe)/RB
For a given transistor, Vbe does not vary significantly during use. As VCC is of fixed value, on
selection of RB, the base current IB is fixed. Therefore this type is called fixed bias type of circuit.
Also for given circuit,
VCC = ICRC + Vce
Therefore,
Vce = VCC - ICRC

The common-emitter current gain of a transistor is an important parameter in circuit design, and
is specified on the data sheet for a particular transistor. It is denoted as β on this page.
Because IC = βIB
we can obtain IC as well. In this manner, operating point given as (VCE,IC) can be set for given
transistor.
Merits:
 It is simple to shift the operating point anywhere in the active region by merely changing
the base resistor (RB).
 A very small number of components are required.
Demerits:
 The collector current does not remain constant with variation in temperature or power
supply voltage. Therefore the operating point is unstable.
 Changes in Vbe will change IB and thus cause RE to change. This in turn will alter the gain
of the stage.
 When the transistor is replaced with another one, considerable change in the value of β
can be expected. Due to this change the operating point will shift.
2)Collector-to-base bias:

This configuration employs negative feedback to prevent thermal runaway and stabilize the
operating point. In this form of biasing, the base resistor RB is connected to the collector instead
of connecting it to the DC source VCC. So any thermal runaway will induce a voltage drop across
the RC resistor that will throttle the transistor's base current.
If Vbe is held constant and temperature increases, then the collector current Ic increases. However,
a larger Ic causes the voltage drop across resistor Rc to increase, which in turn reduces the voltage
across the base resistor Rb. A lower base-resistor voltage drop reduces the base current Ib, which
results in less collector current Ic. Because an increase in collector current with temperature is
opposed, the operating point is kept stable.
Merits:
 Circuit stabilizes the operating point against variations in temperature and β (ie.
replacement of transistor)
Demerits:
 In this circuit, to keep Ic independent of β, the following condition must be met:
which is the case when
 As β-value is fixed (and generally unknown) for a given transistor, this relation can be
satisfied either by keeping Rc fairly large or making Rb very low.
 If Rc is large, a high Vcc is necessary, which increases cost as well as precautions
necessary while handling.
 If Rb is low, the reverse bias of the collector–base region is small, which limits the
range of collector voltage swing that leaves the transistor in active mode.
 The resistor Rb causes an AC feedback, reducing the voltage gain of the amplifier. This
undesirable effect is a trade-off for greater Q-point stability.

3)Voltage divider bias
The voltage divider is formed using external resistors R1 and R2. The voltage across R2 forward
biases the emitter junction. By proper selection of resistors R1 and R2, the operating point of the
transistor can be made independent of β. In this circuit, the voltage divider holds the base voltage
fixed independent of base current provided the divider current is large compared to the base
current. However, even with a fixed base voltage, collector current varies with temperature (for
example) so an emitter resistor is added to stabilize the Q-point, similar to the above circuits with
emitter resistor.
Merits:
 Unlike above circuits, only one dc supply is necessary.
 Operating point is almost independent of β variation.
 Operating point stabilized against shift in temperature.
Demerits:
 As β-value is fixed for a given transistor, this relation can be satisfied either by keeping
RE fairly large, or making R1||R2 very low.
 If RE is of large value, high VCC is necessary. This increases cost as well as
precautions necessary while handling.
 If R1 || R2 is low, either R1 is low, or R2 is low, or both are low. A low R1 raises
VB closer to VC, reducing the available swing in collector voltage, and limiting
how large RC can be made without driving the transistor out of active mode. A
low R2 lowers Vbe, reducing the allowed collector current. Lowering both resistor

values draws more current from the power supply and lowers the input resistance
of the amplifier as seen from the base.
 AC as well as DC feedback is caused by RE, which reduces the AC voltage gain of the
amplifier. A method to avoid AC feedback while retaining DC feedback is discussed
below.
4)Emitter bias:
When a split supply (dual power supply) is available, this biasing circuit is the most effective,
and provides zero bias voltage at the emitter or collector for load. The negative supply VEE is
used to forward-bias the emitter junction through RE. The positive supply VCC is used to reverse-
bias the collector junction. Only two resistors are necessary for the common collector stage and
four resistors for the common emitter or common base stage.
We know that,
VB - VE = Vbe
If RB is small enough, base voltage will be approximately zero. Therefore emitter current is,
IE = (VEE - Vbe)/RE
The operating point is independent of β if RE >> RB/β

Merit:
Good stability of operating point similar to voltage divider bias.
Demerit:
This type can only be used when a split (dual) power supply is available.
Stability Factor:
The degree of success achieved in stabilizing IC in the face of variations in ICO is expressed in
terms of stability factor S and it is defined as the rate of change of IC w.r.t. ICO, keeping ß and
VBE constant.
i.e. S = dIc/dIco at constant ß and VBE (or IB)
From above expression it is obvious that smaller is the value of S, higher is the stability. It is
desirable to have as low stability factor as possible so as to achieve greater thermal stability. The
ideal value of S is unity (because IC includes ICO) but it is never possible to achieve it in practice.
Stability Factor in case of CB circuit,
S = dIc/dIco = d(ßIE + Ico)/dIco 0+1 or S = 1
Stability factor in case of CE circuit
S = dIc/dIco = d[ßIß + (1+ ß) Ico]/dIco 1 + ß taking IB constant.
Stabilization:
It is desirable that once selected, the operating (or Q) point should remain stable i.e. the
operating point should not shift its position owing to change in temperature etc. Unfortunately it
is not possible in practice unless special efforts are made to achieve it. The maintenance of the
operating point stable is called the stabilization.
The stabilization of operating point is essential because of
a) Temperature dependence of IC
(b) Individual variations and
(c) Thermal runaway.

With the increase in temperature, the collector leakage current ICO, the current gain ß tend to
increase and VBE required to produce a given collector current IC tends to decrease. Thus increase
in temperature tends to cause increase in IC.
The value of ß and VBE are not exactly the same for any two transistors even of the same type. So
when a transistor is replaced by another one (even of the same type) the operating point (zero
signals IC and VCE) is shifted.
The collector current IC, being equal to ß IB + (1+ ß ) ICO, increases with the increase in
temperature. This leads to increased power dissipation with further increase in temperature.
Being a cumulative process, it can lead to thermal runaway resulting in burn out of the transistor.
However, if by some modification, IC is made to fall with increase in temperature automatically,
then decrease in the term ß can be made to neutralize the increase in the term (1 +ß ) ICO,
thereby keeping IC almost constant. This will achieve thermal stability resulting in bias stability.
The biasing network associated with the transistor should fulfill the requirements of (i) ensuring
proper zero signal collector current, (ii) ensuring VCE not falling below 0.5 V for Ge transistors
and 1 V for Si transistors at any instant and (iii) ensuring stabilization of operating point (zero
signal IC and VCE)
Bias Compensation techniques:
Diode Compensation:
In the previous section, we looked at how four
parameters (VCC, VBE, ICBO, and ) can
affect the total collector current and,
therefore, the Q-point of the amplifier. Diode
compensation is a technique that is used to
reduce the Q-point variations by selecting a
diode that has temperature characteristics
similar to the transistor. To make sure that the
diode and transistor have the same
temperature characteristics, we can use a BJT
with the same specifications as the amplifier
transistor that is diode-connected. This simply
involves shorting the collector to the base as
shown in the figure to the right for an npn
BJT (this can also be done with pnp BJTs). As
a reminder, the diode symbol and the model
for the forward biased silicon diode are also
shown to the right – remember that the current flows in the direction of the arrow and that, unless

an ideal diode is specified, the diode forward resistance and turn-on voltage must be included in
all calculations.
The diode is connected in the base circuit of
the amplifier as shown in Figure 7.9a,
reproduced to the right. The addition of the
diode in this manner allows temperature
compensation since the VON of the diode
varies in the same fashion as the VBE of the
transistor. If the transistors used in the
amplifier and to construct the diode are
matched, the diode characteristics and base-
emitter junction characteristics will be the
same. Under these circumstances, variations
in VBE due to changes in bias parameters will
effectively be significantly reduced or
cancelled.
Sensistor & Thermistor Compensation:
Sensistor is a resistor whose resistance changes with temperature.
The resistance increases exponentially with temperature[1], that is the temperature coefficient is
positive (eg. 0.7% per degree Celsius).[2]
Sensistors are used in electronic circuits for compensation of temperature influence or as sensors
of temperature for other circuits.[3]
Sensistors are made by using semiconducting silicon and in their operation are similar to PTC-
type thermistors.

2MARKS
1.Why do we choose q point at the center of the loadline?
The operating point of a transistor is kept fixed usually at the center of the active region
in order that the input signal is well amplified. If the point is fixed in the saturation region or the
cut off region the positive and negative half cycle gets clipped off respectively.
2. Name the two techniques used in the stability of the q point .explain.
Stabilization technique: This refers to the use of resistive biasing circuit which
allows IB to vary so as to keep IC relatively constant with variations in Ico,β, and VBE.
Compensation techniques: This refers to the use of temperature sensitive devices such as
thermistors diodes. They provide compensating voltages &currents to maintain operating
point constant.
3. List out the different types of biasing.
1 ) Voltage divider bias
2 ) Base bias
3 ) Emitter feed back bias
4 ) Collector feedback bias
5. What do you meant by thermal runway?
Due to the self heating at the collector junction, the collector current rises. This
causes damage to the device. This phenomenon is called thermal runway.
6. Why is the transistor called a current controlled device?

The output characteristics of the transistor depend on the input current. So the
transistor is called a current controlled device.
7. Define current amplification factor?
It is defined as the ratio of change in output current to the change in input current at
constant other side voltage.
8. What are the requirements for biasing circuits?
The q point must be taken at the Centre of the active region of the output
characteristics.
9. When does a transistor act as a switch?
The transistor acts as a switch when it is operated at either cutoff region or saturation
region
10. What is biasing?
To use the transistor in any application it is necessary to provide sufficient voltage
and current to operate the transistor. This is called biasing.
11. What is operating point?
For the proper operation of the transistor a fixed level of current and voltages are
required. This values of currents and voltages defined at a point at which the transistor
operate is called operating point.
12. What is stability factor?
Stability factor is defined as the rate of change of collector current with respect to
the rate of change of reverse saturation current.
13. What is d.c load line?

The d.c load line is defined as a line on the output characteristics of the transistor
which gives the value of Ic & Vce corresponding to zero signal condition.
14. What are the advantages of fixed bias circuit?
This is simple circuit which uses a few components. The operating point can be
fixed any where on the Centre of the active region
15. Explain about the various regions in a transistor?
The three regions are active region saturation region cutoff region.
16. Explain about the characteristics of a transistor?
Input characteristics: it is drawn between input voltage & input current while keeping
output voltage as constant.
Output characteristics: It is drawn between the output voltage &output current while
keeping input current as constant.
UNIT III
Field Effect Transistor And Its Applications
Field Effect Transistor:
The field effect transistor is a semiconductor device, which depends for its operation on the
control of current by an electric field. There are two of field effect transistors:
1. JFET (Junction Field Effect Transistor)
2. MOSFET (Metal Oxide Semiconductor Field Effect Transistor)

The FET has several advantages over conventional transistor.
1. In a conventional transistor, the operation depends upon the flow of majority and
minority carriers. That is why it is called bipolar transistor. In FET the operation
depends upon the flow of majority carriers only. It is called unipolar device.
2. The input to conventional transistor amplifier involves a forward biased PN
junction with its inherently low dynamic impedance. The input to FET involves a
reverse biased PN junction hence the high input impedance of the order of M-
ohm.
3. It is less noisy than a bipolar transistor.
4. It exhibits no offset voltage at zero drain current.
5. It has thermal stability.
6. It is relatively immune to radiation.
The main disadvantage is its relatively small gain bandwidth product in comparison with
conventional transistor.
Operation of FET:
Consider a sample bar of N-type semiconductor. This is called N-channel and it is electrically
equivalent to a resistance as shown in fig. 1.
Fig. 1
Ohmic contacts are then added on each side of the channel to bring the external connection. Thus
if a voltage is applied across the bar, the current flows through the channel.
The terminal from where the majority carriers (electrons) enter the channel is called source
designated by S. The terminal through which majority carriers leaves the channel is called drain
and designated by D. For an N-channel device, electrons are the majority carriers. Hence the
circuit behaves like a dc voltage VDS applied across a resistance RDS. The resulting current is the
drain current ID. If VDS increases, ID increases proportionally.
Now on both sides of the n-type bar heavily doped regions of p-type impurity have been formed
by any method for creating pn junction. These impurity regions are called gates (gate1 and gate2)
as shown in fig. 2.

Both the gates are internally connected and they
are grounded yielding zero gate source voltage
(VGS =0). The word gate is used because the
potential applied between gate and source
controls the channel width and hence the
current.
As with all PN junctions, a depletion region is
formed on the two sides of the reverse biased
PN junction. The current carriers have diffused
across the junction, leaving only uncovered
positive ions on the n side and negative ions on
the p side. The depletion region width increases
with the magnitude of reverse bias. The
conductivity of this channel is normally zero
because of the unavailability of current carriers.
The potential at any point along the channel
depends on the distance of that point from the
drain, points close to the drain are at a higher
positive potential, relative to ground, then points
close to the source. Both depletion regions are
therefore subject to greater reverse voltage near
the drain. Therefore the depletion region width
increases as we move towards drain. The flow of
electrons from source to drain is now restricted
to the narrow channel between the no
conducting depletion regions. The width of this
channel determines the resistance between drain
and source.
Fig. 2
Field Effect Transistor
Consider now the behavior of drain current ID vs drain source voltage VDS. The gate source
voltage is zero therefore VGS= 0. Suppose that VDS is gradually linearly increased linearly from
0V. ID also increases.

Since the channel behaves as a semiconductor
resistance, therefore it follows ohm's law. The region
is called ohmic region, with increasing current, the
ohmic voltage drop between the source and the
channel region reverse biased the junction, the
conducting portion of the channel begins to constrict
and ID begins to level off until a specific value of
VDS is reached, called the pinch of voltage VP.
At this point further increase in VDS do not produce
corresponding increase in ID. Instead, as VDS
increases, both depletion regions extend further into
the channel, resulting in a no more cross section, and
hence a higher channel resistance. Thus even though,
there is more voltage, the resistance is also greater
and the current remains relatively constant. This is
called pinch off or saturation region. The current in
this region is maximum current that FET can
produce and designated by IDSS. (Drain to source
current with gate shorted).
Fig. 3
As with all pn junctions, when the reverse voltage exceeds a certain level, avalanche breakdown
of pn junction occurs and ID rises very rapidly as shown in fig. 3.
Consider now an N-channel JFET with a reverse gate source voltage as shown in fig. 4.
Fig. 4 Fig. 5
The additional reverse bias, pinch off will occur for smaller values of | VDS |, and the maximum
drain current will be smaller. A family of curves for different values of VGS(negative) is shown
in fig. 5.
Suppose that VGS= 0 and that due of VDS at a specific point along the channel is +5V with

respect to ground. Therefore reverse voltage across either p-n junction is now 5V. If VGS is
decreased from 0 to –1V the net reverse bias near the point is 5 - (-1) = 6V. Thus for any fixed
value of VDS, the channel width decreases as VGS is made more negative.
Thus ID value changes correspondingly. When the gate voltage is negative enough, the depletion
layers touch each other and the conducting channel pinches off (disappears). In this case the
drain current is cut off. The gate voltage that produces cut off is symbolized VGS(off) . It is same
as pinch off voltage.
Since the gate source junction is a reverse biased silicon diode, only a very small reverse current
flows through it. Ideally gate current is zero. As a result, all the free electrons from the source go
to the drain i.e. ID = IS. Because the gate draws almost negligible reverse current the input
resistance is very high 10's or 100's of M ohm. Therefore where high input impedance is
required, JFET is preferred over BJT. The disadvantage is less control over output current i.e.
FET takes larger changes in input voltage to produce changes in output current. For this reason,
JFET has less voltage gain than a bipolar amplifier.
Biasing the Field Effect Transistor
Transductance Curves:
The transductance curve of a JFET is a graph of output current (ID) vs input voltage (VGS) as
shown in fig. 1.
Fig. 1
By reading the value of ID and VGS for a particular value of VDS, the transductance curve can be
plotted. The transductance curve is a part of parabola. It has an equation of

Data sheet provides only IDSS and VGS(off) value. Using these values the transductance curve can
be plotted.
Biasing the FET:
The FET can be biased as an amplifier. Consider the common source drain characteristic of a
JFET. For linear amplification, Q point must be selected somewhere in the saturation region. Q
point is selected on the basis of ac performance i.e. gain, frequency response, noise, power,
current and voltage ratings.
Gate Bias:
Fig. 2, shows a simple gate bias circuit.
Fig. 2
Separate VGS supply is used to set up Q point. This is the worst way to select Q point. The reason
is that there is considerable variation between the maximum and minimum values of FET
parameters e.g.
IDSS VGS(off)
Minimum 4mA -2V
Maximum 13mA -8V
This implies that the minimum and maximum transductance curves are displaced as shown in fig.
3.

Gate bias applies a fixed voltage to the gate.
This fixed voltage results in a Q point that is
highly sensitive to the particular JFET used. For
instance, if VGS= -1V the Q point may very
from Q1 to Q2 depending upon the JFET
parameter is use.
At Q1, ID= 0.016 (1 - (1/8))2
= 12.3 mA
At Q2, ID= 0.004 (1-(1/2))2
= 1 mA.
The variation in drain current is very large.
Fig. 3
Self Bias:
Fig. 4, shows a self bias circuit another way to bias a FET.
Only a drain supply is used and no gate supply. The idea
is to use the voltage across RS to produce the gate source
reverse voltage.
This is a form of a local feedback similar to that used
with bipolar transistors. If drain current increases, the
voltage drop across RS increases because the ID RS
increases. This increases the gate source reverse voltage
which makes the channel narrow and reduces the drain
current. The overall effect is to partially offset the
original increase in drain current. Similarly, if ID
decreases, drop across RS decreases, hence reverse bias
decreases and ID increases.
Fig. 4
Since the gate source junction is reverse biased, negligible gate current flows through RG and so
the gate voltage with respect to ground is zero.
VG= 0;
The source to ground voltage equals the product of the drain current and the source resistance.

VS= ID R S.
The gate source voltage is the difference between the gate voltage and the source voltage.
VGS = VG – VS = 0 – IDRS
VGS = -ID RS.
This means that the gate source voltage equals the negative of the voltage across the source
resistor. The greater the drain current, the more negative the gate source voltage becomes.
Rearranging the equation:
ID = -VGS / RS
The graph of this equation is called self base line a shown in Fig. 5.
Fig. 5

The operating point on transductance curve is the
intersection of self bias line and transductance curve.
The slope of the line is (-1 / RS). If the source resistance
is very large (-1 / RS is small) then Q-point is far down
the transductance curve and the drain current is small.
When RS is small, the Q point is far up the transductance
curve and the drain current is large. In between there is
an optimum value of RS that sets up a Q point near the
middle of the transductance curve.
The transductance curve varies widely for FET (because
of variation in IDSS and VGS(off)) as shown in fig. 6. The
actual curve may be in between there extremes. A and B
are the optimum points for the two extreme curves. To
find the optimum resistance RS, so that Q-point is correct
for all the curves, A and B points are joined such that it
passes through origin.
The slope of this line gives the resistance value RS( VGS
= -ID RS). The current IQ is such that IA > IQ > IB. Here A,
Q and B all points are in straight line.
Fig. 6
Consider the case where a line drawn to pass between points A and B does not pass through the
origin. The equation VGS = - ID RS is not valid. The equation of this line is VGS = VGG – ID RS.
Such a bias relationship may be obtained by adding a fixed bias to the gate in addition to the
source self bias as shown in fig. 7.
Fig. 7
In this circuit.

VGG = RS IG + VGS + ID RS
Since RS IG = 0;
VGG = VGS + ID RS
or VGS = VGG– ID RS
Voltage Divider Bias :
The biasing circuit based on single power supply is shown in fig. 1. This is similar to the voltage
divider bias used with a bipolar transistor.
Fig. 1
The Thevenin voltage VTH applied to the gate is
The Thevenin resistance is given as
The gate current is assumed to be negligible. VTH is the dc voltage from gate to ground.

The drain current ID is given by
and the dc voltage from the drain to ground is VD = VDD – ID RD.
If VTH is large enough to swamp out VGS the drain current is approximately constant for any
JFET as shown in fig. 2.
Fig. 2
There is a problem in JFET. In a BJT, VBE is approximately 0.7V, with only minor variations
from one transistor to other. In a FET, VGS can vary several volts from one JFET to another. It is
therefore, difficult to make VTH large enough to swamp out VGS. For this reason, voltage divider
bias is less effective with, FET than BJT. Therefore, VGS is not negligible. The current increases
slightly from Q2 to Q1. However, voltage divider bias maintains ID nearly constant.
Consider a voltage divider bias circuit shown in fig. 3.
Difference in ID (min) and ID (max) is less
VD (max) = 30 – 2.13 * 4.7 = 20 V
VD (min) = 30 – 2.67 * 4.7 = 17.5 V

Fig. 3
Current Source Bias:
This is another way to produce solid Q point. The aim is to produce a drain current that is
independent of VGS. Voltage divider bias and self bias attempt to do this by swamping out of
variations in VGS.
Using two power supplies:
The current source bias can be used to make ID constant fig. 4.
Fig. 4
The bipolar transistor is emitter biased; its collector current is given by
IC = (VEE – VBE ) / RE.
Because the bipolar transistor acts like a current source, it forces the drain current to equal the
bipolar collector current.
ID = IC
Since IC is constant, both Q points have the same value of drain current. The current source
effectively wipes out the influence of VGS. Although VGS is different for each Q point, it no
longer influences the value of drain current.

Using One power supply:
When only a positive supply is available, the circuit
shown in fig. 5, can be used to set up a constant drain
current.
In this case, the bipolar transistor is voltage divider
biased. Assuming a stiff voltage divider, the emitter and
collector currents are constant for all bipolar transistors.
This forces the FET drain current equal the bipolar
collector current.
Fig. 5
Transductance:
The transductance of a FET is defined as
Because the changes in ID and VGS are equivalent
to ac current and voltage. This equation can be
written as
The unit of gm is mho or siemems.
Typical value of gm is 2000 m A / V.
Fig. 6
The value of gm can be obtained from the transductance curve as shown in fig. 6.
If A and B points are considered, than a change in VGS produces a change in ID. The ratio of ID

and VGS is the value of gm between A and B points. If C and D points are considered, then same
change in VGS produces more change in ID. Therefore, gm value is higher. In a nutshell, gm tells
us how much control gate voltage has over drain current. Higher the value of gm, the more
effective is gate voltage in controlling gate current. The second parameter rd is the drain
resistance.
FET a amplifier
Similar to Bipolar junction transistor. JFET can also be used as an amplifier. The ac equivalent
circuit of a JFET is shown in fig. 1.
Fig. 1
The resistance between the gate and the source RGS is very high. The drain of a JFET acts like a
current source with a value of gm Vgs. This model is applicable at low frequencies.
From the ac equivalent model
The amplification factor µ for FET is defined as

When VGS = 0, gm has its maximum value. The maximum value is designated as gmo.
Again consider the equation,
As VGS increases, gm decreases linearly.
Measuring IDSS and gm, VGS(off) can be determined
FET as amplifier
Fig. 2, shows a common source amplifier.

Fig. 2
When a small ac signal is coupled into the gate it produces variations in gate source voltage. This
produces a sinusoidal drain current. Since an ac current flows through the drain resistor. An
amplified ac voltage is obtained at the output. An increase in gate source voltage produces more
drain current, which means that the drain voltage is decreasing. Since the positive half cycle of
input voltage produces the negative half cycle of output voltage, we get phase inversion in a CS
amplifier.
The ac equivalent circuit is shown in fig. 3.
Fig. 3
The ac output voltage is
vout = - gm v gS RD
Negative sign means phase inversion. Because the ac source is directly connected between the

gate source terminals therefore ac input voltage equals
Vin = Vgs
The voltage gain is given by
The further simplified model of the amplifieris shown in fig. 4.
Fig. 4
Zin is the input impedance. At low frequencies, this is parallel combination of R1|| R2|| RGS. Since
RGS is very large, it is parallel combination of R1 & R2. A Vin is output voltage and RD is the
output impedance.
FET as amplifier
Because of nonlinear transductance curve, a JFET distorts large signals, as shown in fig. 5.
Given a sinusoidal input voltage, we get a non-sinusoidal output current in which positive half
cycle is elongated and negative cycle is compressed. This type of distortion is called Square law
distortion because the transductance curve is parabolic.

Fig. 5 Fig. 6
This distortion is undesirable for an amplifier. One way to minimize this is to keep the signal
small. In that case a part of the curve is used and operation is approximately linear. Some times
swamping resistor is used to minimize distortion and gain constant. Now the source is no longer
ac ground as shown in fig. 6.
The drain current through rS produces an ac voltage between the source and ground. If rS is large
enough the local feedback can swamp out the non-linearity of the curve. Then the voltage gain
approaches an ideal value of RD / rS.
Since RGS approaches infinity therefore, all the drain current flows through rS producing a
voltage drop of gm VgS rS. The ac equivalent circuit is shown in fig. 7.
Fig. 7

The voltage gain reduces but voltage gain is less effective by change in gm. rS must be greater
than 1 / gm only then
JFET Applications
Example-1:
Determine gm for an n-channel JFET with characteristic curve shown in fig. 1.
Fig. 1
Solution:
We select an operating region which is approximately in the middle of the curves; that is,
between vGS = -0.8 V and vGS = -1.2 V; iD = 8.5mA and iD = 5.5 mA. Therefore, the
transductance of the JFET is given by

Design of JFET amplifier:
To design a JFET amplifier, the Q point for the dc bias current can be determined graphically.
The dc bias current at the Q point should lie between 30% and 70% of IDSS. This locates the Q
point in the linear region of the characteristic curves.
The relationship between iD and vGS can be plotted on a dimensionless graph (i.e., a normalized
curve) as shown in fig. 2 .
Fig. 2
The vertical axis of this graph is iD / IDSS and the horizontal axis is vGS / VP. The slope of the
curve is gm.
A reasonable procedure for locating the quiescent point near the center of the linear operating
region is to select IDQ ≈ IDSS / 2 and VGSQ ≈ 0.3VP. Note that this is near the midpoint of the
curve. Next we select vDS ≈ VDD / 2. This gives a wide range of values for vds that keep the
transistor in the pinch –off mode.
The transductance at the Q-point can be found from the slope of the curve of fig.2 and is given
by
Example-2
Determine g m for a JFET where IDSS = 7 mA, VP = -3.5 V and VDD = 15V. Choose a reasonable

location for the Q-point.
Solution:
Let us select the Q-point as given below:
The transconductance, gm, is found from the slope of the curve at the point iD / IDSS = 0.5 and
vGS / VP =0.3. Hence,
JFET Applications
JEFT as Analog Switch:
JFET can be used as an analog switch as shown in fig. 3. It is the major application of a JFET.
The idea is to use two points on the load line: cut off and saturation. When JFET is cut off, it is
like an open switch. When it is saturated, it is like a closed switch.
Fig. 3 Fig. 4
When VGS =0, the JFET is saturated and operates at the upper end of the load line. When VGS is
equal to or more negative than VGS(off) , it is cut off and operates at lower end of the load line
(open and closed switch).This is shown in fig. 4.

Only these two points are used for operation when used as a switch. The JFET is normally
saturated well below the knee of the drain curve. For this reason the drain current is much
smaller than IDSS .
FET as a Shunt Switch:
FET can be used as a shunt switch as shown in fig. 5. When Vcont=0, the JFT is saturated and the
switch is closed When Vcont is more negative FET is like an open switch. The equivalent circuit
is also shown in fig. 5.
Fig. 5
FET as a series switch:
JFET can also be used as series switch as shown in fig. 6. When control is zero, the FET is a
closed switch. When Vcon= negative, the FET is an open switch. It is better than shunt switch.
Fig. 6
Multiplexing:
One of the important application of FET is in analog multiplexer. Analog multiplexer is a circuit
that selects one of the output lines as shown in fig. 7. When control voltages are more negative
all switches are open and output is zero. When any control voltage becomes zero the input is
transmitted to the output.

Fig. 7
Circuit symbols
A variety of symbols are used for the MOSFET. The basic design is generally a line for the
channel with the source and drain leaving it at right angles and then bending back at right angles
into the same direction as the channel. Sometimes three line segments are used for enhancement
mode and a solid line for depletion mode. Another line is drawn parallel to the channel for the
gate.
The bulk connection, if shown, is shown connected to the back of the channel with an arrow
indicating PMOS or NMOS. Arrows always point from P to N, so an NMOS (N-channel in P-
well or P-substrate) has the arrow pointing in (from the bulk to the channel). If the bulk is
connected to the source (as is generally the case with discrete devices) it is sometimes angled to
meet up with the source leaving the transistor. If the bulk is not shown (as is often the case in IC
design as they are generally common bulk) an inversion symbol is sometimes used to indicate
PMOS, alternatively an arrow on the source may be used in the same way as for bipolar
transistors (out for nMOS, in for pMOS).
Comparison of enhancement-mode and depletion-mode MOSFET symbols, along with JFET
symbols (drawn with source and drain ordered such that higher voltages appear higher on the
page than lower voltages):

P-channel
N-channel
JFET MOSFET enh MOSFET enh (no bulk) MOSFET dep
For the symbols in which the bulk, or body, terminal is shown, it is here shown internally
connected to the source. This is a typical configuration, but by no means the only important
configuration. In general, the MOSFET is a four-terminal device, and in integrated circuits many
of the MOSFETs share a body connection, not necessarily connected to the source terminals of
all the transistors.
MOSFET operation
Example application of an N-Channel MOSFET. When the switch is pushed the LED lights up.[2]
Metal–oxide–semiconductor structure on P-type silicon
Metal–oxide–semiconductor structure

A traditional metal–oxide–semiconductor (MOS) structure is obtained by growing a layer of
silicon dioxide (SiO2) on top of a silicon substrate and depositing a layer of metal or
polycrystalline silicon (the latter is commonly used). As the silicon dioxide is a dielectric
material, its structure is equivalent to a planar capacitor, with one of the electrodes replaced by a
semiconductor.
When a voltage is applied across a MOS structure, it modifies the distribution of charges in the
semiconductor. If we consider a P-type semiconductor (with NA the density of acceptors, p the
density of holes; p = NA in neutral bulk), a positive voltage, VGB, from gate to body (see figure)
creates a depletion layer by forcing the positively charged holes away from the gate-
insulator/semiconductor interface, leaving exposed a carrier-free region of immobile, negatively
charged acceptor ions (see doping (semiconductor)). If VGB is high enough, a high concentration
of negative charge carriers forms in an inversion layer located in a thin layer next to the
interface between the semiconductor and the insulator. Unlike the MOSFET, where the inversion
layer electrons are supplied rapidly from the source/drain electrodes, in the MOS capacitor they
are produced much more slowly by thermal generation through carrier generation and
recombination centers in the depletion region. Conventionally, the gate voltage at which the
volume density of electrons in the inversion layer is the same as the volume density of holes in
the body is called the threshold voltage.
This structure with P-type body is the basis of the N-type MOSFET, which requires the addition
of an N-type source and drain regions.
MOSFET structure and channel formation
Cross section of an NMOS without channel formed: OFF state

Cross section of an NMOS with channel formed: ON state
A metal–oxide–semiconductor field-effect transistor (MOSFET) is based on the modulation of
charge concentration by a MOS capacitance between a body electrode and a gate electrode
located above the body and insulated from all other device regions by a gate dielectric layer
which in the case of a MOSFET is an oxide, such as silicon dioxide. If dielectrics other than an
oxide such as silicon dioxide (often referred to as oxide) are employed the device may be
referred to as a metal–insulator–semiconductor FET (MISFET). Compared to the MOS capacitor,
the MOSFET includes two additional terminals (source and drain), each connected to individual
highly doped regions that are separated by the body region. These regions can be either p or n
type, but they must both be of the same type, and of opposite type to the body region. The source
and drain (unlike the body) are highly doped as signified by a '+' sign after the type of doping.
If the MOSFET is an n-channel or nMOS FET, then the source and drain are 'n+' regions and the
body is a 'p' region. As described above, with sufficient gate voltage, holes from the body are
driven away from the gate, forming an inversion layer or n-channel at the interface between the p
region and the oxide. This conducting channel extends between the source and the drain, and
current is conducted through it when a voltage is applied between source and drain.
For gate voltages below the threshold value, the channel is lightly populated, and only a very
small subthreshold leakage current can flow between the source and the drain.
If the MOSFET is a p-channel or pMOS FET, then the source and drain are 'p+' regions and the
body is a 'n' region. When a negative gate-source voltage (positive source-gate) is applied, it
creates a p-channel at the surface of the n region, analogous to the n-channel case, but with
opposite polarities of charges and voltages. When a voltage less negative than the threshold
value (a negative voltage for p-channel) is applied between gate and source, the channel
disappears and only a very small subthreshold current can flow between the source and the drain.
The source is so named because it is the source of the charge carriers (electrons for n-channel,
holes for p-channel) that flow through the channel; similarly, the drain is where the charge
carriers leave the channel.
The device may comprise a Silicon On Insulator (SOI) device in which a Buried OXide (BOX) is
formed below a thin semiconductor layer. If the channel region between the gate dielectric and a

Buried Oxide (BOX) region is very thin, the very thin channel region is referred to as an Ultra
Thin Channel (UTC) region with the source and drain regions formed on either side thereof in
and/or above the thin semiconductor layer. Alternatively, the device may comprise a
SEMiconductor On Insulator (SEMOI) device in which semiconductors other than silicon are
employed. Many alternative semicondutor materials may be employed.
When the source and drain regions are formed above the channel in whole or in part, they are
referred to as Raised Source/Drain (RSD) regions.
Modes of operation
The operation of a MOSFET can be separated into three different modes, depending on the
voltages at the terminals. In the following discussion, a simplified algebraic model is used that is
accurate only for old technology. Modern MOSFET characteristics require computer models that
have rather more complex behavior.
For an enhancement-mode, n-channel MOSFET, the three operational modes are:
Cutoff, subthreshold, or weak-inversion mode
When VGS < Vth:
where Vth is the threshold voltage of the device.
According to the basic threshold model, the transistor is turned off, and there is no
conduction between drain and source. In reality, the Boltzmann distribution of electron
energies allows some of the more energetic electrons at the source to enter the channel
and flow to the drain, resulting in a subthreshold current that is an exponential function of
gate–source voltage. While the current between drain and source should ideally be zero
when the transistor is being used as a turned-off switch, there is a weak-inversion current,
sometimes called subthreshold leakage.
In weak inversion the current varies exponentially with gate-to-source bias VGS as given
approximately by:[3][4]
,
where ID0 = current at VGS = Vth and the slope factor n is given by
n = 1 + CD / COX,
with CD = capacitance of the depletion layer and COX = capacitance of the oxide layer. In
a long-channel device, there is no drain voltage dependence of the current once VDS > >
VT, but as channel length is reduced drain-induced barrier lowering introduces drain
voltage dependence that depends in a complex way upon the device geometry (for
example, the channel doping, the junction doping and so on). Frequently, threshold
voltage Vth for this mode is defined as the gate voltage at which a selected value of
current ID0 occurs, for example, ID0 = 1 μA, which may not be the same Vth-value used in
the equations for the following modes.
Some micropower analog circuits are designed to take advantage of subthreshold
conduction.[5][6][7]
By working in the weak-inversion region, the MOSFETs in these
circuits deliver the highest possible transconductance-to-current ratio, namely: gm / ID = 1
/ (nVT), almost that of a bipolar transistor.[8]

The subthreshold I–V curve depends exponentially upon threshold voltage, introducing a
strong dependence on any manufacturing variation that affects threshold voltage; for
example: variations in oxide thickness, junction depth, or body doping that change the
degree of drain-induced barrier lowering. The resulting sensitivity to fabricational
variations complicates optimization for leakage and performance.[9][10]
MOSFET drain current vs. drain-to-source voltage for several values of VGS − Vth; the boundary
between linear (Ohmic) and saturation (active) modes is indicated by the upward curving
parabola.
Cross section of a MOSFET operating in the linear (Ohmic) region; strong inversion region
present even near drain
Cross section of a MOSFET operating in the saturation (active) region; channel exhibits pinch-
off near drain
Triode mode or linear region (also known as the ohmic mode[11][12]
)
When VGS > Vth and VDS < ( VGS - Vth )
The transistor is turned on, and a channel has been created which allows current to flow
between the drain and the source. The MOSFET operates like a resistor, controlled by the
gate voltage relative to both the source and drain voltages. The current from drain to
source is modeled as:

where μn is the charge-carrier effective mobility, W is the gate width, L is the gate length
and Cox is the gate oxide capacitance per unit area. The transition from the exponential
subthreshold region to the triode region is not as sharp as the equations suggest.
Saturation or active mode[13][14]
When VGS > Vth and VDS > ( VGS - Vth )
The switch is turned on, and a channel has been created, which allows current to flow
between the drain and source. Since the drain voltage is higher than the gate voltage, the
electrons spread out, and conduction is not through a narrow channel but through a
broader, two- or three-dimensional current distribution extending away from the interface
and deeper in the substrate. The onset of this region is also known as pinch-off to
indicate the lack of channel region near the drain. The drain current is now weakly
dependent upon drain voltage and controlled primarily by the gate–source voltage, and
modeled very approximately as:
The additional factor involving λ, the channel-length modulation parameter, models
current dependence on drain voltage due to the Early effect, or channel length
modulation. According to this equation, a key design parameter, the MOSFET
transconductance is:
,
where the combination Vov = VGS - Vth is called the overdrive voltage.[15]
Another key
design parameter is the MOSFET output resistance rO given by:
.
rout is the inverse of gds where . VDS is the expression in saturation
region.
If λ is taken as zero, an infinite output resistance of the device results that leads to
unrealistic circuit predictions, particularly in analog circuits.
As the channel length becomes very short, these equations become quite inaccurate. New
physical effects arise. For example, carrier transport in the active mode may become
limited by velocity saturation. When velocity saturation dominates, the saturation drain
current is more nearly linear than quadratic in VGS. At even shorter lengths, carriers
transport with near zero scattering, known as quasi-ballistic transport. In addition, the
output current is affected by drain-induced barrier lowering of the threshold voltage.

Darlington transistor
Circuit diagram of a Darlington pair using NPN transistors
In electronics, the Darlington transistor (often called a Darlington pair) is a compound
structure consisting of two bipolar transistors (either integrated or separated devices) connected
in such a way that the current amplified by the first transistor is amplified further by the second
one.'.'[1]
This configuration gives a much higher current gain (written β, hfe, or hFE) than each
transistor taken separately and, in the case of integrated devices, can take less space than two
individual transistors because they can use a shared collector. Integrated Darlington pairs come
packaged singly in transistor-like packages or as an array of devices (usually eight) in an
integrated circuit.
The Darlington configuration was invented by Bell Laboratories engineer Sidney Darlington in
1953. He patented the idea of having two or three transistors on a single chip, sharing a
collector.[2]
A similar configuration but with transistors of opposite type (NPN and PNP) is the Sziklai pair,
sometimes called the "complementary Darlington."
Behaviour
A Darlington pair behaves like a single transistor with a high current gain (approximately the
product of the gains of the two transistors). In fact, integrated devices have three leads (B, C and
E), broadly equivalent to those of a standard transistor.
A general relation between the compound current gain and the individual gains is given by:
If β1 and β2 are high enough (hundreds), this relation can be approximated with:

A typical modern device has a current gain of 1000 or more, so that only a small base current is
needed to make the pair switch on. However, this high current gain comes with several
drawbacks.
One drawback is an approximate doubling of base-emitter voltage. Since there are two junctions
between the base and emitter of the Darlington transistor, the equivalent base-emitter voltage is
the sum of both base-emitter voltages:
For silicon-based technology, where each VBEi is about 0.65 V when the device is operating in
the active or saturated region, the necessary base-emitter voltage of the pair is 1.3 V.
Another drawback of the Darlington pair is its increased saturation voltage. The output transistor
is not allowed to saturate (i.e. its base-collector junction must remain reverse-biased) because its
collector-emitter voltage is now equal to the sum of its own base-emitter voltage and the
collector-emitter voltage of the first transistor, both positive quantities in normal operation. (In
symbols, VCE2 = VBE2 + VCE1, so VC2 > VB2 always.) Thus the saturation voltage of a
Darlington transistor is one VBE (about 0.65 V in silicon) higher than a single transistor
saturation voltage, which is typically 0.1 - 0.2 V in silicon. For equal collector currents, this
drawback translates to an increase in the dissipated power for the Darlington transistor over a
single transistor.
Another problem is a reduction in switching speed, because the first transistor cannot actively
inhibit the base current of the second one, making the device slow to switch off. To alleviate this,
the second transistor often has a resistor of a few hundred ohms connected between its base and
emitter terminals.[1]
This resistor provides a low impedance discharge path for the charge
accumulated on the base-emitter junction, allowing a faster transistor turn-off.
The Darlington pair has more phase shift at high frequencies than a single transistor and hence
can more easily become unstable with negative feedback (i.e., systems that use this configuration
can have poor phase margin due to the extra transistor delay).
Darlington pairs are available as integrated packages or can be made from two discrete
transistors; Q1 (the left-hand transistor in the diagram) can be a low power type, but normally Q2
(on the right) will need to be high power. The maximum collector current IC(max) of the pair is
that of Q2. A typical integrated power device is the 2N6282, which includes a switch-off resistor
and has a current gain of 2400 at IC=10A.
A Darlington pair can be sensitive enough to respond to the current passed by skin contact even
at safe voltages. Thus it can form the input stage of a touch-sensitive switch.
FET BIASING:

Unlike BJTs, thermal runaway does not occur with FETs, as already discussed in our blog.
However, the wide differences in maximum and minimum transfer characteristics make ID
levels unpredictable with simple fixed-gate bias voltage. To obtain reasonable limits on
quiescent drain currents ID and drain-source voltage VDS, source resistor and potential divider
bias techniques must be used. With few exceptions, MOSFET bias circuits are similar to those
used for JFETs. Various FET biasing circuits are discussed below:
Fixed Bias.
DC bias of a FET device needs setting of gate-source voltage VGS to give desired drain current ID
. For a JFET drain current is limited by the saturation current IDS. Since the FET has such a high
input impedance that no gate current flows and the dc voltage of the gate set by a voltage divider
or a fixed battery voltage is not affected or loaded by the FET.
Fixed dc bias is obtained using a battery VQG. This battery ensures that the gate is always
negative with respect to source and no current flows through resistor RG and gate terminal that is
IG =0. The battery provides a voltage VGS to bias the N-channel JFET, but no resulting current is
drawn from the battery VGG. Resistor RG is included to allow any ac signal applied through
capacitor C to develop across RG. While any ac signal will develop across RG, the dc voltage
drop across RG is equal to IG RG i.e. 0 volt.
The gate-source voltage VGS is then
VGS = - vG – vs = – vGG – 0 = – VGG

The drain -source current ID is then fixed by the gate-source voltage as determined by equation.
This current then causes a voltage drop across the drain resistor RD and is given as VRD = ID
RD and output voltage, Vout = VDD – ID RD
Self-Bias:
This is the most common method for biasing a JFET. Self-bias circuit for N-channel JFET is
shown in figure.
Since no gate current flows through the reverse-biased gate-source, the gate current IG = 0 and,
therefore,vG = iG RG = 0
The gate-source voltage is then
VGs = VG - Vs = 0 – ID Rs = – ID Rs
So voltage drop across resistance Rs provides the biasing voltage VGg and no external source is
required for biasing and this is the reason that it is called self-biasing.

The operating point (that is zero signal ID and VDS) can easily be determined from equation and
equation given below :
VDS = VDD – ID (RD + RS)
Thus dc conditions of JFET amplifier are fully specified. Self biasing of a JFET stabilizes its
quiescent operating point against any change in its parameters like transconductance. Let the
given JFET be replaced by another JFET having the double conductance then drain current will
also try to be double but since any increase in voltage drop across Rs, therefore, gate-source
voltage, VGS becomes more negative and thus increase in drain current is reduced.
Potential-Divider Biasing:
fet-potential-divider-biasing
A slightly modified form of dc bias is provided by the circuit shown in figure. The resistors RGl
and RG2 form a potential divider across drain supply VDD. The voltage V2 across RG2 provides
the necessary bias. The additional gate resistor RGl from gate to supply voltage facilitates in
larger adjustment of the dc bias point and permits use of larger valued RS.

The gate is reverse biased so that IG = 0 and gate voltage
VG =V2 = (VDD/R G1 + R G2 ) *RG2
And
VGS = vG – vs = VG - ID Rs
The operating point can be determined as
ID = (V2 – VGS)/ RS
And
VDS = VDD – ID (RD + RS)
MOSFET-Metal Oxide Semiconductor Field Effect Transistor:
Transistor,
MOSFET-Schematic symbol
Metal-oxide-semiconductor field-effect transistor (MOSFET) is an important semiconductor
device and is widely employed in many circuit applications. Since it is constructed with the gate
terminal insulated from the channel, it is sometimes called insulated gate FET (IGFET). Like, a
JFET, a MOSFET is also a three terminal (source, gate and drain) device and drain current in it is

also controlled by gate bias. The operation of MOSFET is similar to that of JFET. It can be
employed in any of the circuits covered for the JFET and, therefore, all the equations apply
equally well to the MOSFET and JFET in amplifier connections. However, MOSFET has lower
capacitance and input impedance much more than that of a JFET owing to small leakage current.
In case of a MOSFET the positive voltage may be applied to the gate and still the gate current
remains zero.
MOSFETs are of two types namely
(i) Enhancement type MOSFET or E-MOSFET and
(ii) Depletion enhancement MOSFET or DE-MOSFET.
In the depletion-mode construction a channel is physically constructed and a current between
drain and source is due to voltage applied across the drain-source terminals. The enhancement
MOSFET structure has no channel formed during its construction. Voltage is applied to the gate,
in this case, to develop a channel of charge carriers so that a current results when a voltage is
applied across the drain-source terminals.
Advantages of FET over BJT are:
a) No minority carriers
b) High input impedance
c) It is a voltage controlled device
d) Better thermal stability
Effect of Source and Drain Series Resistance
 The analysis so far neglects the effects of the source/drain series resistance, and the entire voltage is
assumed to drop along the channel.
 However, for modern day MOSFETs, this effect cannot be ignored, due to smaller diffusion cross-sections
and smaller drain currents.
 The extrinsic (measured) voltages can be related to the intrinsic (device) voltages
by the following equations:

where are the source and drain resistances respectively.
 The extrinsic transconductance is related to the intrinsic transconductance
where is the intrinsic drain conductance.
 Similarly, the extrinsic drain conductance is related to the intrinsic drain conductance
UNIT IV
AMPLIFIERS AND OSCILLATORS
Differential amplifier
A differential amplifier is a type of electronic amplifier that multiplies the difference between
two inputs by some constant factor (the differential gain).
Differential amplifier symbol
The inverting and non-inverting inputs are distinguished by "−" and "+" symbols (respectively)
placed in the amplifier triangle. Vs+ and Vs− are the power supply voltages; they are often
omitted from the diagram for simplicity, but of course must be present in the actual circuit.

Differential Amplifiers:
Differential amplifier is a basic building block of an op-amp. The function of a differential
amplifier is to amplify the difference between two input signals.
How the differential amplifier is developed? Let us consider two emitter-biased circuits as shown
in fig. 1.
Fig. 1
The two transistors Q1 and Q2 have identical characteristics. The resistances of the circuits are
equal, i.e. RE1 = R E2, RC1 = R C2 and the magnitude of +VCC is equal to the magnitude of –VEE.
These voltages are measured with respect to ground.
To make a differential amplifier, the two circuits are connected as shown in fig. 1. The two +VCC
and –VEE supply terminals are made common because they are same. The two emitters are also
connected and the parallel combination of RE1 and RE2 is replaced by a resistance RE. The two
input signals v1 & v2 are applied at the base of Q1 and at the base of Q2. The output voltage is
taken between two collectors. The collector resistances are equal and therefore denoted by RC =
RC1 = RC2.
Ideally, the output voltage is zero when the two inputs are equal. When v1 is greater then v2 the
output voltage with the polarity shown appears. When v1 is less than v2, the output voltage has
the opposite polarity.
The differential amplifiers are of different configurations.
The four differential amplifier configurations are following:
1. Dual input, balanced output differential amplifier.
2. Dual input, unbalanced output differential amplifier.

3. Single input balanced output differential amplifier.
4. Single input unbalanced output differential amplifier.
Fig. 2
These configurations are shown in fig. 2, and are defined by number of input signals used and the way an output
voltage is measured. If use two input signals, the configuration is said to be dual input, otherwise it is a single input
configuration. On the other hand, if the output voltage is measured between two collectors, it is referred to as a
balanced output because both the collectors are at the same dc potential w.r.t. ground. If the output is measured at
one of the collectors w.r.t. ground, the configuration is called an unbalanced output.
A multistage amplifier with a desired gain can be obtained using direct connection between successive stages of
differential amplifiers. The advantage of direct coupling is that it removes the lower cut off frequency imposed by the
coupling capacitors, and they are therefore, capable of amplifying dc as well as ac input signals.

Dual Input, Balanced Output Differential Amplifier:
The circuit is shown in fig. 1, v1 and v2 are the two inputs, applied to the bases of Q1 and Q2
transistors. The output voltage is measured between the two collectors C1 and C2 , which are at
same dc potentials.
D.C. Analysis:
To obtain the operating point (ICC and VCEQ) for differential amplifier dc equivalent circuit is
drawn by reducing the input voltages v1 and v2 to zero as shown in fig. 3.
Fig. 3
The internal resistances of the input signals are denoted by RS because RS1= RS2. Since both
emitter biased sections of the different amplifier are symmetrical in all respects, therefore, the
operating point for only one section need to be determined. The same values of ICQ and VCEQ can
be used for second transistor Q2.
Applying KVL to the base emitter loop of the transistor Q1.

The value of RE sets up the emitter current in transistors Q1 and Q2 for a given value of VEE. The
emitter current in Q1 and Q2 are independent of collector resistance RC.
The voltage at the emitter of Q1 is approximately equal to -VBE if the voltage drop across R is
negligible. Knowing the value of IC the voltage at the collector VCis given by
VC =VCC – IC RC
and VCE = VC – VE
= VCC – IC RC + VBE
VCE = VCC + VBE – ICRC (E-2)
From the two equations VCEQ and ICQ can be determined. This dc analysis applicable for all types
of differential amplifier.
Example - 1
The following specifications are given for the dual input, balanced-output differential amplifier
of fig.1:
RC = 2.2 kΩ, RB = 4.7 kΩ, Rin 1 = Rin 2 = 50 Ω , +VCC = 10V, -VEE = -10 V, βdc =100 and VBE =
0.715V.
Determine the operating points (ICQ and VCEQ) of the two transistors.
Solution:
The value of ICQ can be obtained from equation (E-1).
The voltage VCEQ can be obtained from equation (E-2).
The values of ICQ and VCEQ are same for both the transistors.

Dual Input, Balanced Output Difference Amplifier:
The circuit is shown in fig. 1 v1 and v2 are the two inputs, applied to the bases of Q1 and Q2
transistors. The output voltage is measured between the two collectors C1 and C2, which are at
same dc potentials.
Fig. 1
A.C. Analysis :
In previous lecture dc analysis has been done to obtain the operatiing point of the two transistors.
To find the voltage gain Ad and the input resistance Ri of the differential amplifier, the ac
equivalent circuit is drawn using r-parameters as shown in fig. 2. The dc voltages are reduced to
zero and the ac equivalent of CE configuration is used.

Fig. 2
Since the two dc emitter currents are equal. Therefore, resistance r'e1 and r'e2 are also equal and
designated by r'e . This voltage across each collector resistance is shown 180° out of phase with
respect to the input voltages v1 and v2. This is same as in CE configuration. The polarity of the
output voltage is shown in Figure. The collector C2 is assumed to be more positive with respect
to collector C1 even though both are negative with respect to to ground.
Applying KVL in two loops 1 & 2.
Substituting current relations,
Again, assuming RS1 / b and RS2 / b are very small in comparison with RE and re' and therefore
neglecting these terms,

Solving these two equations, ie1 and ie2 can be calculated.
The output voltage VO is given by
VO = VC2 - VC1
= -RC iC2 - (-RC iC1)
= RC (iC1 - iC2)
= RC (ie1 - ie2)
Substituting ie1, & ie2 in the above expression
Thus a differential amplifier amplifies the difference between two input signals. Defining the
difference of input signals as vd = v1 – v2 the voltage gain of the dual input balanced output
differential amplifier can be given by
(E-2)
Differential Input Resistance:
Differential input resistance is defined as the equivalent resistance that would be measured at
either input terminal with the other terminal grounded. This means that the input resistance Ri1
seen from the input signal source v1 is determined with the signal source v2 set at zero. Similarly,
the input signal v1 is set at zero to determine the input resistance Ri2 seen from the input signal
source v2. Resistance RS1 and RS2 are ignored because they are very small.

Substituting ie1,
Similarly,
The factor of 2 arises because the re' of each transistor is in series.
To get very high input impedance with differential amplifier is to use Darlington transistors.
Another ways is to use FET.
Output Resistance:
Output resistance is defined as the equivalent resistance that would be measured at output
terminal with respect to ground. Therefore, the output resistance RO1 measured between collector
C1 and ground is equal to that of the collector resistance RC. Similarly the output resistance RO2
measured at C2 with respect to ground is equal to that of the collector resistor RC.
RO1 = RO2 = RC (E-5)
The current gain of the differential amplifier is undefined. Like CE amplifier the differential
amplifier is a small signal amplifier. It is generally used as a voltage amplifier and not as current
or power amplifier.

Difference Amplifiers
A dual input, balanced output difference amplifier circuit is shown in fig. 1.
Fig. 1
Inverting & Non – inverting Inputs:
In differential amplifier the output voltage vO is given by
VO = Ad (v1 – v2)
When v2 = 0, vO = Ad v1
& when v1 = 0, vO = - Ad v2
Therefore the input voltage v1 is called the non inventing input because a positive voltage v1
acting alone produces a positive output voltage vO. Similarly, the positive voltage v2 acting alone
produces a negative output voltage hence v2 is called inverting input. Consequently B1 is called
noninverting input terminal and B2 is called inverting input terminal.
Common mode Gain:
A common mode signal is one that drives both inputs of a differential amplifier equally. The
common mode signal is interference, static and other kinds of undesirable pickup etc.
The connecting wires on the input bases act like small antennas. If a differential amplifier is
operating in an environment with lot of electromagnetic interference, each base picks up an
unwanted interference voltage. If both the transistors were matched in all respects then the
balanced output would be theoretically zero. This is the important characteristic of a differential
amplifier. It discriminates against common mode input signals. In other words, it refuses to
amplify the common mode signals.

The practical effectiveness of rejecting the common signal depends on the degree of matching
between the two CE stages forming the differential amplifier. In other words, more closely are
the currents in the input transistors, the better is the common mode signal rejection e.g. If v1 and
v2 are the two input signals, then the output of a practical op-amp cannot be described by simply
v0 = Ad (v1 – v2 )
In practical differential amplifier, the output depends not only on difference signal but also upon
the common mode signal (average).
vd = (v1 – vd )
and vC = ½ (v1 + v2 )
The output voltage, therefore can be expressed as
vO = A1 v1 + A2 v2
Where A1 & A2 are the voltage amplification from input 1(2) to output under the condition that
input 2 (1) is grounded.
The voltage gain for the difference signal is Ad and for the common mode signal is AC.
The ability of a differential amplifier to reject a common mode signal is expressed by its
common mode rejection ratio (CMRR). It is the ratio of differential gain Ad to the common mode
gain AC.
Date sheet always specify CMRR in decibels CMRR = 20 log CMRR.
Therefore, the differential amplifier should be designed so that r is large compared with the ratio
of the common mode signal to the difference signal. If r = 1000, vC = 1mV, vd = 1 m V, then

It is equal to first term. Hence for an amplifier with r = 1000, a 1m V difference of potential
between two inputs gives the same output as 1mV signal applied with the same polarity to both
inputs.
Dual Input, Unbalanced Output Differential Amplifier:
In this case, two input signals are given however the output is measured at only one of the two-
collector w.r.t. ground as shown in fig. 2. The output is referred to as an unbalanced output
because the collector at which the output voltage is measured is at some finite dc potential with
respect to ground..
Fig. 2
In other words, there is some dc voltage at the output terminal without any input signal applied.
DC analysis is exactly same as that of first case.
AC Analysis:
The output voltage gain in this case is given by

The voltage gain is half the gain of the dual input, balanced output differential amplifier. Since at
the output there is a dc error voltage, therefore, to reduce the voltage to zero, this configuration is
normally followed by a level translator circuit.
Differential amplifier with swamping resistors:
By using external resistors R'E in series with each emitter, the dependence of voltage gain on
variations of r'e can be reduced. It also increases the linearity range of the differential amplifier.
Fig. 3, shows the differential amplifier with swamping resistor R'E. The value of R'E is usually
large enough to swamp the effect of r'e.
Fig. 3

Biasing of Differential Amplifiers
Constant Current Bias:
In the dc analysis of differential amplifier, we have seen that the emitter current IE depends upon
the value of bdc. To make operating point stable IE current should be constant irrespective value
of bdc.
For constant IE, RE should be very large. This also increases the value of CMRR but if RE value
is increased to very large value, IE (quiescent operating current) decreases. To maintain same
value of IE, the emitter supply VEE must be increased. To get very high value of resistance RE
and constant IE, current, current bias is used.
Figure 5.1
Fig. 1, shows the dual input balanced output differential amplifier using a constant current bias.
The resistance RE is replace by constant current transistor Q3. The dc collector current in Q3 is
established by R1, R2, & RE.
Applying the voltage divider rule, the voltage at the base of Q3 is

Because the two halves of the differential amplifiers are symmetrical, each has half of the current
IC3.
The collector current, IC3 in transistor Q3 is fixed because no signal is injected into either the
emitter or the base of Q3.
Besides supplying constant emitter current, the constant current bias also provides a very high
source resistance since the ac equivalent or the dc source is ideally an open circuit. Therefore, all
the performance equations obtained for differential amplifier using emitter bias are also valid.
As seen in IE expressions, the current depends upon VBE3. If temperature changes, VBE changes
and current IE also changes. To improve thermal stability, a diode is placed in series with
resistance R1as shown in fig. 2.

Fig. 2
This helps to hold the current IE3 constant even though the temperature changes. Applying KVL
to the base circuit of Q3.
Therefore, the current IE3 is constant and independent of temperature because of the added diode
D. Without D the current would vary with temperature because VBE3 decreases approximately by
2mV/° C. The diode has same temperature dependence and hence the two variations cancel each
other and IE3 does not vary appreciably with temperature. Since the cut – in voltage VD of diode
approximately the same value as the base to emitter voltage VBE3 of a transistor the above
condition cannot be satisfied with one diode. Hence two diodes are used in series for VD. In this
case the common mode gain reduces to zero.
Some times zener diode may be used in place of diodes and
resistance as shown in fig. 3. Zeners are available over a wide
range of voltages and can have matching temperature
coefficient
The voltage at the base of transistor QB is
Fig. 3
The value of R2 is selected so that I2 » 1.2 IZ(min) where IZ is the minimum current required to
cause the zener diode to conduct in the reverse region, that is to block the rated voltage VZ.

Current Mirror:
The circuit in which the output current is forced to equal the input current is said to be a current
mirror circuit. Thus in a current mirror circuit, the output current is a mirror image of the input
current. The current mirror circuit is shown in fig. 4.
Fig. 4
Once the current I2 is set up, the current IC3 is automatically established to be nearly equal to I2.
The current mirror is a special case of constant current bias and the current mirror bias requires
of constant current bias and therefore can be used to set up currents in differential amplifier
stages. The current mirror bias requires fewer components than constant current bias circuits.
Since Q3 and Q4 are identical transistors the current and voltage are approximately same

For satisfactory operation two identical transistors are necessary.
Oscillators
Oscillators:
An oscillator may be described as a source of alternating voltage. It is different than amplifier.
An amplifier delivers an output signal whose waveform corresponds to the input signal but
whose power level is higher. The additional power content in the output signal is supplied by the
DC power source used to bias the active device.
The amplifier can therefore be described as an energy converter, it accepts energy from the DC
power supply and converts it to energy at the signal frequency. The process of energy conversion
is controlled by the input signal, Thus if there is no input signal, no energy conversion takes
place and there is no output signal.
The oscillator, on the other hand, requires no external signal to initiate or maintain the energy
conversion process. Instead an output signals is produced as long as source of DC power is
connected. Fig. 1, shows the block diagram of an amplifier and an oscillator.

Fig. 1
Oscillators may be classified in terms of their output waveform, frequency range, components, or
circuit configuration.
If the output waveform is sinusoidal, it is called harmonic oscillator otherwise it is called
relaxation oscillator, which include square, triangular and saw tooth waveforms.
Oscillators employ both active and passive components. The active components provide energy
conversion mechanism. Typical active devices are transistor, FET etc.
Passive components normally determine the frequency of oscillation. They also influence
stability, which is a measure of the change in output frequency (drift) with time, temperature or
other factors. Passive devices may include resistors, inductors, capacitors, transformers, and
resonant crystals.
Capacitors used in oscillators circuits should be of high quality. Because of low losses and
excellent stability, silver mica or ceramic capacitors are generally preferred.
An elementary sinusoidal oscillator is shown in fig. 2. The inductor and capacitors are reactive
elements i.e. they are capable of storing energy. The capacitor stores energy in its electric
field.Whenever there is voltage across its plates,and the inductor stores energy in its magnetic
field whenever current flows through it. Both C and L are assumed to be loss less. Energy can be
introduced into the circuit by charging the capacitor with a voltage V as shown in fig. 2. As long
as the switch S is open, C cannot discharge and so i=0 and V=0.
Fig. 2

Now S is closed at t = to, This means V rises from 0 to V, Just before closing inductor current
was zero and inductor current cannot be changed instantaneously. Current increases from zero
value sinusoidally and is given by
The capacitor losses its charge and energy is simply transferred from capacitor to inductor
magnetic field. The total energy is still same. At t = t1, all the charge has been removed from the
capacitor plates and voltage reduces to zero and at current reaches to its maximum value. The
current for t> t1 charges C in the opposite direction and current decreases. Thus LC oscillation
takes places. Both voltage and current are sinusoidal though no sinusoidal input was applied. The
frequency of oscillation is
The circuit discussed is not a practical oscillator because even if loss less components were
available, one could not extract energy with out introducing an equivalent resistance. This would
result in damped oscillations as shown in fig. 3.
Fig. 3
These oscillations decay to zero as soon as the energy in the tank is consumed. If we remove too
much power from the circuit, the energy may be completely consumed before the first cycle of
oscillations can take place yielding the over damped response.
It is possible to supply energy to the tank to make up for all losses (coil losses plus energy
removed), thereby maintaining oscillations of constant amplitude.
Since energy lost may be related to a positive resistance, it follows that the circuit would gain
energy if an equivalent negative resistance were available. The negative resistance, supplies

whatever energy the circuit lose due to positive resistance. Certain devices exhibit negative
resistance characteristics, an increasing current for a decreasing voltage. The energy supplied by
the negative resistance to the circuit, actually comes from DC source that is necessary to bias the
device in its negative resistance region.
Another technique for producing oscillation is to use positive feedback considers an amplifier
with an input signal vin and output vO as shown in fig. 4.
Fig. 4
The amplifier is inverting amplifier and may be transistorized, or FET or OPAMP. The output is
180° out of phase with input signal vO= -A vin.(A is negative)
Now a feedback circuit is added. The output voltage is fed to the feed back circuit. The output of
the feedback circuit is again 180° phase shifted and also gets attenuated. Thus the output from
the feedback network is in phase with input signal vin and it can also be made equal to input
signal.
If this is so, Vf can be connected directly and externally applied signal can be removed and the
circuit will continue to generate an output signal. The amplifier still has an input but the input is
derived from the output amplifier. The output essentially feeds on itself and is continuously
regenerated. This is positive feedback. The over all amplification from vin to vf is 1 and the total
phase shift is zero. Thus the loop gain A β is equal to unity.
When this criterion is satisfied then the closed loop gain is infinite. i.e. an output is produced
without any external input.
vO = A verror
= A (v in + v f )
= A (vin + β vO)
or (1-A β )vO = A vin

or
When A β = 1, vO / vin=
The criterion A β = 1 is satisfied only at one frequency.This is known as backhausen criterion.
The frequency at which a sinusoidal oscillator will operate is the frequency for which the total
phase shift introduced, as the signal proceeds form the input terminals, through the amplifier and
feed back network and back again to the input is precisely zero or an integral multiple of 2p.
Thus the frequency of oscillation is determined by the condition that the loop phase shift is zero.
Oscillation will not be sustained, if at the oscillator frequency, A β <1 or A β>1. Fig. 5, show the
output for two different contions A β < 1 and A β >1.
Fig. 5
If Aβ is less than unity then Aβ vin is less than vin, and the output signal will die out, when the
externally applied source is removed. If Aβ>1 then A b vinis greater than vin and the output
voltage builds up gradually. If A β = 1, only then output voltage is sine wave under steady state
conditions.
In a practical oscillator, it is not necessary to supply a signal to start the oscillations. Instead,
oscillations are self-starting and begin as soon as power is applied. This is possible because of
electrical noise present in all passive components.
Therefore, as soon as the power is applied, there is already some energy in the circuit at fo, the
frequency for which the circuit is designed to oscillate. This energy is very small and is mixed

with all the other frequency components also present, but it is there. Only at this frequency the
loop gain is slightly greater than unity and the loop phase shift is zero. At all other frequency the
Barkhausen criterion is not satisfied. The magnitude of the frequency component fo is made
slightly higher each time it goes around the loop. Soon the fo component is much larger than all
other components and ultimately its amplitude is limited by the circuits own non-lineareties
(reduction of gain at high current levels, saturation or cut off). Thus the loop gain reduces to
unity and steady stage is reached. If it does not, then the clipping may occur.
Practically, Aβ is made slightly greater than unity. So that due to disturbance the output does not
change but if Aβ = 1 and due to some reasons if Aβ decreases slightly than the oscillation may
die out and oscillator stop functioning. In conclusion, all practical oscillations involve:
 An active device to supply loop gain or negative resistance.
 A frequency selective network to determine the frequency of oscillation.
 Some type of non-linearity to limit amplitude of oscillations.
Example - 1
The gain of certain amplifier as a function of frequency is A (jω) = -16 x 106
/ jω. A feedback
path connected around it has β(j ω ) = 103
/ (20 x 103
+ jω )2
. Will the system oscillate? If so, at
what frequency ?
Solution:
The loop gain is
To determine, if the system will oscillate, we will first determine the frequency, if any, at which
the phase angle of equals to 0° or a multiple of 360°. Using phasor algebra, we have

This expression will equal -360° if ,
Thus, the phase shift around the loop is -360° at ω = 2000 rad/s. We must now check to see if the
gain magnitude |A β| = 1 at ω = 2 x 103
. The gain magnitude is
Substituting ω = 2 x 103
, we find
Thus, the Barkhausen criterion is satisfied at ω = 2 x 103
rad/s and oscillation occurs at that
frequency (2 x 103
/ 2 π= 318 .3 Hz).
Harmonic Oscillators
According to Barkhausen criterion, a feedback type oscillator, having Aβ as loop gain, works if
Aβ is made slightly greater than unity. As discussed in previous lectures, all practical oscillations
involve:
 An active device to supply loop gain or negative resistance.
 A frequency selective network to determine the frequency of oscillation.
 Some type of non-linearity to limit amplitude of oscillations.
Harmonic Oscillator:
One feedback type harmonic oscillator circuit is shown in fig. 1.

Fig. 1 Fig. 2
The dc equivalent circuit is shown in fig. 2. The dc operating point is set by selecting VCC, RB
and RE. The ac equivalent circuit is also shown in fig. 3.
Fig. 3
The transformer provides 180° phase shift to ensure positive feedback so that at the desired
frequency of oscillation, the total phase shift from vin to vx is made equal to 0° and magnitudes

are made equal by properly selecting the turns ratio. RE also controls and stabilizes the gain
through negative feedback. C2 and the transformers equivalent inductance make up a resonant
circuit that determines the frequency of oscillation.
C1 is used to block dc (Otherwise the base would be directly tied to VCC) through the low dc
resistance of transformer primary. C1 has negligible reactance at the frequency of oscillation,
therefore it is not apart of the frequency-determining network, the same applies to C2.
In this circuit, there is an active device suitably biased to provide necessary gain. Since the active
device produces loop phase shift 180º (from base to collector), a transformer in the feedback
loop provides an additional 180º to yield to a loop phase shift of 0º. The feedback factor is
equivalent to the transformer's turns ratio. There is also a turned circuit, to determine the
frequency of oscillation.
The load is in parallel with C2 and the transformer. If the load is resistive, which is usually the
case, the Q of the tuned circuit and the loop gain are both affected, this must be taken into
account when determining the minimum gain required for oscillation. If the load has a capacitive
component, then the value of C2 should be reduced accordingly.
The RC Phase Shift Oscillator:
At low frequencies (around 100 KHz or less), resistors are usually employed to determine the
frequency oscillation. Various circuits are used in the feedback circuit including ladder network.
Fig. 4
A block diagram of a ladder type RC phase shift oscillation is shown in fig. 4. It consists of three
resistor R and C capacitors. If the phase shift through the amplifier is 180º, then oscillation may
occur at the frequency where the RC network produces an additional 180 phase shift.

To find the frequency of oscillation, let us neglect the loading of the phase shift network. Writing
the KV equations,

For phase shift equal to 180o between Vx and VO, imaginary term of Vx / VO must be zero.
Therefore,
This is the frequency of oscillation. Substituting this frequency in Vx / VO expression.
In order to ensure the oscillation, initially |Aβ| >1 and under study state Aβ =1. This means the
gain of the amplifier should be initially greater than 29 (so that Aβ >1) and under steady stat
conditions it reduces to 29.
This oscillator can be realized using FET amplifier as shown in fig. 5. The feedback circuit is
same as discussed above.
Fig. 5 Fig. 6

The input impedance of FET is very high so that there is no loading of the feedback circuit. In
this circuit, the feedback is voltage series feedback.
Vx =VGS +VS or VGS = Vx - V
The same circuit can be realizing using OPAMP. The circuit is shown in fig. 6. The input
impedance is very high and there is no overloading of feedback circuit. The OPAMP is
connected in an inverting configuration and drives three cascaded RC sections. The inverting
amplifier causes a 180° phase shift in the signal passing through it. RC network is used in the
feedback to provide additional 180° phase shift. Therefore, the total phase shift in the signal, of a
particular frequency, around the loop will equal 360° and oscillation will occur at that frequency.
The gain necessary to overcome the loss in the RC network and bring the loop gain up to 1 is
supplied by the amplifier. The gain is given by
Note that input resistor to the inverting amplifier is also the last resistor of the RC feedback
network.
Example -1:
Design a RC phase shift oscillator that will oscillate at 100 Hz.
Solution:
An RC phase shift oscillator using OPAMP is shown in fig. 7. OPAMP is used as an inverting amplifier and provides
180° phase shift. RC network is used in the feedback to provide additional 180° phase shift.
Fig. 7
For an RC phase shift oscillator the frequency is given by

Let C = 0.5 µF. Then
Therefore, Rf= 29 R = 29 (1300Ω) = 37.7 kΩ.
The completed circuit is shown in fig. 7. Rf is made adjustable so the loop gain can be set
precisely to 1.
Example - 2
For the network shown in fig. 8 prove that
This network is used with an OPAMP to form an oscillator. Show that the frequency of
oscillation is f =1 /2πRC and the gain must exceed 3.
Solution:
To find the frequency of oscillation, let us neglect the loading of the phase shift network. Writing
the KV equations,
From equation (E-3),
Fig. 8
Substituting I1 in equation (E-4),.
Solving this equation we get,

Therefore, from equation (E-1),
Putting , we get,
For phase shift equal to 180° between vf and vo, imaginary term of vf / vo must be zero.
Therefore,
This is the frquency of oscillation. Substituting this frequency in vf / vo expression, we get,
This shows that 0° phase shift from vo to vf can be obtained if
and the gain of the feedback circuit becomes 1/3. Therefore, oscillation takes place if the gain of
the amplifier exceeds 3.
Transistor Phase Shift Oscillator:

At low frequencies (around 100 kHz or less), resistors and capacitors are usually employed to
determine the frequency of oscillation. Fig. 1 shows transistorized phase shift oscillator circuit
employing RC network. If the phase shift through the common emitter amplifier is 180°, then the
oscillation may occur at the frequency where the RC network produces an additional 180° phase
shift.
Since a transistor is used as the active element, the output across R of the feedback network is
shunted by the relatively low input resistance of the transistor, because input diode is a forward
biased diode
Fig. 1
Hence, instead of employing voltage series feedback, voltage shunt feedback is used for a
transistor phase shift oscillator. The load resistance RL is also connected via coupling capacitor.
The equivalent circuit using h-parameter is shown in fig. 2.
Fig. 2

For the circuit, the load resistance RL may be lumped with RC and the effective load resistance
becomes R'L(= RC || RL). The two h-parameters of the CE transistor amplifier, hoe and hre are
neglected.
The capacitor C offers some impedance at the frequency of oscillation and, therefore, it is kept as
it is, while the coupling capacitor behaves like ac short. The input resistance of the transistor is
Ri≈hie. Therefore the resistance R3 is selected such that R=R3+Ri=R3+hie. This choice makes the
three R C selections alike and simplifies the calculation. The effect of biasing resistor R1 , R2, &
REon the circuit operation is neglected.
Since this is a voltage shunt feedback, therefore instead of finding VR /VO, we should find the
current gain of the feedback loop.
The simplified equivalent circuit is shown in fig. 3.
Fig. 3
Applying KVL,

Since I3 and Ib must be in phase to satisfy Barkhausen criterion, therefore
Also initially I3 > Ib, therefore, for oscillation to start,

Therefore, the two conditions must be satisfied for oscillation to start and sustain.
Example - 1
(a). Show that the OPAMP phase shifter shown in fig. 4
.
(b) Cascade two identical phase shifters of the type sown in fig. 4. Complete the loop with an
inverting amplifier. Show that the system will oscillate at the frequency f = 1 / 2πRC provided
that the amplifier gain exceeds unity.
(c) Show that the circuit produces two quadrature sinusoids (sine wave differing in phase by
90°).
Fig. 4
Solution:
(a)The voltage the non-inverting terminal input of the OPAM is given by
Since the differential input voltage of OPAMP is negligible small, therefore, the voltage at the
inverting terminal is also given by
The input impedance of the OPAMP is very large, therefore,

or Vi - 2V2 = -VO
Substituting v2 in above equation, we get,
Substituting XC, we get
Therefore,
and the phase angle between VO and Vi is given by
The magnitude of VO / Vi is unity for all frequencies and the phase shift provided by this circuit
is 0° for R = 0 and –180° for R −> infinity.
(b). If two such phase shifters are connected in cascade and an inverting amplifier with gain ß is
connected in the feedback loop, then the net loop gain becomes
Loop gain = Gain of phase shifter 1 x Gain of phase shifter 2 x β
= 1 x 1x β
= β
Therefore, the oscillation takes place if gain β =1, but it is kept >1 so that the losses taking place
in the amplifier can be compensated.

The total phase shift around the loop is given by
total phase shift = -2 tan-1
(ωRC) - 2 tan-1
(ωRC) + 180°
Further, for oscillation to take place the net phase shift around the loop would be 0°.Therefore,
-2 tan-1
(ωRC) - 2 tan-1
(ωRC) + 180° =0
or ωRC = 1
or f = 1 / 2πR C
(c). The phase shift provided by amplifier in the feedback path is 180°, therefore, the phase shift
provided by the phase shifters should also be 180° to have 360° or 0° phase shift. Thus ,the phase
shift provided by the individual shifter will be 90° as both are identical. Therefore, the sine wave
produces by two phase shifters are 90° apart and the circuit produces two quadrature sinusoids.
Wien Bridge Oscillator:
The Wien Bridge oscillator is a standard oscillator circuit for low to moderate frequencies, in the
range 5Hz to about 1MHz. It is mainly used in audio frequency generators.
The Wien Bridge oscillator uses a feedback circuit
called a lead lag network as shown in fig. 1.
At very low frequencies, the series capacitor looks
open to the input signal and there is no output signal.
At very high frequencies the shunt capacitor looks
shorted, and there is no output. In between these
extremes, the output voltage reaches a maximum
value. The frequency at which the output is
maximized is called the resonant frequency. At this
frequency, the feedback fraction reaches a maximum
value of 1/3.
At very low frequencies, the phase angle is positive,
and the circuit acts like a lead network. On the other
hand, at very high frequencies, the phase angle is
negative, and the circuit acts like a lag network. In
between, there is a resonant frequency fr at which the
phase angle equals 0°.
The output of the lag lead network is
Fig. 1

The gain of the feedback circuit is given by
The phase angle between Vout and Vinis given by

These equations shows that maximum value of gain occurs at XC = R, and phase angle also
becomes 0°. This represents the resonant frequency of load lag network. Fig. 2, shows the gain
and phase vs frequency.
Fig. 2
How Wien Bridge Oscillator Works:
Fig. 3, shows a Wien Bridge oscillator. The operational amplifier is used in a non-inverting
configuration, and the lead-lag network provides the feedback. Resistors Rf and R1 determine the
amplifier gain and are selected to make the loop gain equal to 1. If the feedback circuit
parameters are chosen properly, there will be some frequency at which there is zero phase shift
in the signal fed back to non inverting terminal. Because the amplifier is non inverting, it also
contributes zero phase shift, so the total phase shift around the loop is 0 at that frequency, as
required for oscillation.
The oscillator uses positive and negative feedback. The positive feedback helps the oscillations
to build up when the power is turn on. After the output signal reaches the desired level the
negative feedback reduces the loop gain is 1. The positive feedback is through the lead lag
network to the non-inverting input. Negative feedback is through the voltage divider to the
inverting input.

Fig. 3
At power up, the tungsten lamp has a low resistance, and therefore, negative feedback is less. For
this, reason, the loop gain AB is greater than 1, and oscillations can build up at the resonant
frequency fr. As the oscillations build up, the tungsten lamp heats up slightly and its resistance
increases. At the desired output level the tungsten lamp has a resistance R'. At this point
Since the lead lag network has a gain (=B) of 1/3, the loop gain AB equals unity and than the
output amplitude levels off and becomes constant. The frequency of oscillation can be adjusted
by selecting R and C as
The amplifier must have a closed loop cut off frequency well above the resonant frequency, fr.

Fig. 4
Fig. 4, shows another way to represent Wein Bridge oscillator. The lead lag network is the left
side of the bridge and the voltage divider is the right side. This ac bridge is called a Wein Bridge.
The error voltage is the output of the Wein Bridge. When the bridge approaches balance, the
error voltage approaches zero.
Example -1:
Design a Wien-bridge oscillator that oscillates at 25 kHz.
Solution:
Let C1 = C2 = 0.001 µF. Then, the frequency of oscillation is given by,
or,
Let R1 = 10 KΩ. Then,
or, Rf = 20KΩ

Tuned Oscillator:
A variety of oscillator circuits can be built using LC tuned circuits. A general form of tuned
oscillator circuit is shown in fig. 1. It is assumed that the active device used in the oscillator has
very high input resistance such as FET, or an operational amplifier.
Fig. 1 Fig. 2
Fig. 2 shows linear equivalent circuit of fig. 1 using an amplifier with an open circuit gain –Av
and output resistance RO. It is clear from the topology of the circuit that it is voltage series
feedback type circuit.
The loop gain of the circuit –Aβ can be obtained by considering the circuit to be a feedback
amplifier with output taken from terminals 2 and 3 and with input terminals 1 and 3. The load
impedance ZL consists of Z2 in parallel with the series combination of Z1 and Z3. The gain of the
the amplifier without feedback will be given by
The feedback circuit gain is given by
Therefore, the loop gain is given by

If the impedances are pure reactances (either inductive or capacitive), then Z1 = jX1, Z2= jX2 and
Z3= jX3. Then
For the loop gain to be real (zero phase shift around the loop),
X1 + X2 + X3 = 0
and
Therefore, the circuit will oscillate at the resonant frequency of the series combination of X1, X2
and X3. Since –A β must be positive and at leat unity in magnitude, then X1 and X2 must have
the same sign (Av is positive).In other words, they must be the same kind of reactance, either
both inductive or both capacitive.
The Colpitts Oscillator:
Wein bridge oscillator is not suited to high frequencies (above 1MHz). The main problem is the
phase shift through the amplifier.
The alternative is an LC oscillator, a circuit that can be used for frequencies between 1MHz and
500MHz. The frequency range is beyond the frequency limit of most OPAMPs. With an
amplifier and LC tank circuit, we can feedback a signal with the right amplitude and phase is
feedback to sustain oscillations. Fig. 3, shows the circuit of colpitts oscillator.

Fig. 3 Fig. 4
The voltage divider bias sets up a quiescent operating point. The circuit then has a low frequency
voltage gain of rc / r'e where rc is the ac resistance seen by the selector. Because of the base and
collector lag networks, the high frequency voltage gain is less then rc / r'e.
Fig. 4, shows a simplified ac equivalent circuit. The circulating or loop current in the tank flows
through C1 in series with C2. The voltage output equals the voltage across C1. The feedback
voltage vf appears across C2. This feedback voltage drives the base and sustains the oscillations
developed across the tank circuit provided there is enough voltage gain at the oscillation
frequency. Since the emitter is at ac ground the circuit is a CE connection.
Most LC oscillators use tank circuit with a Q greater than 10. The Q of the feedback circuit is
given by
Because of this, the approximate resonant frequency is
This is accurate and better than 1% when Q is greater than 1%. The capacitance C is the
equivalent capacitance the circulation current passes through. In the Colpitts tank the circulating
current flows through C1 in series with C2.
Therefore C = C1 C2 / (C1 +C2)

The required starting condition for any oscillator is A β > 1 at the resonant frequency or A > 1/ β.
The voltage gain A in the expression is the gain at the oscillation frequency. The feedback gain β
is given by
β = vf / vout≈ XC1 / XC2
Because same current flow through C1 and C2, therefore
β = C1/ C2; A > 1/ v; A> C1 / C2
This is a crude approximation because it ignores the impedance looking into the base. An exact
analysis would take the base impedance into account because it is in parallel with C2 .
With small β, the value of A is only slightly larger than 1/β. and the operation is approximately
close A. When the power is switched on, the oscillations build up, and the signal swings over
more and more of ac load line. With this increased signal swing, the operation changes from
small signal to large signal. As this happen, the voltage gain decreases slightly. With light
feedback the value of Aβ can decreases to 1 without excessive clapping.
With heavy feedback, the large feedback signal drives the base into saturation and cut off. This
charges capacitor C3 producing negative dc clamping at the base and changing the operation
from class A to class C. The negative damping automatically adjusts the value of Aβ to 1.
Example - 1
Design a Colpitts oscillator that will oscillate at 100 kHz.
Solution:
Let us choose R1 = Rf = 5 kΩ and C = 0.001 µF. From the frequency expression,
The quality factor (Q) of the LC circuit is given by:
Hartley Oscillator:
Fig. 5, shows Hartley oscillator when the LC tank is resonant, the circulating current flows
through L1 in series with L2. Thus, the equivalent inductance is L = L1 + L2.

Fig. 5
In the oscillator, the feedback voltage is developed by the inductive voltage divider, L1 & L2.
Since the output voltage appears across L1 and the feedback voltage across L2, the feedback
fraction is
β = V / Vout = XL2 / XL1 = L2 / L1
As usual, the loading effect of the base is ignored. For oscillations to start, the voltage gain must
be greater than 1/ β. The frequency of oscillation is given by
Similarly, an opamp based Hartley oscillator circuit is shown in fig. 6.

Fig. 6
Crystal Oscillator:
Some crystals found in nature exhibit the piezoelectric effect i.e. when an ac voltage is applied
across them, they vibrate at the frequency of the applied voltage. Conversely, if they are
mechanically pressed, they generate an ac voltage. The main substances that produce this
piezoelectric effect are Quartz, Rochelle salts, and Tourmaline.
Rochelle salts have greatest piezoelectric activity, for a given ac voltage, they vibrate more than
quartz or tourmaline. Mechanically, they are the weakest they break easily. They are used in
microphones, phonograph pickups, headsets and loudspeakers.
Tourmaline shows the least piezoelectric activity but is a strongest of the three. It is also the most
expensive and used at very high frequencies.
Quartz is a compromise between the piezoelectric activity of Rochelle salts and the strength of
tourmaline. It is inexpensive and easily available in nature. It is most widely used for RF
oscillators and filters.
The natural shape of a quartz crystal is a hexagonal prism with pyramids at the ends. To get a
useable crystal out of this it is sliced in a rectangular slap form of thickness t. The number of
slabs we can get from a natural crystal depends on the size of the slabs and the angle of cut.
Fig. 1
For use in electronic circuits, the slab is mounted between two metal plates, as shown in fig. 1. In
this circuit the amount of crystal vibration depends upon the frequency of applied voltage. By
changing the frequency, one can find resonant frequencies at which the crystal vibrations reach a
maximum. Since the energy for the vibrations must be supplied by the ac source, the ac current is
maximized at each resonant frequency. Most of the time, the crystal is cut and mounted to
vibrate best at one of its resonant frequencies, usually the fundamental or lowest frequency.
Higher resonant frequencies, called overtones, are almost exact multiplies of the fundamental

frequency e.g. a crystal with a fundamental frequency of 1 MHz has a overtones of 2 MHz, 3
MHz and so on. The formula for the fundamental frequency of a crystal is
f = K / t.
where K is a constant that depends on the cut and other factors, t is the thickness of crystal, f is
inversely proportional to thickness t. The thinner the crystal, the more fragile it becomes and the
more likely it is to break because of vibrations. Quartz crystals may have fundamental frequency
up to 10 MHz. To get higher frequencies, a crystal is mounted to vibrate on overtones; we can
reach frequencies up to 100 MHz.
AC Equivalent Circuit:
When the mounted crystal is not vibrating, it is equivalent to a capacitance Cm, because it has
two metal plates separated by dielectric, Cm is known as mounting capacitance.
Fig. 2
When the crystal is vibrating, it acts like a tuned circuit. Fig. 2, shows the ac equivalent circuit of
a crystal vibrating at or near its fundamental frequency. Typical values are L is henrys, C in
fractions of a Pico farad, R in hundreds of ohms and Cm in Pico farads
Ls = 3Hz, Cs = 0.05 pf, Rs = 2K, Cm = 10 pf.
The Q of the circuit is very very high. Compared with L-C tank circuit. For the given values, Q
comes out to be 3000. Because of very high Q, a crystal leads to oscillators with very stable
frequency values.
The series resonant frequency fS of a crystal is the sonant frequency of the LCR branch. At this
frequency, the branch current reaches a maximum value because Ls resonant with CS.
Above fS, the crystal behaves inductively. The parallel resonant frequency is the frequency at
which the circulating or loop current reaches a maximum value. Since this loop current must
flow through the series combination of CS and Cm, the equivalent Cloop is

Since Cloop > CS, therefore, fp > fS.
Since Cm > CS, therefore, Cm || CS is slightly
lesser than CS. Therefore fP is slightly greater
than fS. Because of the other circuit capacitances
that appear across Cm the actual frequency will
lie between fS and fP. fS and fP are the upper and
lower limits of frequency. The impedance of the
crystal oscillator can be plotted as a function of
frequency as shown in fig. 3.
At frequency fS, the circuit behaves like
resistive circuit. At fP the impedance reaches to
maximum, beyond fP, the circuit is highly
capacitive.
The frequency of an oscillator tends to change
slightly with time. The drift is produced by
temperature, aging and other causes. In a crystal
oscillator the frequency drift with time is very
small, typically less than 1 part in 106
per day.
They can be used in electronic wristwatches. If
the drift is 1 part in 1010
, a clock with this drift
will take 30 years to gain or lose 1 sec.
Fig. 3
Crystals can be manufactured with values of fs as low as 10 kHz; at these frequencies the crystal
is relatively thick. On the high frequency side, fs can be as high as 1- MHz; here the crystal is
very thin.
The temperature coefficient of crystals is usually small and can be made zero. When extreme
temperature stability is required, the crystal may be housed in an oven to maintain it at a constant
temperature. The high Q of the crystal also contributes to the relatively drift free oscillation of
crystal oscillators.
Example - 1
The parameters of the equivalent circuit of a crystal are given below:

L = 0.4 H, CS = 0.06 pF, R = 5 kΩ, Cm = 1.0 pF.
Determine the series and parallel resonant frequencies of the crystal.
Solution:
With reference to fig. 2, the admittance of the crystal Y is given by
where,
and
The resonant frequencies are obtained by putting B = 0. Thus,
Consider the term CS R2 / LS = CS R / [L R]. In a crystal, the time constant (L / R) is very much
greater than CS R. Thus the ratio is very much less than 1. For the values given, this ratio is of
the order of10-6
. Neglecting this term in comparison with 2, we get two roots as
where, ωs and ωp are the series and parallel resonant frequencies respectively. Substituting the
values, we get
ωs = 6.45 M Hz. and ωp = 6.64 MHz
Crystal Oscillators:
Fig. 4, shows a colpitts crystal oscillator.

Fi. 4
The capacitive voltage divider produces the feedback voltage for the base of transistor. The
crystal acts like an inductor that resonates with C1 and C2. The oscillation frequency is between
the series and parallel resonant frequencies.
Example-2:
If the crystal of example-1 is used in the oscillator circuit as shown fig. 5, determine the values
of R for the circuit to oscillate.
Fig. 5
Solution:

The equivalent circuit of crystal (discussed earlier) shows that it has a parallel resonant fr
frequency (ωp) at which the impedance becomes maximum. The amplified signal output of the
circuit is applied across the potential divider consisting of R and the crystal circuit. At the
resonant frequency the impedance of crystal becomes maximum (magnitude R) and thus the loop
gain will be greater than or equal to unity. At frequencies away from ωp the loop gain becomes
less than unity. The loop base shift is also zero around ωp. Thus both the conditions required for
sustained oscillations are satisfied and the circuit oscillates.
The value of G of the crystal at ω =ωp is given by
Thus the resistor R should be less than 5x106
Ω.
UNIT V
PULSE CIRCUITS
Clipper Circuits
Clippers:
Clipping circuits are used to select that portion of the input wave which lies above or below
some reference level. Some of the clipper circuits are discussed here. The transfer characteristic
(vo vs vi) and the output voltage waveform for a given input voltage are also discussed.
Clipper Circuit 1:

The circuit shown in fig. 3, clips the input signal above a
reference voltage (VR).
In this clipper circuit,
If vi < VR, diode is reversed biased and does not
conduct. Therefore, vo = vi
and, if vi > VR, diode is forward biased and thus, vo= VR.
The transfer characteristic of the clippers is shown in fig. 4. Fig. 3
Fig. 4
Clipper Circuit 2:
The clipper circuit shown in fig. 5 clips the input signal
below reference voltage VR.
In this clipper circuit,
If vi > VR, diode is reverse biased. vo = vi
and, If vi < VR, diode is forward biased. vo = VR
The transfer characteristic of the circuit is shown in fig. 6. Fig. 5

Fig. 6
Clipper Circuit 3:
To clip the input signal between two independent levels
(VR1< VR2 ), the clipper circuit is shown in fig. 7.
The diodes D1 & D2 are assumed ideal diodes.
For this clipper circuit, when vi ≤ VR1, vo=VR1
and, vi ≥ VR2, vo= VR2
and, VR1 < vi < VR2 vo = vi
The transfer characteristic of the clipper is shown in
fig. 8.
Fig. 7

Fig. 8
Clipper Circuits
Example – 1:
Draw the transfer characteristic of the circuit shown in fig. 9.
Fig. 9
Solution:
When diode D1 is off, i1 = 0, D2 must be ON.

and vo = 10 - 5 x 0.25 = 7.5 V
vp = vo = 7.5 V
Therefore, D1 is reverse biased only if vi < 7.5 V
If D2 is off and D1 is ON, i2 = 0
and vp = 10 ( 0.04 vi - 0.1 ) + 2.5 = 0.4 vi + 1.5
For D2 to be reverse biased,
Between 7.5 V and 21.25 V both the diodes are ON.
Fig. 10
The transfer characteristic of the circuit is shown in fig. 10.

Clipper and Clamper Circuits
Clippers:
In the clipper circuits, discussed so far, diodes are assumed to be ideal device. If third
approximation circuit of diode is used, the transfer characteristics of the clipper circuits will be
modified.
Clipper Circuit 4:
Consider the clipper circuit shown in fig. 1 to clip the input signal above reference voltage
Fig. 1 Fig. 2
When vi < (VR+ Vr), diode D is reverse biased and therefore, vo= vi.
and when vi > ( VR + Vr ), diode D is forward biased and conducts. The equivalent circuit, in this
case is shown in fig. 2.

The current i in the circuit is given by
The transfer characteristic of the circuit is
shown in fig. 3. Fig. 3
Clipper Circuit 5:
Consider the clipper circuit shown in fig. 4, which clips the input signal below the reference level
(VR).
If vi > (VR – Vr), diode D is reverse biased, thus vO = vi and when vi < (vR -Vr), D condcuts and
the equivalent circuit becomes as shown in fig. 5.
Fig. 4 Fig. 5

Therefore,
The transfer characteristic of the circuit
is shown in fig. 6.
Fig. 6
Clipper and Clamper Circuits
Example - 1:
Find the output voltage v out of the clipper circuit of fig. 7(a) assuming that the diodes are
a. ideal.
b. Von = 0.7 V. For both cases, assume RF is zero.

Fig. 7(a) Fig. 7(b)
Solution:
(a). When vinis positive and vin < 3, then vout = vin
and when vin is positive and vin > 3, then
At vin = 8 V(peak), vout = 6.33 V.
When vinis negative and vin > - 4, then vout = vin
When vin is negative and vin < -4, then vout = -4V
The resulting output wave shape is shown in fig. 7(b).
(b). When VON = 0.7 V, vin is positive and vin < 3.7 V, then vout = vin
When vin > 3.7 V, then
When vin = 8V, vout = 6.56 V.
When vin is negative and vin > -4.7 V, then vout = vin
When vin < - 4.7 V, then vout = - 4.7 V
The resulting output wave form is shown in fig. 7(b).
Clamper Circuits:
Clamping is a process of introducing a dc level into a signal. For example, if the input voltage
swings from -10 V and +10 V, a positive dc clamper, which introduces +10 V in the input will
produce the output that swings ideally from 0 V to +20 V. The complete waveform is lifted up

by +10 V.
Negative Diode clamper:
A negative diode clamper is shown in fig. 8, which introduces a negative dc voltage equal to peak value of input in
the input signal.
Fig. 8 Fig. 9
Let the input signal swings form +10 V to -10
V. During first positive half cycle as V i rises
from 0 to 10 V, the diode conducts. Assuming
an ideal diode, its voltage, which is also the
output must be zero during the time from 0 to
t1. The capacitor charges during this period to
10 V, with the polarity shown.
At that Vi starts to drop which means the anode
of D is negative relative to cathode, ( VD = vi -
vc ) thus reverse biasing the diode and
preventing the capacitor from discharging. Fig.
9. Since the capacitor is holding its charge it
behaves as a DC voltage source while the diode
appears as an open circuit, therefore the
equivalent circuit becomes an input supply in
series with -10 V dc voltage as shown in fig.
10, and the resultant output voltage is the sum
Fig. 10

of instantaneous input voltage and dc voltage
(-10 V).
Clamper Circuits
Positive Clamper:
The positive clamper circuit is shown in fig. 1, which introduces positive dc voltage equal to the
peak of input signal. The operation of the circuit is same as of negative clamper.
Fig. 1 Fig. 2
Let the input signal swings form +10 V to -10 V. During first negative half cycle as Vi rises from
0 to -10 V, the diode conducts. Assuming an ideal diode, its voltage, which is also the output
must be zero during the time from 0 to t1. The capacitor charges during this period to 10 V, with
the polarity shown.
After that Vi starts to drop which means the anode of D is negative relative to cathode, (VD= vi -
vC) thus reverse biasing the diode and preventing the capacitor from discharging. Fig. 2. Since
the capacitor is holding its charge it behaves as a DC voltage source while the diode appears as
an open circuit, therefore the equivalent circuit becomes an input supply in series with +10 V dc
voltage and the resultant output voltage is the sum of instantaneous input voltage and dc voltage
(+10 V).
To clamp the input signal by a voltage other than peak value, a dc source is required. As shown
in fig. 3, the dc source is reverse biasing the diode.

The input voltage swings from +10 V to -10 V. In the negative half cycle when the voltage
exceed 5V then D conduct. During input voltage variation from –5 V to -10 V, the capacitor
charges to 5 V with the polarity shown in fig. 3. After that D becomes reverse biased and open
circuited. Then complete ac signal is shifted upward by 5 V. The output waveform is shown in
fig. 4.
Fig. 3 Fig. 4
Clamper (electronics)
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Positive unbiased voltage clamping shifts the amplitude of the input waveform so that all parts of
it are greater than 0V
A clamper is an electronic circuit that prevents a signal from exceeding a certain defined
magnitude by shifting its DC value. The clamper does not restrict the peak-to-peak excursion of
the signal, but moves it up or down by a fixed value. A diode clamp (a simple, common type)
relies on a diode, which conducts electric current in only one direction; resistors and capacitors
in the circuit are used to maintain an altered dc level at the clamper output.
General function
A clamping circuit (also known as a clamper) will bind the upper or lower extreme of a
waveform to a fixed DC voltage level. These circuits are also known as DC voltage restorers.
Clampers can be constructed in both positive and negative polarities. When unbiased, clamping
circuits will fix the voltage lower limit (or upper limit, in the case of negative clampers) to 0
Volts. These circuits clamp a peak of a waveform to a specific DC level compared with a
capacitively coupled signal which swings about its average DC level (usually 0V).
Types
Clamp circuits are categorised by their operation; negative or positive and biased and unbiased.
A positive clamp circuit outputs a purely positive waveform from an input signal; it offsets the
input signal so that all of the waveform is greater than 0V. A negative clamp is the opposite of
this - this clamp outputs a purely negative waveform from an input signal.
A bias voltage between the diode and ground offsets the output voltage by that amount.
For example, an input signal of peak value 5V (VIN = 5V) is applied to a positive clamp with a
bias of 3V (VBIAS = 3V), the peak output voltage will be
VOUT = 2VIN + VBIAS

VOUT = 2 * 5 + 3
VOUT = 13V
Positive unbiased
A positive unbiased clamp
In the negative cycle of the input AC signal, the diode is forward biased and conducts, charging
the capacitor to the peak positive value of VIN. During the positive cycle, the diode is reverse
biased and thus does not conduct. The output voltage is therefore equal to the voltage stored in
the capacitor plus the input voltage again, so VOUT = 2VIN
] Negative unbiased
A negative unbiased clamp
A negative unbiased clamp is the opposite of the equivalent positive clamp. In the positive cycle
of the input AC signal, the diode is forward biased and conducts, charging the capacitor to the
peak value of VIN. During the negative cycle, the diode is reverse biased and thus does not
conduct. The output voltage is therefore equal to the voltage stored in the capacitor plus the input
voltage again, so VOUT = -2VIN
Positive biased
A positive biased clamp
A positive biased voltage clamp is identical to an equivalent unbiased clamp but with the output
voltage offset by the bias amount VBIAS. Thus, VOUT = 2VIN + VBIAS

Negative biased
A negative biased clamp
A negative biased voltage clamp is likewise identical to an equivalent unbiased clamp but with
the output voltage offset in the negative direction by the bias amount VBIAS. Thus, VOUT = -2VIN
- VBIAS
Op-amp circuit
Precision op-amp clamp circuit[1]
The figure shows an op-amp clamp circuit with a non-zero reference clamping voltage. The
advantage here is that the clamping level is at precisely the reference voltage. There is no need to
take into account the forward volt drop of the diode (which is necessary in the preceding simple
circuits as this adds to the reference voltage). The effect of the diode volt drop on the circuit
output will be divided down by the gain of the amplifier, resulting in an insignificant error.
Clamping for input protection
Clamping can be used to adapt an input signal to a device that cannot make use of or may be
damaged by the signal range of the original input.
Principles of operation
The schematic of a clamper reveals that it is a relatively simple device. The two components
creating the clamping effect are a capacitor, followed by a diode in parallel with the load. The
clamper circuit relies on a change in the capacitor‘s time constant; this is the result of the diode
changing current path with the changing input voltage. The magnitude of R and C are chosen so

that is large enough to ensure that the voltage across the capacitor does not discharge
significantly during the diode's "Non conducting" interval. During the first negative phase of the
AC input voltage, the capacitor in the positive clamper charges rapidly. As Vin becomes positive,
the capacitor serves as a voltage doubler; since it has stored the equivalent of Vin during the
negative cycle, it provides nearly that voltage during the positive cycle; this essentially doubles
the voltage seen by the load. As Vin becomes negative, the capacitor acts as a battery of the same
voltage of Vin. The voltage source and the capacitor counteract each other, resulting in a net
voltage of zero as seen by the load.
Biased versus non-biased
By using a voltage source and resistor, the clamper can be biased to bind the output voltage to a
different value. The voltage supplied to the potentiometer will be equal to the offset from zero
(assuming an ideal diode) in the case of either a positive or negative clamper (the clamper type
will determine the direction of the offset. If a negative voltage is supplied to either positive or
negative, the waveform will cross the x-axis and be bound to a value of this magnitude on the
opposite side. Zener diodes can also be used in place of a voltage source and potentiometer,
hence setting the offset at the Zener voltage.
Examples
One common such clamping circuit is the DC restorer circuit in analog television receiver, which
returns the voltage of the signal during the back porch of the line blanking period to 0V. Since
the back porch is required to be at 0V on transmission, any DC or low frequency hum that has
been induced onto the signal can be effectively removed via this method.
Diode Clippers
For a clipping circuit at least two components—an ideal diode and resistor are required and
sometimes a dc battery is also employed for fixing the clipping level. The diode acts as a closed
switch when forward biased and an open switch when reverse biased. The input waveform can
be clipped at different levels by simply changing the voltage of the battery and by interchanging
the positions of the various elements.
Depending on the orientation of the diode, the positive or negative region of the input signal is
―clipped‖ off and accordingly the diode clippers may be positive or negative clippers.
There are two general categories of clippers: series and parallel (or shunt). The series
configuration is defined as one where diode is in series with the load, while the shunt clipper has
the diode in a branch parallel to the load.
1. Positive Clipper
The clipper which removes the positive half cycles of the input voltage is called the positive
clipper. The circuit arrangements for a positive clipper are illustrated in the figure given below.

Positive Series Clipper and Positive Shunt Clipper
The figure illustrates the positive series clipper circuit (that is, diode in series with the load).
From the figure (a) it is seen that while the input is positive, diode D is reverse biased and so the
output remains at zero that is, positive half cycle is clipped off. During the negative half cycle of
the input, the diode is forward biased and so the negative half cycle appears across the output.
Figure (b) illustrates the positive shunt clipper circuit (that is, diode in parallel with the load).
From the figure (b) it is seen that while input side is positive, the diode D is forward biased and
conducts heavily (that is, diode acts as a closed switch). So the voltage drop across the diode or
across the load resistance RL is zero. Thus output voltage during the positive half cycles is zero,
as shown in the output waveform. During the negative half cycles of the input signal voltage, the
diode D is reverse biased and behaves as an open switch. Consequently the entire input voltage
appears across the diode or across the load resistance RL if R is much smaller than RL
Actually the circuit behaves as a voltage divider with an output voltage of [RL / R+ RL] Vmax = -
Vmax when RL >> R
Note: If the diode in figures (a) and (b) is reconnected with reversed polarity, the circuits will
become for a negative series clipper and negative shunt clipper respectively. The negative series
and negative shunt clippers are shown in figures (a) and (b) as given below.
Negative Series Clipper and Negative Shunt Clipper
In the above discussion, the diode is considered to be ideal one. If second approximation for
diode is considered the barrier potential (0.7 V for silicon and 0.3 V for Germanium) of diode,
will be taken into account. Then the output waveforms for positive and negative clippers will be
of the shape shown in the figure below.

Output Waveform – Positive Clipper and Negative Clipper
2. Biased Clipper
Sometimes it is desired to remove a small portion of positive or negative half cycles of the signal
voltage. Biased clippers are employed for this purpose. The circuit diagram for a biased negative
clipper (that is for removing a small portion of each negative half cycle) is illustrated in figure
(a).
Biased Negative Clipper
The action of the circuit is explained below. When the input signal voltage is positive, the diode
D is reverse-biased and behaves as an open-switch, the entire positive half cycle appears across
the load, as illustrated by output waveform [figure (a)]. When the input signal voltage is negative
but does not exceed battery voltage V, the diode D remains reverse-biased and most of the input
voltage appears across the output. When during the negative half cycle of input signal, the signal
voltage exceeds the battery voltage V, the diode D is forward biased i.e conducts heavily. The
output voltage is equal to – V and stays at – V as long as the input signal voltage is greater than
battery voltage V in magnitude. Thus a biased negative clipper removes input voltage when the
input signal voltage exceeds the battery voltage. Clipping can be changed by reversing the
battery and diode connections, as illustrated in figure (b).
Biased Positive Clipper
Some of other biased clipper circuits are given below in the figure. While drawing the wave-
shape of the output basic principle discussed above are followed. The diode has been considered
as an ideal one.

Biased Clipper Circuits
Different Clipping Circuits
3. Combination Clipper
When a portion of both positive and negative of each half cycle of the input voltage is to be
clipped (or removed), combination clipper is employed. The circuit for such a clipper is given in
the figure below.
Combination Clipper
The action of the circuit is summarized below. For positive input voltage signal when input
voltage exceeds battery voltage + V1 diode D1 conducts heavily while diode D2 is reversed biased
and so voltage + V1 appears across the output. This output voltage + V1 stays as long as. the
input signal voltage exceeds + V1. On the other hand for the negative input voltage signal, the
diode D1 remains reverse biased and diode D2 conducts heavily only when input voltage exceeds

battery voltage V2 in magnitude. Thus during the negative half cycle the output stays at – V2 so
long as the input signal voltage is greater than -V2.
Drawbacks of Series and Shunt Diode Clippers
In series clippers, when diode is in ‗off‘ position, there should be no transmission of input signal
to output. But in case of high frequency signals transmission occurs through diode capacitance
which is undesirable. This is the drawback of using diode as a series element in such clippers.
In shunt clippers, when diode is in the ‗off condition, transmission of input signal should take
place to output. But in case of high frequency input signals, diode capacitance affects the circuit
operation adversely and the signal gets attenuated (that is, it passes through diode capacitance to
ground).
Multivibrator
A multivibrator is an electronic circuit used to implement a variety of simple two-state systems
such as oscillators, timers and flip-flops. It is characterized by two amplifying devices
(transistors, electron tubes or other devices) cross-coupled by resistors and capacitors.
There are three types of multivibrator circuit:
 astable, in which the circuit is not stable in either state—it continuously oscillates from
one state to the other. Due to this, it does not require an input (Clock pulse or other).
 monostable, in which one of the states is stable, but the other is not—the circuit will flip
into the unstable state for a determined period, but will eventually return to the stable
state. Such a circuit is useful for creating a timing period of fixed duration in response to
some external event. This circuit is also known as a one shot. A common application is in
eliminating switch bounce.
 bistable, in which the circuit will remain in either state indefinitely. The circuit can be
flipped from one state to the other by an external event or trigger. Such a circuit is
important as the fundamental building block of a register or memory device. This circuit
is also known as a latch or a flip-flop.
In its simplest form the multivibrator circuit consists of two cross-coupled transistors. Using
resistor-capacitor networks within the circuit to define the time periods of the unstable states, the
various types may be implemented. Multivibrators find applications in a variety of systems
where square waves or timed intervals are required. Simple circuits tend to be inaccurate since
many factors affect their timing, so they are rarely used where very high precision is required.
Before the advent of low-cost integrated circuits, chains of multivibrators found use as frequency
dividers. A free-running multivibrator with a frequency of one-half to one-tenth of the reference
frequency would accurately lock to the reference frequency. This technique was used in early
electronic organs, to keep notes of different octaves accurately in tune. Other applications
included early television systems, where the various line and frame frequencies were kept
synchronized by pulses included in the video signal.

Astable multivibrator circuit
Figure 1: Basic BJT astable multivibrator
This circuit shows a typical simple astable circuit, with an output from the collector of Q1, and
an inverted output from the collector of Q2.
Basic mode of operation
The circuit keeps one transistor switched on and the other switched off. Suppose that initially,
Q1 is switched on and Q2 is switched off.
State 1:
 Q1 holds the bottom of R1 (and the left side of C1) near ground (0 V).
 The right side of C1 (and the base of Q2) is being charged by R2 from below ground to
0.6 V.
 R3 is pulling the base of Q1 up, but its base-emitter diode prevents the voltage from
rising above 0.6 .
 R4 is charging the right side of C2 up to the power supply voltage (+V). Because R4 is
less than R2, C2 charges faster than C1.
When the base of Q2 reaches 0.6 V, Q2 turns on, and the following positive feedback loop
occurs:
 Q2 abruptly pulls the right side of C2 down to near 0 V.
 Because the voltage across a capacitor cannot suddenly change, this causes the left side
of C2 to suddenly fall to almost −V, well below 0 V.
 Q1 switches off due to the sudden disappearance of its base voltage.

 R1 and R2 work to pull both ends of C1 toward +V, completing Q2's turn on. The process
is stopped by the B-E diode of Q2, which will not let the right side of C1 rise very far.
This now takes us to State 2, the mirror image of the initial state, where Q1 is switched off and
Q2 is switched on. Then R1 rapidly pulls C1's left side toward +V, while R3 more slowly pulls
C2's left side toward +0.6 V. When C2's left side reaches 0.6 V, the cycle repeats.
Multivibrator frequency
The period of each half of the multivibrator is given by t = ln(2)RC. The total period of
oscillation is given by:
T = t1 + t2 = ln(2)R2 C1 + ln(2)R3 C2
where...
 f is frequency in hertz.
 R2 and R3 are resistor values in ohms.
 C1 and C2 are capacitor values in farads.
 T is period time (In this case, the sum of two period durations).
For the special case where
 t1 = t2 (50% duty cycle)
 R2 = R3
 C1 = C2
Initial power-up
When the circuit is first powered up, neither transistor will be switched on. However, this means
that at this stage they will both have high base voltages and therefore a tendency to switch on,
and inevitable slight asymmetries will mean that one of the transistors is first to switch on. This
will quickly put the circuit into one of the above states, and oscillation will ensue. In practice,
oscillation always occurs for practical values of R and C.
However, if the circuit is temporarily held with both bases high, for longer than it takes for both
capacitors to charge fully, then the circuit will remain in this stable state, with both bases at 0.6

V, both collectors at 0 V, and both capacitors charged backwards to −0.6 V. This can occur at
startup without external intervention, if R and C are both very small. For example, a 10 MHz
oscillator of this type will often be unreliable. (Different oscillator designs, such as relaxation
oscillators, are required at high frequencies.)
Period of oscillation
Very roughly, the duration of state 1 (low output) will be related to the time constant R2C1 as it
depends on the charging of C1, and the duration of state 2 (high output) will be related to the
time constant R3C2 as it depends on the charging of C2. Because they do not need to be the same,
an asymmetric duty cycle is easily achieved.
However, the duration of each state also depends on the initial state of charge of the capacitor in
question, and this in turn will depend on the amount of discharge during the previous state,
which will also depend on the resistors used during discharge (R1 and R4) and also on the
duration of the previous state, etc. The result is that when first powered up, the period will be
quite long as the capacitors are initially fully discharged, but the period will quickly shorten and
stabilise.
The period will also depend on any current drawn from the output and on the supply voltage.
Protective components
While not fundamental to circuit operation, diodes connected in series with the base or emitter of
the transistors are required to prevent the base-emitter junction being driven into reverse
breakdown when the supply voltage is in excess of the Veb breakdown voltage, typically around
5-10 volts for general purpose silicon transistors. In the monostable configuration, only one of
the transistors requires protection.
Figure 2: Basic BJT monostable multivibrator.

Figure 3: Basic BJT bistable multivibrator.
Non-electronic astables
Astable oscillators are usually thought of as electronic circuits, but need not be. Bimetallic strips
are used which switch an electric current on as they cool and off as they heat—flashing
Christmas and car indicator lights may use this mechanism.
Monostable multivibrator circuit
When triggered by an input pulse, a monostable multivibrator will switch to its unstable position
for a period of time, and then return to its stable state. The time period monostable multivibrator
remains in unstable state is given by t = ln(2)R2C1. If repeated application of the input pulse
maintains the circuit in the unstable state, it is called a retriggerable monostable. If further
trigger pulses do not affect the period, the circuit is a non-retriggerable multivibrator.
Bistable multivibrator circuit
Suggested values:
 R1, R2 = 10 kΩ
 R3, R4 = 10 kΩ
This latch circuit is similar to an astable multivibrator, except that there is no charge or discharge
time, due to the absence of capacitors. Hence, when the circuit is switched on, if Q1 is on, its
collector is at 0 V. As a result, Q2 gets switched off. This results in more than half +V volts
being applied to R4 causing current into the base of Q1, thus keeping it on. Thus, the circuit
remains stable in a single state continuously. Similarly, Q2 remains on continuously, if it
happens to get switched on first.
Switching of state can be done via Set and Reset terminals connected to the bases. For example,
if Q2 is on and Set is grounded momentarily, this switches Q2 off, and makes Q1 on. Thus, Set is
used to "set" Q1 on, and Reset is used to "reset" it to off state.

Astable Multivibrator
Introduction
Now that we have seen the bistable multivibrator and then modified it to form a monostable
multivibrator, the next question is, Can we modify it further to use capacitor coupling on both
sides? And what would happen if we did?
Well, of course we can do this; the further question would be, Do we want to? And that depends
on what happens when we build the circuit this way.
Since the use of one capacitor prevents the circuit from remaining stable in one of its two
possible states, it seems likely that with both sides coupled this way the circuit will be unable to
remain stable in either state. That is in fact the case, and in this experiment we will construct and
demonstrate this circuit.
Schematic Diagram
As shown in the schematic diagram here, the astable multivibrator simply extends the
modification that converted the bistable multivibrator to a monostable version of the circuit.
Now, both transistors are coupled to each other through capacitors. Whichever transistor is off at
any moment cannot remain off indefinitely; its base will become forward biased as that capacitor
charges towards +5 volts. Once that happens, that transistor will turn on, thereby turning
the other one off.

3-6 Figure 3-3.—Astable Multivibrator.
When an input signal to one amplifier is large enough, the transistor can be driven into cutoff,
and its collector voltage will be almost V CC. However, when the transistor is driven into
saturation, its collector voltage will be about 0 volts. A circuit that is designed to go quickly from
cutoff to saturation will produce a square or rectangular wave at its output. This principle is used
in multivibrators. Multivibrators are classified according to the number of steady (stable) states
of the circuit. A steady state exists when circuit operation is essentially constant; that is, one
transistor remains in conduction and the other remains cut off until an external signal is applied.
The three types of multivibrators are the ASTABLE, MONOSTABLE, and BISTABLE. The
astable circuit has no stable state. With no external signal applied, the transistors alternately
switch from cutoff to saturation at a frequency determined by the RC time constants of the
coupling circuits. The monostable circuit has one stable state; one transistor conducts while the
other is cut off. A signal must be applied to change this condition. After a period of time,
determined by the internal RC components, the circuit will return to its original condition where
it remains until the next signal arrives. The bistable multivibrator has two stable states. It remains
in one of the stable states until a trigger is applied. It then FLIPS to the other stable condition and
remains there until another trigger is applied. The multivibrator then changes back (FLOPS) to
its first stable state.
Q1. What type circuit is used to produce square or rectangular waves? Q2. What type of
multivibrator does not have a stable state? Q3. What type of multvibrator has one stable state?
Q4. What type of multivibrator has two stable states?
Astable Multivibrator An astable multivibrator is also known as a FREE-
RUNNING MULTIVIBRATOR. It is called free- running because it alternates between two
different output voltage levels during the time it is on. Theoutput remains at each voltage level
for a definite period of time. If you looked at this output on an oscilloscope, you would see
continuous square or rectangular waveforms. The astable multivibrator has two outputs, but NO

inputs. Let's look at the multivibrator in figure 3-3 again. This is an astable multivibrator. The
astable multivibrator is said to oscillate. To understand why the astable multivibrator oscillates,
assume that transistor Q1 saturates and transistor Q2 cuts off when the circuit is energized. This
situation is shown in figure 3-4. We assume Q1 saturates and Q2 is in cutoff because the circuit
is symmetrical; that is, R1 = R4, R2 = R3, C1 = C2, and Q1 = Q2. It is impossible to tell which
transistor will actually conduct when the circuit is energized. For this reason, either of the
transistors may be assumed to conduct for circuit analysis purposes. Figure 3-4.—Astable
multivibrator (Q1 saturated). Essentially, all the current in the circuit flows through Q1; Q1
offers almost no resistance to current flow. Notice that capacitor C1 is charging. Since Q1 offers
almost no resistance in its saturated state, the rate of charge of C1 depends only on the time
constant of R2 and C1 (recall that TC = RC). Notice that the right-hand side of capacitor C1 is
connected to the base of transistor Q2, which is now at cutoff. Let's analyze what is happening.
The right-hand side of capacitor C1 is becoming increasingly negative. If the base of Q2
becomes sufficiently negative, Q2 will conduct. After a certain period of time, the base of Q2
will become sufficiently negative to cause Q2 to change states from cutoff to conduction. The
time necessary for Q2 to become saturated is determined by the time constant R2C1. The next
state is shown in figure 3-5. The negative voltage accumulated on the right side on capacitor C1
has caused Q2 to conduct. Now the following sequence of events takes place almost
instantaneously. Q2 starts conducting and quickly saturates, and the voltage at output 2 changes
from Vapproximately CC to approximately 0 volts. This change in voltage is coupled through
C2 to the base of Q1, forcing Q1 to cutoff. Now Q1 is in cutoff and Q2 is in saturation. This is
the circuit situation shown in figure 3-6.
3-8 Figure 3-5.—Astable multivibrator. Figure 3-6.—Astable multivibrator. (Q2
saturated). Notice that figure 3-6 is the mirror image of figure 3-4. In figure 3-6 the left side of
capacitor C2 becomes more negative at a rate determined by the time constant R3C2. As the left
side of C2 becomes more negative, the base of Q1 also becomes more negative. When the base
of Q1 becomes negative enough to allow Q1 to conduct, Q1 will again go into saturation. The

resulting change in voltage at output 1 will cause Q2 to return to the cutoff state. Look at the
output waveform from transistor Q2, as shown in figure 3-7. The output voltage (from either
output of the multivibrator) alternates from approximately 0 volts to Vapproximately CC,
remaining in each state for a definite period of time. The time may range from a microsecond to
as much as a second or two. VIn some applications, the time period of higher voltage ( CC) and
the time period of lower voltage (0 volts) will be equal. Other applications require differing
higher- and lower-voltage times. For example, timing and gating circuits often have different
pulse widths as shown in figure 3-8.
3-9 Figure 3-7.—Square wave output from Q2. Figure 3-8.—Rectangular waves.
FREQUENCY STABILITY.—Some astable multivibrators must have a high degree of
frequency stability. One way to obtain a high degree of frequency stability is to apply triggers.
Figure 3-9, view (A), shows the diagram of a triggered, astable multivibrator. At time T0, a
negative input trigger to the base of Q1 (through C1) causes Q1 to go into saturation, which
drives Q2 to cutoff. The circuit will remain in this condition as long as the base voltage of Q2 is
positive. The length of time the base of Q2 will remain positive is determined by C3, R3, and R6.
Observe the parallel paths for C3 to discharge. Figure 3-9A.—Triggered astable multivibrator
and output.

View (B) of figure 3-9 shows the waveforms associated with the circuit. At time T1, Q2 comes
out of cutoff and goes into saturation. Also, Q1 is caused to come out of saturation and is cut off.
The base voltage waveform of Q1 shows a positive potential that is holding Q1 at cutoff. This
voltage would normally hold Q1 at cutoff until a point between T2 and T3. However, at time T2
another trigger is applied to the base of Q1, causing it to begin conducting. Q1 goes into
saturation and Q2 is caused to cut off. This action repeats each time a trigger (T2, T4, T6) is
applied.
r
Figure 3-9B.—Triggered astable multivibrator and output.
The prt of the input triggers must be shorter than the natural free-running prt of the astable
multivibrator, or the trigger prf must be slightly higher than the free-running prf of the circuit.
This is to make certain the triggers control the prt of the output.
Monostable Multivibrator The monostable multivibrator (sometimes called a ONE-SHOT
MULTIVIBRATOR) is a square- or rectangular-wave generator with just one stable condition.
With no input signal (quiescent condition) one amplifier conducts and the other is in cutoff. The
monostable multivibrator is basically used for pulse stretching. It is used in computer logic
systems and communication navigation equipment. The operation of the monostable
multivibrator is relatively simple. The input is triggered with a pulse of voltage. The output
changes from one voltage level to a different voltage level. The output remains at this new
voltage level for a definite period of time. Then the circuit automatically reverts to its original
condition and remains that way until another trigger pulse is applied to the input. The monostable
multivibrator actually takes this series of input triggers and converts them to uniform square
pulses, as shown in figure 3-10. All of the square output pulses are of the same amplitude and
time duration.

Figure 3-10.—Monostable multivibrator block diagram.
The schematic for a monostable multivibrator is shown in figure 3-11. Like the astable
multivibrator, one transistor conducts and the other cuts off when the circuit is energized.
Figure 3-11.—Monostable multivibrator schematic.
Recall that when the astable multivibrator was first energized, it was impossible to predict which
transistor would initially go to cutoff because of circuit symmetry. The one-shot circuit is not
symmetrical like the astable multivibrator. Positive voltage VBB is applied through R5 to the base
of Q1. This positive voltage causes Q1 to cut off. Transistor Q2 saturates because of the negative
Vvoltage applied from CC to its base through R2. Therefore, Q1 is cut off and Q2 is saturated
before a trigger pulse is applied, as shown in figure 3-12. The circuit is shown in its stable state.

Figure 3-12.—Monostable multivibrator (stable state).
Let's take a more detailed look at the circuit conditions in this stable state (refer to figure 3-12).
As stated above, Q1 is cut off, so no current flows through R1, and the collector of Q1 Vis at
CC. Q2 is saturated and has practically no voltage drop across it, so its collector is essentially at 0
volts. R5 and R3 form a voltage divider from VBB to the ground potential at the collector of Q2.
The tie point between these two resistors will be positive. Thus, the base of Q1 is held positive,
ensuring that Q1 remains cutoff. Q2 will remain saturated because the base of Q2 is very slightly
negative as a result of the Vvoltage drop across R2. If the collector of Q1 is near CC and the
base of Q2 is near ground, C1 must be charged to nearly VCC volts with the polarity shown. Now
that all the components and voltages have been described for the stable state, let us see how the
circuit operates (see figure 3-13). Assume that a negative pulse is applied at the input terminal.
C2 couples this voltage change to the base of Q1 and starts Q1 conducting. Q1 quickly saturates,
and its collector voltage immediately rises to ground potential. This sharp voltage increase is
coupled through C1 to the base of Q2, causing Q2 to cut off; the collector voltage of Q2
immediately drops to VCC. The voltage divider formed by R5 and R3 then holds the base of Q1
negative, and Q1 is locked in saturation

Figure 3-13.—Monostable multivibrator (triggered).
The one-shot multivibrator has now been turned on by applying a pulse at the input. It will turn
itself off after a period of time. To see how it does this, look at figure 3-13 again. Q1 is held in
saturation by the negative voltage applied through R3 to its base, so the circuit cannot be turned
off here. Notice that the base of Q2 is connected to C1. The positive charge on C1 keeps Q2
cutoff. Remember that a positive voltage change (essentially a pulse) was coupled from the
collector of Q1 when it began conducting to the base of Q2, placing Q2 in cutoff. When the
collector of Q1 switches from -VCC volts to 0 volts, the charge on C1 acts like a battery with its
negative terminal on the collector of Q1, and its positive terminal connected to the base of Q2.
This voltage is what cuts off Q2. C1 will now begin to discharge through Q1 to ground, back
through VCC, through R2 to the other side of C1. The time required for C1 to discharge
depends on the RC time constant of C1 and R2. Figure 3-14 is a timing diagram that shows the
negative input pulse and the resultant waveforms that you would expect to see for this circuit
description.

Figure 3-14.—Waveforms of a monostable multivibrator (triggered).
The only part of the operation not described so far is the short C1 charge time that occurs right
after Q1 and Q2 return to their stable states. This is simply the time required for C1 to gain
electrons on its left side. This charge time is determined by the R1C1 time constant.
Another version of the monostable multivibrator is shown in figure 3-15. View (A) is the circuit
and view (B) shows the associated waveforms. In its stable condition (T0), Q1 is cut off and Q2
is conducting. The input trigger (positive pulse at T1) is applied to the collector of Q1 and
coupled by C1 to the base of Q2 causing Q2 to be cut off. VThe collector voltage of Q2 then
goes CC. The more negative voltage at the collector of Q2 forward biases Q1 through R4. With
the forward bias, Q1 conducts, and the collector voltage of Q1 goes to about 0 volts. C1 now
discharges and keeps Q2 cut off. Q2 remains cut off until C1 discharges enough to allow Q2 to
conduct again (T2). When Q2 conducts again, its collector voltage goes toward 0 volts and Q1 is
cut off. The circuit returns to its quiescent state and has completed a cycle. The circuit remains in
this stable state until the next trigger arrives (T3).

Figure 3-15A.—Monostable miltivibrator and waveshapes. Schematic.
3-14 Figure 3-15B.—Monostable miltivibrator and waveshapes. Waveshapes
Note that R3 is variable to allow adjustment of the gate width. Increasing R3 increases the
discharge time for C1 which increases the cutoff time for Q2. Increasing the value of R3 widens
the gate. To decrease the gate width, decrease the value of R3. Figure 3-16 shows the
relationships between the trigger and the output signal. View (A) of the figure shows the input
trigger; views (B) and (C) show the different gate widths made available by R3. Although the
durations of the gates are different, the duration of the complete cycle remains the same as the

pulse repetition time of the triggers. View (D) of the figure illustrates that the trailing edge of the
positive alternation is variable.
Figure 3-16.—Monostable multivibrator waveforms with a variable gate.
The reason the monostable multivibrator is also called a one-shot multivibrator can easily be
seen. For every trigger pulse applied to the multivibrator, a complete cycle, or a positive and
negative alternation of the output, is completed. Q5. In an astable multivibrator, which
components determine the pulse repetition frequency?
Schmitt trigger
The effect of using a Schmitt trigger (B) instead of a comparator (A).
In electronics, a Schmitt trigger is a comparator circuit that incorporates positive feedback.In
the non-inverting configuration, when the input is higher than a certain chosen threshold, the
output is high; when the input is below a different (lower) chosen threshold, the output is low;
when the input is between the two, the output retains its value. The trigger is so named because
the output retains its value until the input changes sufficiently to trigger a change. This dual

threshold action is called hysteresis, and implies that the Schmitt trigger has some memory. In
fact, the Schmitt trigger is a bistable multivibrator.
Schmitt trigger devices are typically used in open loop configurations for noise immunity and
closed loop positive feedback configurations to implement multivibrators.
Invention
The Schmitt trigger was invented by US scientist Otto H. Schmitt in 1934 while he was still a
graduate student,[1]
later described in his doctoral dissertation (1937) as a "thermionic trigger".[2]
It was a direct result of Schmitt's study of the neural impulse propagation in squid nerves.[2]
Symbol
The symbol for Schmitt triggers in circuit diagrams is a triangle with an inverting or non-
inverting hysteresis symbol. The symbol depicts the corresponding ideal hysteresis curve.
Standard Schmitt trigger
Inverting Schmitt trigger (WRONG IMAGE! Should
have a circle at the right point of the triangle indicating
inversion!
Implementation
A Schmitt trigger can be implemented with a simple tunnel diode, a diode with an "N"-shaped
current–voltage characteristic in the first quadrant. An oscillating input will cause the diode to
move from one rising leg of the "N" to the other and back again as the input crosses the rising
and falling switching thresholds. However, the performance of this Schmitt trigger can be
improved with transistor-based devices that make explicit use of positive feedback to implement
the switching.
Comparator implementation
Schmitt triggers are commonly implemented using a comparator[nb 1]
connected to have positive
feedback (i.e., instead of the usual negative feedback used in operational amplifier circuits). For
this circuit, the switching occurs near ground, with the amount of hysteresis controlled by the
resistances of R1 and R2:

The comparator extracts the sign of the difference between its two inputs. When the non-
inverting (+) input is at a higher voltage than the inverting (−) input, the comparator output
switches to +VS, which is its high supply voltage. When the non-inverting (+) input is at a lower
voltage than the inverting (−) input, the comparator output switches to -VS, which is its low
supply voltage. In this case, the inverting (−) input is grounded, and so the comparator
implements the sign function – its 2-state output (i.e., either high or low) always has the same
sign as the continuous input at its non-inverting (+) terminal.
Because of the resistor network connecting the Schmitt trigger input, the non-inverting (+)
terminal of the comparator, and the comparator output, the Schmitt trigger acts like a comparator
that switches at a different point depending on whether the output of the comparator is high or
low. For very negative inputs, the output will be low, and for very positive inputs, the output will
be high, and so this is an implementation of a "non-inverting" Schmitt trigger. However, for
intermediate inputs, the state of the output depends on both the input and the output. For
instance, if the Schmitt trigger is currently in the high state, the output will be at the positive
power supply rail (+VS). V+ is then a voltage divider between Vin and +VS. The comparator will
switch when V+=0 (ground). Current conservation shows that this requires
and so Vin must drop below to get the output to switch. Once the comparator output has
switched to −VS, the threshold becomes to switch back to high.

Typical hysteresis curve (which matches the curve shown on a Schmitt trigger symbol)
So this circuit creates a switching band centered around zero, with trigger levels . The
input voltage must rise above the top of the band, and then below the bottom of the band, for the
output to switch on and then back off. If R1 is zero or R2 is infinity (i.e., an open circuit), the
band collapses to zero width, and it behaves as a standard comparator. The output characteristic
is shown in the picture on the right. The value of the threshold T is given by and the
maximum value of the output M is the power supply rail.
A practical Schmitt trigger configuration is shown below.

The output characteristic has exactly the same shape of the previous basic configuration, and the
threshold values are the same as well. On the other hand, in the previous case, the output voltage
was depending on the power supply, while now it is defined by the Zener diodes (which could
also be replaced with a single double-anode Zener diode). In this configuration, the output levels
can be modified by appropriate choice of Zener diode, and these levels are resistant to power
supply fluctuations (i.e., they increase the PSRR of the comparator). The resistor R3 is there to
limit the current through the diodes, and the resistor R4 minimizes the input voltage offset caused
by the comparator's input leakage currents (see Limitations of real op-amps).
Schmitt trigger with two transistors
In the positive-feedback configuration used in the implementation of a Schmitt trigger, most of
the complexity of the comparator's own implementation is unused. Hence, it can be replaced
with two cross-coupled transistors (i.e., the transistors that would otherwise implement the input
stage of the comparator). An example of such a 2-transistor-based configuration is shown below.
The chain RK1 R1 R2 sets the base voltage for transistor T2. This divider, however, is affected by
transistor T1, providing higher voltage if T1 is open. Hence the threshold voltage for switching
between the states depends on the present state of the trigger.
For NPN transistors as shown, when the input voltage is well below the shared emitter voltage,
T1 does not conduct. The base voltage of transistor T2 is determined by the mentioned divider.
Due to negative feedback, the voltage at the shared emitters must be almost as high as that set by
the divider so that T2 is conducting, and the trigger output is in the low state. T1 will conduct
when the input voltage (T1 base voltage) rises slightly above the voltage across resistor RE
(emitter voltage). When T1 begins to conduct, T2 ceases to conduct, because the voltage divider
now provides lower T2 base voltage while the emitter voltage does not drop because T1 is now
drawing current across RE. With T2 now not conducting the trigger has transitioned to the high
state.

With the trigger now in the high state, if the input voltage lowers enough, the current through T1
reduces, lowering the shared emitter voltage and raising the base voltage for T2. As T2 begins to
conduct, the voltage across RE rises, further reducing the T1 base-emitter potential and T1 ceases
to conduct.
In the high state, the output voltage is close to V+, but in the low state it is still well above V−.
This may not be low enough to be a "logical zero " for digital circuits. This may require
additional amplifiers following the trigger circuit.
The circuit can be simplified: R1 can be replaced with a short circuit connection, connecting the
T2 base directly to the T1 collector, and R2 can be taken out and replaced with an open circuit.
The key to its operation is that less current flows through RE when T1 is switched on (as a result
of input current into its base) than when T1 is off, because turning T1 on turns T2 off, and T2,
when on, provides more current through RE than does T1. With less current entering RE, the
voltage across it will be lower, and so once current gets going into T1, the input voltage must go
lower to turn T1 back off as now its emitter voltage has been lowered. This Schmitt trigger
buffer can also be turned into a Schmitt trigger inverter and another resistor saved in the process,
by replacing RK2 with a short connection, and connecting Vout to the emitter of T2 instead of its
collector. In this case however, a larger value of resistance should be used for RE as it now serves
as the pull-down resistor on the output, lowering the voltage on the output when the output
should be low, instead of a serving as only a small resistance which is only intended to develop a
small voltage across it that actually adds to the output voltage when it should be at a digital low.
Applications
Schmitt triggers are typically used in open loop configurations for noise immunity and closed
loop positive feedback configurations to implement multivibrators.
Noise immunity
One application of a Schmitt trigger is to increase the noise immunity in a circuit with only a
single input threshold. With only one input threshold, a noisy input signal near that threshold
could cause the output to switch rapidly back and forth from noise alone. A noisy Schmitt
Trigger input signal near one threshold can cause only one switch in output value, after which it
would have to move beyond the other threshold in order to cause another switch.
For example, in Fairchild Semiconductor's QSE15x family of infrared photosensors[3]
, an
amplified infrared photodiode generates an electric signal that switches frequently between its
absolute lowest value and its absolute highest value. This signal is then low-pass filtered to form
a smooth signal that rises and falls corresponding to the relative amount of time the switching
signal is on and off. That filtered output passes to the input of a Schmitt trigger. The net effect is
that the output of the Schmitt trigger only passes from low to high after a received infrared signal
excites the photodiode for longer than some known delay, and once the Schmitt trigger is high, it
only moves low after the infrared signal ceases to excite the photodiode for longer than a similar
known delay. Whereas the photodiode is prone to spurious switching due to noise from the

environment, the delay added by the filter and Schmitt trigger ensures that the output only
switches when there is certainly an input stimulating the device.
Devices that include a built-in Schmitt trigger
As discussed in the example above, the Fairchild Semiconductor QSE15x family of photosensors
use a Schmitt trigger internally for noise immunity. Schmitt triggers are common in many
switching circuits for similar reasons (e.g., for switch debouncing).
The following 7400 series devices include a Schmitt trigger on their input or on each of their
inputs:
 7413: Dual Schmitt trigger 4-input NAND Gate
 7414: Hex Schmitt trigger Inverter
 7418: Dual Schmitt trigger 4-input NAND Gate
 7419: Hex Schmitt trigger Inverter
 74121: Monostable Multivibrator with Schmitt Trigger Inputs
 74132: Quad 2-input NAND Schmitt Trigger
 74221: Dual Monostable Multivibrator with Schmitt Trigger Input
 74232: Quad NOR Schmitt Trigger
 74310: Octal Buffer with Schmitt Trigger Inputs
 74340: Octal Buffer with Schmitt Trigger Inputs and three-state inverted outputs
 74341: Octal Buffer with Schmitt Trigger Inputs and three-state noninverted outputs
 74344: Octal Buffer with Schmitt Trigger Inputs and three-state noninverted outputs
 74(HC/HCT)7541 Octal Buffer with Schmitt Trigger Inputs and Three-State Noninverted
Outputs
 SN74LV8151 is a 10-bit universal Schmitt-trigger buffer with 3-state outputs
A number of 4000 series devices include a Schmitt trigger on inputs, for example:
 4093: Quad 2-Input NAND
 40106: Hex Inverter
 14538: Dual Monostable Multivibrator
 4020: 14-Stage Binary Ripple Counter
 4017: Decade Counter with Decoded Outputs
 4022: Octal Counter with Decoded Outputs
 4093: Quad Dual Input NAND gate
Dual Schmitt input configurable single-gate CMOS logic, AND, OR, XOR, NAND, NOR,
XNOR
 NC7SZ57 Fairchild
 NC7SZ58 Fairchild
 SN74LVC1G57 Texas Instruments

 SN74LVC1G58 Texas Instruments
Use as an oscillator
A Schmitt trigger is a bistable multivibrator, and it can be used to implement another type of
multivibrator, the relaxation oscillator. This is achieved by connecting a single resistor–capacitor
network to an inverting Schmitt trigger – the capacitor connects between the input and ground
and the resistor connects between the output and the input. The output will be a continuous
square wave whose frequency depends on the values of R and C, and the threshold points of the
Schmitt trigger. Since multiple Schmitt trigger circuits can be provided by a single integrated
circuit (e.g. the 4000 series CMOS device type 40106 contains 6 of them), a spare section of the
IC can be quickly pressed into service as a simple and reliable oscillator with only two external
components.
Output and capacitor waveforms for comparator-based relaxation oscillator.
For example, the comparator-based implementation of a relaxation oscillator is shown below.
Here, a comparator-based Schmitt trigger is used in its inverting configuration. That is, the input
and ground are swapped from the Schmitt trigger shown above, and so very negative signals

correspond to a positive output and very positive signals correspond to a negative output.
Additionally, slow negative feedback is added with an RC network. The result, which is shown
on the right, is that the output automatically oscillates from VSS to VDD as the capacitor charges
from one Schmitt trigger threshold to the other.

The UJT as the name implies, is characterized by a single pn junction. It exhibits negative
resistance characteristic that makes it useful in oscillator circuits.
The symbol for UJT is shown in fig. 1. The UJT is having three terminals base1 (B1), base2 (B2)
and emitter (E). The UJT is made up of an N-type silicon bar which acts as the base as shown in
fig. 2. It is very lightly doped. A P-type impurity is introduced into the base, producing a single
PN junction called emitter. The PN junction exhibits the properties of a conventional diode.
Fig. 1
Fig .2
A complementary UJT is formed by a P-type base and N-type emitter. Except for the polarity of
voltage and current the characteristic is similar to those of a conventional UJT.
A simplified equivalent circuit for the UJT is shown in fig. 3. VBB is a source of biasing voltage
connected between B2 and B1. When the emitter is open, the total resistance from B2 to B1 is
simply the resistance of the silicon bar, this is known as the inter base resistance RBB. Since the
N-channel is lightly doped, therefore RBB is relatively high, typically 5 to 10K ohm. RB2 is the
resistance between B2 and point ‗a', while RB1 is the resistance from point ‗a' to B1, therefore the
interbase resistance RBB is
RBB = RB1 + RB2

Fig. 3
The diode accounts for the rectifying properties of the PN junction. VD is the diode's threshold
voltage. With the emitter open, IE = 0, and I1 = I 2 . The interbase current is given by
I1 = I2 = VBB / R BB .
Part of VBB is dropped across RB2 while the rest of voltage is dropped across RB1. The voltage
across RB1 is
Va = VBB * (RB1 ) / (RB1 + RB2 )
The ratio RB1 / (RB1 + RB2 ) is called intrinsic standoff ratio
= RB1 / (RB1 + RB2 ) i.e. Va = VBB .
The ratio is a property of UJT and it is always less than one and usually between 0.4 and 0.85.
As long as IB = 0, the circuit of behaves as a voltage divider.
Assume now that vE is gradually increased from zero using an emitter supply VEE . The diode
remains reverse biased till vE voltage is less than  VBB and no emitter current flows except
leakage current. The emitter diode will be reversed biased.
When vE = VD +VBB, then appreciable emitter current begins to flow where VD is the diode's
threshold voltage. The value of vE that causes, the diode to start conducting is called the peak
point voltage and the current is called peak point current IP.
VP = VD + VBB.

Uni-junction transistor
The graph of fig. 4 shows the relationship between
the emitter voltage and current. vE is plotted on the
vertical axis and IE is plotted on the horizontal axis.
The region from vE = 0 to vE = VP is called cut off
region because no emitter current flows (except for
leakage). Once vE exceeds the peak point voltage, IE
increases, but v E decreases. up to certain point called
valley point (VV and IV). This is called negative
resistance region. Beyond this, IE increases with vE
this is the saturation region, which exhibits a positive
resistance characteristic.
The physical process responsible for the negative
resistance characteristic is called conductivity
modulation. When the vE exceeds VP voltage, holes from P
emitter are injected into N base. Since the P region is
heavily doped compared with the N-region, holes are
injected to the lower half of the UJT.
Fig. 4
The lightly doped N region gives these holes a long lifetime. These holes move towards B1 to
complete their path by re-entering at the negative terminal of VEE. The large holes create a
conducting path between the emitter and the lower base. These increased charge carriers
represent a decrease in resistance RB1, therefore can be considered as variable resistance. It
decreases up to 50 ohm.
Since  is a function of RB1 it follows that the reduction of RB1 causes a corresponding
reduction in intrinsic standoff ratio. Thus as IE increases, RB1 decreases, decreases, and
Va decreases. The decrease in V a causes more emitter current to flow which causes further
reduction in RB1, , and Va. This process is regenerative and therefore Va as well as vE
quickly drops while IE increases. Although RB decreases in value, but it is always positive
resistance. It is only the dynamic resistance between VV and VP. At point B, the entire
base1 region will saturate with carriers and resistance RB1 will not decrease any more. A
further increase in Ie will be followed by a voltage rise.
The diode threshold voltage decreases with temperature and RBB resistance increases with
temperature because Si has positive temperature coefficient.

UJT Relaxation Oscillator:
The characteristic of UJT was discussed in previous lecture. It is having negative resistance
region. The negative dynamic resistance region of UJT can be used to realize an oscillator.
The circuit of UJT relaxation oscillator is shown in fig. 1. It includes two resistors R1 and R2 for
taking two outputs R2 may be a few hundred ohms and R1 should be less than 50 ohms. The dc
source VCC supplies the necessary bias. The interbase voltage VBB is the difference between VCC
and the voltage drops across R1 and R2. Usually RBB is much larger than R1 and R2 so that VBB
approximately equal to V. Note, RB1 and RB2 are inter-resistance of UJT while R1 and R2 is the
actual resistor. RB1 is in series with R1 and RB2 is in series with R2 .
Fig. 1
As soon as power is applied to the circuit capacitor begins to charge toward V. The voltage
across C, which is also VE , rises exponentially with a time constant
= R C
As long as VE < VP, IE = 0. the diode remains reverse biased as long as VE < VP . When the
capacitor charges up to VP , the diode conducts and RB1 decreases and capacitor starts
discharging. The reduction in R B1 causes capacitor C voltage to drop very quickly to the valley
voltage VV because of the fast time constant due to the low value of RB1 and R1. As soon as VE

drops below Va + VD the diode is no longer forward biased and it stops conduction. It now
reverts to the previous state and C begins to charge once more toward VCC .
The emitter voltage is shown in fig. 2, VE rises exponentially toward VCC but drops to a very low
value after it reaches VP. The time for the VE to drop from VP to VV is relatively small and
usually neglected. The period T can therefore be approximated as follows:
Fig. 2

There are two additional outputs possible for the UJT oscillation one of these is the voltage
developed at B1 due to capacitor discharge while the other is voltage developed at B2 as shown
in fig. 3.

When UJT fires (at t = T) Va drops, causing a
corresponding voltage drop at B2. The duration of
outputs at B1 and B2 are determined by C discharge
time.
If R1 is very small, C discharges very quickly and very
narrow pulse is produced at the output. If R1 = 0,
obviously no pulses appear at B1.
If R2 = 0, no pulse can be generated at B2. If R1 is too
large, its positive resistance may swamp the negative
resistance and prevent the UJT form switching back
after it has fired.
R2, in addition to providing a source of pulse at B2, is
useful for temperature stabilization of the UJT's peak
point voltage .
VP = VD + VBB.
As the temperature increases, Vp decreases. The
temperature coefficient of RBB is positive. Rs is
essentially independent of temperature. It is therefore
possible to select R2 so that  VBB increases with
temperature by the same amount as VD decreases. This
provides a constant VP and, in turn, frequency of
oscillation.
Figure 31.3
Selection of R and C:
In the circuit, R is required to pass only the capacitor charging current. At the instant when VP is
reached; R must supply the peak current. It is therefore, necessary, that the current through R
should be slightly greater than the peak point.
Once the UJT fires, VE drops to the valley voltage VV . IE should not be allowed to increases

beyond the valley point IV, otherwise the UJT is taken into saturation region and does not switch
back, R therefore must be selected large enough to ensure that
As long as R is chosen between these extremes, reliable operation results.

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