Maximum power transfer theorem

Maximum power transfer theorem
In electrical engineering, the maximum power transfer theorem states
that, to obtain maximum external power from a source with a finite
internal resistance, the resistance of the load must be equal to the resistance
of the source as viewed from the output terminals. Moritz von
Jacobi published the maximum power (transfer) theorem around 1840, which
is also referred to as "Jacobi's law".[1]
The theorem results in maximum power transfer, and not
maximum efficiency. If the resistance of the load is made larger than the
resistance of the source, then efficiency is higher, since a higher percentage
of the source power is transferred to the load, but the magnitude of the load
power is lower since the total circuit resistance goes up.
If the load resistance is smaller than the source resistance, then most of the
power ends up being dissipated in the source, and although the total power
dissipated is higher, due to a lower total resistance, it turns out that the
amount dissipated in the load is reduced.
The theorem states how to choose (so as to maximize power transfer) the
load resistance, once the source resistance is given, not the opposite. It
does not say how to choose the source resistance, once the load resistance
is given. Given a certain load resistance, the source resistance that
maximizes power transfer is always zero, regardless of the value of the load
resistance.
The theorem can be extended to AC circuits that include reactance, and
states that maximum power transfer occurs when the load impedance is
equal to the complex conjugate of the source impedance.
Norton theorem
Any collection of batteries and resistances with two terminals is electrically
equivalent to an ideal current source i in parallel with a single resistor r. The value
of r is the same as that in the Thevenin equivalent and the current i can be found by
dividing the open circuit voltage by r.

Thévenin's theorm
In circuit theory, Thévenin's theoremfor linear electrical networks states that any combination
of voltage sources, current sources, and resistors with two terminals is electrically equivalent to
a single voltage source V and a single series resistor R. For single frequency AC systems the
theorem can also be applied to general impedances, not just resistors. The theorem was first
discovered by German scientist Hermann von Helmholtz in 1853,[1]
but was then rediscovered in
1883 by French telegraph engineer Léon Charles Thévenin (1857–1926).[2][3]
This theorem states that a circuit of voltage sources and resistors can be converted into
a Thévenin equivalent, which is a simplification technique used in circuit analysis. The
Thévenin equivalent can be used as a good model for a power supply or battery (with the
resistor representing the internal impedance and the source representing the electromotive
force). The circuit consists of an idealvoltage source in series with an ideal resistor.

Any black box containing only voltage sources,currentsources,and other resistors can be converted to a Thévenin
equivalentcircuit, comprising exactly one voltage source and one resistor.

Calculating the Thévenin equivalent
To calculate the equivalent circuit, the resistance and voltage are needed, so two equations are
required. These two equations are usually obtained by using the following steps, but any
conditions placed on the terminals of the circuit should also work:
1. Calculate the output voltage, VAB, when in open circuit condition (no load resistor—
meaning infinite resistance). This is VTh.
2. Calculate the output current, IAB, when the output terminals are short circuited (load
resistance is 0). RTh equals VTh divided by this IAB.
The equivalent circuit is a voltage source with voltage VTh in series with a resistance RTh.
Step 2 could also be thought of as:
2a. Replace voltage sources with short circuits, and current sources with open circuits.
2b. Calculate the resistance between terminals A and B. This is RTh.
The Thévenin-equivalent voltage is the voltage at the output terminals of the original
circuit. When calculating a Thévenin-equivalent voltage, the voltage divider principle is
often useful, by declaring one terminal to be Vout and the other terminal to be at the
ground point.
The Thévenin-equivalent resistance is the resistance measured across points A and B
"looking back" into the circuit. It is important to first replace all voltage- and current-
sources with their internal resistances. For an ideal voltage source, this means replace
the voltage source with a short circuit. For an ideal current source, this means replace
the current source with an open circuit. Resistance can then be calculated across the
terminals using the formulae for series and parallel circuits. This method is valid only for
circuits with independent sources. If there are dependent sources in the circuit, another
method must be used such as connecting a test source across A and B and calculating
the voltage across or current through the test source.

[edit]Example
Step 0:The original circuit
Step 1: Calculating the equivalent
output voltage
Step 2:Calculating the
equivalent resistance
Step 3:The
equivalent circuit
In the example, calculating the equivalent voltage:
(notice that R1 is not taken into consideration, as above
calculations are done in an open circuit condition between A
and B, therefore no current flows through this part, which
means there is no current through R1 and therefore no voltage
drop along this part)
Calculating equivalent resistance:

[edit]
Kirchhoff's current law (KCL)
The current entering any junction is equal to the current leaving that junction. i1 + i4 = i2 + i3
This law is also called Kirchhoff's first law, Kirchhoff's point rule, Kirchhoff's junction
rule (or nodal rule), and Kirchhoff's first rule.
The principle of conservation of electric charge implies that:
At any node (junction) in an electrical circuit, the sum of currents flowing into that node is
equal to the sum of currents flowing out of that node.
or
The algebraic sum of currents in a network of conductors meeting at a point is zero.
Recalling that current is a signed (positive or negative) quantity reflecting direction
towards or away from a node, this principle can be stated as:
n is the total number of branches with currents flowing towards or away from the
node.
This formula is valid for complex currents:

The law is based on the conservation of charge whereby the charge (measured
in coulombs) is the product of the current (in amperes) and the time (in
seconds).
Kirchhoff's voltage law (KVL)
The sum ofall the voltages around the loop is equal to zero. v1 + v2 + v3 - v4 = 0
This law is also called Kirchhoff's second law, Kirchhoff's loop (or mesh) rule,
and Kirchhoff's second rule.
The principle of conservation of energy implies that
The directed sum of the electrical potential differences (voltage) around any closed
circuit is zero.
or
More simply, the sum of the emfs in any closed loop is equivalent to the sum of the
potential drops in that loop.
or
The algebraic sum of the products of the resistances of the conductors and the currents
in them in a closed loop is equal to the total emf available in that loop.

Similarly to KCL, it can be stated as:
Here, n is the total number of voltages measured. The voltages may also be
complex:
This law is based on the conservation of "energy given/taken by potential
field" (not including energy taken by dissipation). Given a voltage potential,
a charge which has completed a closed loop doesn't gain or lose energy as
it has gone back to initial potential level.
This law holds true even when resistance (which causes dissipation of
energy) is present in a circuit. The validity of this law in this case can be
understood if one realizes that a charge in fact doesn't go back to its starting
point, due to dissipation of energy. A charge will just terminate at the
negative terminal, instead of positive terminal. This means all the energy
given by the potential difference has been fully consumed by resistance
which in turn loses the energy as heat dissipation.
To summarize, Kirchhoff's voltage law has nothing to do with gain or loss of
energy by electronic components (resistors, capacitors, etc.). It is a law
referring to the potential field generated by voltage sources. In this potential
field, regardless of what electronic components are present, the gain or loss
in "energy given by the potential field" must be zero when a charge
completes a closed loop.
Ohm's law
From Wikipedia, the free encyclopedia
This article is about the law related to electricity. For other uses, see Ohm's acoustic law.

V, I, and R, the parameters ofOhm's law.
Ohm's law states that the current through a conductor between two points is
directly proportional to the potential difference across the two points. Introducing the constant of
proportionality, the resistance,[1]
one arrives at the usual mathematical equation that describes
this relationship:[2]
where I is the current through the conductor in units of amperes, V is the potential difference
measured across the conductor in units of volts, and R is theresistance of the conductor in
units of ohms. More specifically, Ohm's law states that the R in this relation is constant,
independent of the current.[3]
The law was named after the German physicist Georg Ohm, who, in a treatise published in
1827, described measurements of applied voltage and current through simple electrical
circuits containing various lengths of wire. He presented a slightly more complex equation
than the one above (see History section below) to explain his experimental results. The
above equation is the modern form of Ohm's law.

PrincipleofOperationoftheNPNandPNPTransistor
An npn transistor operation can be described in shorts strokes in the following brief sentences
as follows,
1. the base emitter junction is forward-biased by a base potential,
2. the forward-biasing action results in a small base current that is inputted to the transistor.
3. this small base current causes a large collector current to flow,
4. the collector current is  times the value of the base current,  being the current
amplification factor of the transistor,
5. base and collector current sums up to form the emitter current.
The principle of operation of a pnp transistor is similar to the npn transistor except that the
polarities of the voltages and current applied to the pnp transistor is opposite to that of the npn
transistor.
In the pnp transistor operation the following sequence of events take place

1. the base emitter junction is forward-biased by a base potential,
2. the forward-biasing action results in a small base current that is drawn from the transistor
base,
3. this small base current causes a large collector current to flow,
4. the collector current is b times the value of the base current,
5. base and collector current sum up to form the emitter current.
Take note the base-emitter voltage (VBE) is now in the opposite that of the npn transistor. As a
result of this the base current is now drawn from the base instead of inputted to the base as was
the case for the npn transistor. Likewise the directions of emitter and collector current is now
opposite those for the npn transistor.
What remains the same are the following,
1. IC is still b times greater than IB or IC = b · IB.
2. IE is still the sum of currents IC and IB or,
IE = IC + IB.
The graphic highlights the contrast between operation of the npn and pnp transistor.

Resistor: As you could probably guess fromthe name, a resistor increases the
resistance of a circuit. The main purpose of this is to reduce the flow of electricity in
a circuit. Resistors come in all different shapes and sizes. They dissipate heat as a
result of their opposing electricity, and are therefore rated both in terms of their
resistance (how much they oppose the flow of electrons) and their power capacity
(how much power they can dissipate before becoming damaged.) Generally, bigger
resistors can handle more power. There are also variable resistors, which can have
their resistance adjusted by turning a knob or other device. These are sometimes
called potentiometers
Capacitor: A capacitoris a component made fromtwo (or two sets of)conductive
plates with an insulator between them. The insulator prevents the plates from
touching. When a DC current is applied across a capacitor,positive charge builds on
one plate (or set of plates) and negative charge builds on the other. The charge will
remain until the capacitoris discharged. When an AC current is applied across the
capacitor,it will charge one set of plates positive and the other negative during the
part of the cycle when the voltage is positive; when the voltage goes negative in the
second half of the cycle, the capacitorwill release what it previously charged, and
then charge the opposite way. This then repeats for eachcycle. Since it has the
opposite charge stored in it each time the voltage changes, it tends to oppose the
change in voltage. As you cantell then, if you apply a mixed DC and AC signal across
a capacitor,the capacitorwill tend to block the DC and let the AC flow through. The

strength of a capacitoris called capacitance and is measured in farads (F). (In
practical terms, usually microfarads and the like, since one faradwould be a very
large capacitor!)They are used in all sorts of electronic circuits, especially combined
with resistors and inductors, and are commonly found in PCs.
Inductor: An inductor is essentially a coil of wire. When current flows through an
inductor, a magnetic field is created, and the inductor will store this magnetic energy
until it is released. In some ways, an inductor is the opposite of a capacitor. While a
capacitor stores voltage as electrical energy, an inductor stores current as magnetic
energy. Thus, a capacitoropposes a change in the voltage of a circuit, while an
inductor opposes a change in its current. Therefore, capacitors block DC current and
let AC current pass, while inductors do the opposite. The strength of an inductor is
called--take a wild guess--its inductance, and is measured in henrys (H). Inductors can
have a core of air in the middle of their coils, or a ferrous (iron) core. Being a
magnetic material, the iron core increases the inductance value, which is also
affectedby the material used in the wire, and the number of turns in the coil. Some
inductor cores are straight in shape, and others are closed circles called toroids. The
latter type of inductor is highly efficient because the closed shape is conducive to
creating a stronger magnetic field. Inductors are used in all sorts of electronic
circuits, particularly in combination with resistors and capacitors, and are commonly
found in PCs.
A Zener diode is a special kind of diode which allows current to flow in the forward direction in
the same manner as an ideal diode, but will also permit it to flow in the reverse direction when
the voltage is above a certain value known as the breakdown voltage, "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 due to overheating. In the case of a
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 close to the Zener breakdown
voltage. For example, a diode with a Zener breakdown voltage of 3.2 V will exhibit a voltage
drop of very nearly 3.2 V across a wide range of reverse currents. 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 time
Current-voltage characteristic ofa Zener diode with a breakdown voltage of 17 volts. Notice the change of voltage
scale between the forward biased (positive) direction and the reverse biased (negative) direction.
property.

In a 5.6 V diode,
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".

s the coefficient of a 12 V diode.
Current-voltage characteristic ofa Zener diode with a breakdown voltage of 17 volts. Notice the change of voltage
scale between the forward biased (positive) direction and the reverse biased (negative) direction.
property.

In a 5.6 V diode,
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".

Load line (electronics)
FromWikipedia,thefreeencyclopedia
Jump to: navigation, search
Diode load line.
A load line is used in graphic analysis of circuits, representing the constraint other
parts of the circuit place on a non-linear device, like a diode or transistor. A load line
represents the response of a linear circuit connected to the nonlinear device in
question. The operating point is where the parameters of the nonlinear device and the
parameters of the linear circuit match, according to how they are connected while still
adhering to their internal systems.[1]
In the example on the right, the nonlinear diode is placed in series with a linear circuit
consisting of a resistor and a voltage source. The load line represents the relationship
between current and voltage in the linear part of the circuit while the exponential
represents the relationship between current and voltage in the nonlinear device. Since

the current going through three elements in series should be the same, the operating
point of the circuit will be at the intersection of the exponential with the load line.
In a BJT circuit, the BJT has a different current-voltage (IC-VCE) characteristic
depending on the base current. Placing a series of these curves on the graph shows
how the base current will affect the operating point of the circuit.
The load line can be used for both dc and ac analysis. Once a dc operating point is
defined by the dc load line an ac load line with, in general, a different slope intersects
the dc operating point. In reality there are many ac load lines that vary from the dc
load line to a limiting load line all having a common intersection at the dc operating
point. This limiting load line is generally referred to ac the ac load line and is the load
line of the ac circuit (capacitors shorted, dc sources opened, etc...)
Different between dmosfet and emodfet:
An e-mosfet is and "enhancement" mosfet. A d-mosfet is a "depletion" mosfet. These essentially show what mode the
mosfet operates in when a voltage is applied to the gate. .
An enhancement mode mosfet is normally non-conducting but conducts when the
channel is enhanced by applying a voltage to the gate and pulling carriers into the
channel. A depletion mode mosfet normally conducts but becomes more and more
non-conducting as carriers are depleted or pulled out of the channel by applying a
voltage. The polarity of the voltage depends on whether it is an N channel or P
channel. P channel uses positively doped silicon while N channel uses negatively
doped silicon. N channel fets are used wherever possible because N material
conducts better than P material.
There are basically two types of fet, the jfet and the mosfet. The jfet uses a single
junction to control the channel hence draws some current. Bipolar transistors use
two junctions. In the mosfet (Metal Oxide Semiconducting Field Effect Transistor)
there is no such junction hence draw so little current for control purposes it can be
regarded as zero. The gate is isolated from the channel by a very thin layer of
metal oxide (usually chromium dioxide). An enhacement mode mosfet can be
turned on by applying a voltage then removing the wire to the gate. The channel
will then remain conducting for some time.
JFET operation
The junction gate field-effect transistor (JFET or JUGFET) is the simplest type
of field-effect transistor. It can be used as an electronically-controlledswitch or as a
voltage-controlled resistance. Electric charge flows through a semiconducting channel
between "source" and "drain" terminals. By applying a bias voltage to a "gate" terminal,
the channel is "pinched", so that the electric current is impeded or switched off
completely.

The JFET is a long channel of semiconductor material, doped to contain an abundance
of positive charge carriers (p-type), or of negative carriers (n-type). Contacts at each end formthe source(S) and
drain(D). The gate(G) (control) terminal has doping opposite to that of the channel, w hich surrounds it, so that there is a P-N
junction at the interface. Terminals to connect w ith the outside are usually made ohmic.
FunctionJFET operationis like thatof a garden hose. The flow of water through a hose can be controlled by
squeezingit to reduce the cross section; the flow of electric charge through a JFET is controlledby
constrictingthe current-carryingchannel. The currentalso depends on the electric field betweensource and drain
(analogous to the difference in pressure on either end of the hose)
Conductor, insulator, semiconductor
Solid-state materials can be classified into three groups: insulators, semiconductors and conductors. Insulators are
materials having an electrical conductivity (like diamond: 10-14S/cm); semiconductors have a
conductivity (for silicon it can range from 10-5S/cm to 103S/cm); at last conductors
are materials with high conductivities : (like silver: 106S/cm.)
The electrical properties of a given material depend on the electronic populations of the different allowed bands.
Electrical conduction is the result of electron motion within each band. When an electric field is applied to the material,
electrons start to move in the direction opposed to the direction of the electric field. An empty energy band (in which
there is no free electron) does not of course participate in the formation of an electric current. It is also the case for
a fully occupied band. Indeed, an electron can move provided that, whenever it leaves its site, it can find some free
space elsewhere (another available site within its energy band, called a “hole”), where it can go. A material with fully
occupied or empty energy bands is then an insulator. This is the case when the gap energy exceeds ~9eV, because
for such gaps, the thermal energy at 300K (~25 meV) is clearly insufficient to allow electrons from the valence band to
be promoted to the conduction band. In this case the valence band (and all bands of lower energy) is fully occupied,
and the conduction band is empty.

Figure 2 : Representation of energy bands
A semiconductor is primarily an insulator at 0K. However, since the energy gap is lower compared to insulators
(~1eV), the valence band is slightly thermally populated at room temperature, whereas the conduction band is slightly
depopulated. Since electrical conduction is directly connected to the number of electrons in the “almost empty”
conduction band and to the number of holes in the “almost fully occupied” valence band, it can be expected that the
electrical conductivity of such an intrinsic semiconductor will be very small.
For a conductor, conduction bands and valence bands are not separated and there is therefore no energy gap. The
conduction band is then partially occupied (even at low temperatures), resulting in a “high” electrical conductivity.

Maximum power transfer theorem

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Maximum power transfer theorem