Electronics and modern physics presentation

Topic:
Transistor Biasing for amplifiers
Noor-ul-ain

Transistor Biasing:
The process of applying a voltage and magnitude to the circuit
to ensure faithful amplification is known as transistor biasing.
OR
Transistor biasing is the proper flow of zero signal collector
current and the maintenance of proper collector emitter voltage
during the passage of signal.

FAITHFUL
AMPLIFICATION:
• For transistor biasing, first we should
have faithful amplification. It is the
process of increasing the strength of
weak signal with not any change in its
general shape is known as faithful
amplification.
• For biasing by input signal and faithful
amplification, it is necessary that:
1. proper zero signal collector current
2. Proper Minimum VBE at any instant
3. Proper Minimum VCE at any instant

Proper zero signal
collector current:
• When no input signal is applied, the d.c
current Ic will flow in the collector circuit
due to VBB as shown this is known as zero
signal collector circuit.
• The value of zero signal collector
current should be at least equal to the
maximum collector current due to
AC signal alone.
• Illustration:
• suppose the signal applied to the base of
transistor give peak collector current of 1
milliampere. Now, the zero current should be
equal to 1 mA otherwise there is a cutoff
voltage.

Proper Minimum VBE:
• In order to achieve faithful amplification, VBE should not fall below 0.5 V for
germanium and 0.7 V for silicon transistors. The base current is very small until
the input voltage overcomes the potential barrier at the base-emitter junction.
Once the potential barrier is overcome, the base current and hence collector
current increases sharply. But below potential barrier, the output is not properly
biased, and results in unfaithful amplification.
• Therefore, if base-emitter voltage VBE falls below these values during any part of
the signal, that part will be amplified to lesser extent due to small collector
current. This will result in unfaithful amplification.

Proper
Minimum VCE:
• For faithful amplification,
the collector-emitter
voltage VCE should not fall
below 0.5V for Ge
transistors and 1V for
silicon transistors. This is
called knee voltage.
Otherwise, it is forward
biased and instead of
attracting VCE it repel VCE.
• The value of VCE should
not be less than input
signal, otherwise it is not
amplified.

Stabilization:
The collector current IC in a transistor changes rapidly when
a) Temperature changes
b) Transistor is replaced by another of the same type. This is due to the
inherent variations (𝛽 − 𝑣𝑎𝑙𝑢𝑒) of transistor parameters.
When the temperature changes or the transistor is replaced, the operating
point also changes. However for faithful amplification, it is essential that
operating point remains fixed. This needs to make the operating point
independent of these variations. This is known as stabilization.
“The process of making operating point (zero signal IC and VBE)
independent of temperature changes and variations in transistor parameters is
called stabilization”.
Need for stabilization:
Stabilization of the operating point is necessary due to the following reasons:
(i) Individual variations (iii) Thermal runaway
(ii) Temperature dependence of IC

Temperature dependence of IC:
• The collector leakage current ICBO is greatly influenced (especially in
germanium transistor) by temperature changes. A rise of 10°C doubles
the collector leakage current ICBO which may be as high as 0.2 mA for
low powered germanium transistors. So, it also increases the IC.
IC = β IB + (β + 1) ICBO
Thermal runaway:
The self-destruction of unstabilised transistor is called thermal runaway.
The flow of IC produces heat in the transistor , which increases
temperature ,and it increases ICBO and it will increase the IC again. And
this process repeat again, and in few minutes , increase in IC will burn the
transistor.
To avoid thermal runaway, we decrease IB with temperature and IB
compensate the leakage current and it makes IC constant.

Stability factor:
The rate of change of collector current IC with respect to the
collector leakage current ICO at constant β and IB is called Stability
factor.
S = d IC / d ICO
IC =β IB + (β + 1) ICO
1 = β d IB / d Ic + (β + 1) d ICO / d Ic
1 = β d IB / d Ic + (β + 1) / S ⸪ 1/S = d ICO/ d Ic
S =
𝛽+1
1−𝛽
ⅆ𝐼𝑏
ⅆ𝐼𝑐

There are four methods of transistor biasing for an amplifier.
1) Base resister method .
2) Emitter Base method.
3) Biasing with collector feedback method.
4) Voltage divider bias
Methods of Transistor Biasing:

Base resistor method:
In this method, a high resistance RB
(several hundred kilo ohm) is connected
between the base and positive end of
supply for npn transistor. For pnp
transistor, RB is connected between the
base and negative end of supply. Here,
required zero signal base current is
provided by VCC and it flows through RB
. The base is positive w.r.t emitter. Base
emitter junction is forward biased. We
use the value of RB to get the value of
zero signal base current.
IC = β IB

Circuit Analysis:
To find RB , Collector current flows in the zero signal condition is required: Let
IC is a required zero signal collector current. Consider ABENA a closed circuit.
Now we apply Kirchhoff's voltage law,
VCC = IB RB + VBE
or IB RB = VCC – VBE
⸫ RB =
VCC – VBE
IB
VBE is very small as compared to VCC , then we neglect it:
RB =
VCC
IB
VCC is a known quantity and IB is chosen at some suitable value. Here, RB can
calculate directly and for this reason this method is sometimes called fixed
biased method.

Stability factor:
From above circuit:
(i)
In this method rate of change of IB is independent of rate of change of IC so that
dIB/dIC = 0. putting this value in above equation (i), we get:
Stability factor, S = β + 1
Thus the stability factor in a fixed bias is (β + 1). This means that IC changes
(β + 1) times as much as any change in ICO .

Advantages:
 The biasing circuit is very simple as only one resistor is used.
 Biasing conditions are easy to set and calculations are simple.
 There is no loading of the source by the biasing circuit since no resistor is
employed across base-emitter junction.
DISADVANTAGES:
 This method has poor stabilization. It is because there is no mean to stop a
self increase in collector current due to temperature rise and individual
variations.
 The stability factor is very high. Therefore, there are strong chances of
thermal runaway.
Due to these disadvantages, this method of biasing is rarely active.

Emitter bias method:
In this method, we use base
resistor RB, collector resistor RC and
emitter resistor RE. This circuit differs
from base-bias circuit in two
important respects.
• It uses two d.c voltage sources; one
positive (+VCC), other is negative
(-VEE). Normally these two voltages
are equal.
• There is a resistor RE in the emitter
circuit.

Condensed Diagram:
Now we redraw the circuit as it
usually appears on schematic
diagrams. It means deleting the
battery symbols. This is the reduced
form of emitter-bias circuit. In a
condensed diagram, we deleted
battery symbols. Here, a negative
supply voltage –VEE is applied to the
bottom of RE and a positive voltage
of +VCC to the top of RC.

Circuit Analysis:
Finding the Q-point values (i.e. d.c IC and d.c VCE) for this circuit.
a) Collector current (IC).
Appling Kirchhoff's voltage law to above circuit, we have:
- IB RB – VBE – IE RE + VEE = 0
⸫ VEE = IB RB + VBE + IE RE
Now IC ≃ IE and IC = β IB ⸫
IB ≃
IE
β
Putting IB = IE /β in the above equation, we have,
VEE =
IE
β
RB + IE RE + VBE
or VEE – VBE = IE
RB
β
+ R𝐸
⸫ IE =
VEE – VBE
RE + RB
β
Since IC ≃ IE , then, ⇒ IC =
VEE – VBE
RB

b) Collector Emitter voltage (VCE).
This circuit shows the various voltages of
the emitter bias circuit with respect to
ground.
Emitter voltage is:
VE = −VEE + IE RE
Base voltage is:
VB = VE + VBE
Collector voltage is:
VC = VCC − IC RC
Subtracting VE from VC ,
VC – VE = VCC − IC RC − −VEE + IE RE
Using the approximation IC ≃ IE , we have,
VC – VE = VCC − IC RC − −VEE + IC RE
VCE = VCC − IC RC + VEE − IC RE
or VCE = VCC + VEE – IC (RC + RE)

Alternatively.
Applying Kirchhoff's voltage law to the
collector side of the emitter bias circuit,
VCC − IC RC − VCE − IE RE − (−VEE) = 0
VCC − IC RC − VCE − IE RE + VEE = 0
VCC − IC RC − VCE − IC RE + VEE = 0
⸪ IC ≃ IE
VCC − IC RC − IC RE + VEE = VCE
VCC − IC RC + RE + VEE = VCE
VCE = VCC + VEE – IC RC + RE

Stability factor:
The expression for the collector current IC for the emitter bias circuit is:
IC ≃ IE =
VEE – VBE
RE + RB
β
It is clear that IC is dependent on VBE and β, both changes with temperature.
If RE ≫ RB /β, then expression for IC becomes:
IC =
VEE – VBE
RE
This condition makes IC independent of β.
If VEE ≫ VBE then IC becomes:
IC =
VEE
RE
This condition makes IC independent of VBE.
If IC is independent of β and VBE, the Q-point is not affected by the variations in
these parameters. Thus emitter bias can provide stable Q-point if properly
designed.

Biasing with collector feedback Resistor:
In this method, one end of RB is
connected to the base and the
other end to the collector. Here the
required zero signal base current is
determined not by VCC but by the
collector-base voltage VCB . It is
clear that VCB forward biases the
base emitter junction and hence
base current IB flows through RB.
This causes the zero signal
collector current to flow in the
circuit.

Circuit Analysis:
The required value of RB needed to give the zero signal current IC can be
determined as follows. Referring to the given figure,
VCC = IC RC + IB RB + VBE
or RB =
VCC – VBE – IC RC
IB
RB =
VCC – VBE – β IB RC
IB
( ⸪
IC = β IB )
Alternatively,
VCE = VBE + VCB
or VCB = VCE – VBE
⸪ RB =
VCB
IB
=
VCE – VBE
IB
where IB =
IC
β
Mathematically, here stability factor S for this method is less than (β + 1) i.e.
Stability factor, S < (β + 1)
Therefore, this method provides better stability than the fixed bias.

Advantages:
• It is a simple method as it requires only one resistance RB .
• This circuit provides some stabilization of the operating point as discussed
below:
VCE = VBE + VCB
Suppose the temperature increases. This will increase collector leakage
current and hence the total collector current. But as soon as collector current
increase, VCB decrease i.e. lesser voltage is available across RB . Hence the base
current IB decreases. The smaller IB tends to decrease the collector current to
original value.

Disadvantage:
• The circuit does not provide good stabilization because stability factor is
fairly high, though it is lesser than that of fixed bias. Therefore, the
operating point does change, although to lesser extent, due to temperature
variations and other effects.
• This circuit provides a negative feedback which reduces the gain of the
amplifier as explained hereafter. During the positive half-cycle of the
signal, the collector current increases. The increased collector current
would result in greater voltage drop across RC. This will reduce the base
current and hence collector current.

Stability of Q-point:
We know that β varies directly with temperature and 𝑉𝐵𝐸 varies inversely
with temperature. As the temperature goes up, β goes up and 𝑉𝐵𝐸 goes down.
The increase in β increases 𝐼𝐶 (= β 𝐼𝐵) . The decrease in 𝑉𝐵𝐸 increases 𝐼𝐵which
in turn increases 𝐼𝐶. As 𝐼𝐶 tries to increase, the voltage drop across 𝑅𝐶 (= 𝐼𝐶𝑅𝐶)
also tries to increases. This tends to reduce collector voltage 𝑉𝐶 and, therefore,
the voltage across 𝑅𝐵. The reduced voltage across 𝑅𝐵 reduces 𝐼𝐵 and offsets the
attempted increases in 𝐼𝐶 and attempted decrease in 𝑉𝐶. The result is that the
collector feedback circuit maintains a stable Q-point. The reverse action occurs
when the temperature decreases.

Voltage Divider Bias Method:
This is the most widely used
method of providing biasing and
stabilization to a transistor. In this
method, two resistances 𝑅1 and
𝑅2 are connected across the supply
voltage 𝑉𝐶𝐶 (See Fig.) and provide
biasing. The emitter resistance
𝑅𝐿 provides stabilization. The name
“voltage divider” comes from the
voltage divider formed by 𝑅1 and
𝑅2 . The voltage drop across 𝑅2
forward biases the base-emitter
junction. This causes the base current
and hence collector current flow in
the zero signal conditions.

Circuit Analysis:
Suppose that the current flowing through resistance 𝑅1 is 𝐼1 . As base current
𝐼𝐵 is very small, therefore, it can be assumed with reasonable accuracy that
current flowing through R2 is also I1 .
a) Collector current (IC).
I1 =
VCC
R1+R2
⸪ Voltage across resistance R2 is: V2 = I1 R2
V2 =
VCC
R1+R2
R2
Appling Kirchhoff's voltage law to the base circuit of figure:
V2 = 𝑉𝐵𝐸 + 𝑉𝐸
or V2 = VBE + IE RE
or IE =
V2 − VBE
RE
Since IE ≃ IC
⸪ IC =
V2 − VBE
RE
(i)

b) Collector-Emitter Voltage (VCE).
It is clear from above eq. (i) IC does not depends upon β. But IC depends upon
𝑉𝐵𝐸.
If 𝑉2 ≫ 𝑉𝐵𝐸 then IC is practically independent of 𝑉𝐵𝐸. Thus IC in this circuit is
almost independent of transistor parameters. This ensures good stabilization.
Due to this reason, potential divider bias has become universal method for
providing transistor biasing.
Applying Kirchhoff’s voltage law to the collector side of the circuit,
VCC = IC RC + VCE + IE RE
VCC = IC RC + VCE + IC RE (⸪
IE ≃ IC)
VCC = IC RC + RE + VCE
⸪ VCE = VCC − IC RC + RE

Stabilisation:
In this circuit, excellent stabilisation is provided by RE. Consider the equation
of collector current.{eq.(i)}
IC =
V2 − VBE
RE
V2 = VBE + IC RE
Suppose the collector current IC increases due to rise in temperature. This will
cause the voltage drop across emitter resistance RE to increase. As voltage drop
across R2 (i.e.V2) is independent of IC, therefore, VBE decreases. This causes IB to
decreases. The reduced value of IB tends to restore IC to the original value.

Stability factor:
Applying Kirchhoff’s voltage law to the
base circuit,
Considering VBE to be constant and
differentiating the above equation with
respect to IC ,
(i)

The general expression for stability factor is
Putting the value of from eq. (i) into the expression for S,
Dividing the numerator and denominator of R.H.S of above equation by RE,
(ii)
This equation gives the formula of stability factor S for potential divider bias

Two points should be noted here;
(i) For greater thermal stability, the value of S should be small. We can get this
by making small. If is made very small, then it can be neglected
as compared to 1.
⸪
This is an ideal value of S and leads to the maximum thermal stability.
(ii) The ratio can be made very small by decreasing R0 and increasing
RE. Low value of R0 can be obtained by making R2 very small. But with low
value of R2 , current drawn from VCC will be large. This puts the restriction on
the value of R0. Increasing the value of RE requires greater VCC in order in order
to maintain the same zero signal collector current. Due to these limitations, a
compromise is made in the selection of the values of R0 and RE. Generally, these
values are so selected that S ≃ 10.

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