Transistor
DC Biasing Circuits
Pictures are redrawn (with some modifications) from
Introductory Electronic Devices and Circuits
1
Objectives
• State the purpose of dc biasing circuits.
• Plot the dc load line given the value of VCC and
the total collector-emitter circuit resistance.
• Describe the Q-point of an amplifier.
• Describe and analyze the operations of various
bias circuits:
–
–
–
–
–
base-bias circuits
voltage-divider bias circuits
emitter-bias circuits
collector-feedback bias circuits
emitter-feedback bias circuits
2
Transistor Biasing
The basic function of transistor is amplification. The process of
raising the strength of weak signal without any change in its
general shape is referred as faithful amplification. For faithful
amplification it is essential that:1.
2.
3.
Emitter-Base junction is forward biased
Collector- Base junction is reversed biased
Proper zero signal collector current
The proper flow of zero signal collector current and
the maintenance of proper collector emitter voltage
during the passage of signal is called transistor
biasing.
3
WHY BIASING?
If the transistor is not biased properly, it would work
inefficiently and produce distortion in output signal.
HOW A TRANSISTOR CAN BE BIASED?
A transistor is biased either with the help of battery or
associating a circuit with the transistor. The later method is
more efficient and is frequently used. The circuit used for
transistor biasing is called the biasing circuit.
4
BIAS STABILITY
 Through proper biasing, a desired quiescent operating point of the
transistor amplifier in the active region (linear region) of the
characteristics is obtained. It is desired that once selected the operating
point should remain stable. The maintenance of operating point stable is
called Stabilisation.
 The selection of a proper quiescent point generally depends on the
following factors:
(a) The amplitude of the signal to be handled by the amplifier and
distortion level in signal
(b) The load to which the amplifier is to work for a corresponding
supply voltage
 The operating point of a transistor amplifier shifts mainly with changes
in temperature, since the transistor parameters — β, ICO and VBE (where
the symbols carry their usual meaning)—are functions of temperature.
5
The DC Operating Point
For a transistor circuit to amplify it must be properly biased with dc
voltages. The dc operating point between saturation and cutoff is
called the Q-point. The goal is to set the Q-point such that that it
does not go into saturation or cutoff when an a ac signal is applied.
6
Requirements of biasing network
• Ensuring proper zero signal collector current.
• Ensuring VcE not falling below 0.5V for Ge transistor and 1V for
Silicon transistor at any instant.
• Ensuring Stabilization of operating point. (zero signal IC and VcE)
7
The Thermal Stability of Operating Point (SIco)
Stability Factor S:- The stability factor S, as the change of collector
current with respect to the reverse saturation current, keeping β and
VBE constant. This can be written as:
The Thermal Stability Factor : SIco
SIco = ∂Ic
∂Ico
Vbe, β
This equation signifies that Ic Changes SIco times as fast as Ico
Differentiating the equation of Collector Current IC = (1+β)Ico+ βIb &
rearranging the terms we can write
SIco ═ 1+β
1- β (∂Ib/∂IC)
It may be noted that Lower is the value of S Ico better is the stability
8
Various Biasing Circuits
•
•
•
•
Fixed Bias Circuit
Fixed Bias with Emitter Resistor
Collector to Base Bias Circuit
Potential Divider Bias Circuit
9
Fig 7.1 Typical amplifier operation.
VCC
VB(ac)
IB(ac)
RC
RB
Q1
VCE(ac)
IC(ac)
10
Fig 7.2 A generic dc load line.
IC
I C (sat) 
VCC  VCE
IC 
RC
VCC
RC
VCE (off )  VCC
VCE
11
Fig 7.3 Example 7.1.
Plot the dc load line for the circuit
shown in Fig. 7.3a.
+12 V
IC
RC
2 k
RB
8
IC(sat)
6
Q1
4
VCE(off)
2
2
4
6
8
10
12
VCE
12
Fig 7.4 Example 7.2.
Plot the dc load line for the circuit shown in
Fig. 7.4. Then, find the values of VCE for IC =
1, 2, 5 mA respectively.
+10 V
IC
VCE  VCC  IC RC
RC
1 k
RB
Q1
10
IC (mA)
VCE (V)
8
1
9
6
2
8
4
5
5
2
2
4
6
8
10
VCE
13
Fig 7.6-8 Optimum Q-point with
amplifier operation.
IC
IC(sat)
IB = 50 A
IC  βI B
IC(sat)/2
IB
IB = 40 A
IB = 30 A
Q-Point
IB = 20 A
IB = 10 A
VCC/2
VCC
IB = 0 A
VCE
VCE  VCC  IC RC
14
Fig 7.9 Base bias (fixed bias).
VCC
IC
VCC  VBE
IB 
RB
RB
Output
IB
Input
IC  βI B
RC
VCE  VCC  IC RC
Q1
+0.7 V
VBE
b = dc current gain = hFE
IE
15
Fig 7.10 Example 7.3.
VCC  0.7V 8V  0.7V
IB 

RB
360kΩ
+8 V
 20.28μA
IC
RC
2 k
RB
360 k
 2.028mA
VCE  VCC  I C RC
IB
hFE = 100
+0.7 V
VBE
I C  hFE I B  100  20.28μA 
 8V   2.028mA  2kΩ 
 3.94V
IE
The circuit is midpoint biased.
16
Fig 7.11 Example 7.4.
Construct the dc load line for the circuit shown in Fig. 7.10,
and plot the Q-point from the values obtained in Example
7.3. Determine whether the circuit is midpoint biased.
IC (mA)
I C (sat)
4
VCC
8V


 4mA
RC 2kΩ
VCE  off   VCC  8V
3
Q
2
1
2
4
6
8
10
VCE (V)
17
Fig 7.12 Example 7.6. (Q-point shift.)
The transistor in Fig. 7.12 has values of hFE = 100 when T =
25 °C and hFE = 150 when T = 100 °C. Determine the Qpoint values of IC and VCE at both of these temperatures.
+8 V
I
RB C
360 k
IB
+0.7 V
VBE
RC
2 k
Temp(°C)
25
IB (A)
20.28
IC (mA)
2.028
VCE (V)
3.94
100
20.28
3.04
1.92
hFE = 100 (T = 25C)
hFE = 150 (T = 100C)
IE
18
Fig 7.13 Base bias characteristics. (1)
VCC
IC
Circuit recognition: A single resistor
(RB) between the base terminal and
VCC. No emitter resistor.
RC
RB
Output
IB
Input
Q1
+0.7 V
VBE
Advantage: Circuit simplicity.
Disadvantage: Q-point shift with temp.
IE
Applications: Switching circuits only.
19
Fig 7.13 Base bias characteristics. (2)
VCC
IC
Load line equations:
RC
VCE (off )  VCC
RB
Output
IB
Input
Q1
+0.7 V
VBE
I C (sat )
VCC

RC
IE
Q-point equations:
VCC  VBE
IB 
RB
I C  hFE I B
VCE  VCC  I C RC
20
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.
• 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.
• For small-signal transistors (e.g., not power transistors) with
relatively high values of β (i.e., between 100 and 200), this
configuration will be prone to thermal runaway. In particular, the
stability factor, which is a measure of the change in collector
current with changes in reverse saturation current, is approximately
β+1. To ensure absolute stability of the amplifier, a stability factor of
less than 25 is preferred, and so small-signal transistors have large
stability factors.
Usage:
• Due to the above inherent drawbacks, fixed bias is rarely used in
linear circuits (i.e., those circuits which use the transistor as a
current source). Instead, it is often used in circuits where
transistor is used as a switch. However, one application of fixed
bias is to achieve crude automatic gain control in the transistor by
feeding the base resistor from a DC signal derived from the AC
output of a later stage.
The Potential Divider Bias Circuit
This is the most commonly used arrangement for biasing as it provide good
bias stability. In this arrangement the emitter resistance ‘RE’ provides
stabilization. The resistance ‘RE’ cause a voltage drop in a direction so as to
reverse bias the emitter junction. Since the emitter-base junction is to be
forward biased, the base voltage is obtained from R1-R2 network. The net
forward bias across the emitter base junction is equal to VB- dc voltage drop
across ‘RE’. The base voltage is set by Vcc and R1 and R2. The dc bias
circuit is independent of transistor current gain. In case of amplifier, to avoid
the loss of ac signal, a capacitor of large capacitance is connected across
RE. The capacitor offers a very small reactance to ac signal and so it passes
through the condensor.
23
Fig 7.14 Voltage divider bias. (1)
+VCC
Assume that I2 > 10IB.
VB 
I1
R1
IC
RC
IB
I2
R2
VE  VB  0.7V
Output
Input
IE
RE
R2
VCC
R1  R2
IE 
VE
RE
Assume that ICQ  IE (or
hFE >> 1). Then
VCEQ  VCC  ICQ  RC  RE 
24
Fig 7.15 Example 7.7. (1)
Determine the values of ICQ and VCEQ for the circuit shown in Fig. 7.15.
+10 V
VB  VCC
R2
R1  R2
4.7kΩ
 2.07V
22.7kΩ
VE  VB  0.7V
 2.07V  0.7V  1.37V
 10V 
I1
IC
R1
18 k
RC
3 k
Because ICQ  IE (or hFE >> 1),
IB
hFE = 50
I2
R2
4.7 k
IE
RE
1.1 k
I CQ 
VE 1.37V

 1.25mA
RE 1.1kΩ
VCEQ  VCC  I CQ  RC  RE 
 10V  1.25mA  4.1kΩ   4.87V
25
Fig 7.15 Example 7.7. (2)
Verify that I2 > 10 IB.
+10 V
VB 2.07V
I2 

 440.4μA
R2 4.7kΩ
I1
IC
R1
18 k
RC
3 k
IE
1.25mA
IB 

hFE  1
50+1
 24.51μA
 I 2  10I B
IB
hFE = 50
I2
R2
4.7 k
IE
RE
1.1 k
26
Which value of hFE do I use?
Transistor specification sheet may list any
combination of the following hFE: max. hFE,
min. hFE, or typ. hFE. Use typical value if
there is one. Otherwise, use
hFE (ave)  hFE (min)  hFE (max)
27
Example 7.9
A voltage-divider bias circuit has the following values:
R1 = 1.5 k, R2 = 680 , RC = 260 , RE = 240  and
VCC = 10 V. Assuming the transistor is a 2N3904,
determine the value of IB for the circuit.
VB  VCC
R2
680Ω
 10V 
 3.12V
R1  R2
2180Ω
VE  VB  0.7V  3.12V  0.7V  2.42V
I CQ
VE 2.42V
 IE 

 10mA
RE 240Ω
hFE ( ave )  hFE (min)  hFE (max)  100  300  173
IB 
IE
10mA
 57.5μA
hFE (ave)  1 174

28
Stability of Voltage Divider
Bias Circuit
The Q-point of voltage divider bias circuit is less
dependent on hFE than that of the base bias (fixed
bias).
For example, if IE is exactly 10 mA, the range of hFE is
100 to 300. Then
At hFE  100, I B 
At hFE
IE
10mA

 100μA and I CQ  I E  I B  9.90mA
hFE  1
101
IE
10mA
 300, I B 

 33μA and I CQ  I E  I B  9.97mA
hFE  1
301
ICQ hardly changes over the entire range of hFE.
29
Fig 7.18 Load line for voltage
divider bias circuit.
IC (mA)
I C (sat)
25
VCC
10V


 20mA
RC  RE 260Ω+240Ω
20
Circuit values are from
Example 7.9.
15
10
VCE (off )  VCC  10V
5
2
4
6
8
10
12
VCE (V)
30
Fig 7.19-20 Base input resistance. (1)
VCC
VE  I E RE  I B (hFE  1) RE
VCC
RIN (base)
I1
R1
IC
RC
I1
I2
R2
IE
RIN(base)
RE
I2
 hFE RE
R1
IB
R2
VE

 (hFE  1) RE
IB
0.7 V
IB
May be ignored.
RIN(base)
31
Fig 7.19-20 Base input resistance. (2)
VCC
I1
VB 

R1
IB
I2
R2
VB
IB

R2 // RIN (base)
R1  R2 // RIN (base)
R2 //  hFE RE 
VCC
R1  R2 //  hFE RE 
REQ
R1  REQ
VCC
VCC
REQ  R2 //  hFE RE 
RIN(base)
32
Fig 7.21 Example 7.11.
VCC=20V
REQ  R2 //  hFE RE 
 10kΩ//  50 1.1kΩ   8.46kΩ
VB  VCC
I1
R1
68k
IC
RC
6.2k
hFE = 50
I2
R2
10k
IE
RE
1.1k
REQ
R1  REQ
8.46kΩ
  20V 
 2.21V
68kΩ  8.46kΩ
I CQ  I E 

VE VB  0.7V

RE
RE
2.21V  0.7V
 1.37mA
1.1kΩ
VCEQ  VCC  I CQ  RC  RE 
 20V  1.37mA  7.3kΩ   9.99V
33
Fig 7.24 Voltage-divider bias
characteristics. (1)
+VCC
Circuit recognition: The
voltage divider in the base
circuit.
I1
R1
IC
RC
IB
Output Disadvantages: Requires
more components than most
other biasing circuits.
Input
I2
R2
Advantages: The circuit Qpoint values are stable
against changes in hFE.
IE
RE
Applications: Used primarily
to bias linear amplifier.
34
Merits:
• 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.
Usage:
The circuit's stability and merits as above make it widely used for linear
circuits.
Fig 7.24 Voltage-divider bias
characteristics. (2)
+VCC
VCC
Load line I

equations: C (sat ) RC  RE
VCE (off )  VCC
I1
R1
IC
RC
IB
Q-point equations (assume
that hFERE > 10R2):
Output
VB  VCC
R2
R1  R2
VE  VB  0.7V
Input
I2
R2
IE
RE
I CQ  I E 
VE
RE
VCEQ  VCC  I CQ  RC  RE 
36
Other Transistor Biasing
Circuits
• Emitter-bias circuits
• Feedback-bias circuits
– Collector-feedback bias
– Emitter-feedback bias
37
Fig 7.25-6 Emitter bias.
+VCC
IC
Assume that the transistor
operation is in active region.
VEE  0.7V
IB 
RB   hFE  1 RE
RC
IB
Q1
Input
Output
IC  hFE I B
I E   hFE  1 I B
VCE  VCC  IC RC  I E RE  VEE
RB
RE
IE
Assume that hFE >> 1.
VCE  VCC  IC  RC  RE   VEE
-VEE
38
Fig 7.27 Example 7.12.
+12 V
Determine the
values of ICQ and
VCEQ for the
amplifier shown in IC
Fig.7.27.
IB
IB 
RC
750

12V  0.7V
RB  (hFE  1) RE
11.3V
 37.47μA
100Ω+2011.5kΩ
I CQ  hFE I B  200  37.47μA
 7.49mA
Q1
Output
VCEQ  VCC  I C  RC  RE   (VEE )
hFE = 200
 24V  7.49mA  750Ω  1.5kΩ 
Input
RB
100
IE
RE
1.5k
-12 V
 7.14V
39
Load Line for
Emitter-Bias Circuit
IC
I C (sat)
IC(sat)
VCC  (VEE ) VCC  VEE


RC  RE
RC  RE
VCE (off )  VCC   VEE   VCC  VEE
VCE(off)
VCE
40
Fig 7.28 Emitter-bias
characteristics. (1)
+VCC
IC
Circuit recognition: A split (dualpolairty) power supply and the base
resistor is connected to ground.
RC
IB
Q1
Input
RB
RE
IE
-VEE
Advantage: The circuit Q-point
values are stable against changes in
hFE.
Output
Disadvantage: Requires the use of
dual-polarity power supply.
Applications: Used primarily to bias
linear amplifiers.
41
Fig 7.28 Emitter-bias
characteristics. (2)
+VCC
IC
Load line equations:
I C (sat )
RC
VCC  VEE

RC  RE
VCE (off )  VCC  VEE
IB
Q1
Input
Output
Q-point equations:
I CQ
RB
RE
IE
-VEE
VBE  VEE
  hFE 
RB   hFE  1 RE
VCEQ  VCC  I CQ  RC  RE   VEE
42
The Collector to Base Bias Circuit
VCC
RC
Ic
RF
C
Ib
This
configuration
employs
negative
feedback to prevent thermal runaway and
stabilize the operating point. In this form of
biasing, the base resistor RF 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.
B
+ V
BE
-
EI
E
43
Fig 7.29 Collector-feedback
bias.
+VCC
RC
RB
IB
IC
VCC   IC  I B  RC  I B RB  VBE
VCC  VBE
IB 
(hFE  1) RC  RB
ICQ  hFE I B
VCEQ  VCC   hFE  1 I B RC
 VCC  I CQ RC
IE
44
Fig 7.30 Example 7.14.
+10 V
RC
1.5 k
RB
180 k
hFE = 100
Determine the values of ICQ and VCEQ for the
amplifier shown in Fig. 7.30.
VCC  VBE
IB 
RB   hFE  1 RC
10V  0.7V

 28.05μA
180kΩ  1011.5kΩ
I CQ  hFE I B  100  28.05μA
 2.805mA
VCEQ  VCC  (hFE  1) I B RC
 10V  101 28.05μA 1.5kΩ
 5.75V
45
Circuit Stability of
Collector-Feedback Bias
+VCC
hFE increases
IC increases (if IB is the same)
RC
RB
IB
VCE decreases
IC
IE
IB decreases
IC does not increase that much.
Good Stability. Less dependent
on hFE and temperature.
46
Collector-Feedback
Characteristics (1)
+VCC
RC
RB
IB
Circuit recognition: The base
resistor is connected between
the base and the collector
terminals of the transistor.
Advantage: A simple circuit
with relatively stable Q-point.
IC
IE
Disadvantage: Relatively poor
ac characteristics.
Applications: Used primarily to
bias linear amplifiers.
47
Collector-Feedback
Characteristics (2)
+VCC
Q-point relationships:
IB 
RC
RB
IB
IC
VCC  VBE
(hFE  1) RC  RB
ICQ  hFE I B
VCEQ  VCC  ICQ RC
IE
48
Fig 7.31 Emitter-feedback bias.
+VCC
RB
IC
RC
IB 
VCC  VBE
RB   hFE  1 RE
ICQ  hFE I B
I E   hFE  1 I B
IB
VCEQ  VCC  I C RC  I E RE
IE
RE
 VCC  I CQ  RC  RE 
49
Fig 7.32 Example 7.15.
+VCC
IB 
VCC  VBE
16V  0.7V

RB   hFE  1 RE 680kΩ  511.6kΩ
 20.09μA
RB
680k
RC
6.2k
ICQ  hFE I B  50  20.09μA  1mA
VCEQ  VCC  I CQ  RC  RE 
 16V  1mA  7.8kΩ   8.2V
hFE = 50
RE
1.6k
50
Circuit Stability of
Emitter-Feedback Bias
+VCC
hFE increases
IC increases (if IB is the same)
RB
IC
RC
VE increases
IB
IB decreases
IE
RE
IC does not increase that much.
IC is less dependent on hFE and
temperature.
51
Emitter-Feedback
Characteristics (1)
+VCC
RB
IC
RC
Advantage: A simple circuit
with relatively stable Q-point.
IB
IE
Circuit recognition: Similar to
voltage divider bias with R2
missing (or base bias with RE
added).
Disadvantage: Requires more
components than collectorfeedback bias.
RE
Applications: Used primarily to
bias linear amplifiers.
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Emitter-Feedback
Characteristics (2)
+VCC
Q-point relationships:
IB 
RB
IC
RC
ICQ  hFE I B
VCEQ  VCC  ICQ  RC  RE 
IB
IE
VCC  VBE
RB  (hFE  1) RE
RE
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Summary
•
•
•
•
•
DC Biasing and the dc load line
Base bias circuits
Voltage-divider bias circuits
Emitter-bias circuits
Feedback-bias circuits
– Collector-feedback bias circuits
– Emitter-feedback bias circuits
54