Chapter 7
DC Biasing Circuits
Pictures are redrawn (with some modifications) from
Introductory Electronic Devices and Circuits
By
Robert T. Paynter
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
Fig 7.1 Typical amplifier operation.
VCC
VB(ac)
IB(ac)
RC
RB
Q1
VCE(ac)
IC(ac)
3
Fig 7.2 A generic dc load line.
IC
I C (sat) 
VCC  VCE
IC 
RC
VCC
RC
VCE (off )  VCC
VCE
4
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
5
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
6
Fig 7.6-8 Optimum Q-point with
amplifier operation.
IC
IC(sat)
IB = 50 A
I C  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
7
Fig 7.9 Base bias (fixed bias).
VCC
IC
VCC  VBE
IB 
RB
RB
Output
IB
Input
I C  βI B
RC
VCE  VCC  IC RC
Q1
+0.7 V
VBE
b = dc current gain = hFE
IE
8
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.
9
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)
10
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
11
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.
12
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
13
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 
14
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
15
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  10 I B
IB
hFE = 50
I2
R2
4.7 k
IE
RE
1.1 k
16
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)
17
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

18
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.
19
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)
20
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)
21
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)
22
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
23
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.
24
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 
25
Other Transistor Biasing
Circuits
• Emitter-bias circuits
• Feedback-bias circuits
– Collector-feedback bias
– Emitter-feedback bias
26
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
27
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
28
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
29
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.
30
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
31
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
I CQ  hFE I B
VCEQ  VCC   hFE  1 I B RC
 VCC  I CQ RC
IE
32
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
33
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.
34
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.
35
Collector-Feedback
Characteristics (2)
+VCC
Q-point relationships:
IB 
RC
RB
IB
IC
VCC  VBE
(hFE  1) RC  RB
I CQ  hFE I B
VCEQ  VCC  I CQ RC
IE
36
Fig 7.31 Emitter-feedback bias.
+VCC
RB
IC
RC
VCC  VBE
IB 
RB   hFE  1 RE
I CQ  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 
37
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
I CQ  hFE I B  50  20.09μA  1mA
VCEQ  VCC  I CQ  RC  RE 
 16V  1mA  7.8kΩ   8.2V
hFE = 50
RE
1.6k
38
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.
39
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.
40
Emitter-Feedback
Characteristics (2)
+VCC
Q-point relationships:
IB 
RB
IC
RC
I CQ  hFE I B
VCEQ  VCC  ICQ  RC  RE 
IB
IE
VCC  VBE
RB  (hFE  1) RE
RE
41
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
42