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Chapter 7DC Biasing Circuits

Pictures are redrawn (with some modifications) from Introductory Electronic Devices and Circuits

ByRobert T. Paynter

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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

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Fig 7.1 Typical amplifier operation.

RB

RC

Q1

VCCVB(ac)

IB(ac)

VCE(ac)

IC(ac)

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Fig 7.2 A generic dc load line.

IC

VCE

(sat)CC

CC

VI

R

(off )CE CCV V

CC CEC

C

V VI

R

5

Fig 7.3 Example 7.1.

RB

RC2 k

Q1

+12 V

VCE2 4 6 8 10 12

2

4

6

8

IC

IC(sat)

VCE(off)

Plot the dc load line for the circuit shown in Fig. 7.3a.

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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.

RB

RC1 k

Q1

+10 V

VCE2 4 6 8 10

2

4

6

8

IC

10 IC (mA) VCE (V)

1 9

2 8

5 5

CE CC C CV V I R

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Fig 7.6-8 Optimum Q-point with amplifier operation.

βC BI I

CE CC C CV V I R

VCE

IB = 0 A

IB = 10 A

IB = 20 A

IB = 30 A

IB = 40 A

IB = 50 A

IC

Q-Point

VCCVCC/2

IC(sat)

IC(sat)/2

IB

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Fig 7.9 Base bias (fixed bias).

CC BEB

B

V VI

R

βC BI I

CE CC C CV V I R

RC

RB

+0.7 V

IC

IB

IE

Input

Output

VBE

VCC

Q1

= dc current gain = hFE

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Fig 7.10 Example 7.3.

RC2 k

RB360 k

+0.7 V

IC

IB

IEVBE

+8 V

hFE = 100

0.7V 8V 0.7V

360kΩ

20.28μA

CCB

B

VI

R

100 20.28μA

2.028mAC FE BI h I

8V 2.028mA 2kΩ

3.94V

CE CC C CV V I R

The circuit is midpoint biased.

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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.

VCE (V)2 4 6 8 10

1

2

3

4

IC (mA)

Q

(sat )

8V4mA

2kΩCC

CC

VI

R

off 8VCCCEV V

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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 Q-point values of IC and VCE at both of these temperatures.

RC2 k

RB360 k

+0.7 V

IC

IB

IEVBE

+8 V

hFE = 100 (T = 25C)hFE = 150 (T = 100C)

Temp(°C) IB (A) IC (mA) VCE (V)

25 20.28 2.028 3.94

100 20.28 3.04 1.92

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Fig 7.13 Base bias characteristics. (1)

RC

RB

+0.7 V

IC

IB

IE

Input

Output

VBE

VCC

Q1 Advantage: Circuit simplicity.

Disadvantage: Q-point shift with temp.

Applications: Switching circuits only.

Circuit recognition: A single resistor (RB) between the base terminal and VCC. No emitter resistor.

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Fig 7.13 Base bias characteristics. (2)

RC

RB

+0.7 V

IC

IB

IE

Input

Output

VBE

VCC

Q1

(sat )

(off )

CCC

C

CE CC

VI

R

V V

Load line equations:

Q-point equations:

CC BEB

B

C FE B

CE CC C C

V VI

R

I h I

V V I R

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Fig 7.14 Voltage divider bias. (1)

R1

R2 RE

RC

+VCC

Input

Output

I1

I2 IE

IB

IC

Assume that I2 > 10IB.

2

1 2B CC

RV V

R R

0.7VE BV V

EE

E

VI

R

Assume that ICQ IE (or hFE >> 1). Then

CEQ CC CQ C EV V I R R

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Fig 7.15 Example 7.7. (1)Determine the values of ICQ and VCEQ for the circuit shown in Fig. 7.15.

R118 k

R24.7 k

RE1.1 k

RC3 k

+10 V

I1

I2IE

IB

IC

hFE = 50

2

1 2

4.7kΩ10V 2.07V

22.7kΩ

B CC

RV V

R R

0.7V

2.07V 0.7V 1.37VE BV V

Because ICQ IE (or hFE >> 1),

1.37V1.25mA

1.1kΩE

CQE

VI

R

10V 1.25mA 4.1kΩ 4.87V

CEQ CC CQ C EV V I R R

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Fig 7.15 Example 7.7. (2)Verify that I2 > 10 IB.

R118 k

R24.7 k

RE1.1 k

RC3 k

+10 V

I1

I2IE

IB

IC

hFE = 50

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2.07V440.4μA

4.7kΩBVIR

1.25mA

1 50+1

24.51μA

EB

FE

II

h

2 10 BI I

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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

(ave) (min) (max)FE FE FEh h h

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Example 7.9A 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.

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1 2

680Ω10V 3.12V

2180ΩB CC

RV V

R R

0.7V 3.12V 0.7V 2.42VE BV V

2.42V10mA

240ΩE

CQ EE

VI I

R

( ) (min) (max) 100 300 173FE ave FE FEh h h

(ave)

10mA57.5μA

1 174E

BFE

II

h

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Stability of Voltage DividerBias 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

10mAAt 100, 100μA and 9.90mA

1 101E

FE B CQ E BFE

Ih I I I I

h

10mAAt 300, 33μA and 9.97mA

1 301E

FE B CQ E BFE

Ih I I I I

h

ICQ hardly changes over the entire range of hFE.

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Fig 7.18 Load line for voltage divider bias circuit.

2 4 6 8 10 12

5

10

15

20

25

IC (mA)

VCE (V)

(sat )

10V20mA

260Ω+240ΩCC

CC E

VI

R R

(off ) 10VCE CCV V

Circuit values are from Example 7.9.

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Fig 7.19-20 Base input resistance. (1)

R1

R2 RE

RC

VCC

I1

I2IE

IB

IC

RIN(base)

R1

R2

I1

I2

VCC

0.7 V

IB RIN(base)

( 1)E E E B FE EV I R I h R

(base) ( 1)EIN FE E

B

FE E

VR h R

I

h R

May be ignored.

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Fig 7.19-20 Base input resistance. (2)

IB

R1

R2

I1

I2

VCC

IB RIN(base)

VB

2 (base)

1 2 (base)

2

1 2

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//

//

//

//

//

INB CC

IN

FE ECC

FE E

EQCC

EQ FE EEQ

R RV V

R R R

R h RV

R R h R

RV

R R h RR R

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Fig 7.21 Example 7.11.

2 //

10kΩ// 50 1.1kΩ 8.46kΩ

EQ FE ER R h R

1

8.46kΩ20V 2.21V

68kΩ 8.46kΩ

EQB CC

EQ

RV V

R R

0.7V

2.21V 0.7V1.37mA

1.1kΩ

E BCQ E

E E

V VI I

R R

20V 1.37mA 7.3kΩ 9.99V

CEQ CC CQ C EV V I R R

R168k

R210k

RE1.1k

RC6.2k

VCC=20V

I1

I2

IE

IC

hFE = 50

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Fig 7.24 Voltage-divider bias characteristics. (1)

R1

R2 RE

RC

+VCC

Input

Output

I1

I2 IE

IB

IC

Circuit recognition: The voltage divider in the base circuit.

Advantages: The circuit Q-point values are stable against changes in hFE.

Disadvantages: Requires more components than most other biasing circuits.

Applications: Used primarily to bias linear amplifier.

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Fig 7.24 Voltage-divider bias characteristics. (2)

R1

R2 RE

RC

+VCC

Input

Output

I1

I2 IE

IB

IC

Load line equations: (sat )

(off )

CCC

C E

CE CC

VI

R R

V V

Q-point equations (assume that hFERE > 10R2):

2

1 2

0.7V

B CC

E B

ECQ E

E

CEQ CC CQ C E

RV V

R R

V V

VI I

R

V V I R R

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Other Transistor Biasing Circuits

• Emitter-bias circuits• Feedback-bias circuits

– Collector-feedback bias– Emitter-feedback bias

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Fig 7.25-6 Emitter bias.Assume that the transistor operation is in active region.

RC

RE

RB

IC

IE

IBQ1

Input

Output

+VCC

-VEE

0.7V

1EE

BB FE E

VI

R h R

C FE BI h I

1E FE BI h I

CE CC C C E E EEV V I R I R V

Assume that hFE >> 1.

CE CC C C E EEV V I R R V

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Fig 7.27 Example 7.12.

RC750

RE1.5k

RB100

IC

IE

IB Q1

Input

Output

+12 V

-12 V

hFE = 200

Determine the values of ICQ and VCEQ for the amplifier shown in Fig.7.27.

12V 0.7V

( 1)

11.3V37.47μA

100Ω+201 1.5kΩ

BB FE E

IR h R

200 37.47μA

7.49mA

CQ FE BI h I

( )

24V 7.49mA 750Ω 1.5kΩ

7.14V

CEQ CC C C E EEV V I R R V

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Load Line forEmitter-Bias Circuit

(sat )

( )CC EE CC EEC

C E C E

V V V VI

R R R R

( )CE off CC EE CC EEV V V V V

VCE

IC

IC(sat)

VCE(off)

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Fig 7.28 Emitter-bias characteristics. (1)

RC

RE

RB

IC

IE

IBQ1

Input

Output

+VCC

-VEE

Circuit recognition: A split (dual-polairty) power supply and the base resistor is connected to ground.

Advantage: The circuit Q-point values are stable against changes in hFE.

Disadvantage: Requires the use of dual-polarity power supply.

Applications: Used primarily to bias linear amplifiers.

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Fig 7.28 Emitter-bias characteristics. (2)

RC

RE

RB

IC

IE

IBQ1

Input

Output

+VCC

-VEE

Load line equations:

(sat )

(off )

CC EEC

C E

CE CC EE

V VI

R R

V V V

Q-point equations:

1BE EE

CQ FEB FE E

CEQ CC CQ C E EE

V VI h

R h R

V V I R R V

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Fig 7.29 Collector-feedback bias.

RB

RC

+VCC

IC

IE

IB

CC C B C B B BEV I I R I R V

( 1)CC BE

BFE C B

V VI

h R R

CQ FE BI h I

1CEQ CC FE B C

CC CQ C

V V h I R

V I R

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Fig 7.30 Example 7.14.

Determine the values of ICQ and VCEQ for the amplifier shown in Fig. 7.30.

RB

RC1.5 k

+10 V

180 k

hFE = 100

1

10V 0.7V28.05μA

180kΩ 101 1.5kΩ

CC BEB

B FE C

V VI

R h R

100 28.05μA

2.805mA

CQ FE BI h I

( 1)

10V 101 28.05μA 1.5kΩ

5.75V

CEQ CC FE B CV V h I R

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Circuit Stability ofCollector-Feedback Bias

RB

RC

+VCC

IC

IE

IB

hFE increases

IC increases (if IB is the same)

VCE decreases

IB decreases

IC does not increase that much.

Good Stability. Less dependent on hFE and temperature.

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Collector-FeedbackCharacteristics (1)

RB

RC

+VCC

IC

IE

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.

Disadvantage: Relatively poor ac characteristics.

Applications: Used primarily to bias linear amplifiers.

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Collector-FeedbackCharacteristics (2)

RB

RC

+VCC

IC

IE

IB

Q-point relationships:

( 1)CC BE

BFE C B

V VI

h R R

CQ FE BI h I

CEQ CC CQ CV V I R

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Fig 7.31 Emitter-feedback bias.

RB RC

+VCC

RE

IB

IE

IC

1CC BE

BB FE E

V VI

R h R

CQ FE BI h I

CEQ CC C C E E

CC CQ C E

V V I R I R

V I R R

1E FE BI h I

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Fig 7.32 Example 7.15.

RB680k

RC6.2k

+VCC

RE1.6k

hFE = 50

16V 0.7V

1 680kΩ 51 1.6kΩ

20.09μA

CC BEB

B FE E

V VI

R h R

50 20.09μA 1mACQ FE BI h I

16V 1mA 7.8kΩ 8.2V

CEQ CC CQ C EV V I R R

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Circuit Stability ofEmitter-Feedback Bias

hFE increases

IC increases (if IB is the same)

VE increases

IB decreases

IC does not increase that much.

IC is less dependent on hFE and temperature.

RB RC

+VCC

RE

IB

IE

IC

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Emitter-FeedbackCharacteristics (1)

Circuit recognition: Similar to voltage divider bias with R2 missing (or base bias with RE added).

Advantage: A simple circuit with relatively stable Q-point.

Disadvantage: Requires more components than collector-feedback bias.

Applications: Used primarily to bias linear amplifiers.

RB RC

+VCC

RE

IB

IE

IC

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Emitter-FeedbackCharacteristics (2)

RB RC

+VCC

RE

IB

IE

IC

Q-point relationships:

( 1)CC BE

BB FE E

V VI

R h R

CQ FE BI h I

CEQ CC CQ C EV V I R R

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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