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Chapter 5:
BJT AC Analysis
1
BJT Transistor Modeling
•
A model is an equivalent circuit that represents the AC
characteristics of the transistor.
•
A model uses circuit elements that approximate the behavior of
the transistor.
•
There are two models commonly used in small signal AC
analysis of a transistor:
–
–
re model
Hybrid equivalent model
2
The re Transistor Model
BJTs are basically current-controlled devices, therefore the re model uses a
diode and a current source to duplicate the behavior of the transistor.
One disadvantage to this model is its sensitivity to the DC level. This model is
designed for specific circuit conditions.
3
Common-Base Configuration
I c  I e
re 
26 mV
Ie
Input impedance:
Z i  re
Output impedance:
Z o  
Voltage gain:
AV 
R L R L

re
re
Current gain:
A i    1
4
Common-Emitter Configuration
The diode re model can be
Input impedance:
replaced by the resistor re.
I e  Z
i1I rbe  I b
Output impedance:
26 mV
re Z  r  
oI o
e
Voltage gain:
AV  
RL
re
Current gain:
A i   ro  
more…
5
Common-Collector Configuration
Use the common-emitter model for the common-collector configuration.
6
The Hybrid Equivalent Model
The following hybrid parameters are developed and used for
modeling the transistor. These parameters can be found in a
specification sheet for a transistor.
•
•
•
•
hi = input resistance
hr = reverse transfer voltage ratio (Vi/Vo)  0
hf = forward transfer current ratio (Io/Ii)
ho = output conductance  
7
Simplified General h-Parameter Model
•
•
•
•
hi = input resistance
hr = reverse transfer voltage ratio (Vi/Vo)  0
hf = forward transfer current ratio (Io/Ii)
ho = output conductance  
8
Common-Emitter re vs. h-Parameter Model
Common-Emitter
h ie   re
h fe   ac
Common-Base
h ib  re
h fb     1
9
The Hybrid p Model
The hybrid p model is most useful for analysis of highfrequency transistor applications.
At lower frequencies the hybrid p model closely approximate
the re parameters, and can be replaced by them.
10
Common-Emitter Fixed-Bias Configuration
•
•
•
•
•
•
The input is applied to the base
The output is from the collector
High input impedance
Low output impedance
High voltage and current gain
Phase shift between input and
output is 180
11
Common-Emitter Fixed-Bias Configuration
AC equivalent
re model
12
Common-Emitter Fixed-Bias Calculations
Input impedance:
Z i  R B ||  re
Z i   re R E  10 re
Output impedance:
Z o  R C || rO
Z o  R C ro  10R C
Voltage gain:
Av 
Vo
(R || r )
 C o
Vi
re
Av  
RC
ro  10R C
re
Current gain:
I
 R B ro
Ai  o 
I i (ro  R C )(R B   re )
A i   ro  10R C , R B  10 re
Current gain from voltage gain:
Ai  A v
13
Zi
RC
Common-Emitter Voltage-Divider Bias
re model requires you to determine , re, and ro.
14
Common-Emitter Voltage-Divider Bias Calculations
Input impedance:
R   R 1 || R 2
Z i  R  ||  re
Output impedance:
Z o  R C || ro
Z o  R C ro  10R C
Voltage gain:
Av 
Vo  R C || ro

Vi
re
Av 
Vo
R
  C ro  10R C
Vi
re
Current gain:
I
 R ro
Ai  o 
I i (ro  R C )(R    re )
I
R 
Ai  o 
r  10R C
I i R    re o
I
A i  o   ro  10R C , R   10 re
Ii
Current gain from voltage gain:
Z
Ai  A v i
RC
15
Common-Emitter Emitter-Bias Configuration
(Unbypassed RE)
16
Impedance Calculations
Input impedance:
Z i  R B || Z b
Z b   re  (  1)R E
Z b  (re  R E )
Z b  R E
Output impedance:
Zo  R C
17
Gain Calculations
Voltage gain:
Av 
Vo
R C

Vi
Zb
Av 
Vo
RC

Vi
re  R E Z b  (re  R E )
Av 
Vo
R
  C Z b  R E
Vi
RE
Current gain:
I
R B
Ai  o 
I i R B  Zb
Current gain from voltage gain:
Ai  A v
18
Zi
RC
Emitter-Follower Configuration
•
•
•
This is also known as the common-collector configuration.
The input is applied to the base and the output is taken from the
emitter.
There is no phase shift between input and output.
19
Impedance Calculations
Input impedance:
Z i  R B || Z b
Z b   re  (  1)R E
Z b  (re  R E )
Z b  R E
Output impedance:
Z o  R E || re
Z o  re R E  re
20
Gain Calculations
Voltage gain:
Vo
RE

Vi R E  re
V
A v  o  1 R E  re , R E  re  R E
Vi
Av 
Current gain:
Ai  
R B
R B  Zb
Current gain from voltage gain:
Ai  A v
Zi
RE
21
Common-Base Configuration
•
•
•
•
•
•
•
The input is applied to the
emitter.
The output is taken from the
collector.
Low input impedance.
High output impedance.
Current gain less than unity.
Very high voltage gain.
No phase shift between input
and output.
22
Calculations
Input impedance:
Z i  R E || re
Output impedance:
Zo  R C
Voltage gain:
Av 
Vo R C R C


Vi
re
re
Current gain:
I
A i  o    1
Ii
23
Common-Emitter Collector Feedback Configuration
•
•
•
•
This is a variation of the common-emitter fixed-bias
configuration
Input is applied to the base
Output is taken from the collector
There is a 180 phase shift between input and output
24
Calculations
Input impedance:
Zi 
re
1 RC

 RF
Output impedance:
Z o  R C || R F
Voltage gain:
Av 
Vo
R
 C
Vi
re
Current gain:
I
R F
Ai  o 
Ii
R F  R C
I
R
Ai  o  F
Ii
RC
25
Collector DC Feedback Configuration
•
•
•
•
This is a variation of the
common-emitter, fixed-bias
configuration
The input is applied to the base
The output is taken from the
collector
There is a 180 phase shift
between input and output
26
Calculations
Input impedance:
r
Zi 
e
1 RC

 RF
Output impedance:
Z o  R C || R F
Voltage gain:
Av 
Vo
R
 C
Vi
re
Current gain:
I
R F
Ai  o 
Ii
R F  R C
I
R
Ai  o  F
RC
I
i
27
Two-Port Systems Approach
This approach:
• Reduces a circuit to a two-port system
• Provides a “Thévenin look” at the output terminals
• Makes it easier to determine the effects of a changing load
With Vi set to 0 V:
Z Th  Z o  R o
The voltage across
the open terminals is:
E Th  A vNL Vi
where AvNL is the
no-load voltage
gain.
28
Effect of Load Impedance on Gain
This model can be applied to
any current- or voltagecontrolled amplifier.
Adding a load reduces the
gain of the amplifier:
Av 
Vo
RL

A vNL
Vi R L  R o
Ai  A v
Zi
RL
29
Effect of Source Impedance on Gain
The fraction of
applied signal that
reaches the input of
the amplifier is:
Vi 
R i Vs
Ri  Rs
The internal resistance of the signal source reduces the
overall gain:
A vs 
Vo
Ri

A vNL
Vs R i  R s
30
Combined Effects of RS and RL on Voltage Gain
Effects of RL:
Vo R L A vNL

Vi
RL  Ro
R
Ai  A v i
RL
Av 
Effects of RL and RS:
Vo
Ri
RL

A vNL
Vs R i  R s R L  R o
R  Ri
A is   A vs s
RL
A vs 
31
Cascaded Systems
•
•
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The output of one amplifier is the input to the next amplifier
The overall voltage gain is determined by the product of gains of
the individual stages
The DC bias circuits are isolated from each other by the
coupling capacitors
The DC calculations are independent of the cascading
The AC calculations for gain and impedance are interdependent
32
R-C Coupled BJT Amplifiers
Input impedance, first stage:
Z i  R 1 || R 2 || re
Output impedance, second stage:
Zo  R C
Voltage gain:
A v1 
R C || R 1 || R 2 ||  re
re
A V2 
RC
re
A v  A v1 A v 2
33
Cascode Connection
This example is a CE–CB
combination. This arrangement
provides high input impedance
but a low voltage gain.
The low voltage gain of the
input stage reduces the Miller
input capacitance, making this
combination suitable for highfrequency applications.
34
Darlington Connection
The Darlington circuit provides a very high
current gain—the product of the individual
current gains:
D = 12
The practical significance is that the circuit
provides a very high input impedance.
35
DC Bias of Darlington Circuits
Base current:
V  VBE
I B  CC
R B   DR E
Emitter current:
I E  ( D  1)I B   DI B
Emitter voltage:
VE  I E R E
Base voltage:
VB  VE  VBE
36
Feedback Pair
This is a two-transistor circuit that operates like a
Darlington pair, but it is not a Darlington pair.
It has similar characteristics:
• High current gain
• Voltage gain near unity
• Low output impedance
• High input impedance
The difference is that a Darlington
uses a pair of like transistors,
whereas the feedback-pair
configuration uses complementary
transistors.
37
Current Mirror Circuits
Current mirror circuits
provide constant current
in integrated circuits.
38
Current Source Circuits
Constant-current sources can be built using FETs, BJTs, and
combinations of these devices.
VGS = 0V
ID = IDSS = 10 mA
I VIZC  VBE
I  I E E
RE
39
more…
Fixed-Bias Configuration
Input impedance:
Z i  R B || h ie
Output impedance:
Z o  R C || 1 / h oe
Voltage gain:
Av 
Vo
h R || 1 / h o e
  fe C
Vi
h ie
Current gain:
I
A i  o  h fe
Ii
Z i  R B || h ie
40
Voltage-Divider Configuration
Input impedance:
Z i  R || h ie
Output impedance:
Zo  R C
Voltage gain:
h R || 1/h oe 
A v   fe C
h ie
Current gain:
Ai  
h fe R 
R   h ie
41
Unbypassed Emitter-Bias Configuration
Input impedance:
Z b  h fe R E
Z i  R B || Z b
Output impedance:
Zo  R C
Voltage gain:
Av  
RC
RE
Current gain:
Ai 
Current gain from voltage gain:
h fe R B
R B  Zb
Ai  A v
42
Zi
RC
Emitter-Follower Configuration
Input impedance:
Z b  h fe R E
Z i  R o || Z b
Output impedance:
Z b  h fe R E
Z i  R o || Z b
h
Z o  R E || ie
h fe
Voltage gain:
Av 
Vo
RE

Vi R E  h ie / h fe
Current gain:
Ai 
h fe R B
R B  Zb
Ai  A v
Zi
RE
43
Common-Base Configuration
Input impedance:
Z i  R E || h ib
Output impedance:
Zo  R C
Voltage gain:
Av 
Vo
h R
  fb C
Vi
h ib
Current gain:
I
A i  o  h fb  1
Ii
44
Complete Hybrid Equivalent Model
•
•
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Current gain, Ai
Voltage gain, Av
Input impedance, Zi
Output impedance, Zo
45
Troubleshooting
Check the DC bias voltages
 If not correct, check power supply, resistors, transistor. Also
check the coupling capacitor between amplifier stages.
Check the AC voltages
 If not correct check transistor, capacitors and the loading
effect of the next stage.
46
Practical Applications
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Audio Mixer
Preamplifier
Random-Noise Generator
Sound Modulated Light Source
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