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Chapter 5:
BJT AC Analysis
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5.3 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 three models commonly used in small signal AC analysis of a
transistor:
AC equivalent
– re model
circuit
– Hybrid equivalent model
– Hybrid ∏ model
AC
network
Sketch an AC network:
1. Remove DC supplies
(replaced by short)
2. The coupling capacitor
and bypass capacitor can
be replaced by a short 2
5.4 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.
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Common-Base Configuration
I c  I e
re 
26 mV
IE
Input impedance: Low
Z i  re
Output impedance: High
Z o  
Voltage gain: voltage amplification
AV 
R L R L

re
re
re model for CB configuration
Current gain: No current amplification
A i    1
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Common-Emitter Configuration
Input impedance: higher than CB
Z i  re
Output impedance: lower than CB
Z o  ro  
Voltage gain: Voltage amplification，
AV  
RL
re
Vo and Vi are 180° out of phas
Current gain: Current amplification
A i   ro  
re model for CE configuration
The diode re model can be
replaced by the resistor re.
I e    1I b  I b
re 
26 mV
Ie
re model requires you to
determine , re, and ro.
Use the common-emitter model for the common-collector configuration.
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5.5 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  
Simplified General H-Parameter Model: Approximate hybrid equivalent model
•
•
•
•
hi = input resistance
hr = reverse transfer voltage ratio (Vi/Vo)  0
hf = forward transfer current ratio (Io/Ii)
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ho = output conductance  
re Model vs. h-Parameter Model
Common-Emitter
h ie   re
h fe   ac
Common-Base
h ib  re
h fb     1
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5.6 The Hybrid p Model
The hybrid p model is most useful for analysis of high-frequency transistor
applications.
At lower frequencies the hybrid p model closely approximate the re parameters,
and can be replaced by them.
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AC Analysis with Equivalent models
Section 5.8 CE with fix-bias
Section 5.9 CE with voltage-divider bias
Section 5.10 CE with emitter bias
CE
Section 5.14 CE with dc collector feedback bias
Section 5.13 CE with collector feedback
Section 5.11 CC: Emitter follower
Section 5.12 CB
Amplification
circuit
DC analysis
to determine re
AC unknowns
AC equivalent circuit
with re model
Calculate:
•Impedance
•Input impedance
•Output impedance
•Gain
•Voltage gain
•Current gain
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5.8 Common-Emitter Fixed-Bias Configuration
AC network
•
•
•
•
•
•
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
AC equivalent with re model
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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
CE amplifiers:
Current gain from voltage gain:
• High input impedance
Z
• Low output impedance
Ai  A v i
RC
• High voltage and current gain
• Phase shift between input and
output is 180
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5.9 Common-Emitter Voltage-Divider Bias
re model requires you to determine , re, and ro.
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
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5.10 Common-Emitter Emitter-Bias Configuration
(Unbypassed RE)
Input impedance:
Zi  RB || Zb
Zb   re  (   1) RE
Output impedance:
Zo  R C
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
Zi
RC
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5.13 Common-Emitter Collector Feedback Configuration
Input impedance:
Zi 
re
1 RC

 RF
Output impedance:
Z o  R C || R F
Voltage gain:
Av 
•
•
•
•
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
Vo
R
 C
Vi
re
Current gain:
I
R F
Ai  o 
Ii
R F  R C
I
R
Ai  o  F
Ii
RC
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5.14 Collector DC Feedback Configuration
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5.11 Emitter-Follower Configuration (CC)
•
•
•
Emitter-follower is also
Input impedance:
Voltage gain:
known as the commonZ i  R B || Z b
V
RE
collector configuration.
Av  o 
Vi R E  re
The input is applied to the
Z b   re  (  1)R E
base and the output is
V
Z b  (re  R E )
A v  o  1 R E  re , R E  re  R E
taken from the emitter.
Vi
Z b  R E
There is no phase shift
Current gain:
R B
between input and output. Output impedance:
A 
Z o  R E || re
Z o  re R E  re
i
R B  Zb
Current gain from voltage gain:
Ai  A v
Zi
RE
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5.12 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.
Input impedance:
Z i  R E || re
Voltage gain:
Output impedance:
Av 
Zo  R C
Vo R C R C


Vi
re
re
Current gain:
I
A i  o    1
Ii
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5.17 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.
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5.16 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
Vo =
RL
A v NL Vi
RL + Ro
Zi
RL
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5.16 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
Vo = A vNL Vi  A vNL
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
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5.16 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 
Vo =
R i Vs
RL
RL
A vNL Vi =
A v NL
RL + Ro
RL + Ro
Ri + Rs
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 
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5.19 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
Z i  Z i1
Z o  Z on
A vT  A v1  A v2  A v3  A vn
A iT   A vT
Z i1
A v1 , A v2 , A v3 , , A vn
are loaded gains
RL
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R-C Coupled BJT Amplifiers
Input impedance, first stage:
Zi = Zi1 = R1 || R 2 || βre1
Output impedance, second stage:
Zo = R C2
Voltage gain:
A V1 = -
R C1 || Z i2 R C1 || R 3 || R 4 || βre2
=
re1
re1
A V2 = -
R C2
re2
AV = AV1 AV2
Zi2 = R 3 || R 4 || βre2
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Cascode Connection: CE–CB
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
high-frequency applications.
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5.20 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.
5.21 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
• Low 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.
PNP
D = 12
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5.22 Current Mirror Circuits
Current mirror circuits provide constant
current in integrated circuits.
I X = I E + 2I B = I E + 2
IE =
Current mirror circuit with higher output impedance.
IE β + 2
=
IE
β
β
V -V
β
I X  I X = CC BE
β+2
RX
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5.23 Current Source Circuits
Constant-current sources can be built using FETs, BJTs, and combinations of these
devices.
IE  IC
I  IE 
VZ  VBE
RE
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Summary of Chapter 5
•
AC analysis
– Load line analysis
– Mathematical analysis by small signal model
•
AC analysis method by small signal model
– DC analysis to determine re
– AC equivalent circuit by re model
– Calculation impedance and gain
•
•
•
•
CE amplifier
CB amplifier
CC amplifier
Cascaded amplifier system
– Effect of Rs and RL
– CE-CB
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