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Chapter 5
BJT AC Analysis
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 two models commonly used in small
signal AC analysis of a transistor:
re model
Hybrid equivalent model
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.
Common-Emitter Configuration
The diode re model can be replaced by the resistor re.
Ie    1 Ib  Ib
26 mV
re 
Ie
Common-Emitter Configuration
Input impedance:
Zi  re
Output impedance:
Zo  ro  
Voltage gain:
AV  
RL
re
Current gain:
Ai   ro 
Common-Base Configuration
Input impedance:
re 
26 mV
Ie
Zi  re
Output impedance:
Zo  
Voltage gain:
AV 
 RL RL

re
re
Current gain:
Ai    1
Common-Collector Configuration
Input impedance:
Zi  (  1)re
Output impedance:
Zo  re || RE
Voltage gain:
AV 
RE
RE  re
Current gain:
Ai  β  1
5.5 Common-Emitter Fixed-Bias Configuration






The input is applied to the base.
The output is taken from the collector.
High input impedance
Low output impedance
High voltage and current gain
Phase shift between input and output is 180.
Common-Emitter
Fixed-Bias
Configuration
AC equivalent
re,model
Common-Emitter
Fixed-Bias
Calculations
Input
impedance:
Output
impedance:
Zi  RB||β| e
Zi  βre
Zo  RC||rO
Zo  RC
Av 
Voltage gain:
RE 10 βr e
RC
re
Current gain:
ro 10 RC
Io
βRB ro

I i (ro  RC )(R B  βre )
Ai  β
ro 10 RC
Vo
(R ||r )
 C o
Vi
re
Av  
Ai 
Current gain
from voltage gain:
ro 10 RC , RB 10 βr e
Ai   AV
Zi
RC
5.6 Common-Emitter Voltage-Divider Bias
re model requires you to
determine , re, and ro.
Common-Emitter
Voltage-Divider Bias
Calculations
Input impedance
R   R1 || R2
Zi  R  || βre
Voltage gain
Av 
Vo  RC || ro

Vi
re
Av 
Vo
R
 C
Vi
re
ro 10R C
Output impedance
Zo  RC || ro
Zo  RC
ro 10RC
Current gain
Io
R ro

I i (ro  RC )(R   re )
I
R 
Ai  o 
r 10R
I i R   re o C
Ai 
Ai 
Io
  ro 10RC , R10 re
Ii
Current gain from Av
Ai   Av
Zi
RC
5.7 Common-Emitter Emitter-Bias Configuration
Impedance Calculations
Input impedance:
Zi  RB || Zb
Zb  re  (   1)RE
Zb  (re  RE )
Zb  RE
Output impedance:
Zo  RC
Gain Calculations
Voltage gain:
Av 
Vo
R
 C
Vi
Zb
Av 
Vo
RC

Vi
re  RE
Av 
Vo
R
 C
Vi
RE
Zb (re  RE )
Z b   RE
Current gain:
Ai 
Io
RB

Ii RB  Zb
Current gain from Av:
Ai   Av
Zi
RC
5.8 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.
Impedance
Calculations
Input impedance:
Zi  RB ||Z b
Zb  βre  (β  1)RE
Zb  β(re  RE )
Zb  βRE
Output impedance:
Zo  RE||re
Zo  re
RE  re
Gain Calculations
Voltage gain:
Av 
Vo
RE

Vi RE  re
Av 
Vo
1
Vi
RE  re , RE  re  RE
Current gain:
Ai  
βRB
RB  Z b
Current gain from voltage gain:
Ai   Av
Zi
RE
5.9 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
Calculations
Input impedance:
Zi  RE || re
Output impedance:
Zo  RC
Voltage gain:
Av 
Vo RC RC


Vi
re
re
Current gain:
Ai 
Io
   1
Ii
5.10 CE Collector Feedback Configuration
•
•
•
•
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 the input and output
Calculations
Input impedance:
Output impedance:
Voltage gain:
Av 
Zi 
Zo  RC || RF
Vo
R
 C
Vi
re
Current gain:
Ai 
Io
βRF

Ii
RF  βRC
Ai 
Io
R
 F
Ii
RC
re
1 RC

β RF
5.11 Collector DC Feedback Configuration
This is a variation of the commonemitter, 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.
Calculations
Input impedance:
Zi 
re
1 RC

β RF
Output impedance:
Zo  RC||RF
Voltage gain:
Av 
Vo
R
 C
Vi
re
Current gain:
Ai 
Io
 RF

Ii
RF   RC
Ai 
Io
R
 F
Ii
RC
5.12 Effect of Source Impedance on Gain
The amplitude of the
applied signal that
reaches the input of
the amplifier is:
Vi 
RiVs
R i  Rs
The internal resistance of the signal source reduces the overall gain:
Avs 
Vo
Ri

AvNL
Vs Ri  Rs
Combined Effects of RS and RL on Voltage Gain
Effects of RL:
Av 
Vo RL AvNL

Vi RL  Ro
Ai   Av
Ri
RL
Avs 
Effects of RL and RS:
Vo
Ri
RL

AvNL
Vs Ri  Rs RL  Ro
Ais   Avs
Rs  R i
RL
5.15 Two-Port Systems Approach
With Vi set to 0 V:
ZTh  Zo  Ro
The voltage across the open terminals is:
where AvNL is the no-load voltage gain.
ETh  AvNLVi
Effect of Load Impedance on Gain
 This model can be applied to any amplifier.
 Adding a load reduces the gain of the amplifier:
Av 
Vo
RL

AvNL
Vi RL  Ro
Ai   Av
Zi
RL
5.16 Cascaded Systems
 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.
R-C Coupled BJT Amplifiers
Voltage gain: Av1 
RC || R1 || R2 || βRe
re
Av2 
RC
re
Av  Av1 Av2
Output impedance, second stage:
Zi  R1 || R2 || Re
Input impedance, first stage:
Zo  RC
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 high-frequency
applications.
5.17 Darlington Connection
The Darlington circuit provides
very high current gain, equal to the
product of the individual current
gains:
D = 1 2
The practical significance is that
the circuit provides a very high
input impedance.
DC Bias of Darlington Circuits
Base current:
IB 
VCC  VBE
RB   D RE
Emitter current:
IE  (D  1)IB  DIB
Emitter voltage:
VE  IE RE
Base voltage:
VB  VE  VBE
5.18 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.
Ch.5 Summary
Current Mirror Circuits
Current mirror
circuits provide
constant current in
integrated circuits.
Ch.5 Summary
Current Source Circuits
Constant-current sources can be built using FETs, BJTs, and
combinations of these devices.
I  IE 
VZ  VBE
RE
IE  IC
Ch.5 Summary
Current Source Circuits
VGS = 0V
ID = IDSS = 10 mA
Ch.5 Summary
Fixed-Bias
Input impedance:
Zi  RB || hie
Output impedance:
Zo  RC || 1/ hoe
Voltage gain:
Av 
Vo
h R || 1/ ho e 
  fe C
Vi
hie
Current gain:
Ai 
Io
 hfe
Ii
Ch.5 Summary
Voltage-Divider Configuration
Input impedance:
Zi  R || hie
Output impedance:
Zo  RC
Voltage gain:
Av  
Current gain:
hfe RC || 1/hoe 
hie
Ai  
hfeR 
R   hie
Ch.5 Summary
Emitter-Follower Configuration
Input impedance:
Zb  hfeRE
Zi  Ro || Zb
Z b  h fe R E
Z i  R o || Z b
Output impedance:
Zo  RE ||
hie
hfe
Voltage gain:
Av 
Vo
RE

Vi RE  hie / hfe
Ai 
Current gain:
hfeRB
RB  Z b
Ai   Av
Zi
RE
Ch.5 Summary
Common-Base Configuration
Input impedance:
Zi  RE || hib
Output impedance:
Zo  RC
Voltage gain:
Av 
Vo
h R
  fb C
Vi
hib
Current gain:
Ai 
Io
 hfb  1
Ii
5.19 The Hybrid Equivalent Model
Hybrid parameters are developed and used for modeling the
transistor. These parameters can be found on a transistor’s
specification sheet:
hi = input resistance
hr = reverse transfer voltage ratio (Vi/Vo)  0
hf = forward transfer current ratio (Io/Ii)
ho = output conductance
Ch.5 Summary
Simplified General h-Parameter Model
hi = input resistance
hf = forward transfer current ratio (Io/Ii)
Ch.5 Summary
re vs. h-Parameter Model
Common-Emitter
hie  βre
hfe  βac
Common-Base
hib  re
hfb  α  1
5.22 The Hybrid  Model
The hybrid pi model is most useful for analysis
of high-frequency transistor applications.
At lower frequencies the hybrid pi model closely
approximate the re parameters, and can be
replaced by them.
5.24 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.