BJT AC Analysis
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
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Common-Base Configuration
I c = αI e
re =
26 mV
Ie
Input impedance:
Zi= r e
Output impedance:
Z o≃∞ Ω
Voltage gain:
AV =
αR L R L
≃
re
re
Current gain:
Ai = − α≃− 1
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Common-Emitter Configuration
The diode re model can be
replaced by the resistor re.
I e= (β+ 1 )I b≃βI b
re =
26 mV
Ie
more…
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Common-Emitter Configuration
Input impedance:
Z i = βr e
Output impedance:
Z o= r o≃∞ Ω
Voltage gain:
RL
AV = −
re
Current gain:A = β∣
i
r
o=
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
∞
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Common-Collector Configuration
Input impedance:
Z i = ( β+ 1 )r e
Output impedance:
Z o= r e∣∣ R E
Voltage gain:
RE
AV =
R E+ r e
Current gain:
Ai = β + 1
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
The Hybrid Equivalent Model
The following hybrid parameters are developed and used
for modeling the transistor. These parameters can be found
on the 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
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Simplified General h-Parameter Model
•
•
hi = input resistance
hf = forward transfer current ratio (Io/Ii)
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
re vs. h-Parameter Model
Common-Emitter
hie = βr e
h fe= β ac
Common-Base
hib = r e
h fb = − α≃− 1
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
The Hybrid  Model
The hybrid  model is most useful for analysis of highfrequency transistor applications.
At lower frequencies the hybrid  model closely
approximate the re parameters, and can be replaced by
them.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Common-Emitter Fixed-Bias Configuration
AC equivalent
re model
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Common-Emitter Fixed-Bias Calculations
Input impedance:
Z i = R B ∣∣ βr e
Z i ≃ βr e∣R ≥ 10 βr
E
e
Output impedance:
Z o = RC ∣∣r O
Z o ≃ RC ∣r ≥ 10 R
o
C
Voltage gain:
Vo
( R ∣∣r )
=− C o
Vi
re
RC
Av= −
∣
r e r o ≥ 10RC
Av=
Current gain:
I o βR B r o
Ai = =
I i (r o + R C )( R B+ βr e )
Ai ≃ β∣r ≥ 10R , R ≥ 10 βr
o
C
B
e
Current gain from voltage gain:
Ai = − A v
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Zi
RC
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Common-Emitter Voltage-Divider Bias
re model requires you to determine , re, and ro.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Common-Emitter Voltage-Divider Bias
Input impedance:
Calculations
R' = R 1∣∣ R 2
Z i = R '∣∣ βr e
Output impedance:
Z o = RC ∣∣r o
Z o ≃ RC ∣r ≥ 10R
o
C
Voltage gain:
V o − RC∣∣r o
=
V i re
V
R
A v = o ≃− C ∣r ≥ 10R
C
Vi
re o
Av=
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Current gain:
'
Io β R ro
Ai = =
I i ( r o + R C )( R' + βr e )
I o β R'
¿
Ai = ≃ '
∣r ≥ 10R
o
C
I i R + βr e
I
'
Ai = o ¿β∣r ≥ 10R , { R≥ 10 βr e
o
C
Ii
Current gain from voltage gain:
Zi
Ai = − A v
RC
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Common-Emitter Emitter-Bias
Configuration
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Impedance Calculations
Input impedance:
Z i = R B∣∣ Z b
Z b = βr e + ( β + 1) R E
Z b≃ β ( re + R E )
Z b ≃ βR E
Output impedance:
Z o= RC
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Gain Calculations
Voltage gain:
Av=
Vo
=−
βRC
Vi
Zb
V
R
Av= o = − C
∣
Vi
r e + R E Z b= β( r e + R E )
Vo
RC
Av =
¿−
∣
Vi
R E Z b ≃βR E
Current gain:
Ai =
Io
βR B
=
I i RB + Zb
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Current gain from voltage gain:
Ai = − A v
Zi
RC
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Impedance Calculations
Input impedance:
Z i = R B∣∣ Z b
Z b = βr e + ( β + 1) R E
Z b≃ β ( re + R E )
Z b ≃ βR E
Output impedance:
Z o = R E ∣∣r e
Z o ≃r e∣R >> r
E
e
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Gain Calculations
Voltage gain:
V o RE
=
Vi
R E+ r e
V
A v = o ≃1∣ R >> r , R + r ≃ R
E
e
E
e
E
Vi
Av=
Current gain:
Ai ≃−
βR B
R B+ Z b
Current gain from voltage gain:
Z
Ai = − A v i
RE
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Calculations
Input impedance:
Z i = R E∣∣r e
Output impedance:
Z o= RC
Voltage gain:
V o αR C R C
Av=
=
≃
Vi
re
re
Current gain:
Ai =
Io
= − α ≃− 1
Ii
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Calculations
Input impedance:
Zi=
re
1 RC
+
β RF
Output impedance:
Z o≃RC ∣∣ R F
Voltage gain:
Av=
Vo
R
=− C
Vi
re
Current gain:
I o βR F
=
Ii
R F + βR C
I
R
Ai = o ≃ F
Ii
RC
Ai =
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Calculations
Input impedance:
Zi=
re
1 RC
+
β RF
Output impedance:
Z o≃RC ∣∣ R F
Voltage gain:
Av=
Vo
R
=− C
Vi
re
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Current gain:
I o βR F
Ai =
=
Ii
R F + βR C
I
R
Ai = o ≃ F
Ii
RC
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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 V i
where AvNL is the
no-load voltage
gain.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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:
Vo
RL
Av=
=
A
V i R L + R o vNL
Zi
Ai = − A v
RL
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Effect of Source Impedance on Gain
The fraction of
applied signal that
reaches the input of
the amplifier is:
Ri V s
V i=
Ri+ Rs
The internal resistance of the signal source reduces the
overall gain:
A vs=
Vo
Ri
=
A
V s Ri + R s vNL
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Combined Effects of RS and RL on Voltage
Gain
Effects of RL:
V o R L A vNL
Av=
=
V i R L+ R o
R
Ai = − A v i
RL
Effects of RL and RS:
V o Ri
RL
A vs=
=
A
V s Ri + R s R L + R o vNL
R + Ri
Ais = − A vs s
RL
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
R-C Coupled BJT Amplifiers
Input impedance, first stage:
Z i = R 1∣∣ R 2∣∣ βre
Output impedance, second stage:
Z o= RC
Voltage gain:
A v1=
R C∣∣ R 1∣∣ R 2∣∣ βr e
re
R
AV2 = C
re
A v = A v1 A v2
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
DC Bias of Darlington Circuits
Base current:
V CC − V BE
I B=
R B+ β D R E
Emitter current:
I E = ( β D+ 1) I B≃ β D I B
Emitter voltage:
V E= I E R E
Base voltage:
V B= V E+ V BE
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Current Mirror Circuits
Current mirror circuits
provide constant current
in integrated circuits.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Current Source Circuits
Constant-current sources can be built using FETs, BJTs, and
combinations of these devices.
IE  IC
I ≃ I
E=
V
Z
− V
RE
BE
more…
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Current Source Circuits
VGS = 0V
ID = IDSS = 10 mA
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Fixed-Bias Configuration
Input impedance:
Z i = R B∣∣hie
Output impedance:
Z o= RC ∣∣1/h oe
Voltage gain:
Av=
h fe (R C∣∣1 / ho e )
Vo
=−
Vi
hie
Current gain:
Ai =
Io
≃h fe
Ii
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Z i = R B∣∣hie
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Voltage-Divider Configuration
Input impedance:
Z i = R '∣∣ hie
Output impedance:
Z o≃RC
Voltage gain:
h fe (R C∣∣1/h oe )
Av= −
h ie
Current gain:
Ai = −
hfe R'
'
R + hie
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Emitter-Follower Configuration
Input impedance:
Z b = h fe R E
Z i = R o∣∣ Z b
Output impedance:
Z o ≃ R E ∣∣
hie
h fe
Z b = h fe R E
Z i = R o∣∣ Z b
Voltage gain:
Av=
Vo
RE
=
V i R E + hie / hfe
Current gain:
Ai =
h fe R B
R B+ Z b
Zi
Ai = − A v
RE
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Common-Base Configuration
Input impedance:
Z i = R E∣∣h ib
Output impedance:
Z o= RC
Voltage gain:
Av=
Vo
h R
= − fb C
Vi
h ib
Current gain:
Io
Ai = = h fb≃− 1
Ii
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
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.
Electronic Devices and Circuit Theory, 10/e
Robert L. Boylestad and Louis Nashelsky
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.