Chapter 5:
BJT AC Analysis
Islamic University of Gaza
Dr. Talal Skaik
Copyright ©2009 by Pearson Education, Inc.
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
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 Dr. Talal Skaik 2014
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
BJT Transistor Modeling
3 Dr. Talal Skaik 2014
Removal of the dc supply and
insertion of the short-circuit
equivalent for the capacitors.
Capacitors chosen with very
small reactance at the frequency
of application → replaced by
low-resistance or short circuit.
Copyright ©2009 by Pearson Education, Inc.
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
BJT Transistor Modeling
4 Dr. Talal Skaik 2014
Circuit redrawn for small-
signal ac analysis
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
The re Transistor Model
5 Dr. Talal Skaik 2014
Common Emitter Configuration
1
11
beii
b b
be e e c b e b b e
b e
b ebei e e
b b
VVZ
I I
V I r I I r I I r
I r
I rVZ r r
I I
Copyright ©2009 by Pearson Education, Inc.
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
The re Transistor Model Common Emitter Configuration
26 e
E
mVr
I
6 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
The re Transistor Model
Common Emitter Configuration
7 Dr. Talal Skaik 2014
0
0
1C
CE
CE
C
Islope
V r
Vr
I
The output resistance r is
typically in the range of
40 kΩ to 50 kΩ
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Common-Base Configuration
8 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Common-Base
Configuration
9 Dr. Talal Skaik 2014
The output resistance
r0 is quite high.
typically extend into
the megaohm range.
Common Base re
equivalent circuit
Copyright ©2009 by Pearson Education, Inc.
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Common Emitter Fixed Bias Configuration
10 Dr. Talal Skaik 2014
Common-emitter fixed-bias
configuration.
Network after the removal of the effects
of VCC, C1 and C2.
Copyright ©2009 by Pearson Education, Inc.
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Common Emitter Fixed Bias Configuration
11 Dr. Talal Skaik 2014
Substituting the re model into the network.
Copyright ©2009 by Pearson Education, Inc.
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Common Emitter Fixed Bias Configuration
12 Dr. Talal Skaik 2014
o C
io C o o C o
e e
o C o Cv v r 10R
i e e
V (R ||r ) , , V (R ||r )r r
V (R ||r ) RA , A
V r r
ib b
V VI I
Input impedance:
Output impedance:
Voltage gain:
eE r10Rei
eBi
rZ
r||RZ
Co
O
R10rCo
Co
RZ
r||RZ
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Common Emitter Fixed Bias Configuration
13 Dr. Talal Skaik 2014
Demonstrating the 180°phase shift between input and
output waveforms.
o C ov
i e
V (R ||r )A
V r
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Example 5.1
14 Dr. Talal Skaik 2014
Determine re, Zi (with ro=∞), Zo (with ro=∞),
Av (with ro=∞).
Repeat with ro=50 kΩ.
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Example 5.1 - Solution
15 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Common-Emitter
Voltage-Divider Bias
re model requires you to determine , re, and ro.
16 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Common-Emitter Voltage-Divider Bias
Input impedance:
Output impedance:
Voltage gain:
ei
21
r||RZ
R||RR
Co 10RrCo
oCo
RZ
r||RZ
17 Dr. Talal Skaik 2014
o C
io C o o C o
e e
o C o Cv v r 10R
i e e
V (R ||r ) , , V (R ||r )r r
V (R ||r ) RA , A
V r r
ib b
V VI I
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Example 5.2
18 Dr. Talal Skaik 2014
Determine re, Zi , Zo (with ro=∞), Av (with
ro=∞). Repeat with ro=50 kΩ.
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Example 5.2 - Solution
19 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Common-Emitter
Emitter-Bias Configuration
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Copyright ©2009 by Pearson Education, Inc.
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Impedance Calculations
E
i B b
1
1
for R
Z R ||Z
i b e e E
i b e b E
ib e E
b
b e E e E
b E e
V I r I R
V I r I R
VZ r R
I
Z r R r R
Z R r
Input impedance:
Output impedance:
o CZ R
21 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
o
o
o Cv
i b
b e E
o Cv
i e E
b E
o Cv
i E
V
V
V RA
V Z
substituting Z (r R )
V RA
V r R
and for the approximation Z R
V RA
V R
o C b C
iC
b
I R I R
VR
Z
Gain Calculations
Voltage gain:
22 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Example 5.3
23 Dr. Talal Skaik 2014
Determine re, Zi , Zo , Av . ignore ro for ro ≥ 10(RC+RE)
Without CE (unbypassed):
Copyright ©2009 by Pearson Education, Inc.
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Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
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.
24 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Impedance Calculations
Input impedance:
i B b
b e E
b e E
b E E e
Z R ||Z
Z r ( 1)R
Z (r R )
Z R (for R >>r )
25 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Impedance Calculations
Output impedance:
E e
e b
o
o E e o e R r
, I =( +1)I
( +1)
( +1)
( +1)
sin ( +1)
To determine Z , is set to zero
Z R ||r , Z r
ib
b
i
b
ie
e E
ie
e E
i
VI
Z
V
Z
VI
r R
ce
VI
r R
V
26 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Gain Calculations
Voltage gain:
E e E e E
Eo
E e
o Ev
i E e
ov R r , R r R
i
RV V
R r
V RA
V R r
VA 1
V
i
27 Dr. Talal Skaik 2014
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Example 5.7
28 Dr. Talal Skaik 2014
Determine re, Zi , Zo , Av .
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458 • All rights reserved.
Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky
Example 5.7 - solution
29 Dr. Talal Skaik 2014