Chapter 5:

BJT AC Analysis
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.

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
Effect of Load Impedance on Gain

This model can be applied to

any current- or voltage-
controlled amplifier.

Adding a load reduces the

gain of the amplifier:
Vo RL
Av   A vNL
Vi RL  Ro
Zi
Ai  A v
RL

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky 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:
R i Vs
Vi 
Ri  Rs

The internal resistance of the signal source reduces the

overall gain:
Vo Ri
A vs   A vNL
Vs R i  R s

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
Combined Effects of RS and RL on Voltage
Gain
Effects of RL:
Vo R L A vNL
Av  
Vi RL  Ro
R
Ai  A v i
RL

Effects of RL and RS:

Vo Ri RL
A vs   A vNL
Vs R i  R s R L  R o
R  Ri
A is   A vs s
RL

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky 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 Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
R-C Coupled BJT Amplifiers
This image cannot currently be display ed.

Input impedance, first stage:

Z i  R 1 || R 2 ||  re

Output impedance, second stage:

Zo  R C

Voltage gain:
R C || R 1 || R 2 ||  re
A v1 
re
RC
A V2 
re
A v  A v1 A v 2

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
R-C Coupled BJT Amplifiers
Draw the ac equivalent circuit and calculate the voltage gain, input resistance and
output resistance for the cascade BJT amplifier in above Figure. Let the parameters
are:

VCC  20V ,  Q1   Q 2  200, V BE ( ON )  0.7V , r0  

R1  R3  15k, R2  R4  4.7 k, RC1  RC 2  2.2k, RE1  R E 2  1k

Solution

Dc Analysis

I BQ1  19.89A I BQ 2  19.89A

I CQ1  3.979mA I CQ 2  3.979mA
1re1   2 re 2  1.307 k

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
R-C Coupled BJT Amplifiers
Ac Analysis:
The voltage gain at Q1 is:

AV 1  0.153(2.2k // 957.36)  102.06

The voltage gain at Q2 is

AV 2  0.153( 2.2k )  336.6

The overall gain is then,
AV  AV 1 AV 2  ( 102.06)( 336.6)  34,353
The input resistance is:
Ri  R1 // R2 // Br e  957.36

The o/p resistance is: Ro  RC 2  2.2k

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky 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 high-
frequency applications.

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
Cascode Connection

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky 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:
bD = b1b2
The practical significance is that the circuit
provides a very high input impedance.

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
DC Bias of Darlington Circuits
This image cannot currently be display ed.

Base current:
V  VBE
I B  CC
R B   DR E

Emitter current:
I E  ( D  1)I B   D I B

Emitter voltage:
VE  I E R E

Base voltage:
VB  VE  VBE

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
AC small signal of Darlington Circuits

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky 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 Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
DC Analysis of Feedback Pair

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
AC Analysis of Feedback Pair

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky 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 Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
Current Mirror Example

Find I?

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.
Current Mirror More Configurations

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky 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.

VZ  VBE IE  IC
I  IE 
RE
more…

Electronic Devices and Circuit Theory, 10/e Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky 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 Copyright ©2009 by Pearson Education, Inc.
Robert L. Boylestad and Louis Nashelsky Upper Saddle River, New Jersey 07458 • All rights reserved.