Chapter 5: BJT AC Analysis

Chapter 5: BJT AC Analysis

Copyright ©2009 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458 • All rights reserved.

Electronic Devices and Circuit Theory, 10/eRobert L. Boylestad and Louis Nashelsky

BJT Transistor ModelingBJT 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



The rThe ree Transistor Model Transistor Model

• BJTs are basically current-controlledcurrent-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-Base ConfigurationCommon-Base Configuration

Input impedance:Input impedance:

Output impedance:Output impedance:

Voltage gain:Voltage gain:

Current gain:Current gain:

ec I I e

e I

mV 26r

ei rZ

oZ

e

L

e

LV r

R

r

RA

1A i



Common-Emitter ConfigurationCommon-Emitter Configuration

bbe III 1

The diode re model can be replaced by the resistor re.

more…more…

ee I

mV 26r



Common-Emitter ConfigurationCommon-Emitter Configuration





ei rZ

oo rZ

e

LV r

RA

oriA



Common-Collector ConfigurationCommon-Collector Configuration





ei rZ )1(

Eeo RrZ ||

eE

EV rR

RA

1iA



The Hybrid Equivalent ModelThe Hybrid Equivalent ModelThe 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



Simplified General h-Parameter ModelSimplified General h-Parameter Model

• hi = input resistance• hf = forward transfer current ratio (Io/Ii)



rree vs. h-Parameter Model vs. h-Parameter Model

acfe

eie

h

rh

Common-EmitterCommon-Emitter

Common-BaseCommon-Base

1h

rh

fb

eib



The Hybrid The Hybrid Model Model

The hybrid model is most useful for analysis of high-frequency transistor applications.

At lower frequencies the hybrid model closely approximate the re parameters, and can be replaced by them.



Common-Emitter Fixed-Bias ConfigurationCommon-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



Common-Emitter Fixed-Bias ConfigurationCommon-Emitter Fixed-Bias Configuration

AC equivalent

re model



Common-Emitter Fixed-Bias CalculationsCommon-Emitter Fixed-Bias Calculations

Co 10Rre

Cv

e

oC

i

ov

r

RA

r

)r||(R

V

VA

eBCo r10R ,10Rri

eBCo

oB

i

oi

A

)r)(RR(r

rR

I

IA

C

ivi R

ZAA

Current gain from voltage gain:

Input impedance:

Output impedance:

Voltage gain: Current gain:

eE r10Rei

eBi

rZ

r||RZ

Co

O

R10rCo

Co

RZ

r||RZ



Common-Emitter Voltage-Divider BiasCommon-Emitter Voltage-Divider Bias

re model requires you to determine , re, and ro.



Common-Emitter Voltage-Divider Bias Common-Emitter Voltage-Divider Bias CalculationsCalculations


Input impedance:

Output impedance:

Voltage gain:

Current gain:

ei

21

r||RZ

R||RR

Co 10RrCo

oCo

RZ

r||RZ

Co 10Rre

C

i

ov

e

oC

i

ov

r

R

V

VA

r

r||R

V

VA

eCo

Co

r10R ,10Rri

oi

10Rrei

oi

eCo

o

i

oi

I

IA

rR

R

I

IA

)rR)(R(r

rR

I

IA

C

ivi R

ZAA



Common-Emitter Emitter-Bias Common-Emitter Emitter-Bias ConfigurationConfiguration



Impedance CalculationsImpedance Calculations

Eb

Eeb

Eeb

bBi

RZ

)R(rZ

1)R(rZ

Z||RZ

Input impedance:

Output impedance:Co RZ



Gain CalculationsGain Calculations


Voltage gain:

Current gain:

Eb

Eeb

RZE

C

i

ov

)R(rZEe

C

i

ov

b

C

i

ov

R

R

V

VA

Rr

R

V

VA

Z

R

V

VA

bB

B

i

oi ZR

R

I

IA

C

ivi R

ZAA



Emitter-Follower ConfigurationEmitter-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 CalculationsImpedance Calculations

Input impedance:

Output impedance:

eE rReo

eEo

rZ

r||RZ

Eb

Eeb

Eeb

bBi

RZ

)R(rZ

1)R(rZ

Z||RZ



Gain CalculationsGain Calculations


Voltage gain:

Current gain:

EeEeE RrR ,rRi

ov

eE

E

i

ov

1V

VA

rR

R

V

VA

bB

Bi ZR

RA

E

ivi R

ZAA




• 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.



CalculationsCalculations

eEi r||RZ

Co RZ

e

C

e

C

i

ov r

R

r

R

V

VA

1I

IA

i

oi

Input impedance:

Output impedance:

Voltage gain:

Current gain:



Common-Emitter Collector Feedback Common-Emitter Collector Feedback ConfigurationConfiguration

• 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




F

C

ei

R

R1

rZ

FCo R||RZ

e

C

i

ov r

R

V

VA

C

F

i

oi

CF

F

i

oi

R

R

I

IA

RR

R

I

IA

Input impedance:

Output impedance:

Voltage gain:

Current gain:



Collector DC Feedback ConfigurationCollector 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




F

C

ei

R

R1

rZ

FCo R||RZ

e

C

i

ov r

R

V

VA

C

F

i

oi

CF

F

i

oi

R

R

I

IA

RR

R

I

IA

Input impedance:

Output impedance:

Voltage gain: Current gain:



Two-Port Systems ApproachTwo-Port Systems ApproachThis 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

ooTh RZZ

ivNLTh VAE

With Vi set to 0 V:

The voltage across the open terminals is:

where AvNL is the no-load voltage gain.



Effect of Load Impedance on GainEffect of Load Impedance on Gain

L

ivi R

ZAA

This model can be applied to any current- or voltage-controlled amplifier.

Adding a load reduces the gain of the amplifier:

vNLoL

L

i

ov A

RR

R

V

VA



Effect of Source Impedance on GainEffect of Source Impedance on Gain

si

sii RR

VRV

The fraction of applied signal that reaches the input of the amplifier is:

vNLsi

i

s

ovs A

RR

R

V

VA

The internal resistance of the signal source reduces the overall gain:



Combined Effects of RCombined Effects of RSS and R and RLL on Voltage on Voltage

GainGainEffects of RL:

Effects of RL and RS:

L

ivi

oL

vNLL

i

ov

R

RAA

RR

AR

V

VA

L

isvsis

vNLoL

L

si

i

s

ovs

R

RRAA

ARR

R

RR

R

V

VA



Cascaded SystemsCascaded 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 AmplifiersR-C Coupled BJT Amplifiers

Co RZ

Input impedance, first stage:

Output impedance, second stage:

Voltage gain:

e21i r||R||RZ

2v1vv

e

C2V

e

e21C1v

AAA

r

RA

r

r||R||R||RA



Cascode ConnectionCascode 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.



Darlington ConnectionDarlington Connection

The Darlington circuit provides a very high current gain—the product of the individual current gains:

D = 12

The practical significance is that the circuit provides a very high input impedance.



DC Bias of Darlington CircuitsDC Bias of Darlington Circuits

BDBDE II)1(I

EEE RIV

EDB

BECCB RR

VVI

Base current:

Emitter current:

Emitter voltage:

Base voltage:

BEEB VVV



Feedback PairFeedback 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.



Current Mirror CircuitsCurrent Mirror Circuits

Current mirror circuits provide constant current in integrated circuits.



Current Source CircuitsCurrent Source CircuitsConstant-current sources can be built using FETs, BJTs, and combinations of these devices.

IE IC

E

BEZE R

VVII

more…more…



Current Source CircuitsCurrent Source Circuits

VGS = 0VID = IDSS = 10 mA



Fixed-Bias ConfigurationFixed-Bias Configuration

ieBi h||RZ

ieBi h||RZ

oeCo h/1||RZ

ie

oCfe

i

ov h

eh/1||Rh

V

VA

fei

oi h

I

IA

Input impedance:

Output impedance:

Voltage gain:

Current gain:



Voltage-Divider ConfigurationVoltage-Divider Configuration

ie

fei hR

RhA

iei h||RZ

Co RZ

ie

oeCfev h

1/h||RhA

Input impedance:

Output impedance:

Voltage gainVoltage gain:

Current gain:



Emitter-Follower ConfigurationEmitter-Follower Configuration

boi

Efeb

Z||RZ

RhZ

boi

Efeb

Z||RZ

RhZ

Input impedance:

Output impedance:

Voltage gain:

Current gain:

fe

ieEo h

h||RZ

feieE

E

i

ov h/hR

R

V

VA

E

ivi

bB

Bfei

R

ZAA

ZR

RhA




ibEi h||RZ

Co RZ

ib

Cfb

i

ov h

Rh

V

VA

1hI

IA fb

i

oi

Input impedance:

Output impedance:

Voltage gain:

Current gain:



TroubleshootingTroubleshooting

Check the DC bias voltagesCheck the DC bias voltages

If not correct, check power supply, resistors, transistor. Also check the coupling capacitor between amplifier stages.

Check the AC voltagesCheck the AC voltages

If not correct check transistor, capacitors and the loading effect of the next stage.

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Chapter 5: BJT AC Analysis