1 Chapter 5: BJT AC Analysis. BJT Transistor Modeling 2 A model is an equivalent circuit that represents the AC characteristics of the transistor. A model

11

Chapter 5: Chapter 5: BJT AC AnalysisBJT AC Analysis

BJT Transistor ModelingBJT Transistor Modeling

22

• 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

33

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-Base ConfigurationCommon-Base Configuration

Input impedance:

Output impedance:

Voltage gain:

Current gain:

44

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

55

ee I

mV 26r

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

bbe II1I

Input impedance:

Output impedance:

Voltage gain:

Current gain:

ei rZ

oo rZ

e

LV r

RA

oriA

more…more…

Common-Collector ConfigurationCommon-Collector Configuration

66

Use the common-emitter model for the common-collector configuration.

The Hybrid Equivalent ModelThe Hybrid Equivalent Model

77

The following hybrid parameters are developed and used for modeling the transistor. These parameters can be found in a 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

88

• hi = input resistance• hr = reverse transfer voltage ratio (Vi/Vo) 0 • hf = forward transfer current ratio (Io/Ii)• ho = output conductance

99

Common-Emitter rCommon-Emitter ree 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

1010

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

1111

• 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

1212

AC equivalent

re model

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

1313

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

1414

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

Common-Emitter Voltage-Divider Bias CalculationsCommon-Emitter Voltage-Divider Bias Calculations

1515


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 ConfigurationCommon-Emitter Emitter-Bias Configuration(Unbypassed R(Unbypassed REE))

1616

1717

Impedance CalculationsImpedance Calculations

Eb

Eeb

Eeb

bBi

RZ

)R(rZ

1)R(rZ

Z||RZ

Input impedance:

Output impedance:

Co RZ

1818

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

1919

• 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.

2020

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

2121

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


2222

• 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

2323

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 ConfigurationCommon-Emitter Collector Feedback Configuration

2424

• 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


2525

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

2626

• 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


2727

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 Approach

2828

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

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

2929

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

3030

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 Gain on Voltage Gain

3131

Effects 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

3232

R-C Coupled BJT AmplifiersR-C Coupled BJT Amplifiers

Co RZ

3333

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

3434

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

3535

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

3636

EDB

BECCB RR

VVI

Base current:

Emitter current:

Emitter voltage:

Base voltage:

BEEB VVV

Feedback PairFeedback Pair

3737

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

3838

Current mirror circuits provide constant current in integrated circuits.

Current Source CircuitsCurrent Source Circuits

3939

Constant-current sources can be built using FETs, BJTs, and combinations of these devices.

VGS = 0VID = IDSS = 10 mA

IE IC

E

BEZE R

VVII

more…more…

Fixed-Bias ConfigurationFixed-Bias Configuration

ieBi h||RZ

4040

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

4141

ie

fei hR

RhA

iei h||RZ

Co RZ

ie

oeCfev h

1/h||RhA

Input impedance:

Output impedance:

Voltage gainVoltage gain:

Current gain:

Unbypassed Emitter-Bias ConfigurationUnbypassed Emitter-Bias Configuration

4242

bBi

Efeb

Z||RZ

RhZ

Co RZ

E

Cv R

RA

C

ivi R

ZAA

bB

Bfei ZR

RhA

Input impedance:

Output impedance:

Voltage gain:

Current gain: Current gain from voltage gain:

Emitter-Follower ConfigurationEmitter-Follower Configuration

boi

Efeb

Z||RZ

RhZ

boi

Efeb

Z||RZ

RhZ

4343

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


4444

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:

Complete Hybrid Equivalent ModelComplete Hybrid Equivalent Model

• Current gain, Ai

• Voltage gain, Av

• Input impedance, Zi

• Output impedance, Zo

4545

TroubleshootingTroubleshooting

4646

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.

Practical ApplicationsPractical Applications

• Audio Mixer

• Preamplifier

• Random-Noise Generator

• Sound Modulated Light Source

4747

Documents

1 Chapter 5: BJT AC Analysis. BJT Transistor Modeling 2 A model is an equivalent circuit that represents the AC characteristics of the transistor. A model