BJT AC Analysis

BJT AC AnalysisBJT AC Analysis

Chapter 5

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Electronic Devices and Circuit TheoryElectronic Devices and Circuit Theory

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Ch.5 Summary

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

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Ch.5 Summary

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.

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Ch.5 Summary

Common-Base Configuration

ee I

mV26 r

ei rZ

oZ

e

L

e

LV r

R

r

RA

1iA

Input impedance:

Output impedance:

Voltage gain:

Current gain:

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Ch.5 Summary

Common-Emitter Configuration

bbe II I 1

ee I

mV26 r

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

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Ch.5 Summary

Common-Emitter Configuration

ei rZ

oo rZ

e

LV r

RA

oriA

Input impedance:

Output impedance:

Voltage gain:

Current gain:

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Ch.5 Summary

Common-Collector Configuration

ei rZ )1(

Eeo RrZ ||

eE

EV rR

RA

1βAi

Input impedance:

Output impedance:

Voltage gain:

Current gain:

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Ch.5 Summary

The Hybrid Equivalent Model

Hybrid parameters are developed and used for modeling the transistor. These parameters can be found on a transistor’s specification sheet:

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

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Ch.5 Summary

Simplified General h-Parameter Model

hi = input resistancehf = forward transfer current ratio (Io/Ii)

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Ch.5 Summary

re vs. h-Parameter Model

acfe

eie

βh

βrh

Common-Emitter

Common-Base

1

αh

rh

fb

eib

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Ch.5 Summary

The Hybrid Model

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

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

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Ch.5 Summary

Common-Emitter Fixed-Bias Configuration

The input is applied to the baseThe output is taken from the collector

High input impedanceLow output impedance

High voltage and current gain

Phase shift between input and output is 180

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Ch.5 Summary

Common-Emitter Fixed-Bias Configuration

AC equivalent

re,model

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Ch.5 Summary

Common-Emitter Fixed-Bias Calculations

Co Rre

Cv

e

oC

i

ov

r

RA

r

)||r(R

V

VA

10

eBCo βr, RRri

eBCo

oB

i

oi

βA

)βr)(RR(r

rβR

I

IA

1010

C

iVi R

ZAA Current gain

from voltage gain:

Input

impedance:

Output

impedance:

Voltage gain:

Current gain:

eE βrRei

eBi

βrZ

||β|RZ

10

Co

O

RrCo

Co

RZ

||rRZ

10

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Ch.5 Summary

Common-Emitter Voltage-Divider Bias

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

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Ch.5 Summary

Common-Emitter Voltage-Divider Bias Calculations

Input impedance

ei

21

βr||RZ

R||RR

Output impedance

Co 10RrCo

oCo

RZ

r||RZ

Voltage gain

Co 10Rre

C

i

ov

e

oC

i

ov

r

R

V

VA

r

r||R

V

VA

Current gain

eCo

Co

r10R ,10Rri

oi

10Rrei

oi

eCo

o

i

oi

I

IA

rR

R

I

IA

)rR)(R(r

rR

I

IA

Current gain from Av

C

ivi R

ZAA

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Ch.5 Summary

Common-Emitter Emitter-Bias Configuration

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Ch.5 Summary

Impedance Calculations

Eb

Eeb

Eeb

bBi

RZ

)R(rZ

1)R(rZ

Z||RZ

Input impedance:

Output impedance:

Co RZ

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Ch.5 Summary

Gain Calculations

Current gain from Av:

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

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Ch.5 Summary

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.

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Ch.5 Summary

Impedance Calculations

Input impedance:

Output impedance:eE rReo

eEo

rZ

||rRZ

Eb

Eeb

Eeb

b Bi

βRZ

)Rβ(rZ

)R(ββrZ

||ZRZ

1

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Ch.5 Summary

Gain Calculations

Current gain from voltage gain:

Voltage gain:

Current gain:

EeEeE Rr, RrRi

ov

eE

E

i

ov

V

VA

rR

R

V

VA

1

bB

Bi ZR

βRA

E

ivi R

ZAA

Electronic Devices and Circuit TheoryBoylestad

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Ch.5 Summary

Common-Base ConfigurationThe 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

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Ch.5 Summary

Calculations

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:

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Ch.5 Summary

Common-Emitter Collector Feedback Configuration

• 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 the input and output

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Ch.5 Summary

Calculations

F

C

ei

RR

β

rZ

1

FCo R||RZ

e

C

i

ov r

R

V

VA

C

F

i

oi

CF

F

i

oi

R

R

I

IA

βRR

βR

I

IA

Input impedance:

Output impedance:

Voltage gain:

Current gain:

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Ch.5 Summary

Collector DC FeedbackConfiguration

• The input is applied to the base

• The output is taken from the collector

• There is a 180 phase shift between input and output

This is a variation of the common-emitter, fixed-bias configuration

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Ch.5 Summary

Calculations

F

C

ei

RR

β

rZ

1

FCo ||RRZ

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:

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Ch.5 Summary

Two-Port Systems Approach

ooTh RZZ

With Vi set to 0 V:

The voltage across the open terminals is:

where AvNL is the no-load voltage gain

ivNLTh VAE

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Ch.5 Summary

Effect 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

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Ch.5 Summary

Effect of Source Impedance on Gain

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

si

sii RR

VRV

vNLsi

i

s

ovs A

RR

R

V

VA

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

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Ch.5 Summary

Combined Effects of RS and RL on Voltage Gain

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

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Ch.5 Summary

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

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Ch.5 Summary

R-C Coupled BJT Amplifiers

Co RZ

Input impedance, first stage:

Output impedance, second stage:

Voltage gain:

ei RRRZ |||| 21

21

2

211

||||||

vvv

e

Cv

e

eCv

AAA

r

RA

r

RRRRA

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Ch.5 Summary

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.

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Ch.5 Summary

Darlington Connection

The Darlington circuit provides very high current gain, equal to the product of the individual current gains:

D = 1 2

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

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Ch.5 Summary

DC Bias of Darlington Circuits

BDBDE III )1(

EEE RIV

EDB

BECCB RR

VVI

Base current:

Emitter current:

Emitter voltage:

Base voltage:

BEEB VVV

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Ch.5 Summary

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.

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Ch.5 Summary

Current Mirror Circuits

Current mirror circuits provide constant current in integrated circuits.

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Ch.5 Summary

Current Source Circuits

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

IE ICE

BEZE R

VVII

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Ch.5 Summary

Current Source Circuits

VGS = 0VID = IDSS = 10 mA

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Ch.5 Summary

Fixed-Bias

ieBi hRZ ||

oeCo hRZ /1||

ie

oCfe

i

ov h

ehRh

V

VA

/1||

fei

oi h

I

IA

Input impedance:

Output impedance:

Voltage gain:

Current gain:

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Ch.5 Summary

Voltage-Divider Configuration

ie

fei hR

RhA

iei h||RZ

Co RZ

ie

oeCfev h

1/h||RhA

Input impedance:

Output impedance:

Voltage gaingain:

Current gain:

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Ch.5 Summary

Emitter-Follower Configuration

boi

Efeb

Z||RZ

RhZ

boi

Efeb

ZRZ

RhZ

||

Input impedance:

Output impedance:

Voltage gain:

Current gain:

fe

ieEo h

hRZ ||

feieE

E

i

ov hhR

R

V

VA

/

E

ivi

bB

Bfei

R

ZAA

ZR

RhA

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Ch.5 Summary

Common-Base Configuration

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:

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Ch.5 Summary

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.