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FALL2012-2013

Course Teacher : Bishwajit Debnath

AIUB

Department of Electrical and Electronics Engineering

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BJT Transistor Modeling

A model is an equivalent circuit that represents theAC characteristics of the transistor.

A model uses circuit elements that approximate thebehavior of the transistor.

There are two models commonly used in smallsignal AC analysis of a transistor:

r e model Hybrid equivalent model

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The r e Transistor Model

BJTs are basically current-controlled devices;

Therefore the r e model uses a diode and a current source toduplicate 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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The r e Transistor Model

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Common-Base Configuration

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Common-Base Configuration

Input impedance:

Output impedance:

ec II e

eI

mV26r

ei rZ

oZ

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Common-Base Configuration

Voltage gain:

Current gain:

ec II e

eI

mV26r

e

L

e

LV r

R rR

A

1A i

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Common-Emitter Configuration

b b e I I I 1

ee

I

mV26r

The diode r e model can bereplaced by the resistor r e.

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Common-Emitter Configuration

Input impedance:

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Common-Emitter Configuration

Output impedance:

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Common-Emitter Configuration

Voltage gain:

R L

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Common-Emitter Configuration

Current gain:

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Common-Emitter Configuration

Model

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Common-Emitter Configuration

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Common-Collector Configuration

Input impedance:

Output impedance:

Voltage gain:

Current gain:

e i r Z )1(

E e o R r Z ||

eE

EV

rR

R A

1 iA

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The Hybrid Equivalent Model

The following hybrid parameters are developed and usedfor modeling the transistor. These parameters can be foundon the specification sheet for a transistor.

h i = input resistance h r = reverse transfer voltage ratio (V i/Vo) 0 h f = forward transfer current ratio (I o/I i) h o = output conductance

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Simplified General h-Parameter Model

h i = input resistance h f = forward transfer current ratio (I o/I i)

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r e vs. h-Parameter Model

acfe

eie

h

rh

Common-Emitter

Common-Base

1h

rh

fb

eib

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The Hybrid Model

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

At lower frequencies the hybrid model closelyapproximate the r e parameters, and can be replacedby them.

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Common-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

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Common-Emitter Fixed-Bias Configuration

AC equivalent

r e model

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Common-Emitter Fixed-Bias Calculations

Co 10R re

Cv

e

oC

i

ov

r

R A

r

)r||(R

V

VA

eBCo r10R ,10R ri

eBCo

oB

i

oi

A)r)(R R (r

rR

I

IA

C

ivi

R

ZAA

Current gain from voltage gain:

Input impedance:

Output impedance:

Voltage gain: Current gain:

eE r10R ei

eBi

rZ

r||R Z

Co

O

R 10rCo

Co

R Zr||R Z

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Common-Emitter Voltage-Divider Bias

r e model requires you to determine , r e, and r o.