Chapter 7: BJT Transistor Modeling Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458

Chapter 7: BJT Transistor Modeling

Robert BoylestadDigital Electronics

Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458

All rights reserved.

Slide 1




Transistor Modeling

A model is an equivalent circuit that represents the AC characteristics of the transistor.It uses circuit elements that approximate the behavior of the transistor.

There are 2 models commonly used in small signal AC analysis of a transistor:

• re model• hybrid equivalent model

Slide 2




Important Parameters

Zi, Zo, Av, Ai are important parameters for the analysis of the Ac characteristics of a transistor circuit.

Slide 3




Input Impedance, Zi[Formula

7.1]

To determine Ii: insert a “sensing resistor”

then calculate Ii: [Formula 7.2]

Ii

ViZi

Rsense

ViVsIi

Slide 4




Output Impedance, Zo

[Formula 7.5]

To determine Io: insert a “sensing resistor”

then calculate Io: [Formula 7.4]

Io

VoZo

Rsense

VoVIo

Slide 5




Voltage Gain, Av[Formula

7.6]

For an amplifier with no load:

[Formula 7.7]

Note: the no-load voltage gain (AVNL) is always greaterthan the loaded voltage gain (AV).

Vi

VoAv

it)(opencircuRVi

VoA

LVNL

Slide 6




Current Gain, Ai[Formula

7.9]

The current gain (Ai) also be calculated using the voltage gain (Av):

[Formula 7.10]

Ii

IoAi

LR

ZiAvAi

Slide 7




Phase Relationship

The phase relationship between input and output depends on the amplifier configuration circuit.

Common – Emitter ~ 180 degrees

Common - Base ~ 0 degrees

Common – Collector ~ 0 degrees

Slide 8




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.

Using a PNP transistor the Common-Base configuration and the re model:

The emitter is the input and the collector is the output.This model indicates: Ic = Ie

Slide 9




Common – Base Configuration

Slide 10




re

[Formula 7.11]

where IE is the DC current.

Ee

I

26mVr

Slide 11




Common-Base re Model

The diode in the previously shown re model can be replaced by the resistor re.

Slide 12




Impedance in Common-Base Configuration

The re model indicates:

The input impedance (Zi) is quite small:

[Formula 7.12]

The output impedance (Zo) is quite large:

[Formula 7.13]

erZi

Zo

Slide 13




Gain calculations for the Common-Base using the re model

Voltage Gain:

[Formula 7.14]

Current Gain:

[Formula 7.15]

The phase relationship between input and output is 0 degrees.

e

L

e

L

r

R

r

RAv

1 Ai

Slide 14




NPN Common-Base Configuration

The npn transistor will use the same calculation. The only difference is that the voltage polarities and current directions will be the opposite.

Slide 15




Common-Emitter Configuration

The base current is the input and the collector is the output.This model indicates:

[Formula 7.16]

[Formula 7.17]

[Formula 7.18]IbIe

IbIe

IbIc

)1(

Slide 16




Impedance in Common-Emitter Configuration

The input impedance (Zi):

[Formula 7.19]

The output impedance (Zo):

[Formula 7.20]

erZi

Zo

roZo

Slide 17




Gain calculations for the Common-Emitter using the re model

Voltage Gain (Av): [Formula 7.21]

Current Gain (Ai): [Formula 7.22]

e

L

r

RAv

roAi

Slide 18




Common-Collector Configuration

The Common-Emitter Model is used for Common-Collector.

Slide 19




Hybrid Equivalent Model

The hybrid parameters: hie, hre, hfe, hoe are developed and used to model the transistor. These parameters can be found in a specification sheet for a transistor.

Slide 20




General h-Parameters for any Transistor Configuration

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

Slide 21




Simplified General h-Parameter Model

The above model can be simplified based on these approximations:

hr 0 therefore hrVo = 0 and ho

Slide 22




Common-Emitter re vs. h-Parameter Model

hie = rehfe = hoe = 1/ro

Slide 23




Common-Emitter h-Parameters

[Formula 7.28]

[Formula 7.29]

acfe

eie

h

rh

Slide 24




Common-Base re vs. h-Parameter Model

hib = rehfb = -

Slide 25




Common-Base h-Parameters

[Formula 7.30]

[Formula 7.31]

1

fb

eib

h

rh

Documents

Chapter 7: BJT Transistor Modeling Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458