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Chapter 7 BJT Transistor Modeling

Faculty of Electrical and Electronic Eng.

Topic objectives

- At the end of the course you will be able to
- Understand about the small signal analysis of

circuit network using re model and hybrid

equivalent model - Understand the relationship between those two

available model for small signal analysis

- INTRODUCTIONTRANSISTOR MODELING
- To begin analyze of small-signal AC response of

BJT amplifier the knowledge of modeling the

transistor is important. - The input signal will determine whether its a

small signal (AC) or large signal (DC) analysis. - The goal when modeling small-signal behavior is

to make of a transistor that work for

small-signal enough to keep things linear

(i.e. not distort too much) 3 - There are two models commonly used in the small

signal analysis - a) re model
- b) hybrid equivalent model

How does the amplification be done?

- Conservation output power of a system cannot be

large than its input and the efficiency cannot be

greater than 1 - The input dc plays the important role for the

amplification to contribute its level to the ac

domain where the conversion will become as

?Po(ac)/Pi(dc) - Simply speaking

Disadvantages

- Re model
- Fails to account the output impedance level of

device and feedback effect from output to input - Hybrid equivalent model
- Limited to specified operating condition in order

to obtain accurate result

DC supply ? 0 potential

- O/p coupling capacitor ? s/c
- Large values
- Block DC and pass AC signal

- I/p coupling capacitor ? s/c
- Large values
- Block DC and pass AC signal

- Bypass
- capacitor ? s/c
- Large values

Voltage-divider configuration under AC analysis

Redraw the voltage-divider configuration after

removing dc supply and insert s/c for the

capacitors

Modeling of BJT begin HERE!

AC bias analysis 1) Kill all DC sources 2)

Coupling and Bypass capacitors are short cct. The

effect of there capacitors is to set a lower

cut-off frequency for the cct. 3) Inspect the

cct (replace BJTs with its small signal modelre

or hybrid). 4) Solve for voltage and current

transfer function, i/o and o/p impedances.

- IMPORTANT PARAMETERS
- Input impedance, Zi
- Output impedance, Zo
- Voltage gain, Av
- Current gain, Ai
- Input Impedance, Zi(few ohms ? M?)
- The input impedance of an amplifier is the value

as a load when connecting a single source to the

I/p of terminal of the amplifier.

Two port system-determining input impedance Zi

- The input impedance of transistor can be

approximately determined using dc biasing because

it doesnt simply change when the magnitude of

applied ac signal is change.

Demonstrating the impact of Zi

Example 6.1 For the system of Fig. Below,

determine the level of input impedance

Output Impedance, Zo (few ohms ? 2M?) The output

impedance of an amplifier is determined at the

output terminals looking back into the system

with the applied signal set to zero.

Example 6.2 For the system of Fig. below,

determine the level of output impedance

Example 6.3 For the system of Fig. below,

determine Zo if V600mV, Rsense10k? and Io10?A

Example 6.4 Using the Zo obtained in example

6.3, determine IL for the configuration of Fig

below if RL2.2 k? and Iamplifier6 mA.

- Voltage Gain, AV
- DC biasing operate the transistor as an

amplifier. Amplifier is a system that having the

gain behavior. - The amplifier can amplify current, voltage and

power. - Its the ratio of circuits output to circuits

input. - The small-signal AC voltage gain can be

determined by

By referring the network below the analysis are

Example 6.5 For the BJT amplifier of fig. below,

determine a)Vi b) Ii c) Zi d) Avs

- Current Gain, Ai
- This characteristic can be determined by

- re TRANSISTOR MODEL
- employs a diode and controlled current source to

duplicate the behavior of a transistor. - BJT amplifiers are referred to as

current-controlled devices. - Common-Base Configuration
- ?Common-base BJT transistor
- ?re model
- ?re equivalent cct.

Therefore, the input impedance, Zi re that less

than 50O. For the output impedance, it will be as

follows

isolation part, Zire

Zo ? ??

The common-base characteristics

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- Example 6.6 For a common-base configuration in

figure - below with IE4mA, ?0.98 and AC signal of 2mV is
- applied between the base and emitter terminal
- Determine the Zi b) Calculate Av if RL0.56k?
- c) Find Zo and Ai

Solution

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- Example 6.7 For a common-base configuration in

previous - example with Ie0.5mA, ?0.98 and AC signal of

10mV is - applied, determine
- Zi b) Vo if RL1.2k? c) Av d)Ai e) Ib

- Common-Emitter Configuration
- ?Common-emitter BJT transistor
- ?re model
- ?re equivalent cct.
- Still remain controlled-current source (conducted

between collector and base terminal) - Diode conducted between base and emitter terminal

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The output graph

Output impedance Zo

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- Example 6.8 Given ?120 and IE(dc)3.2mA for a

common- - emitter configuration with ro ? ?, determine
- Zi b)Av if a load of 2 k? is applied c) Ai with

the 2 k? load

- Example 6.9 Using the npn common-emitter

configuration, - determine the following if ?80, IE(dc)2 mA and

ro40 k? - Zi b) Ai if RL 1.2k ? c) Av if RL1.2k ?

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Hybrid Equivalent Model

- re model is sensitive to the dc level of

operation that result input resistance vary with

the dc operating point - Hybrid model parameter are defined at an

operating point that may or may not reflect the

actual operating point of the amplifier

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.

Determination of parameter

H22 is a conductance!

General h-Parameters for any Transistor

Configuration

hi input resistance hr reverse transfer

voltage ratio (Vi/Vo) hf forward transfer

current ratio (Io/Ii) ho output conductance

Common emitter hybrid equivalent circuit

Common base hybrid equivalent circuit

Simplified General h-Parameter Model

The model can be simplified based on these

approximations hr ? 0 therefore hrVo 0 and

ho ? ? (high resistance on the output)

Simplified

Common-Emitter re vs. h-Parameter Model

hie ?re hfe ? hoe 1/ro

Common-Emitter h-Parameters

Formula 7.28 Formula 7.29

Common-Base re vs. h-Parameter Model

hib re hfb -?

Common-Base h-Parameters

Formula 7.30 Formula 7.31