Lecture 12

Small AC Signal Analysis of BJT

BJT 1-1

Outline Introduction to small AC signal analysis of BJT

The re Transistor Model • BJT configurations

The Hybrid π Equivalent Model The re Model vs. The Hybrid π Equivalent Model

BJT 1-2

Problem on DC analysis of BJT

Given the device characteristics as shown in figure, determine VCC, RB, and RC for the fixed bias configuration

BJT 1-3

Solution

From the load line

BJT 1-4

BJT Transistor Modeling

BJT AC model is an equivalent circuit that represents the AC characteristics of the BJT transistor

The 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 π equivalent model

BJT 1-5

BJT AC Analysis

BJT 1-6

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 Recall: the ac resistance of a diode can be

determined by the equation rac = 26 mV/ID, where ID is the dc current through the diode at the Q (quiescent) point

One disadvantage of this model is its sensitivity to the DC level. This model is designed for specific circuit conditions

BJT 1-7

Common-Base Configuration

BJT 1-8

ee

I

mV 26r

Input impedance:

Output impedance:

Voltage gain:

Current gain:

ec I I

ei rZ

oZ

e

L

ee

L

i

oV

r

R

rI

R

V

VA eI

1 iA

RL

Forward-biased junction

Example For a common-base configuration, as shown in the

figure, with IE = 4 mA, α = 0.98, and an ac signal of 2 mV applied between the base and emitter terminals: (a) Determine the input impedance.

(b) Calculate the voltage gain if a load of 0.56 kΩ is connected to the output terminals.

(c) Find the output impedance and current gain.

BJT 1-9

Solution

BJT 1-10

Common-Emitter Configuration

BJT 1-11

bbe III 1

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

e

eI

mV 26r

Common-Emitter Configuration

BJT 1-12

Input impedance:

Output impedance:

Voltage gain:

Current gain:

e

B

ii rZIV

oo rZ

e

LV

r

RA VV

i

o

oriA

IIi

o

RL

Vo

The Hybrid π Equivalent Model The hybrid π model is most useful for analysis of high-frequency

transistor applications

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

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

BJT 1-13

• hi = input resistance

• hr = reverse transfer voltage ratio (Vi/Vo) 0

• hf = forward transfer current ratio (Io/Ii)

• ho = output conductance

The Hybrid π Equivalent Model

BJT 1-14

- Short-circuit input impedance parameter

- Open-circuit reverse transfer voltage ratio parameter - Short-circuit forward transfer current ratio parameter - Open-circuit output admittance parameter

Simplified General h-Parameter Model

BJT 1-15

• hi = input resistance

• hf = forward transfer current ratio (Io/Ii)

- hr and ho has slight impact on values of Zi, Zo,Av and Ai

- hr very small (≈ 0) and ho very large (∞)

re vs. h-Parameter Model

BJT 1-16

fe

eie

h

rh

Common-Emitter

Common-Base

1

fb

eib

h

rh

e

BJT 1-17

Lecture Summary

Covered material Introduction to small AC signal analysis of BJT

The re Transistor Model The Hybrid π Equivalent Model

Material to be covered next lecture

Continue BJT analysis with small AC signal Common-Emitter configuration

• Analysis using various biasing circuits

Effect of source/load impedance on current and voltage gain

Introduction to cascaded systems