Lecture 15 Small AC Signal Analysis of BJTeng.staff.alexu.edu.eg/.../spring_2018/Lecture_15_BJT.pdfOutline Introduction to small AC signal analysis of BJT The r e Transistor Model

Lecture 15

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

Problems on DC analysis of BJT Example (1)

Determine the dc bias voltage VCE and the current IC for the voltage-divider configuration shown in the figure. (use exact and approximate methods)

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Solution Using Exact Analysis Method

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Solution (cont’d)

Return to the example:

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Solution (cont’d)

BJT 1-6

Solution (cont’d)

Using Approximate Analysis Method

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The condition that will define whether the approximate approach can be applied

Solution (cont’d)

Return to the example: Testing:

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Solution (cont’d)

BJT 1-9

• Now, compare between obtained results by the exact and approximate methods

• Using the exact approach: ICQ =0.85 mA VCEQ=12.22 V

Problems on DC analysis of BJT

Example (2) Make dc analysis for determining the voltage VCB

and the current IB for the common-base configuration as shown in figure

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Solution

Applying Kirchhoff’s voltage law to the input circuit yields

Applying Kirchhoff’s voltage law to the output circuit gives

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Problems on DC analysis of BJT

Example (3) Given the device characteristics as shown in

figure, determine VCC, RB, and RC for the fixed bias configuration

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Solution

From the load line

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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

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BJT AC Analysis

BJT 1-15

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 1-16

Common-Base Configuration

BJT 1-17

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.

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Solution

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Common-Emitter Configuration

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bbe III 1

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

e

eI

mV 26r

Common-Emitter Configuration

BJT 1-21

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 1-22

• 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 1-23

- 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 1-24

• 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 1-25

fe

eie

h

rh

Common-Emitter

Common-Base

1

fb

eib

h

rh

e

BJT 1-26

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