INTRODUCTION: TRANSISTOR 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 it’s a small

signal (AC) or largesignal (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 modelb) 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 η=Po(ac)/Pi(dc)

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

VS

VCC

C1

C2

C3

+

-

Vo

RS

Vi

+

-RE

RCR1

R2

VS

+

-

Vo

RS

V i

+

-

RCR1

R2

•I/p coupling capacitor s/c• Large values• Block DC and pass AC signal • Bypass

capacitor s/c•Large values

DC supply “0” potential

Voltage-divider configuration under AC analysis

Redraw the voltage-divider configuration after removing dc

supply and insert s/c for the capacitors

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

VS

RSR2 R1 Rc

Transistor small-signal ac

equivalent cct

Vo

Zi

Ii

Zo

Io

Vi

+ +

- -

B

E

C

Redrawn for small-signal AC analysis

Modeling of BJT begin

HERE!

VS

+

-

Vo

RS

V i

+

-

RCR1

R2

AC bias analysis :

1) Kill all DC sources

2) Coupling and Bypass capacitors are short cct. The effect of these capacitors is to set a lower cut-off frequency for the cct.

3) Inspect the cct (replace BJTs with its small signal model:re 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 MΩ)

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.

VS Two-portsystem

Vi

Rsense

IiZi

+

-

Determining Zi

+

-

sense

isi

R

VVI

−=

i

ii

I

VZ =

Two port system-determining input impedance Zi

• The input impedance of transistor can be approximately determined using dc biasing because it doesn’t simply change when the magnitude of applied ac signal is change.

Output Impedance, Zo (few ohms 2MΩ)

The output impedance of an amplifier is determined at the output terminals looking back into the system with the applied signal set to zero.

Two-portsystem

Rsource

Vs=0V

Rsense

V

+

-

+

-

Io

ZoVo

Determining Zo

sense

oo

R

VVI

−=

o

oo

I

VZ =

cctopen become ZRZ oLo ⇒≥R LZ o=R o

Iam p lifie r

IR o

IL

RoL

Lo

II

RRFor

≥≥

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.• It’s the ratio of circuit’s output to circuit’s input.• The small-signal AC voltage gain can be determined by:

i

ov

V

VA =

VS AvNLVi

Rsource

Zi

+

-

+

-Vo

+

-

Determining the no load voltage gain

By referring the network below the analysis are:

cct)(open ΩRi

oLvNL

V

VA

load no

∞==

vNLARZ

Z

V

VA

:resistance sourcewith

si

i

s

ovs

+==

Current Gain, Ai

• This characteristic can be determined by:

i

oi

I

IA =

BJTamplifier

Vi

Zi

+

-

Vo

+

-

Ii

RL

Determining the loaded current gain

Io

L

ivi

R

ZAA −=

Li

io

ii

Lo

RV

ZV

Z/V

R/V −=−=

L

oo

R

VI −=

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 transistorre modelre equivalent cct.

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

0VVo

i12

0VVi

i11

o12i11i

o

o

V

Vh

I

Vh

VhIhV

====

====

====

====

++++====

0AIo

o22

0VVo

i21

o

o22i21O

o

o

V

Ih

I

Ih

, 0VV Solving

VhIhI

====

====

====

====

====++++====

H22 is a conductance!

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

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 = βrehfe = βhoe = 1/ro