Prepared by

Mr.R.Suresh , AP/EEE

Ms.S.KARKUZHALI,A.P/EEE

(EC 8353)

Electron Devices and Circuits

BJT small signal model – Analysis of CE, CB, CC amplifiers- Gain and frequency response –MOSFET small signal model– Analysis of CS and Source follower – Gain and frequency response- High frequency analysis.

BJT: Two port network, Transistor hybridmodel, determination of h- parameters,conversion of h-parameters, generalizedanalysis of transistor amplifier model usingh-parameters, Analysis of CB, CE and CCamplifiers using exact and approximateanalysis, Comparison of transistor amplifiers.

FET: Generalized analysis of small signalmodel, Analysis of CG, CS and CD amplifiers,comparison of FET amplifiers.

Agenda•Small Signal Analysis

• Hybrid h-Parameter model for an amplifier

• Hybrid Parameters or h-parameters

•Transistor Hybrid Model

•Analysis of Transistor Amplifier using Complete h- Parameter Model

•Analysis of Transistor Amplifier using simplified h-Parameter Model

We represent the transistor amplifier circuit in the form of a two port network as shown in fig. • This two port network represent the transistor in any one of its three configurations (CE,CB,CC).

•

Small Signal Analysis of Amplifiers

• Small signal response is analyzed using the h-parameter model

• Response of an amplifier depends on frequency considerations.

• Frequency response curves of RC Coupled amplifier , DC amplifier is

shown.

•There are 3 regions of frequency : low , mid and high

•The difference between high and low frequency is the bandwidth

RC Coupled Amplifier

DC Amplifier

Hybrid h-Parameter model for an amplifier

The equivalent circuit of a transistor can be dram using simple

approximation by retaining its essential features.

These equivalent circuits will aid in analyzing transistor

circuits easily and rapidly.

A transistor can be treated as a two part network. The terminal

behavior of any two part network can be specified by the

terminal voltages V1 & V2 at parts 1 & 2 respectively and

current i1 and i2, entering parts 1 & 2, respectively, as shown

in figure.

Two Port Network

•Of these four variables V­1, V2, i1 and i2, two can be selected as independent variables and

the remaining two can be expressed in terms of these independent variables. This leads to

various two part parameters out of which the following three are more important.

Hybrid Parameters or h-parametersIf the input current i1 and output Voltage V2 are takes as independent variables, the input

voltage V1 and output current i2 can be written as

V1 = h11 i1 + h12 V2

i2 = h21 i1 + h22 V2

The four hybrid parameters h11, h12, h21 and h22 are defined as follows.

h11 = [V1 / i1] with V2 = 0

= Input Impedance with output part short circuited.

h22 = [i2 / V2] with i1 = 0

= Output admittance with input part open circuited.

h12 = [V1 / V2] with i1 = 0

= reverse voltage transfer ratio with input part open circuited.

h21 = [i2 / i1] with V2 = 0

= Forward current gain with output part short circuited.

The dimensions of h – parameters are as follows:

h11 - Ω

h22 – mhos

h12, h21 – dimension less.

as the dimensions are not alike, (i.e) they are hybrid in nature, and these

parameters are called as hybrid parameters.

The Hybrid Model for Two-port Network:-

V1 = h11 i1 + h12 V2

I2 = h1 i1 + h22 V2

↓

V1 = h1 i1 + hr V2

I2 = hf i1 + h0 V2

The Hybrid Model for Two-port Network:-

Transistor Hybrid Model

Use of h – parameters to describe a transistor have the following advantages:

•h – parameters are real numbers up to radio frequencies .

•They are easy to measure

•They can be determined from the transistor static characteristics curves.

•They are convenient to use in circuit analysis and design.

•Easily convert able from one configuration to other.

•Readily supplied by manufactories.

Transistor Hybrid Model CE Configuration

In common emitter transistor configuration, the input signal is applied between the base

and emitter terminals of the transistor and output appears between the collector and emitter

terminals. The input voltage (Vbe) and the output current (ic) are given by the following

equations:

Vbe = hie.ib + hre.Vc

ie = hfe.ib + hoe.Vc

Transistor Hybrid Model CE Configuration

Transistor Hybrid Model CB Configuration

Where hie =(∂f1/∂iB)Vc = (∂vB/∂iB)Vc = (ΔvB /ΔiB)Vc = (vb / ib)Vc

hre =(∂f1/∂vc)IB = (∂vB/∂vc) IB = (ΔvB /Δvc) IB = (vb /vc) IB

hfe =(∂f2/∂iB)Vc = (∂ic /∂iB)Vc = (Δ ic /ΔiB)Vc = (ic / ib)Vc

hoe= (∂f2/∂vc)IB = (∂ic /∂vc) IB = (Δ ic /Δvc) IB = (ic /vc) IB

The same theory is extended to other configurations including CB and CC

Hybrid Model and Equations for the transistor in three different configurations are are given below.

Analysis of Transistor Amplifier using Complete h-

Parameter Model

In the h-parameter model consider the load Resistance RL and input signal Vs. The

expressions for Current gain, Voltage gain ,input and output impedance are:

1. Current Gain:

Ai=-hf/(1+hoRL)

Where Ai is the current amplification or current gain

The overall current gain taking source resistance is given by:

Ais=Ai * (Rs/Zi + Rs)

where

Zi input impedance

Rs source resistance

Analysis of Transistor Amplifier using Complete h-Parameter Model

2)Input Impedance(Zi)

Zi= hi+hrAiRL

3) Voltage Gain(Av):

Av=(Ai * RL)/ Zi

Voltage gain taking source resistance is given by

Avs=(Av * Zi)/(Zi+Rs)

4) Output Admittance(Yo)

Yo=ho-hf * hr/(hi+Rs)

Analysis of Transistor Amplifier using simplified h-

Parameter Model

Common Emitter Configuration

Fixed Bias configuration:

Input Impedance Zi = RB || hie

Output Impedance Zo=RC || (1/hoe)

Voltage gain Av=-hfe * (RC || (1/hoe) /hie

Current Gain Ai=hfe * RB/(RB + hie)

Voltage Divider Configuration:

Input impedance Zi=(RB1 || RB2)|| hie

Output Impedance Zo=RC ||(1/hoe)

Voltage gain Av=-hfe * [RC || (1/hoe)]/hie

Current gain Ai=hfe * (RB1||RB2)/(RB1|| RB2) + hie

25

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.

26

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!

27

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

28

29

30

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

31

Common-Emitter re vs. h-Parameter Model

hie = re

hfe =

hoe = 1/ro

32

Common-Emitter h-Parameters

[Formula 7.28]

[Formula 7.29]acfe

eie

h

rh

33

Common-Base re vs. h-Parameter Model

hib = re

hfb = -

34

Common-Base h-Parameters

[Formula 7.30]

[Formula 7.31]1

fb

eib

h

rh

SMALL-SIGNAL LOW-FREQUENCY OPERATION OF TRANSISTORS

Hybrid Parameters and Two-Port NetworkFor the hybrid equivalent model to be described, the parameters aredefined at an operating point that may or may not give an actual pictureof the operating condition of the amplifier. The quantities hie , hre , hfe

and hoe are called the hybrid parameters and are the components of asmall-signal equivalent circuit. The description of the hybrid equivalentmodel begins with the general two-port system.

Two-port system representation (Black model realisation)

EQUIVALENT CIRCUITS THROUGH HYBRID PARAMETERS

AS A TWO-PORT NETWORKFor the transistor, even though it has three basic configurations, they are all four-terminal configurations, and thus, the resulting equivalent circuit will have the sameformat. The h-parameter will however change with each configuration. To distinguishwhich parameter has been used or which is available, a second subscript has beenadded to the h-parameter notation.(i) For the common-base configuration: the lower case letter b(ii) For the common-emitter configuration: the lower case letter e(iii) For the common-collector configuration: the lower case letter c

Complete hybrid equivalent model

TRANSISTOR AS AMPLIFIER

An n–p–n transistor in the common-base bias mode

EXPRESSIONS OF CURRENT GAIN, INPUT RESISTANCE, VOLTAGE

GAIN AND OUTPUT RESISTANCEThe h-parameter equivalent circuit of a transistor amplifier having a voltage source Vg, with its input resistance Rg connected to the input terminals and a load resistance RLconnected to the output terminals.

h-Parameter equivalent circuit of a transistor

EXPRESSIONS OF CURRENT GAIN, INPUT RESISTANCE, VOLTAGE

GAIN AND OUTPUT RESISTANCECurrent Gain (AI)

Input Resistance (RI)

EXPRESSIONS OF CURRENT GAIN, INPUT RESISTANCE, VOLTAGE

GAIN AND OUTPUT RESISTANCEVoltage Gain:- Voltage gain or voltage amplification is defined as the ratio of the output voltage V2 to the input voltage V1.

Where,

Output Resistance (RO)

FREQUENCY RESPONSE FOR CE AMPLIFIER WITH AND WITHOUT

SOURCE IMPEDANCEAt different frequencies of the input signal, the performance of the device isdifferent. The analysis till now has been limited to the mid-frequency spectrum.Frequency response of an amplifier refers to the variation of the magnitude andphase of the amplifier with frequency.

a) Gain vs. frequency for a CE amplifier (b) Phase angle

vs. frequency for a CE amplifier

EMITTER FOLLOWER

The emitter follower transistor is a design which is basically a CC amplifier.

Current gain:

An emitter follower configuration with biasing

Input resistance:

Voltage gain:

Output resistance

The emitter follower is used for impedance matching.

Figure Small-signal equivalent circuit for FETs.

Figure FET small-signal equivalent circuit that accounts for the dependence of iD on vDS.

Figure Determination of gm and rd. See Example 5.5.

Figure Common-source amplifier.

For drawing an a c equivalent circuit of Amp.

•Assume all Capacitors C1, C2, Cs as short circuit elements for ac signal

•Short circuit the d c supply

•Replace the FET by its small signal model

LgsmLoo

gs

o

v

RvgRiv

v

vA

gain, Voltage

dDLLmgs

o

vrRRRg

v

vA ,

Dd

Dd

Ddo Rr

RrRrZ

imp., put Out

21 imp., Input RRRZ

Gin

A C Equivalent Circuit

Simplified A C Equivalent Circuit

)R||(rgAv Ddm

DR10r D,m

dRgAv

)R||(rgAv Ddm

This is a CS amplifier configuration therefore the input is on the gate and the output is on the drain.

21 R||RZi

Dd R||rZo

DdD

10RrRZo

Figure vo(t) and vin(t) versus time for the common-source amplifier of Figure 5.28.

Figure Common-source amplifier.

An Amplifier Circuit using MOSFET(CS Amp.)

Figure Small-signal equivalent circuit for the common-source amplifier.

A small signal equivalent circuit of CS Amp.

Figure vo(t) and vin(t) versus time for the common-source amplifier of Figure 5.28.

Figure Gain magnitude versus frequency for the common-source amplifier of Figure 5.28.

Figure Source follower.

Figure Small-signal ac equivalent circuit for the source follower.

Figure Equivalent circuit used to find the output resistance of the source follower.

Figure Common-gate amplifier.