Sem I 0809/rosdiyana

Chapter 5:BJT Small-Signal Analysis

Contents

Common-Emitter fixed-bias configuration Voltage divider bias CE Emitter bias Emitter-follower configuration Common-base configuration Collector-feedback configuration Hybrid equivalent circuit and model

• re transistor model – employs a diode and controlled current source to duplicate the behavior of a transistor in the region of interest.

• The re and hybrid models will be used to analyze small-signal AC analysis of standard transistor network configurations.

Ex: Common-base, common-emitter and common-collector configurations.

• The network analyzed represent the majority of those appearing in practice today.

BJT Small Signal Analysis

AC equivalent of a network is obtained by:

1. Setting all DC sources to zero

2. Replacing all capacitors by s/c equiv.

3. Redraw the network in more convenient and logical form

Common-Emitter (CE) Fixed-Bias Configuration

The input (Vi) is applied to the base and the output (Vo) is from the collector.

The Common-Emitter is characterized as having high input impedance and low output impedance with a high voltage and current gain.

Removing DC effects of VCC and Capacitors

Common-Emitter (CE) Fixed-Bias Configuration

re Model

Determine , re, and ro: and ro: look in the specification sheet for the transistor or test the transistor using a curve tracer.re: calculate re using dc analysis:

Ee I

26mVr

Common-Emitter (CE) Fixed-Bias Configuration

Impedance Calculations

Input Impedance: Output Impedance:

eBi r||RZ

eB ei r10RrZ

Or||RZ Co

c o 10roZ RRc

Common-Emitter (CE) Fixed-Bias Configuration

Gain Calculations

Voltage Gain (Av):

Current Gain (Ai):

Current Gain from Voltage Gain:

e

oC

i

ov r

)r||(R

V

VA

Coe

Cv 10Rrr

RA

)r)(RR(r

rR

I

IA

eBCo

oB

i

oi

eBCoi r10R ,10RrA

C

ivi R

ZAA

Common-Emitter (CE) Fixed-Bias Configuration

Voltage Gain

e

CvCo

e

oC

eb

oCbv

eb i

oCbO

i

Ov

r

RA 10Ror r if

r

)r||(R

βrI

)r||(RβIA

βrIV

)r||(RβIV

V

VA

Common-Emitter (CE) Fixed-Bias Configuration

Current gain

C

ivi

Bo

Bo

i

oi

eBCo

eBCo

Bo

i

oi

eB

B

Co

o

i

b

b

o

i

oi

eB

B

i

b

eB

iBb

Co

o

b

o

Co

boo

R

ZAA

ooequation t thisusecan or we

βRr

βRr

I

IA

,βr10R and 10R r if

βrRRr

βRr

I

IA

βrR

R

Rr

βr

I

I

I

I

I

IA

βrR

R

I

I and

βrR

IRI

Rr

βr

I

I and

Rr

βIrI

circuitsoutput andinput the toruledivider -current

theapplyingby determined isgain current The

Common-Emitter (CE) Fixed-Bias Configuration

Phase Relationship

The phase relationship between input and output is 180 degrees. The negative sign used in the voltage gain formulas indicates the inversion.

Common-Emitter (CE) Fixed-Bias Configuration

CE – Voltage-Divider Bias Configuration

re Model

You still need to determine , re, and ro.

CE – Voltage-Divider Bias Configuration

Impedance Calculations

Input Impedance: Output Impedance:

21

2121

RR

RRR||RR

er||RZi

oC r||RZo

C C 10RroRZo

CE – Voltage-Divider Bias Configuration

Gain Calculations

Voltage Gain (Av):

Current Gain (Ai):

Current Gain from Voltage Gain:

e

oC

i

ov r

r||R

V

VA

Coe

C

i

ov 10Rrr

R

V

VA

)rR)(R(r

rR

I

IA

eCo

o

i

oi

Coei

oi 10RrrR

Rβ

I

IA

eCoi

oi r10R ,10RrI

IA

C

ivi R

ZAA

CE – Voltage-Divider Bias Configuration

Voltage Gain

e

C vCo

e

oC v

oCe

io

e

ib

oCbO

r

RA 10Ror r if

r

)r ||(RA

)r ||(Rβr

VβV

βr

VI

)r ||)(RI (βV

CE – Voltage-Divider Bias Configuration

Current gain

e

eo

o

i

oi

Co

eCo

o

i

oi

B21

βrR'

βR'

βrR'r

rβR'

I

IA

,R10rfor

βrR'Rr

rβR'

I

IA

RR||RR'

format. same thehave

gain willcurrent for theequation the,R' the

for except ion,configurat bias-fixedemitter -

common that similar to so isnetwork thesince

CE – Voltage-Divider Bias Configuration

C

iVi

i

oi

i

oi

e

R

ZAA

optionan as

I

IA

R'

βR'

I

IA

,r10R' if And

CE – Voltage-Divider Bias Configuration

Phase Relationship

A CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias.

CE – Voltage-Divider Bias Configuration

CE Emitter-Bias Configuration

Unbypassed RE

re Model

Again you need to determine , re.

CE Emitter-Bias Configuration

Impedance Calculations

Input Impedance: Output Impedance:

Eeb 1)R(rZ

)R(rZ Eeb

eE Eb rRRZ

bBi Z||RZ Co RZ

CE Emitter-Bias Configuration

Defining the input impedance of a transistor with an unbypassed emitter resistor

Eb

eE

Eeb

Eeb

ib

Ebebi

Eeebi

βRZ

toreduced becan aboveeqn ,ran greater thmuch is R since

βRβrZ

1,an greater thnormally is β since

R)1β(βrI

VZ

RI)1β(βrIV

RIβrIV

:sideinput the toKVL Applying

CE Emitter-Bias Configuration

Voltage Gain (Av):

Current Gain (Ai):

Current Gain from Voltage Gain:

Gain Calculations

b

C

i

ov Z

R

V

VA

)R(rZRr

R

V

VA

EebEe

C

i

ov

EbE

C

i

ov RZR

R

V

VA

bB

B

i

oi ZR

R

I

IA

C

ivi R

ZAA

or

CE Emitter-Bias Configuration

Voltage Gain

E

C

i

oV

Eb

Ee

C

i

oV

Eeb

b

C

i

oV

Cb

i

CbCoo

b

ib

R

R

V

VA

βRion Zapproximat for the and

Rr

R

V

VA

gives )Rβ(r Zngsubstituti

Z

βR

V

VA

RZ

Vβ

RβIRIV

Z

VI

CE Emitter-Bias Configuration

Current Gain

CR

ZAA

ZR

R

I

I

I

I

I

IA

I

I

II

ZR

R

I

I

ZR

IRI

:inresult llcircuit wiinput the toruledivider -current theApplying .II

ion approximat permit the to Z toclose often too is R of magnitude The

ivi

bB

B

i

b

b

o

i

oi

b

o

bo

bB

B

i

b

bB

iBb

ib

bB

CE Emitter-Bias Configuration

Phase RelationshipA CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias.

CE Emitter-Bias Configuration

Bypassed RE

This is the same circuit as the CE fixed-bias configuration and therefore can be solved using the same re model.

CE Emitter-Bias Configuration

Emitter-Follower Configuration

You may recognize this as the Common-Collector configuration. Indeed they are the same circuit. Note the input is on the base and the output is from the emitter.

re Model

You still need to determine and re.

Emitter-Follower Configuration

Impedance Calculations

Input Impedance:

bBi Z||RZ

Eeb 1)R(rZ

)R(rZ Eeb

Eb RZ

Emitter-Follower Configuration

Calculation for the current Ie

Ee

ie

eee

Ee

i

Ee

ie

b

b

ibe

b

ib

Rr

VI

rβ

βr1)β(

βr and

β1)β(but R1)β(

βrV

1)Rβ(βr

1)Vβ(I

gives for Z gsubtitutin

Z

V1)β(1)Iβ(I

Z

VI

Emitter-Follower Configuration

Impedance Calculations (cont’d)Output Impedance:

eEo r||RZ eE

eo rRrZ

Ee

ie Rr

VI

ionconfiguratfollower emitter for the impedenceoutput theDefining

Emitter-Follower Configuration

Gain CalculationsVoltage Gain (Av):

Current Gain (Ai):

Current Gain from Voltage Gain:

eE

E

i

ov rR

R

V

VA

EeEeEi

ov RrR ,rR 1

V

VA

bB

Bi ZR

RA

E

ivi R

ZAA

Emitter-Follower Configuration

Voltage gain

1V

VA

RrR

,ran greater thmuch usually R

rR

R

V

VA

rR

VRV

i

ov

EeE

eE

eE

E

i

ov

eE

iEo

Emitter-Follower Configuration

Current Gain

E

ivi

bB

Bi

bB

B

i

b

b

o

i

oi

b

o

beo

bB

B

i

b

bB

iBb

R

ZAAor

ZR

RA

,)1( since

ZR

R)1(

I

I

I

I

I

IA

)1(I

I

I)1(II

ZR

R

I

I

ZR

IRI

Emitter-Follower Configuration

Phase RelationshipA CC amplifier or Emitter Follower configuration has no phase shift between input and output.

Vo

Emitter-Follower Configuration

Common-Base (CB) Configuration

The input (Vi) is applied to the emitter and the output (Vo) is from the collector.

The Common-Base is characterized as having low input impedance and high output impedance with a current gain less than 1 and a very high voltage gain.

re Model

You will need to determine and re.

Common-Base (CB) Configuration

Impedance Calculations

Input Impedance: Output Impedance:

eEi r||RZ Co RZ

Common-Base (CB) Configuration

Gain Calculations

Voltage Gain (Av):

Current Gain (Ai):

e

C

e

C

i

ov r

R

r

R

V

VA

1I

IA

i

oi

Common-Base (CB) Configuration

Voltage & Current gain

e

C

e

C

i

oV

Ce

io

e

ie

Ce

CcCoo

r

R

r

Rα

V

VA

Rr

VαV

r

VI

RαI

)RI(RIV

1I

IA

III

II

i

oi

ieo

ie

Common-Base (CB) Configuration

Phase Relationship

A CB amplifier configuration has no phase shift between input and output.

Vo

Common-Base (CB) Configuration

Collector DC Feedback Configuration

The network has a dc feedback resistor for increased stability, yet the capacitor C3 willshift portions of the feedback resistance to the input and output sections of the networkin the ac domain. The portion of RF shifted to the input or output side will be determinedby the desired ac input and output resistance levels.

Substituting the re equivalent circuit into the ac equivalent network

eβr||RZ F1i oF2Co r||R||RZ

2|| FCo RRZ

Collector DC Feedback Configuration

Impedance Calculations

Input Impedance: Output Impedance:

Voltage Gain

e

CF2

i

ov

Co

e

CF2o

i

ov

e

io

e

ib

bo

CF2o

r

R||R

V

VA

,10Rrfor

r

R||R||r

V

VA

R'βr

VβV

βr

VI

R'βIV

R||R||rR'

Collector DC Feedback Configuration

Current Gain

C

iV

i

oi

F2o

Ci

oi

CF2oF1

F2oF1

i

oi

F1eF1eF1

eF1C

F1

i

oi

eF

F1

Ci

b

b

o

i

oi

Cb

o

C

bo

F2o

eF

F

i

b

eF

iFb

R

ZA

I

IA or

R||rR

1

β

I

IA

RR||rR

)R||(rβR

I

IA

RβrR,βrn larger thamuch usually is R since

βrRRR'

βRR'

I

IA

βrR

R.

RR'

βR'

I

I.

I

I

I

IA

,gain current the

RR'

βR'

I

Ior

RR'

βIR'I

R||rR' using sideoutput for the and

βrR

R

I

Ior

βrR

IRI

sideinput For the

Collector DC Feedback Configuration

Approximate Hybrid Equivalent Circuit

The h-parameters can be derived from the re model:

hie = re hib = rehfe = hfb = -hoe = 1/ro

The h-parameters are also found in the specification sheet for the transistor.

Hybrid equivalent model re equivalent model

Approximate Common-Emitter Equivalent Circuit

Hybrid equivalent model re equivalent model

Approximate Common-Base Equivalent Circuit

Troubleshooting

1. Check the DC bias voltages – if not correct check power supply, resistors, transistor. Also check to ensure that the coupling capacitor between amplifier stages is OK.

2. Check the AC voltages – if not correct check transistor, capacitors and the loading effect of the next stage.

Practical Applications

• Audio Mixer

• Preamplifier

• Random-Noise Generator

• Sound Modulated Light Source