ANALOGUE ELECTRONICS I

EMT 112/4

Basic BJT Amplifiers (Part 1)

Analog Signals & Linear Amplifiers Analog signals

Natural analog signals: physical sense (hearing, touch, vision) Electrical analog signals: e.g. output from microphone, output signal from

compact disc – form of time-varying currents & voltages Magnitude: any value which vary continuously with time

Analog circuits Electronic circuits which produce analog signals E.g. linear amplifier

Linear amplifier Magnifies input signal & produce output signal that is larger & directly

proportional to input signal

DC voltage source

Amplifier LoadSignal source

DC powera) Low signal powerb) High signal power

(a) (b)

Block diagram of a compact disc player system

The Bipolar Linear Amplifier

To use circuit as an amplifier, transistor needs to be biased with DC voltage at quiescent point (Q-point) transistor is biased in forward active region

Time-varying output voltage is directly proportional to & larger than time-varying input voltage linear amplifier

(a) Bipolar transistor inverter circuit; (b) inverter transfer characteristics

The Bipolar Linear Amplifier

Summary of notation

Variable Meaning

iB, vBE Total instantaneous values

IB, VBE DC values

ib, vbe Instantaneous ac values

Ib, Vbe Phasor values

Graphical Analysis & AC Equivalent Circuit

(D) Common-emitter transistor characteristics, dc load line, and sinusoidal variation in base current, collector current, and collector-emitter voltage

RC

RB

vs

vO

VBB

VC

C

(C) Common-emitter circuit with time varying signal source in series with base dc source

iB

iC

vBE

vCE

Fig. C

Fig. D

Graphical Analysis & AC Equivalent Circuit Base on Fig. C & D

(time-varying signals linearly related & superimposed on dc values)

If signal source, vs = 0:

(4)

(3)

(2)

(1)

beBEQBE

ceCEQCE

cCQC

bBQB

vVv

vVv

iIi

iIi

(6) loop) E-(C

(5) loop) E-(B

CEQCCQCC

BEQBBQBB

VRIV

VRIV

Graphical Analysis & AC Equivalent Circuit

For B-E loop, considering time varying signals:

Rearrange:

Base on (5), left side of (7) is 0. So:

For C-E loop, considering time varying signals:

Base on (6), left side of (11) is 0. So:

(7) )()( beBEQBbBQBEBBsBB vVRiIvRivV

(8) sbeBbBEQBBQBB vvRiVRIV

(9) beBbs vRiv

(11)

(10)

ceccCEQCCQCC

ceCEQCcCQCECCCC

vRiVRIV

vVRiIvRiV

)()(

(12) 0 cecc vRi

Graphical Analysis & AC Equivalent Circuit

Definition of small signal Small signal : ac input signal voltages and

currents are in the order of ±10 percent of Q-point voltages and currents.

e.g. If dc current is 10 mA, the ac current (peak-to-peak) < 0.1 mA.

Graphical Analysis & AC Equivalent Circuit

Rules for ac analysis Replacing all capacitors by short circuits Replacing all inductors by open circuits Replacing dc voltage sources by ground

connections Replacing dc current sources by open circuits

RC

RB

vs

vO

vce

vbe

ic

ib

+

+

--

AC equivalent circuit of C-E with npn transistor

Graphical Analysis & AC Equivalent Circuit

Equations Input loop

Output loop

beBbs vRiv

beT

BQb v

V

Ii

0 ceCc vRi

bc ii

0.026 V

Small-signal hybrid- equivalent circuit

Using transconductance (gm) parameter

gm=ICQ/VT

r=VT/ICQ

vbe = ibrπ

rπ

= diffusion resistance /base-emitter input resistance

1/rπ

= slope of iB – VBE curve

BQFCQ

CQ

TF

BQ

T

b

be

II

I

V

I

Vr

i

v

,

)( b

b

I

i

Using common-emitter current gain (β) parameter

Small-signal hybrid- equivalent circuit

How to construct Small-signal hybrid-

Place a terminal for the transistor

Common Terminal as ground

B

E

C

We know that

i across B ib

i across C βib i across E (β+1)ib

rπ between B -E

RC

RB

vs

vO

VBB

VCC

B

E

C

βibrπ

Small-signal equivalent circuit

Cbemceo RVgVV sB

be VRr

rV

B

Cms

ov Rr

rRg

V

VA

gain, voltage signal Small

B C

E

rVs

RB

RC

Vo

Ic

Ib gmVbeVbe Vce

+ +

--

Small-signal hybrid- equivalent circuit

Output signal voltage

Input signal voltage

RC

RB

vs

vO

VBB

VC

C

Example

Given : = 100, VCC = 12V

VBE = 0.7V, RC = 6k,

RB = 50k, and VBB = 1.2V

Calculate the small-signal voltage gain.

Small-signal hybrid- equivalent circuit

Solutions

AR

VVI

B

onBEBBBQ 10

50

7.02.1)(

mAAII BQCQ 1)10(100

VRIVV CCQCCCEQ 6)6)(1(12

kI

Vr

CQ

T 6.21

)026.0)(100(

VmAV

Ig

T

CQm /5.38

026.0

1

4.11

B

Cms

ov Rr

rRg

V

VA

1.

2.

3.

4.

5.

6.

Hybrid- Model and Early Effect

transconductance parameter

current gain parameter

ro=VA/ICQ

ro = small-signal transistor output resistanceVA = early voltage

Early Voltage (VA)

Hybrid- Model and Early Effect

Early Voltage (pg 299)

Basic Common-Emitter Amplifier Circuit

vs

RS

R1

R2

RC

CCvO

VCCExample

Given : = 100, VCC = 12V

VBE(on) = 0.7V, RS = 0.5k,

RC = 6k, R1 = 93.7k, R2 = 6.3k

and VA = 100V.

Calculate the small-signal voltage gain.

Como RrVgV

s

S

VRrRR

rRRV

21

21

Co

S

ms

ov Rr

RrRR

rRRg

V

VA

21

21

Coo RrR

rRRRi 21

B C

E

R1 \\ R2

Vs

RS

RCrOr gmV

Vo

Ri Ro

Solution

Small-signal equivalent circuit

Self-Reading

Textbook: Donald A. Neamen, ‘MICROELECTRONICS Circuit Analysis & Design’,3rd Edition’, McGraw Hill International Edition, 2007

Chapter 5:The Bipolar Junction Transistor

Page: 334-339

Chapter 6: Basic BJT Amplifiers

Page: 370-388.

ExerciseThe circuit parameters in Figure are changed to VCC = 5V, R1=35.2kΩ, R2=5.83kΩ, RC=10kΩ and RS =0, β =100, VBE(on) =0.7V and VA =100V. Determine the quiescent collector current and collector-emitter voltage and find the small-signal voltage gain.

Ans: ICQ = 0.21mA, VCEQ =2.9V, Av =-79.1)