BJT Common-Emitter Amplifier

By:Syahrul Ashikin

School of Electrical System Engineering

Objectives

To understand and familiar with dc analysis of bipolar transistor circuits.

To study common-emitter amplifier in term of ac analysis and familiar with general characteristic of this circuit.

Basic common-emitter circuit

R1

R2

RC

CC

vs

VCC

vo

Voltage divider biasing

Coupling capacitor ->dc isolation between amplifier

and signal source

Emitter at ground -> common emitter

Rules in dc analysis

Replacing all capacitors by open circuit.

Replacing all inductors by short circuit.

Replacing ac voltage source by short circuit or ground connection.

Replacing ac current source by open circuit.

Dc analysis

The circuit can be analyzed by forming a Thevenin equivalent circuit.

CC acts as an open circuit to dc.

RC

VCC

RTH

VTH

Thevenin circuit analysis

We know that,

Thevenin resistance, RTH is:

Thevenin voltage, VTH is:

Apply KVL around B-E loop;

The collector current, ICQ is then:

BQCQ II BQEQ II )1(

21 RRRTH

CCTH VRR

RV

21

2

0)( onBETHBQTH VRIV

TH

onBETHBQ R

VVI )(

TH

onBETH

BQCQ

R

VV

II

)(

Cont. Thevenin circuit analysis

Apply KVL to collector-emitter loop;

Thus, Q-point of the amplifier circuit is the coordinate between ICQ and VCEQ.

0 CEQCCQCC VRIV

CBQCC

CCQCCCEQ

RIV

RIVV

Rules in 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

AC analysis-small-signal equivalent circuit-

Inside the transistor

Small-signal hybrid-π parameters Small-signal input

resistance, rπ

Transconductance, gm

Small-signal output resistance, ro

Control voltage, Vπ

Output voltage, Vo

Input resistance, Ri

sS

VRrRR

rRRV

21

21

CQ

T

I

Vr

T

CQm V

Ig

CQ

Ao I

Vr

Como RrVgV

rRRRi 21

Small-signal hybrid-π parameters

Output resistance, Ro

Voltage gain, Av

Coo RrR

Co

S

ms

ov Rr

RrRR

rRRg

V

VA

21

21

Example 1 Given

VCC=12V,RS=0.5kΩ, R1=93.7kΩ, R2=6.3kΩ, RC=6kΩ, β=100, VBE(on)=0.7V and VA=100V.

Determine small-signal voltage gain, input resistance and output resistance of the circuit.

R1

R2

RC

CC

vs

VCC

voR1

Solution Example 1

1st step: DC solution Find Q-point values. ICQ = 0.95mA VCEQ=6.31V.

Cont Solution Example 1 2nd step: AC solution Small-signal hybrid-π parameters are:

VmAV

Ig

T

CQm /5.36

026.0

95.0

kI

Vr

CQ

T 74.295.0

)100)(026.0(

kI

Vr

CQ

Ao 105

95.0

100

Cont Solution Example 1

Small-signal voltage gain is:

Input resistance, Ri is:

krRRRi 87.174.29.521

)(21

21

Co

S

ms

ov Rr

RrRR

rRRg

V

VA

163)6105(5.074.29.5

74.29.5)5.36(

vA

Cont Solution Example 1

O/p resistance, Ro -> by setting independent source Vs = 0 -->no excitation to input portion, Vπ=0, so gmVπ=0 (open cct). kRrR Coo 68.56105

Common-emitter circuit with emitter resistor

Why we need to add emitter resistor, RE in the circuit design?

Without RE, when β increases or decreases -> ICQ and VCEQ also vary, thus Q-point will be shifted and makes the circuit unstable.

By adding RE, there will be not much shift in Q-point is stabilized even with variation of β. Moreover, the voltage gain is less dependent on transistor current gain in ac analysis.

Common-emitter circuit with emitter resistor

R1

R2

RC

CC

vs

VCC

vo

RE

Emitter resistor

Thevenin circuit analysis

Apply KVL around B-E loop,

RC

VCC

RTH

VTH

RE

0)1(

0

)(

)(

EonBETHBQTH

EEQonBETHBQTH

RVRIV

RIVRIV

)()1( onBETHETHBQ VVRRI

ETH

onBETHBQ RR

VVI

)1()(

Thevenin circuit analysis We will get collector current as:

Apply KVL around C-E loop to find VCEQ,

0 EEQCEQCCQCC RIVRIV

ETH

onBETH

BQCQ

RR

VV

II

)1()(

ECBQCC

EBQCBQCC

EEQCCQCCCEQ

RRIV

RIRIV

RIRIVV

)1(

)1(

Ac analysis-small-signal equivalent circuit-

Small-signal hybrid-π parameters

The ac output voltage is: (if we consider equivalent circuit with current gain β)

Input voltage equation:

Input resistance looking into the base of BJT, Rib:

Input resistance to the amplifier is:

Cbo RIV )(

Ebbbin RIIrIV )(

Eb

inib Rr

I

VR )1(

ibi RRRR 21

Small-signal hybrid-π parameters

By voltage divider, we get relate Vin and Vs:

Small-signal voltage gain is then:

If Ri>>RS and if (1+β)RE >> rπ, voltage gain is:

sSi

iin V

RR

RV

Si

i

E

C

s

ov RR

R

Rr

R

V

VA

)1(

E

C

E

C

s

ov R

R

R

R

V

VA

)1(

Exact value

Approximate value

Example 2 Given VCC=10V, R1=56kΩ,

R2=12.2kΩ, RC=2kΩ, RE=0.4kΩ, RS=0.5kΩ, VBE(on)=0.7V, β=100 and VA=∞.

a) Sketch Thevenin equivalent circuit.

b) Determine Q-points.

c) Sketch and label small-signal equivalent hybrid-π circuit.

d) Find small-signal voltage gain, AV.

R1

R2

RC

CC

vs

VCC

vo

RE

RS

Common-emitter circuit with positive and negative voltage biasing

Biasing with dual supplies in desirable in some applications because: Eliminate coupling capacitor Allow dc input voltages as input signals.

Example 3 A simple transistor circuit biased with both

+ve and –ve dc voltages is shown in figure below. Given β=100 and VBE(on)=0.7V. Calculate IEQ, ICQ and VCEQ.

Solution Example 3

For dc analysis, set vs=0 so that base terminal is at ground potential.

KVL around B-E loop,

So, emitter current:

Collector current:

VRIV EEQonBE )(0

mAR

VVI

E

onBEEQ 15.2

2

)7.05()( )(

mAII EQCQ 13.215.2101

100

1

Cont solution example 3

Apply KVL around C-E loop yields

Rearrange the equation to find VCEQ;

VRIVRIV EECEQCCQ

V

RIRIVVV EEQCCQCEQ

15.2)2)(15.2()5.1)(13.2()55(

)(

Example 4

Let β=120, R1=175kΩ, R2=250kΩ, RC=10kΩ, RE=20kΩ and VBE(on)=0.7V.

For the given circuit,i) Find RTH, VTH and Q-points.ii) Sketch dc load line

Solution Example 4

1st: Sketch Thevenin equivalent circuit to find RTH and VTH. RTH = 103kΩ & VTH = 1.6V

2nd: Apply KVL around B-E loop to find equation for IBQ. Then, find ICQ and IEQ. IBQ = 3.92μA ICQ = 0.471mA & IEQ = 0.474mA

3rd: Apply KVL around C-E loop to find equation for VCEQ. VCEQ = 3.8V

4th: Sketch dc load line and indicate the Q-points. Find IC(max) at y-axis and VCE(cutoff)= VCC=V+-V-=18V at x-axis.