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Page 1: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

SMALL-SIGNAL HYBRID-Π EQUIVALENT

CIRCUIT

Page 2: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Content

BJT – Small Signal AmplifierBJT complete Hybrid equivalent circuit

BJT approximate Hybrid model

ObjectivesDevelop the small-signal models of transistor that are used in analysis of linear amplifier.

Page 3: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Basic knowledge..

Ohm’s Law

Kirchoff’s Law

Thevenin and Norton’s Theorem

All electronic circuit analysis require these for mathematical manipulation.

Page 4: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Small signal hybrid- equivalent circuit of bipolar transistor

Need to develop a small-signal equivalent cct -- use hybrid- model because is closely related to the physic of transistor.

Treat transistor as two-port network.

Page 5: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

2-port system

AC analysis require simplification of transistors as 2-port system.

Simplification leads to new parameters / definitions.

Page 6: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

2-port system cont..

‘Single ended’ 2-port system has 1 input port shorted to 1 output port.

Alternative view =>system has a common input/output port.

Three terminal device device which only three connection leads, i.e transistor falls into this category.

Page 7: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Single-ended 2-port network

Page 8: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Differential 2-port network

The ‘differential 2-port’ network will be the basis for forthcoming analysis of all types of transistors (BJT and FET).

Page 9: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Port variables2-port network analysis is all about current and voltage by breaking down voltage direction (-ve to +ve or +ve to –ve) and current direction (to or from).

Each current and voltage has 2 possible

directions.

Page 10: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

2-port variables

Below are the equations for BJT’s derived from 2-port network simplification.

ceoebfec

cerebiebe

VhIhI

VhIhV

Page 11: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Small signal hybrid-π equivalent circuit

Based on 2-port network, 1 input port and 1 output port shorted together to form a common port of both input and output.

Transistor has input and output ports shorted (emitter) resulting a small-signal 2-port hybrid- π network.

Page 12: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Cont..

Figure shows iB vs. vBE with small-time varying signal superimposed at Q-pt.

Since sinusoidal signals are small, the slope at Q-pt treated as a constant, has units of conductance.

The inverse of this conductance is small-signal resistance, rπ

Page 13: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Cont..We can relate small-signal input base current to small-signal input voltage by:

Finding rπ from Q-point slope lead to:

rπ also known as diffusion resistance and is a function of Q-point parameters.

riv bbe

CQ

T

BQ

T

b

be

I

V

I

Vr

i

v

Page 14: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Cont.. Now, we consider the output terminal characteristic of BJT.

Assume o/p collector current is independent of collector-emitter voltage collector-current is a function of base-emitter voltage, so the equation:

From eq 5.2 in Chapter 5 Neaman,

BE

ptQBE

CC v

v

ii

.

T

BESC V

vIi exp

Page 15: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Cont..After substitution and rearrange the above, we obtain:

The term ICQ / VT is a conductance. Since this term relates current in collector to a voltage in B-E circuit, it is called transconductance and is written:

Transconductance also a function of Q-pt parameters and directly proportional to dc bias current.

T

CQ

ptQT

BES

TptQBE

C

V

I

V

vI

Vv

i

exp.1

T

CQm V

Ig

Page 16: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Cont..

Using these new parameters develop a simplified small-signal hybrid-π equivalent cct for npn BJT.

Phasor components given in parentheses.

This circuit can be inserted into ac equivalent circuit shown previously.

Page 17: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Small-signal hybrid- equivalent circuit using transconductance

Transconductance parameter

gm=ICQ/VT

r=VT/ICQ

Page 18: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Cont..We can relate small-signal collector current to small-signal base current for o/p of equivalent cct.

Where

β is called ac common-emitter current gain.

Thus:

b

ptQB

Cc i

i

ii .

ptQB

C

i

i

bc ii

Page 19: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

ib(Ib )

Current gain parameter

Small-signal hybrid- equivalent circuit using common-emitter current gain

Page 20: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Small-signal circuit parameters

Page 21: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Small-signal voltage gain

Combine BJT equivalent cct to ac equivalent cct.

Page 22: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Small-signal voltage gainVoltage gain, Av = ratio of o/p voltage to i/p voltage.

Small-signal B-E voltage is called control voltage, Vbe or V.

The dependent current source is gmV flows through RC produce –ve C-E voltage at the output.

Cbemceo RVgVV

Page 23: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Cont..

From the input portion of the circuit:

The small-signal voltage gain is:

sB

be VRr

rV

B

Cms

ov Rr

rRg

V

VA

Page 24: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Example 1

Given : = 100, VCC = 12V

VBE = 0.7V, RC = 6k, VT=0.026V, RB = 50k and

VBB = 1.2V

Calculate the small-signal

voltage gain.

Page 25: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

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.

Page 26: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Example 2

Given VCC=5V, VBB=2V, RB=650kΩ, RC=15kΩ, β=100 and VBE(on)=0.7V. Determine a) Q-points, b) gm and r

c) voltage gain.

Page 27: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Early effect

Early Voltage (VA)

Page 28: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Early voltageFigure above show current-voltage characteristic for constant values of B-E voltage.

The curves are linear with respect to C-E voltage in forward-active mode.

The slope is due to base-width modulation effect Early Effect.

When the curves extrapolated at zero current, they meet a point on –ve voltage axis, vce = -VA. VA --- Early voltage with typical value in range of 50 < VA

< 300V.

Page 29: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Hybrid-π equivalent circuit with Early Effect

Early Effect => collector current, iC is dependent to collector-emitter voltage, vCE (refer Chapter 5-Neaman):

The output resistance, rO:

Substitute and rearrange both equation,

A

CE

T

BESC V

v

V

vIi 1.exp

ptQC

CEO i

vr

A

CQ

ptQAT

BES

O V

I

VV

vI

r

1.exp

1

Page 30: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Cont..

Hence, small-signal transistor output resistance, rO become:

rO is equivalent to Norton resistance rO is parallel with dependent current sources.

CQ

AO I

Vr

Page 31: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Modified bipolar equivalent circuits including rO

due to Early Effect.

Transconductance parameter

Current gain parameter

ro=VA/ICQ

Page 32: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Self study for pnp transistor

From Neaman textbook,Ac equivalent circuit – pg 386

Transconductance and current gain – pg 386 & 387

Small-signal hybrid-π equivalent circuit – pg 387

Do example 6.3

Page 33: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Expanded hybrid-π equivalent circuit

Include 2 additional resistance, rb and rμ.

rb series resistance of semiconductor material.Since rb << rμ., rb is neglected (short cct) at low freq.

rμ reverse-biased diffusion resistance of B-C junction. Typically in megaohms and neglected (open cct). Normally, in hybrid-π model, we neglect both rb and rμ.

Page 34: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

Other small-signal parameters -h parameter

h-parameter -> relate small-signal terminal currents and voltages of 2-port network.The linear r/ship between terminal currents and voltages are:

Where:i for inputr for reversef for forwardo for outpute for common-emitter

ceoebfec

cerebiebe

VhIhI

VhIhV

Page 35: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

h-parameter

These equations represent KVL at input and KCL at output applied to h-parameter model for common-emitter BJT.

Page 36: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives.

h-parameter in relation to hybrid-π