1 LECTURE 1: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT OF BIPOLAR TRANSISTOR (BJT) By: Syahrul...

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LECTURE 1:SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT OF

BIPOLAR TRANSISTOR (BJT)

By:Syahrul Ashikin Azmi

PPKSE

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Lecture’s content

• Objectives– Develop the small-signal models of transistor that are

used in analysis of linear amplifier.

• BJT – Small Signal AmplifierSmall-signal hybrid-π equivalent circuit of BJTSmall-signal hybrid-π equivalent circuit using

transconductanceSmall-signal hybrid-π equivalent circuit using common

current gainSmall-signal voltage gainHybrid- π equivalent circuit including Early EffectExpanded hybrid- π equivalent circuitOther small-signal parameters and equivalent circuits

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Basic knowledge..

• Ohm’s Law

• Kirchoff’s Law

• Thevenin and Norton’s Theorem

• All electronic circuit analysis require these for mathematical manipulation.

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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.

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**2-port system**

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

• Simplification leads to new parameters / definitions.

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Small signal hybrid- equivalent circuit of bipolar transistor **2-port system**

• ‘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.

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**2-port system**

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**2-port system**

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

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**2-port system**• 2-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.

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Small signal hybrid-π equivalent circuit of bipolar transistor cont..

• 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.

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• 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

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• 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. VT is known as thermal voltage.

riv bbe

CQ

T

BQ

T

b

be

I

V

I

Vr

i

v

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Small signal hybrid-π equivalent circuit of bipolar transistor

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

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• 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

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• 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.

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Small-signal hybrid- equivalent circuit using transconductance

Transconductance parameter

gm=ICQ/VT

r=VT/ICQ

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Small-signal hybrid- equivalent circuit using transconductance

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

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ib(Ib )

Current gain parameter

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

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Small-signal voltage gain cont..

• Combine BJT equivalent cct to ac equivalent cct.

Small-signal hybrid-π model

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• Voltage gain, Av = ratio of o/p voltage to i/p voltage.

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

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

Cbemceo RVgVV

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• From the input portion of the circuit, using voltage divider:

• The small-signal voltage gain is:

s

B

be VRr

rV

B

Cms

ov Rr

rRg

V

VA

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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.

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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.

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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.

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Hybrid-π equivalent circuit including Early effect

Early Voltage (VA)

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Hybrid-π equivalent circuit including Early effect

**Early voltage**

• Figure 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.

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Hybrid-π equivalent circuit including 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

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Hybrid-π equivalent circuit including Early effect 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

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Modified bipolar equivalent circuits including rO due to Early Effect.

Transconductance parameter

Current gain parameter

ro=VA/ICQ

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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

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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.

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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 input– r for reverse– f for forward– o for output– e for common-emitter

• Equation 1: KVL at input, hie in series with dependent voltage source, hreVce

• Equation 2: KCL at output, hoe is in parallel with dependent current source, hfeIb.

ceoebfec

cerebiebe

VhIhI

VhIhV

Equation 1

Equation 2

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h-parameter

Common-emitter transistor h-parameter model of C-E BJT

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h-parameter

h-parameter in relation with hybrid-π are shown below:

1 LECTURE 1: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT OF BIPOLAR TRANSISTOR (BJT) By: Syahrul...

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