Lecture6(20-3-11)

7/27/2019 Lecture6(20-3-11)

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EE 332

DEVICES AND CIRCUITS II

Lecture 6

Small-Signal Modeling and Linear Amplification (1)

Introduction to Amplifiers

• BJT is an excellent amplifier when biased in forward-active region

• FET can be used as amplifier if operated in pinch-off or saturation

region.

• In these regions, transistors can provide high voltage, current and

power gains.

• Bias is provided to stabilize the operating point in desired operation

region.

• Q-point also determines

– Small-signal parameters of transistor

– Voltage gain, input resistance, output resistance

– Maximum input and output signal amplitudes

– Power consumption

BJT Amplifier

Lecture Goals

Understanding of concepts related to:

• Transistors as linear amplifiers

• dc and ac equivalent circuits

• Use of coupling and bypass capacitors and inductors to modify dc and

ac equivalent circuits

• Small-signal voltages and currents

• Small-signal models for diodes and transistors

• Identification of common-source and common-emitter amplifiers

• Amplifier characteristics such as voltage gain, input and output

resistances and linear signal range

• Rule-of-thumb estimates for voltage gain of common-emitter and

common-source amplifiers.

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BJT Amplifier

BJT is biased in active region by dc voltage source V BE . Q-point is

set at ( I C , V CE )=(1.5 mA, 5 V) with I B = 15 μA.

Total base-emitter voltage is: bev

BE V

BE v +=

Collector-emitter voltage is: This gives the

load line

C RC i

CE v −=10

BJT Amplifier (contd.)

•If changes in operating currents and voltages are small enough,

then I C and V CE waveforms are undistorted replicas of input signal.

•Small voltage change at base causes large voltage change at

collector. Voltage gain is given by:

•Minus sign indicates 1800 phase shift between input and output

signals.

2061802060008.0

18065.1

bev

cev−=∠=

∠

∠==v A

MOSFET Amplifier

BJT Amplifier (contd.)

8 mV peak change in v BE gives 5 μA change in i B and 0.5 mA change in iC .

0.5 mA change in iC gives 1.65 V change in vCE .

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MOSFET Amplifier

Coupling and Bypass Capacitors

Coupling and Bypass Capacitors

•C 1 and C 3 are large coupling capacitors or dc blocking capacitors,

their reactance at signal frequency is negligible.

• C 2 is bypass capacitor, provides low impedance path for ac current

from emitter to ground, removing RE (required for good Q-point

stability) from circuit when ac signals are considered.

•AC coupling through capacitors is used to inject ac input signal and

extract output signal without disturbing Q-point

•Capacitors provide negligible impedance at frequencies of interest

and provide open circuits at dc.

MOSFET Amplifier

MOSFET is biased in active region by dc voltage source V GS .

Q-point is set at ( I D, V DS )=(1.56 mA, 4.8 V) with V GS =3.5 V.

Total gate-source voltage is:

1 V p-p change in vGS gives 1.25 mA p-p change in iD and 4

V p-p change in vDS .

gsv

GS V

GS v +=

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DC and AC Analysis

• DC analysis:

– Find dc equivalent circuit by replacing all capacitors by open circuits

and inductors by short circuits.

– Find Q-point from dc equivalent circuit by using appropriate large-

signal transistor model.

• AC analysis:

– Find ac equivalent circuit by replacing all capacitors by short circuits,

inductors by open circuits, dc voltage sources by ground connectionsand dc current sources by open circuits.

– Replace transistor by small-signal model

– Use small-signal ac equivalent to analyze ac characteristics of amplifier.

– Combine end results of dc and ac analysis to yield total voltages and

currents in the network.

AC Equivalent for BJT Amplifier

k Ω100k Ω3.43

k Ω30k Ω1021

==

==

RC

R R

R R B

R

DC and AC Equivalents for MOSFET

Amplifier dc equivalent

ac equivalentSimplified ac equivalentSimplified ac equivalent

DC Equivalent for BJT Amplifier

• All capacitors in original amplifier circuits are replaced by open

circuits, disconnecting v I , R

I , and R3 from circuit.

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Small-Signal Operation of Diode


(contd.)

⎥⎥⎥⎥

⎥

⎦

⎤

⎢⎢⎢⎢

⎢

⎣

⎡

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎥⎥⎥⎥

⎥

⎦

⎤

⎢⎢⎢⎢

⎢

⎣

⎡

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

++++−⎟⎟ ⎠

⎞

⎜⎜⎝

⎛

=

−⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +=+∴

...

3

61

2

21exp1exp

1exp

T V d v

T V d v

T V d v

T V Dv

S I

T V DV

S I

T V

d v

DV

S I

d i

D I

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ = 1exp

T V Dv

S I

Di

Subtracting I D from both sides of the equation,

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

++++= ...

3

61

2

21)(

T V d v

T V d v

T V d v

S I

D I

d i

For id to be a linear function of signal voltage vd ,

This represents the requirement for small-signal operation of the diode.

V05.02 =<<T

V d v

d v

d g

D I

Di

T V d v

S I

D I

d i +=⇒+=

⎟⎟⎟

⎠

⎜⎜⎜

⎝

)( ⎞⎛

Current-Controlled Attenuator

Magnitude of ac voltage vo

developed across diode can be

controlled by value of dc bias current applied to diode.


• The slope of the diode characteristic at the Q-point is called the

diode conductance and is given by:

• g d is small but non-zero for I D = 0 because slope of diode

equation is nonzero at origin.

• Diode resistance is given by:

D I D

I

T V D I

d g

T V

S I

D I

T V DV

T V S

I

poQ Dv Di

d g

40V025.0

exp

int

==≅

+==

−∂

∂=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

For I D>> I S

d g d

r 1

=

∴

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Lecture6(20-3-11)

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