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Linear Amplifiers (2)

• Symbol for a single-ended

input linear voltage amplifier.

• Ideally provides linearvoltage gain regardless of

the amplitude of the input

signal

• Real amplifiers have power 

supplies that limit the

amplitude of the output

• If input is too large, output

clamps

Transfer Characteristics (1)

Plot of amplifier output versus amplifier input

Transfer Characteristics (2)

• Gain = Slope

• To operate amplifier in its linear region, the inputmust be kept small enough

Real Transfer Characteristics

• Each circle represents

a different DC

component for the

input and output

signals – called an

operating point

• Location of operating

point has an effect on

• input signal range

• amplifier gain magnitude

• amount of distortion

Operating Point (1)

Voltage gain, output DC voltage, allowable input

magnitude range are affected

Operating Point (2)

Derivative of

transfercharacteristic

gives measure

of amplifier gain

linearity (and

distortion)

Input and output signal amplitude ranges are

maximized when operating point is near middle of

linear region

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Signal Convention (1)

• DC magnitudes in uppercase symbol and

subscript

 – Example: ID, VD

• Ac signal quantities in lowercase symbol &

subscript

 – Example: id(t), vd(t)

• Total DC + ac signal quantities in lowercase

symbol, uppercase subscript

 – Example: iD(t), vD (t)

Signal Convention (2)In general

vD(t) = VD + vd(t)

iC(t) = IC + ic(t)

Superposition

• If the amplifier is linear, superposition can be

applied. Each component can be determined

seperately.

• Determine the DC magnitude of the output using

DC model (i.e capacitors are open circuited,

inductors are short circuited)

 – Example: IO, VO

• Determine the ac signal component of the output

using the ac model (i.e., DC sources are killed and

capacitors are short circuited, inductors are open

circuited) as

 – Example: vo(t) = Av vi(t)

Amplifier Classification

CurrentCurrentCurrent

TransresistanceVoltageCurrent

TransconductanceCurrentVoltage

VoltageVoltageVoltage

TypeOutputInput

+

vi

-

+

vo

-

Ideal Voltage Amplifier 

Avi

+

R oAvi

+

vi-

+

vo-

R i

+

Real Voltage Amplifier 

Loaded Ideal Voltage Amplifier 

Avi

+

vi-

+

vo-

+

R LR s

vs

+

Av

v

s

o=

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Loaded Voltage Amplifier 

R o

Avi

+

vi-

+

vo-

R i

+

R L

R s

vs

+

Lo

L

is

i

s

o

R R 

R 

R R 

R A

v

v

++=

Ideal Current Amplifier 

Real Current Amplifier 

Aii

ii io

Aiiii io

R i R o

Loaded Ideal Current Amplifier 

Ai

i

s

o=

Aii R Lii

R sisio

Loaded Current Amplifier 

Aii R Lii

R Sisio

R i R o

Lo

o

is

s

s

o

R R 

R 

R R 

R A

i

i

++=

To determine Input Resistance R i

R oAvi

+

vi-

+

vo-

R i

+

• Apply input voltage vi(or input current ii)

• Determine the input

current ii (or inputvoltage vi)

Then

R i = vi / iiAiiii io

R i R o

ii

+

vi-

Voltage Amplifier 

Current Amplifier 

To determine Output Resistance R o

R oAvi

+

vi-

+

vx-

R i

+

• Kill the input signal

(set vi or ii to zero)

• Apply a test voltage

vx to the output node• Determine the current

ix that the source

delivers to the circuit

Then

R o = vx / ix

Aiiii ix

R i R o

ii

+

vi-

Voltage Amplifier 

Current Amplifier 

+

vx-

ix