320 Amp Models

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320-amp-models.tex Page 1

ECE 320

Amplifier Models

ECE 320 - Linear Active Circuit Design Phyllis R. Nelson

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2-Port Networks

A 2-port network is any circiut with two pairs of wires connecting to the outside world. (Each

port is a pair of wires.) The standard notation used for the voltages and currents in a 2-port

network is shown below.

2-port

network

+

-v2

+

-v1

i1 i2

Just as there are two completely equivalent models for a 1-port network (the Thevenin and

Norton equivalent circuits), there are multiple equivalent models for a 2-port network. We will

consider the z, y, g, and h parameter models. (There are also s and abcd parameters.)


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z Parameters

+

-v2

+

-v1

i1 i2

z12i2

z21i1z11 z22

+

+

v1 = z11i1 + z12i2

v2 = z21i1 + z22i2


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z11 =v1i1

i2=0

= open-circuit input resistance

z12 =v1i2

i1=0

= reverse open-circuit transresistance

z21 =v2

i1i2=0

= forward open-circuit transresistance

z22 =v2i2

i1=0

= open-circuit output resistance

All of the zij are in Ohms.


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y Parameters

+

-v2

+

-v1

i1 i2

y12v2

y21v11y11

1y22

i1 = y11v1 + y12v2

i2 = y21v1 + y22v2


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y11 =i1v1

v2=0

= short-circuit input conductance

y12 =i1v2

v1=0

= reverse short-circuit transconductance

y21 =i2

v1

v2=0

= forward short-circuit transconductance

y22 =i2v2

v1=0

= open-circuit output conductance

All of the yij are in Siemens.


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g Parameters

+

-v2

+

-v1

i2

+

g12i2

g21v1g221

g11

i1 = g11v1 + g12i2

v2 = g21v1 + g22i2


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g11 =i1v1

i2=0

= open-circuit input conductance

g12 =i1i2

v1=0

= reverse short-circuit current gain

g21 =v2

v1

i2=0

= forward open-circuit voltage gain

g22 =v2i2

v1=0

= short-circuit output resistance

g12 and g21 are dimensionless, while g11 is in Siemens and g22 is in Ohms.


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h Parameters

+

-

v2

+

-

v1

i1 i2

h12v2

h21i1h11 1

h22+

v1 = h11i1 + h12v2

i2 = h21i1 + h22v2


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h11 =v1i1

v2=0

= short-circuit input resistance

h12 = v1

v2

i1=0

= reverse open-circuit voltage gain

h21 =i2

i1

v2=0

= forward short-circuit current gain

h22 =i2v2

i1=0

= open-circuit output conductance

h12 and h21 are dimensionless, while h11 is in Ohms and h22 is in Siemens.


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IEEE Alternative Subscript Notation

11 i for input

12 r for reverse transfer

21 f for forward transfer

22 o for output


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Amplifiers

An amplifier is a special case of a 2-port network having an input port and an output port.

Amplifiers are considered to be one-directional, producing a scaled copy of the input signal at the

output port.

Standard amplifier models are used in system design in much the same way as the Thevenin

and Norton models: they provide the simplest possible description of the properties of a more

complex circuit. Thus, the parameters of the standard amplifier models are used in specifications.


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The circuit below shows an amplifier, together with a model for the source that drives it, and the

load. The definitions of a number of commonly-used parameters are also given.

+

+

RL

RL

vivS

+

-vo

+

-

io

iiInput voltage gain: Av =

vovi

Overall voltage gain: Avs =vovS

Current gain: Ai =ioii

Transresistance: Rm = voiiInput transconductance: Gm =

iovi

Input power gain: Ap =popi

=vovi

ioii= AvAi

Overall power gain: Aps=

po

ps

=vovs

ioii= AvsAi


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Amplifier Models

There are four equivalent amplifier models. Each one can be derived from one of the 2-port

network parameterizations by setting the parameter with the subscript 21 to zero, renaming v1. v2

and i1 to vi, vo and ii, changing the direction of i2 and naming the new current io. Thus there are

four amplifier models, which are discussed in detail on the next few slides.


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Voltage Amplifier

+

vS

RS

Ri+

-

vi

+

-Avovi

Ro

+

vo

-

RL

io

Avo =

vo

viio=0

= open circuit voltage gain

The voltage amp comes from the g-parameter 2-port model. The figure below shows how.

+

-v2

+

-v1

i2

+

g12i2

g21v1g221

g11

0

viRi

io

vo

Ro

Avovi


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+

vS

RS

Ri+

-

vi+-A

vo

vi

Ro

+

vo

-

RL

io

The voltage amplifier, together with its source and load, are used to connect the specific

amplifier model with quantities describing the amplifiers performance.

Av =vovi=

RL

Ro +RL

Avo = input voltage gain

Avs =vo

vS

=vo

vi

vi

vS

= Ri

RS+RiAv = overall voltage gain

Ai =ioii=

vo/Rovi/Ri

=RiRo

vovi=

RiRo

Av = current gain


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Current Amplifier

+

vS

RS

RiRo

+

vo

-

RLii

Aisii

io

Ais =ioii

vo=0

= short circuit current gain

Ai =ioii=

Ro

Ro +RL

Ais = input current gain


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Transconductance Amplifier

+

vS

RS

RiRo

+

vo

-

RL

Gmsvi

+

vi

-

io

Gms =iovi

vo=0

= short circuit transconductance

Gm =iovi=

Ro

Ro +RL

Gms = input transconductance


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Transresistance Amplifier

+

vS

RS

Ri+-Rmoii

Ro

+

vo

-

RLii

io

Rmo =voii

Io=0

= open circuit transconductance

Rm =voii=

RL

RL +Ro

Rmo = input transconductance


d l P

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Conversion Between Amplifier Models

Lets find the component values of a voltage amp that is equivalent to a given current amp.

+

vS

RS

RiRo

+

vo

-

RLii

Aisii

io

+

vS

RS

Ri+

-

vi+-Avovi

Ro

+

vo

-

RL

io

Current Amp Voltage Amp

Neither Ro or Ri needs a new value, although Ro changes from parallel- to series-connected.

Avo =voviio=0

=

RoAisiivi =

RoAisvi/ii =

RoRiA

is

Note that this final expression contains only component values, and that all the voltages and

currents have been eliminated.


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