EE 230 Lecture 33 Spring 2010

# EE 230 Lecture 33 Spring 2010 - EE 230 Lecture 33 Small...

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EE 230 Lecture 33 Small Signal Operation of Nonlinear Networks

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Assume a one-port device has an I-V relationship given by the equation Determine the small-signal model of this device at V=2V. Quiz 33 2 I = 5V
And the number is ? 1 3 8 4 6 7 5 2 9 ?

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Assume a one-port device has an I-V relationship given by the equation Determine the small-signal model of this device at V=2V. Quiz 33 2 I = 5V Solution: Q SS SS V=V I iv V = 2 10 20 Q -1 V=V AV VV I V V = == Small signal model that of a conductor of value 20AV -1
Methods of Analysis of Nonlinear Circuits Will consider three different analysis requirements and techniques for some particularly common classes of nonlinear circuits 1. Circuits with continuously differential devices Interested in obtaining transfer characteristics of these circuits or outputs for given input signals 2. Circuits with piecewise continuous devices interested in obtaining transfer characteristics of these circuits or outputs for a given input signals 3. Circuits with small-signal inputs that vary around some operating point Interested in obtaining relationship between small-signal inputs and the corresponding small-signal outputs. Will assume these circuits operate linearly in some suitably small region around the operating point Other types of nonlinearities may exist and other types of analysis may be required but we will not attempt to categorize these scenarios in this course Review from Last Time:

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Circuits with small-signal inputs that vary around some operating point This is one of the most useful classes of circuits that exist Use is driven by goal to use nonlinear devices ( at fundamental device level, that’s all we have that provide power gain) to perform linear signal processing functions Concept of “systems” with small-signal inputs that vary around some operating point throughout the electrical engineering field and in many other fields as well Although the concepts will be introduced in the context of electronic circuits, the principles and mathematics are generally applied Review from Last Time:
Small-Signal Principle y x Q-point X Q Y Q Linear Model at Q-point X QINT y=f(x) y=f(x) Q Q x=x Q y-y f x-x x = () Q QQ x=x f x = Review from Last Time:

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Small-Signal Principle y = iV Q V=V defn I y V = def SS = i i def SS v V i SS v SS Q SS SS V=V I iv V = Review from Last Time:
A Small Signal Equivalent Circuit 2-Terminal Nonlinearl Device f(x) Small-Signal Principle Q V=V I y V = y = iV The small-signal model of this 2-terminal electrical network is a resistor of value 1/y One small-signal parameter characterizes this one-port but it is dependent on Q-point Review from Last Time:

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Small signal analysis example [] () R V V t V 2L W μ C V V T SS M OX DD OUT 2 sin + = ω V IN =V M sin ω t V M is small R V V t V 1- V V 2L W μ C V V T SS M T SS OX DD OUT 2 2 sin + + = Recall that if x is small ( ) 2 1+x 1+2x R V V t 2V 1- V V 2L W μ C V V T SS M T SS OX DD OUT
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## This note was uploaded on 02/01/2012 for the course EE 230 taught by Professor Mina during the Fall '08 term at Iowa State.

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EE 230 Lecture 33 Spring 2010 - EE 230 Lecture 33 Small...

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