TheveninNortonpp1

# TheveninNortonpp1 - THEVENINS AND NORTONS THEOREMS These...

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These are some of the most powerful analysis results to be discussed. They permit us to hide information that is not relevant and concentrate on what is important to the analysis THEVENIN’S AND NORTON’S THEOREMS

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http://angelfire.com/ab3/mjramp/index.html Low distortion audio power amplifier rom PreAmp voltage ) To speakers TO MATCH SPEAKERS AND AMPLIFIER IT IS MUCH EASIER TO CONSIDER THIS EQUIVALENT CIRCUIT! TO MATCH SPEAKERS AND AMPLIFIER ONE SHOULD ANALYZE THIS CIRCUIT + - R TH V REPLACE AMPLIFIER BY SIMPLER “EQUIVALENT” Courtesy of M.J. Renardson
LINEAR CIRCUIT May contain independent and dependent sources with their controlling variables PART A independent and dependent sources B a b _ O v + i THEVENIN’S EQUIVALENCE THEOREM Resistance Equivalent Thevenin Source Equivalent Thevenin TH TH R v B a b _ O v + i + TH R TH v A Thevenin Equivalent Circuit for PART A A SIMILAR EQUIVALENCE RESULT IS PRESENTED NEXT

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LINEAR CIRCUIT May contain independent and dependent sources with their controlling variables PART A independent and dependent sources B a b _ O v + i NORTON’S EQUIVALENCE THEOREM Resistance Equivalent Thevenin Source Equivalent Thevenin N N R i B a b _ O v + i N R N i A Norton Equivalent Circuit for PART A
Examples of Valid and Invalid Partitions

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OUTLINE OF PROOF - version 1 If Circuit A is unchanged then the current should be the same FOR ANY Vo USE SOURCE SUPERPOSITION SC i + All independent sources set to zero in A O i = = O O TH i v R DEFINE SC O i i i + = O SC TH O v i R v i + = ; SC TH OC OC O i R v v v i + = = = 0 ) 0 ( CIRCUIT OPEN : CASE SPECIAL SC OC TH i v R = TH OC SC R v i = i R v v i R v i TH OC O SC TH O = + = HOW DO WE INTERPRET THIS RESULT?
OUTLINE OF PROOF - version 2 2. Result must hold for “every valid Part B” that we can imagine 1. Because of the linearity of the models, for any Part B the relationship between Vo and the current, i, has to be of the form n i m v O + = * 3. If part B is an open circuit then i=0 and. .. OC v n = 4. If Part B is a short circuit then Vo is zero. In this case OC TH O v i R v + = How do we interpret this? OC SC v i m + = * 0 TH SC OC R i v m = = LINEAR CIRCUIT May contain independent and dependent sources with their controlling variables PART A independent and dependent sources B a b _ O v + i i O v OC v SC i

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This is the Thevenin equivalent circuit for the circuit in Part A OC TH O v i R v + = For ANY circuit in Part B The voltage source is called the THEVENIN EQUIVALENT SOURCE The resistance is called the THEVENIN EQUIVALENT RESISTANCE R TH i + _ O v OC v + _ PART A MUST BEHAVE LIKE THIS CIRCUIT LINEAR CIRCUIT May contain independent and dependent sources with their controlling variables PART A ANY B a b _ O v + i THEVENIN APPROACH
Norton Approach SC i TH R + O v a b i Norton TH O TH OC TH OC O R v R v i i R v v = = LINEAR CIRCUIT May contain independent and dependent sources with their controlling variables PART A ANY B a b _ O v + i SC TH OC i R v = Source Equivalent Norton SC i Part A for tion Representa Equivalent Norton

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R TH i + _ O v
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## This note was uploaded on 12/01/2011 for the course EE 2120 taught by Professor Aravena during the Fall '08 term at LSU.

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TheveninNortonpp1 - THEVENINS AND NORTONS THEOREMS These...

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