04-Circuit%20Theorems

04-Circuit%20Theorems - EECS 215 Circuit Theorems Linearity...

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EECS 215 Circuit Theorems
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Linearity A circuit is linear if output is proportional to input A function f(x) is linear if f(ax)=af(x) All Circuit Elements In 215 are Linear Resistors V=IR V(I) is linear, I(V) is linear Linearly Dependent Sources Capacitors Inductors We will examine theorems and principles that apply to linear circuits to simplify analysis
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Linearity – Additive property The output current or voltage of a linear circuit can be expressed as a linear combination of inputs (current or voltage) y=f(x 1 +x 2 +x 3 )=k 1 x 1 + k 2 x 2 + k 3 x 3 y is output current or voltage x i are input current or voltage k i are proportionality constants, depending on circuit elements Note: k i can be unitless, in Ω , or in S , depending on y, x i units x 1 x 3 x 2 Inputs k 1 k 2 k 3 y=k 1 x 1 +k 2 x 2 +k 3 x 3
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Superposition The voltage across/current through an element in a linear circuit is the algebraic sum from each independent source acting alone Step by step procedure: 1) Turn off all all independent sources except 1. Find the output voltage and/or current due to that source using nodal or mesh analysis 2) Repeat step (1) for all independent
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04-Circuit%20Theorems - EECS 215 Circuit Theorems Linearity...

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