04 - Circuit Theorems

# 04 - Circuit Theorems - EECS 215 Circuit Theorems Linearity...

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EECS 215 Circuit Theorems J. Phillips EECS 215 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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J. Phillips EECS 215 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 , 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 J. Phillips EECS 215 Linearity – Additive property Illustration Examine dependence of v 0 on inputs v s and i s v s v 0 + - R 1 R 2 i s Relate v 0 to v s
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04 - Circuit Theorems - EECS 215 Circuit Theorems Linearity...

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