lecture19

# lecture19 - EE 205 Coifman First Order circuits i (t) +...

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EE 205 Coifman 19-1 First Order circuits + - v(t) i(t) L Resistors and sources + - v(t) i N (t) R N L GL di t dt it i t NN () +() = Three factors contribute to our solution: 1) The input(s) driving the circuit (e.g., v T (t)) 2) The values of the circuit parameters (e.g., R T and C) 3) The initial stored energy (initial condition) (e.g., v(0)) We’ve done part 3, now go pack to part 1 and consider sinusoidal inputs (why sinusoids?), this is the "Forced response" (why?) e.g., I t u t NA () = [] cos ω note, this is a "causal" sinusoid

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EE 205 Coifman 19-2 For the moment, assume we start with no stored charge (then, we will use superposition to combine the Forced and Natural responses) GL di t dt it I t t NA () +() =≥ cos , ω 0 Thus, LHS must be a sinusoid of frequency ω , so, I t F =+ cos ωφ or converting to Fourier coefficients, a t b t cos sin ωω
EE 205 Coifman 19-3 now quit looking ahead. .. it I GL tG L t t A () = + () + 1 0 2 ω ωω cos sin , and adding in the natural response. .. Ke I GL L t t tGL A =+ + + 1 0 2 cos sin ,

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EE 205 Coifman 19-4 Kids these days. ..
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## This note was uploaded on 07/17/2008 for the course EE 205 taught by Professor Coifman during the Spring '08 term at Ohio State.

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lecture19 - EE 205 Coifman First Order circuits i (t) +...

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