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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 i(t) L G L di t dt i t i t N N ( ) + ( ) = ( ) 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 I t u t N A ( ) = [ ] ( ) 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) G L di t dt i t I t t N A ( ) + ( ) = cos , ω 0 Thus, LHS must be a sinusoid of frequency ω , so, i t I t F ( ) = + ( ) cos ω φ or converting to Fourier coefficients, i t a t b t ( ) = + cos sin ω ω
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EE 205 Coifman 19-3 now quit looking ahead... i t I GL t GL t t A ( ) = + ( ) + ( ) 1 0 2 ω ω ω ω cos sin , and adding in the natural response...
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