11 - AC Steady State

11 - AC Steady State - EECS 215 AC Steady State AC Circuit...

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EECS 215 AC Steady State J. Phillips EECS 215 AC Circuit Analysis What happens when you drive a circuit with a sinusoidal input? For example, V in =V 0 cos( ω t) From SOC analysis thusfar we have transient response and steady state response natural solution and forced solution Steady state response is the forced solution Can be used for any periodic signal (Fourier series!)
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J. Phillips EECS 215 AC Circuit Analysis Using Our Current Tools () 2 2 2 0 12 1 0 2 2 0 1 00 1/2 0 11 1 2( ) 2 1 cos( ) 1 cc c c General Differential Equation VV i RR R Vi L t LC C t LC t i R f t tC t L C t L LC Now i I t ft C αω α ω ∂∂ +  ++ = +  ∂  = + =   + = = = =− 1 sin( ) cos( ) , () , cos ( ) s in cf R It I t LC Trial Forced Solutionof formof f t f t f t vt A t B t ωω +  ′′ =+ i o (t)=I 0 cos( ω t) C R 2 R 1 L J. Phillips EECS 215 AC Circuit Analysis Using Our Current Tools 2 2 2 1 0 22 s 1 2s i n ( ) c o s ( ) cos( ) sin( ) 1 2 s i n ()2 c o s sin( ) cos( ) cf c General Differential Equation t R VI tI t L C t AtBt At B t C BtAt ω ω = +  −−  −+ =   1 1 1 22 2 2 10 0 2 2 0 sin( ) cos( ) cos( ) sin( ) 2 1 2 2 1 2
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This note was uploaded on 04/04/2008 for the course EECS 215 taught by Professor Phillips during the Winter '08 term at University of Michigan.

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11 - AC Steady State - EECS 215 AC Steady State AC Circuit...

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