22-AC Steady State 1

22-AC Steady State 1 - teady tate AC Analysis I...

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Unformatted text preview: teady tate AC Analysis I Steady-State AC Analysis I Fred Terry all, 2008 Fall, 2008 1 Material Order Alexander & Sadiku Chapters 9, 10, 14 ecture: Somewhat Different Order than Lecture: Somewhat Different Order than Text Chapters oday: Big Picture (Part of Chp 14) Today: Big Picture (Part of Chp 14) Finding AC Steady State Response Relationship to Transient Response/Differential Equations 2 AC Circuit Analysis Objective: Find the Steady-State Response of a inear Circuit to a Fixed AC Signal Linear Circuit to a Fixed AC Signal V in (t)=V cos( t) he Steady tate Response is the orced Solution The Steady-State Response is the Forced Solution of the Differential Equation for the Circuit hy Do This? Why Do This? Through Fourier Series, this gives us the response to ANY periodic signal Directly Useful for All Analog Circuit Design, Understanding Clock Skew on Digital Lines, etc. 3 Example: General RLC Problem C L 2 2 1 2 1 2 1 1 c c c General Differential Equation V V i R R R V i L t LC C t LC t V i + + + = + i o (t)=I cos( t)u(t) ( ) ( ) 2 2 1 1 2 1 2 ( ) 2 c c c V V i R V i f t t C t L C t R R L + + = + = + = R 2 R 1 1/2 1 cos( ) LC Now i I t = = ater we will use the following 1 ( ) f t C = 1 sin( ) cos( ) ( ), ( ), ( ) ( ) cos ( ) sin ( ) R I t I t LC Trial Forced Solutionof formof f t f t f t v t A t B t + = + Later, we will use the following...
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22-AC Steady State 1 - teady tate AC Analysis I...

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