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Chapter 10- Chapter 10-1 Circuit Theory Circuit Theory 2 Chapt er 10 Si nusoi dal St eady- st at e Anal ysi s O Ì [email protected] ac. kr . ¨ ° â ª * : : : H°â ª * , , Pr of essor Roger Howe Pr of essor Roger Howe ( UCB) ( UCB)

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Objectives Si nusoi dal st eady st at e anal ysi s of l i near ci r cui t s Fr equency domai n anal ysi s of l i near ci r cui t s Li near ci r cui t s? Si nusoi ds?
Sinusoidal Function Review Angular frequency (rad/s) ) ( 1 , π 2 ω : θ : ω : ) θ ω cos( ) ( Hz T f f V t V t v m m = = + = Peak value, Phase angle (degrees or rads)

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Why are Sinusoids Important? Any per i odi c si gnal v( t ) can be expr essed as a sum of si nusoi dal si gnal s by a Four i er ser i es expansi on The r esponse of a l i near ci r cui t s t o a si nusoi dal i nput , as a f unct i on of i t s f r equency, w, l eads t o i nsi ght s i nt o t he behavi or of t he ci r cui t s Li near ci r cui t s?
Linear Circuits Theor em: sol ut i ons f or vol t ages and cur r ent s i n a l i near ci r cui t ( i . e. one consi st i ng of R, L, C, and dependent s sour ces) wi t h a si nusoi dal si gnal as t he i nput ar e: Li near ci r cui t s Phase and ampl i t ude shi f t ed si nusoi d at t he same ϖ Li near i t y : f ( k 1 * c 1 +K 2 * c 2 ) =k 1 f ( c 1 ) + k 2 f ( c 2 )

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x 1 ( t ) = si n( t ) y 1 ( t ) = 2si n( t - π / 4) Fr equency 1 Graphical representation of linear circuits
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