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10 - AC Circuits and Phasors

10 - AC Circuits and Phasors - EECS 215 AC Circuits and...

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EECS 215 AC Circuits and Phasors J. Phillips EECS 215 Introduction Objective: Find steady state response of a linear circuit to fixed AC signal Sinusoidal input experienced in practice Any time varying periodic signal can be represented by a series of sinusoids (Fourier Series) What happens if we solve by directly substitution? amplitude V m = frequency angular = ω ( ) φ ω + = t V v m s sin phase = φ
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J. Phillips EECS 215 Phasors Sinusoids may be alternatively represented by a complex number containing magnitude and phase info φ jy x z + = φ φ j re r z = = 2 2 y x r + = x y 1 tan = φ φ cos r x = φ sin r y = φ φ φ sin cos j e j ± = ± ( ) ( ) ( ) ( ) t j j t j m m Ve e e V t V t v ω φ ω φ ω Re Re cos = = + = tion representa phasor V e V V m j m = = = φ φ J. Phillips EECS 215 Phasor Math Addtion ( ) ( ) 2 1 2 1 2 1 y y j x x z z + + + = + ( ) ( ) 2 1 2 1 2 1 y y j x x z z + = ( ) 2 1 2 1 2 1 φ φ + = r r z z ( ) 2 1 2 1 2 1 φ φ = r r z z = 2 φ r z φ = = r jy x z Subtraction Multiplication Division
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