lecture3 - Boise State University Department of Electrical...

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Unformatted text preview: Boise State University Department of Electrical and Computer Engineering ECE 212 Circuit Analysis and Design Lecture #3: The Phasor Transform III Lecture Objectives : 1. To define the concept of a phasor and to give it a physical interpretation using a rotating space vector 2. To derive the phasors of the derivative and integral of a sinusoidal waveform Polar-to-Rectangular and Rectangular-to-Polar Conversions : z = | z | = | z | cos + j | z | sin = a + jb z = a + jb = a 2 + b 2 tan 1 b a = | z | = tan 1 b a = { atan b/a if a atan b/a 180 o if a Example of a Transform: The Logarithm Transform Real Domain- Real Domain a ln- x = ln a b ln- y = ln b c = ab = e ln ab = e z ln- 1 - z = x + y = ln a + ln b = ln ab Concept of a Phasor : v ( t ) = V m cos( t + o ) = 2 V cos( t + o ) = R e { 2 V cos( t + o ) + j (anything) } = R e { 2 V cos( t + o ) + j 2 V sin( t + o ) }...
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This document was uploaded on 11/01/2011 for the course ECE 212 at Boise State.

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lecture3 - Boise State University Department of Electrical...

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