Lecture 20-22_v2 - Spring 2011 ECE 2100, Cornell...

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Unformatted text preview: Spring 2011 ECE 2100, Cornell University, Prof. A. Molnar 1 Lectures 20-22 Phasors and their uses Frequency-domain analysis Spring 2011 ECE 2100, Cornell University, Prof. A. Molnar 2 Generalizing complex exp. Can describe a complex exponential as either magnitude and phase (polar) or as a weighted sum of real, imaginary (cartesian) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 t B t A t V t m t m t V t m t V sin cos sin sin cos cos cos- =- = + = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 t j jB A t V t j jm m t V t j j m j t j m t V exp exp sin cos exp exp exp + = + = = + = Can describe a sinusoid either by magnitude and phase (polar) or as a weighted sum of sine, cosine (cartesian) cos( t) sin( t) A B m real imag A B m Spring 2011 ECE 2100, Cornell University, Prof. A. Molnar 3 The phasor transform Converting phase/mag to Cartesian (complex notation): Converting complex cartesian to angle + magnitude ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 sin , cos exp exp m B m A t j jB A j t j m t V = = + = + = Allows intra-conversion between complex numbers and magnitude/phase real imag A B m ( 29 ( 29 ( 29 ( 29 ( 29( 29 =- + = + = + = + =- A B jB A jB A B A m t j jB A j t j m t V 1 2 2 tan exp exp...
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This note was uploaded on 06/10/2011 for the course ECE 2100 taught by Professor Kelley/seyler during the Spring '05 term at Cornell University (Engineering School).

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Lecture 20-22_v2 - Spring 2011 ECE 2100, Cornell...

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