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Lecture 22

# Lecture 22 - Lectures 22 Phasors and their uses...

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Unformatted text preview: Lectures 22 Phasors and their uses 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 ϖ ϖ φ ϖ φ ϖ φ ϖ 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 ϖ ϖ φ φ ϖ φ φ ϖ 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( ω t) sin( ω t) A B m φ real imag A B m φ The phasor transform • Converting phase/mag to Cartesian (complex notation): • Converting complex cartesian to angle + magnitude ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 φ φ ϖ φ ϖ 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...
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Lecture 22 - Lectures 22 Phasors and their uses...

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