EE_365_200708FA_homework_07_solution

# EE_365_200708FA_homework_07_solution - 1 sc sa sb s EE 365...

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1 Homework 07 Solution © Jeffrey Mayer 2005-2007. All rights reserved. EE 365 Fall 2007 s ϕ sa a s sb b s sc c s 2 cos( ) 2 cos( 120 ) 2 cos( 120 ) sa s e is sb s e is sc s e is i I t i I t i I t ω ϕ ω ϕ ω ϕ = + = + + ° = + ° ( , ) ( , ) ( , ) ( , ) cos( ) 2 cos( ) cos( 120 ) 2 cos( 120 ) cos( 120 ) 2 cos( 120 ) 2 cos( ) cos( 120 )cos( 120 ) cos( 120 gs s gsa s gsb s gsc s s s s e is s s s e is s s s e is s s e is s e is s t t t t n I t n I t n I t I n t t ϕ ϕ ϕ ϕ ϕ ω ϕ ϕ ω ϕ ϕ ω ϕ ω ϕ ϕ ω ϕ ϕ = + + = + + + ° ⋅ + + ° + ° ⋅ + ° = + + + ° + + ° + ° F F F F [ ] ( ) 3 2 )cos( 120 ) 2 cos ( ) e is s s s e is t n I t ω ϕ ϕ ω ϕ + ° = + + Maximum mmf occurs when the argument of the cos(·) is zero: (0 ) 0 s is s is t ϕ ϕ ϕ ϕ + ⋅ + = = − Track a constant value of the wave: ( ) s e is t K ϕ ω ϕ + + = ( ) s e is K t ϕ ω ϕ = + [ ] ( ) s e is s e d d K t dt dt d dt ϕ ω ϕ ϕ ω = + = − 1.

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