Lecture 25-27_v2

Lecture 25-27_v2 - Spring 2011 ECE 2100 Cornell University...

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Unformatted text preview: Spring 2011 ECE 2100, Cornell University, Prof. Molnar 1 Lecture 25-27 Sinusoidal power, complex conjugate power matching, Mutual Inductance and transformers Spring 2011 ECE 2100, Cornell University, Prof. Molnar 2 Definitions of power in sinusoids • Instantaneous power: – power being transferred at a given moment in time – Can be either positive or negative, – depending upon time, phase shift • Average power: – Over a given cycle – Due to in-phase part of voltage, current – Equivalent to the RMS alue of current squared ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 Z I Z A A Z P t t A Z t P t A t A Z t P t A Z t V I e Z ZI V t V t I t P t A t I RMS avg j Re Re 2 1 cos 2 1 2 2 sin sin 2 2 cos 1 cos 2 1 cos cos cos cos 2 2 2 2 = = = +- + + = + + + = + + = ⇒ = = = + = θ φ ϖ θ φ ϖ θ φ ϖ θ φ ϖ θ φ ϖ φ ϖ θ Always pos. “Real” Both pos, neg. Spring 2011 ECE 2100, Cornell University, Prof. Molnar 3 Example 2 4 6 8 10 12 14 V(t) I(t) P(t) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 R A e R A P t R A t I t V t P t R A t I e R V R V I e CA P t CA t I t V t P t CA t I Ce V CV j I e L A P t L A t I t V t P t L A t I e L V L j V I t A t V j Ravg R R R j R j Cavg C C C j C j Lavg L L L j L 2 Re 2 2 cos 1 2 cos Re 2 2 sin 2 sin Re 2 2 sin 2 sin cos 2 2 2 2 2 2 2 2 2 2 2 = = + = = = ⇒ = = = =- = =- = ⇒ = = =...
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Lecture 25-27_v2 - Spring 2011 ECE 2100 Cornell University...

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