EE40Lecture 17Venkat AnantharamThevenin EquivalentRoot Mean Square (rms) ValuesPower: Instantaneous and Time-AverageMaximum Average Power TransferSlide 1EE40 Spring 2008 Venkat AnantharamEE40Lecture 17Venkat Anantharam3/05/08 Reading: Chap. 5: phasors. Chap. 6: Bode plots.Slide 2EE40 Spring 2008 Venkat AnantharamThevenin Equivalentf=60 Hz4.8231.10k2090-k65.290-k65.20 10V −∠=⎟⎠⎞⎜⎝⎛°∠Ω+°∠Ω°∠Ω°∠==OCTHVV20kΩ+-1µF10V ∠ 0°VC+-+-ZTHVTHZR= R= 20kΩ = 20kΩ∠0°ZC= 1/j (2πf x 1µF) = 2.65kΩ∠-90°4.8262.20k2090-k65.290-k65.20k20 ||C−∠=⎟⎠⎞⎜⎝⎛°∠Ω+°∠Ω°∠Ω⋅°∠Ω°== ZZZRTHSlide 3EE40 Spring 2008 Venkat AnantharamRoot Mean Square (rms) Values• rms valued defined as• Assuming a sinusoid gives• Using a trigonometric identity gives• Evaluating at limits givesdttvTvToRMS∫= )(12T = perioddttvTvTomRMS∫+= )(cos122θωdttTvvTomRMS∫++= )]22cos(1[22θω2mRMSvv =)]2sin(21)22sin(21[22θθωωwTTTvvmRMS−++=Slide 4EE40 Spring 2008 Venkat AnantharamPower: Instantaneous and Time-AverageFor a Resistor• The instantaneous power is• The time-average power isFor an Impedance • The instantaneous power is• The time-average power is• The reactive power at 2ω isRtvtitvtp2)()()()( ==RvdttvTRdtRtvTdttpTPrmsTTTAVE202020])(1[1)(1)(1====∫∫∫)()()( titvtp=}Re{)()(1)(1*00rmsrmsTTAVEdttitvTdttpTP IV ⋅===∫∫titv ()(}Im{*rmsrmsQ IV ⋅=222)(rmsrmsAVEIVQP ⋅=+Slide 5EE40 Spring 2008 Venkat AnantharamMaximum Average Power Transfer+-ZTHVTHZLOAD• Maximum time average power occurs when• This presents a resistive impedance to the source• Power transferred is*THLOADZZ =*THTHtotalZZZ +=RVRPrmsAVE221**}2Re{}Re{
View Full Document
Unlocking...