EE40 Lecture 17 Venkat Anantharam 3 05 08 Reading Chap 5 phasors Chap 6 Bode plots EE40 Spring 2008 Slide 1 Venkat Anantharam Thevenin Equivalent 10V 0 20k 1 F ZTH VC VTH f 60 Hz ZR R 20k 20k 0 ZC 1 j 2 f x 1 F 2 65k 90 2 65k 90 VTH VOC 10V 0 1 31 82 4 2 65k 90 20k 0 20k 0 2 65k 90 ZTH Z R Z C 2 62 82 4 2 65k 90 20k 0 EE40 Spring 2008 Slide 2 Venkat Anantharam Root Mean Square rms Values rms valued defined as T vRMS 1 2 v t dt T o T period Assuming a sinusoid gives T vRMS 1 2 2 v cos t dt m T o Using a trigonometric identity gives 2 T vRMS v m 1 cos 2 t 2 dt 2T o Evaluating at limits gives 2 vRMS v 1 1 sin 2 T 2 m T sin 2 2T 2 2w EE40 Spring 2008 Slide 3 vRMS vm 2 Venkat Anantharam Power Instantaneous and Time Average For a Resistor The instantaneous power is v t 2 p t v t i t R The time average power is PAVE 1 T T T T 2 vrms 1 v t 2 1 1 2 0 p t dt T 0 R dt R T 0 v t dt R For an Impedance v t i t The instantaneous power is p t v t i t The time average power isT PAVE 1 T T 1 p t dt v t i t dt Re V I rms rms 0 T 0 The reactive power at 2 is Q Im Vrms I rms EE40 Spring 2008 Slide 4 2 PAVE Q 2 Vrms I rms 2 Venkat Anantharam Maximum Average Power Transfer ZTH ZLOAD VTH Maximum time average power occurs when Z LOAD Z TH This presents a resistive impedance to the source Z total ZTH Z TH Power transferred is PAVE EE40 Spring 2008 2 V V Re VI Re V 12 rms 2R R Slide 5 Venkat Anantharam
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