Find the Thévenin Equivalent Circuit to the Left of Terminals

Question

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The Answer is

\begin{array} { l } Z _ { \mathrm { a } } = \mathrm { R } _ { 1 } + Z _ { \mathrm { L } 3 } + Z _ { \mathrm { L } 1 } = 6 + \mathrm { j } 26 \Z _ { \mathrm { b } } = Z _ { \mathrm { L } 2 } + \mathrm { R } _ { 2 } + Z _ { \mathrm { C } 1 } = 9 + \mathrm { j } 11 \V _ { t h } = V _ { s } imes \frac { Z _ { M } } { Z _ { a } } = 21.9209 + \mathrm { j } 71.6760 \V _ { o } = V _ { t h } imes \frac { R _ { L } } { Z _ { t h } + R _ { L } } = 15.1058 + \mathrm { j } 40.1490 = 42.8967 \angle 69.3815 ^ { \circ } \mathrm { V }\end{array}

clear all;

\mathrm { ZL } = 19 \mathrm { j } ; \mathrm { ZL } 2 = 21 \mathrm { j } ; \mathrm { ZM } = 16 \mathrm { j } ; \mathrm { R } 1 = 6 ; \mathrm { R } 2 = 9 ; \mathrm { ZL } 3 = 7 \mathrm { j } ; \mathrm { ZC1 } = - 10 \mathrm { j } ; \mathrm { RL } = 15 ; \mathrm { ZMM } = \mathrm { abs } ( \mathrm { ZM } )

;

\mathrm { Vm } = 125 ; \mathrm { phi } = 60

;

\mathrm { Vs } = \mathrm { P } 2 \mathrm { Rd }

(Vm, phi)

\mathrm { Za } = \mathrm { R } 1 + \mathrm { ZL } 3 + \mathrm { ZL } 1

\mathrm { Zb } = \mathrm { ZL } 2 + \mathrm { R } 2 + \mathrm { ZCl }

Vth

= \mathrm { Vs }

*

\mathrm { ZM } / \mathrm { Za }

\mathrm { Zth } = \mathrm { Zb } + \mathrm { ZMM } ^ { \wedge } 2 / \mathrm { Za }

Voa

= \mathrm { Vth } \star \mathrm { RL } / ( \mathrm { Zth } + \mathrm { RL } )

Voap=R2P (Voa)

Essay