ECE 202 Lesson 2

ECE 202 Lesson 2 - ECE 202 Circuit Theory 2 Lesson 2 Phasor...

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Unformatted text preview: ECE 202 Circuit Theory 2 Lesson 2 Phasor Representation of Sinusoidal Waveforms Phasor Impedances Generating Phasor Circuits Euler's Formula e jx = cos x + j sin x x = t + e j ( t + ) = cos ( t + ) + j sin ( t + ) Ae j ( t + ) = A cos ( t + ) + jA sin ( t + ) 2 Sinusoidal Waveforms Ae j ( t + ) = A cos ( t + ) + jA sin ( t + ) j ( t + ) A cos ( t + ) = Re Ae j ( t + ) A sin ( t + ) = Im Ae 3 Phasor j ( t + ) Re j e jt A cos ( t + ) = Re Ae = Ae j ( t + ) Im j e jt A sin ( t + ) = Im Ae = Ae The phasor Ae j carries the amplitude and phase information of a sinusoidal waveform 4 Phasor Impedance of Resistor v ( t ) = Ve jt i(t) R + v(t) - v( t) = R i( t) Ve jt = R Ie jt V =R I i ( t ) = Ie jt 5 Phasor Impedance of Inductor v ( t ) = Ve jt i(t) L + v(t) - v ( t ) = L di ( t ) dt Ve jt = Lj Ie jt V = j L I i ( t ) = Ie jt 6 Phasor Impedance of Capacitor v ( t ) = Ve jt i(t) C + v(t) - i ( t ) = C dv ( t ) dt Ie jt = Cj Ve jt V 1 = I jC i ( t ) = Ie jt 7 Generating Phasor Circuits i(t) R + v(t) i(t) L + v(t) i(t) C + v(t) I I I R + V j L + V 1/(j C) + V - 8 ...
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ECE 202 Lesson 2 - ECE 202 Circuit Theory 2 Lesson 2 Phasor...

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