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ECE201_Lecture31

# ECE201_Lecture31 - EE201 Linear Circuit Analysis I Lecture...

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1 EE201 Linear Circuit Analysis I Lecture 31 Topic: Phasors, Ohm’s Phasor Law for R, L, & C; KVL & KCL 1. Phasor (1) Definition: a complex number representation of sinusoidal signals at a fixed freq. (2) Notation: bold face capital letter (underscored capital letter for handwriting) e.g. V or V (3) rectangular vs. polar coordinate: polar is preferred. e.g. V = V m φ (4) meaning: a complex number , used to represent a real sinusoidal function of time t at a fixed frequency of ω . e.g., I = 10 ∠ − 90 ° , V = I 1 + j , find v(t). First, treat I & V as complex numbers, V = 10 ∠ − 90 ° 1 + j = 10 ∠ − 90 ° 2 45 ° = 5 2 ∠ − 135 ° Then, treat V as a representation of v(t). v ( t ) = Re 5 2 e j ω t 135 ° ( ) { } = 5 2 cos ω t 135 ° ( ) Notice the Re{ } and “ ω t” during the V to v(t) expansion. 2. What is the difference between a phasor and a shorthand notation of a complex #? A phasor is a complex number that represents a sinusoidal function of time t .

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ECE201_Lecture31 - EE201 Linear Circuit Analysis I Lecture...

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