ECE201_Lecture37

# ECE201_Lecture37 - ECE201 Linear Circuit Analysis I Lecture...

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1 ECE201 Linear Circuit Analysis I Lecture 37 Topic: Average Power and Effective Value 1. Effective Value of a Signal (1) Intuitive definition: I eff , the effective value of a periodic current i(t), is the value of a dc signal applied to a 1 resistor, such that P ave,R due to the dc signal and P ave,R due to the ac signal are equal. (2) Mathematical Definition: Left: p(t) = i 2 (t) R, P ave1 = 1 T p( τ ) d 0 T = R T i 2 ( ) 0 T Right: = I eff 2 P ave2 = 1 T p( ) 0 T = 1 T (I 2 R) o T = I 2 R Set P ave1 = P ave 2 , I = 1 T o T i 2 ( τ )d τ In general, F = 1 T o T f 2 ( τ )d τ Where f(t) is a periodic signal with a fundamental period of T. F eff is also called the rms (root-mean-square) value of f(t).

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2 (3) Example: Compute the effective value of the waveform below. 4 2 0 1 2 3 4 5 6 7 t v(t) ...
3 (4) Effective value of a general sinusoidal signal: Let v(t) = V m cos( ω t+ θ ) V V m : maximum or peak value of v(t). v 2 (t) = V m 2 cos ω t + θ ( ω t + θ ( ) = V m 2 2 cos0 + V m 2 2 cos 2 ω t + 2 θ ( ) The fundamental period of v(t) is T = 2 π ω .

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## This note was uploaded on 04/19/2011 for the course ECE 201 taught by Professor All during the Spring '08 term at Purdue.

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ECE201_Lecture37 - ECE201 Linear Circuit Analysis I Lecture...

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