ECE201_Lecture37

ECE201_Lecture37 - ECE201 Linear Circuit Analysis I Lecture...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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).
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 (3) Example: Compute the effective value of the waveform below. 4 2 0 1 2 3 4 5 6 7 t v(t) ...
Background image of page 2
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 .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

ECE201_Lecture37 - ECE201 Linear Circuit Analysis I Lecture...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online