RMS_summary - Average and Effective (RMS) Values –...

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Unformatted text preview: Average and Effective (RMS) Values – SUMMARY (Jackson: Ch 18, Appendix 2‐6) Average Values 1 ∫ x( t ) dt T0 find period⇒area⇒average x= T Effective (RMS) Values 2 1T ∫ x( t ) dt T0 T⇒S⇒M⇒R Some hints and work‐saving shortcuts… a) Time shifting to a convenient part of the cycle / convenient origin X RMS = ( ) t α t’ = t+α b) Use geometry and geometric integration to advantage A t 2 2 2 t A t x( t ) = A − c) Separate AC and DC components and combine later If x( t ) = A + B + C + ... x = A + B + C + ... X RMS = 2 2 2 ARMS + BRMS + C RMS + ... 2 2 2A 2A 4A 4A 4 A2 t , x( t ) = A2 − 2 t + 2 t 2 ; versus x( t ) = t , x( t ) = 2 t 2 T T T T T ( ) 2 ( ) iff A, B, C… are all different frequencies! Remember… ⎛T ⎞ ⎜ ∫ x( t ) dt ⎟ ⎝0 ⎠ 2 ≠ ∫ ( x( t )) dt T 2 0 Denard Lynch Oct 2008 ...
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This note was uploaded on 09/25/2010 for the course EE 201 taught by Professor Linch during the Spring '10 term at University of Saskatchewan- Management Area.

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