RMS_combination - Average and Effective(RMS Values of...

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Average and Effective (RMS) Values of Composite Waveforms Denard Lynch Page 1 of 3 Nov. 1, 2008 For a waveform composed of a number of components, for example: x(t) = a(t) + b(t) + c(t) + … (1) the average and effective values may be determined from the average and effective values (respectively) of the components as follows: x( t ) = a( t ) + b( t ) + c( t ) + ... (2) X RMS = A RMS 2 + B RMA 2 + C RMA 2 + ... (3) However , the components must be fully described over the period in question so that the composite expression given in (1) is indeed true. Consider the following example where we may want to know the RMS value of the waveform: We can see three distinct waveform shapes that make up the overall period in this case, and we know, from previous work, that each has a specific RMS value in relation to the peak, A ( 3 ,A, 2 , respectively) iff they were a repetitive waveform of period T/3 . If we happen to use these directly as the RMS values of a(t), b(t) and c(t), we would get: X RMS = A 3 2 + A ( ) 2 + A 2 2 = 5 6 A which is incorrect!.
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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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RMS_combination - Average and Effective(RMS Values of...

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