Electronic Measurements

Average and effective values

Last Modification: April 16, 2013

The average (or mean) and effective (or RMS) values, are common used terms to indicate the magnitude of a periodic signal. This can be a voltage, current, power or another quantity. This article lists the equations for the average and effective values for a number of different waveforms. You can find the background on this subject in the article Theory & definitions.

Random waveform

The mean and RMS value of a random waveform can be calculated with the equations below:
calculation of the average value of a random signal[equ. 1]     calculation of the effective value of a random signal[equ. 2]

In these equations is a(t) the signal function. This can be interchanged with a voltage v(t), current i(t), power p(t) or another quantity. Amean and ARMS must than be replaced by the corresponding quantity. With emphasis must be mentioned that the RMS-value may only be calculated for the voltage and current. For other quantities is the RMS-value meaningless.


Waveforms

Here below is a list of common waveforms and their derivatives for the mean and RMS values.

Duty-cycle

De duty-cycle δ is expressed as coefficient and is always smaller than 1. Often a duty-cycle will be expressed as a percentage: to obtain the coefficient, the percentage-number must be divided by 100. If a waveform has more than one with declarations δx, is the total of widths never greater than 1.

Average value sine wave

The average value of a sine-shaped voltage or current is 0. But, often in literature, the value vpk*π/2 (≈0,637*vpk) is used. This is not the real value of the average values of a sine, but the average of the absolute values of a sine. To avoid confusion, there has to be a clear indication which average value is meant.


Form factor

The form factor is the ratio between the effective and average value:
calculation form factor[equ. 3]
Sometimes when the formfactor is calculated the result will be infinitive. This is the case with pure alternating voltages with an average value of 0. An exception is then made by using the absolute values. For a sine wave the form factor will become π/(2*√2) ≈1,11.


Crest factor

The crest factor is the ratio between the (absolute) peak value and the effective value:
calculation crest factor[equ. 4]

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