Root Mean Square - RMS of Common Waveforms

RMS of Common Waveforms

Waveform Equation RMS
DC, constant
Sine wave
Square wave
Modified square wave
Triangle wave
Sawtooth wave
Pulse train
Notes:
t is time
f is frequency
a is amplitude (peak value)
D is the duty cycle or the percent(%) spent high of the period (1/f)
{r} is the fractional part of r

Waveforms made by summing known simple waveforms have an RMS that is the root of the sum of squares of the component RMS values, if the component waveforms are orthogonal (that is, if the average of the product of one simple waveform with another is zero for all pairs other than a waveform times itself).

RMS_{Total} = \sqrt {{{RMS_1}^2 + {RMS_2}^2 + \cdots + {RMS_n}^2} }

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