## Appendix A. Calculating RMS value

RMS stands for Root Mean Square, which shows what it is: the square
root of the mean of the squares. Let's assume we take n samples. The value
of sample x will be v(x∙T/n) where T is the period of the signal. The RMS
value is the square root of the average of the square of all samples (x
ranging from 0 thru n-1):

Next, we replace xT/n by t: t = xT/n. This means we also have to
change the range of the sum sign: if x=0, t=0; if x=n-1, t=(n-1)T/n = T when
n is very large. The calculation becomes more accurate if n nears
infinite:

Multiply both the numerator and the denominator by the time step
between each sample (which nears zero when n nears infinite), and we get the
following equation:

In case of a sinusoidal signal, v(t) = A sin(2∙π∙f∙t) where A is the
amplitude of the signal.

v^{2}(t) =
A^{2}sin^{2}(2∙π∙f∙t). You
may have learned in high school that sin^{2}(x) =
0.5(1-cos(2x)). So: