Amplitude Measurements, Root Mean Square Value, VRMS

The RMS value of an alternating current is that current which will give the same heating effect as the equivalent direct current. The RMS value of y=f(x) over the range x=a to x=b is given by:

RMS value =

The mean or average value of a waveform between x=a to x=b is given by:

AVG value =

For simple tones (sinusoidal waveforms) the relationships between RMS value, AVG value, peak and peak-to-peak value are given in Table 6.

from value	multiplication factor to value
	average	RMS	peak	peak-to-peak
average	1.0	1.11	1.57	3.14
RMS	0.9	1.0	1.414	2.828
peak	0.637	0.707	1.0	2.0
peak-to-peak	0.32	0.3535	0.5	1.0

Table 6: Peak-to-peak, RMS and AVG value conversion for sinusoidal waveforms:

Coding bits/sample: n	8	16	18	20	22	24	32
FS ratio: N/1	28	216	218	220	222	224	232
FS ratio: dB	48	96	108	120	132	144	192
Note: dB (FS) = 20 * lg(N) = 20 * lg(2n) = 20*0.3010*n

Table 7. Full Scale Range (dB FS) available at different digital word lengths (bits/sample).