Amplitude Measurements, Root Mean Square Value, VRMS

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).