Amplitude Measurements, Root Mean Square Value, VRMS

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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 = 625.png

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

AVG value = 626.png

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).