# 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).