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AC units Conversion

We are often concerned with the average value or level of a signal over some time period. Vibrations of course, tend to produce signals that look like sine waves. But the average value of any sine wave over one cycle is zero. So that is not very useful. If we just dealt with pure sine waves, we could simply report the peak value. E.g. for x = Asin( $\omega$ t)we could just report A (sometimes called single amplitude, and abbreviated as p, pk, or SA). Or we could report the peak-to-peak, which would be 2A in this case (sometimes called double amplitude, and abbreviated as pp, pk-pk, or DA). Many times, of course, we do not have pure sine waves, and it is useful to distinguish between signals which spent a lot of time at the peak value and only a little time near zero and those which spend a lot of time near zero and only a little time near the peak. A simple method is to simply take the average of the absolute value, namely ${\frac{{1}}{{T}}}$ $\int$ | f ( $\omega$ t) | dt. This has the advantage that it is easy to do in hardware - absolute value is a rectifier (a few diodes) and averaging is a low pass filter (a few resistors and capacitors). Some companies refer to this value value as the average value of the signal, although it is not the same as an arithmetic mean. The most common method of reporting levels is the RMS level, which stands for root-mean-square. This is defined as $\sqrt{{\frac{1}{T}\int f(t)^{2}dt}}$ . For a pure sine wave, there is a one-to-one relationship between these four different measures, as defined in the table below.

To-> RMS Peak PP Avg

from

RMS 1 $\sqrt{{2}}$ = 1.41 2 $\sqrt{{2}}$ = 2.83 ${\frac{{2\sqrt{2}}}{{\pi}}}$ = 0.900

Peak ${\frac{{\sqrt{2}}}{{2}}}$ = 0.707 1 2 ${\frac{{2}}{{\pi}}}$ = 0.637

Peak-to-Peak ${\frac{{\sqrt{2}}}{{4}}}$ = 0.353 0.5 1 ${\frac{{1}}{{\pi}}}$ = 0.318

Average ${\frac{{\pi}}{{2\sqrt{2}}}}$ = 1.11 ${\frac{{\pi}}{{2}}}$ = 1.57 $\pi$ = 3.14 1

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To->	RMS	Peak	PP	Avg
from
RMS	1	$\sqrt{{2}}$ = 1.41	2 $\sqrt{{2}}$ = 2.83	${\frac{{2\sqrt{2}}}{{\pi}}}$ = 0.900
Peak	${\frac{{\sqrt{2}}}{{2}}}$ = 0.707	1	2	${\frac{{2}}{{\pi}}}$ = 0.637
Peak-to-Peak	${\frac{{\sqrt{2}}}{{4}}}$ = 0.353	0.5	1	${\frac{{1}}{{\pi}}}$ = 0.318
Average	${\frac{{\pi}}{{2\sqrt{2}}}}$ = 1.11	${\frac{{\pi}}{{2}}}$ = 1.57	$\pi$ = 3.14	1