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Crest Factor

The ratio of the peak amplitude to the average amplitude or RMS value of any periodically varying function. For a sine wave the crest factor is 1.414, and for a square wave the crest factor is 1. So the peak amplitude of a pure sine wave can be determined by multiplying the RMS value times 1.414. It also works out that the RMS value can be determined by multiplying the peak value times .707. This concept is important to understand in a variety of circumstances. One that we come into contact with regularly is when working with level meters. A peak reading meter is by definition not going to show us RMS levels and vice versa. Some meters do show both, which gives the engineer a good opportunity to compare the peak to average levels (or Crest Factor) of their material. This is of crucial importance in mastering work.

For you math/physics nuts, this relates to the fact that you can take the sin of Pi divided by 4 and get .707.

Sin π/4 = .707

A sin wave is a 360 degree repeating waveform. If you assume you start at zero degrees then you are at “peak” value 90 degrees into the wave. 90 degrees is 1/4 of the way through the 360 degree cycle. It’s based on a circle (which also has 360 degrees) so that’s where Pi comes in. Pi divided by 4 = .785398. The sin of that is .707107. Similarly at 270 degrees into the 360 sine wave you are at the maximum negative value. So you can also look at the equation this way:

Sin (3π/4)

Pi multiplied by 3 = 9.42478, divide that by 4 and you have 2.365619. Well, guess what the sin of 2.365619 is? Answer = .700411. Essentially we’re back at our .707 number. It’s just off a little due to the rounding necessary when working with the value of Pi(π).

To reverse the process (start with the RMS value and solve for peak value) we can invert the equation.

1/(sin (π/4)) = 1.414 – 1/(sin (3π/4) = 1.414

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