# Error in the "Measurements of AC magnitude" page.

#### Puddy Tat

Joined May 10, 2007
1

You have the form factor listed incorrectly twice once in the text, once in the review/summary section as being the ratio of the crest (peak) to the average value.

It is actually the ratio of the RMS value to the average value. In in the case of a sine wave the form factor is supposed to be 1.11 = .707/.637.

While I don't have a specific reference giving this equation handy. The following IEEE paper, mentions on pg 207 (page 4 of the paper) that the form factor of a sine wave is 1.11.

R.E. Morrison, Parameters that influence power quality on industrial frequency AC traction systems, Proceedings of the IEEE Power Engineering Society Transmission and Distribution Conference, vol. 1, pp. 204-209, Summer 2001.

While I was looking up how a form factor was calculated I found several sites mentioning that it was the ratio of RMS to average, which does give the expected value of 1.11. While looking around for a more offical site I came across yours which appears to be in error. Using your calculation gives an incorrect value of ~1.57 for the form factor of a sine wave waveform.

#### recca02

Joined Apr 2, 2007
1,212
i agree with the above statement.
form factor for sine wave is 1.11 (remember using it in a transformer derivation)
also it is ratio of rms to average as stated.

#### Dave

Joined Nov 17, 2003
6,969
Thanks for the correction, it does appear as though you are correct. I assume the error may have propagated from the crest factor explanation.

Dave

#### Dcrunkilton

Joined Jul 31, 2004
422
I propose the following changes:

for full text. Excerpts follow.

Original text:

The form factor of an AC waveform is the ratio of its peak value divided by its average value. Square-shaped waveforms always have crest and form factors equal to 1, since the peak is the same as the RMS and average values. Sinusoidal waveforms have crest factors of 1.414 (the square root of 2) and form factors of 1.571 (π/2). Triangle- and sawtooth-shaped waveforms have crest values of 1.732 (the square root of 3) and form factors of 2.

New Text:
The form factor of an AC waveform is the ratio of its RMS value divided by its average value. Square-shaped waveforms always have crest and form factors equal to 1, since the peak is the same as the RMS and average values. Sinusoidal waveforms have an RMS value of 0.707 (the reciprocal of the square root of 2) and a form factor of 1.11 (0.707/0.636). Triangle- and sawtooth-shaped waveforms have RMS values of 0.577 (the reciprocal of the square root of 3) and form factors of 1.15 (0.577/0.5).

REVIEW:

Original text:The form factor of an AC waveform is the ratio of its peak (crest) value to its average value.

New Text:
The form factor of an AC waveform is the ratio of its RMS value to its average value.

I will make the above changes in a week if we receive no complaints about the proposed changes, sooner if we receive agreement with the changes.

I will list Puddy Tat as the contributor on the contributors page, Appendix A-2, unless this is a screen name rather than a real name.