# Understanding crest factor of a voltmeter

I was studying signals and systems and came across the crest factor which is defined as the ratio of Vmax of the signal to the rms value of the voltage with the dc component removed. It then proceeds to says that a voltmeter with high crest factor is able to read accurately rms values of signals whose waveforms differ from sinusoids, in particular, signals with low duty factor. My question is what does this mean, as far as I knew crest factor was defined for periodic signals, how do I relate to the crest factor of a voltmeter?

For a sinusoid, the peak or "crest" is sqrt(2) times higher than the RMS value. For other waveshapes, it can be much higher. The crest factor spec is telling you how high the peaks of a signal can be relative to the RMS of the signal for the voltmeter to still accurately measure the RMS.

Many modern RMS voltmeters sample the waveform many times per cycle, and perform the RMS calculation in firmware digitally. Each reading is squared, these square values low pass filtered, then the square root taken of this low pass filtered result.

The individual readings are linear, and have some fixed resolution and maximum value that can be converted. To get RMS, samples at the peaks of the waveform still need to be within the measurement range. However, the average can't be so low relative to the peaks that you get significant quantization noise. The meter manufacturer has done all these calculations and is telling you how extreme the peaks can be for the meter to still live up to whatever accuracy it is claiming.

• How do meters behave when measuring a frequency components which are high relative to the sample rate? I would think that a meter which took "snapshot" samples of unfiltered signals at "random" times could do a pretty good job of taking RMS measurements of any frequency the sample-and-hold amplifier could handle, but I have no idea if they do any such thing. Mar 25, 2014 at 15:07
• @Supe: The sample frequency needs to be "high" relative to the signal frequency to get good RMS. Put another way, the harmonics of the signal matter in determining RMS, so the signal needs to be sampled fast enough to properly measure the highest relevant harmonic. Since it's hard to know that that is, higher is better. Usually you want to sample at a few kHz at least to get good RMS of 60 Hz power signals, for example. 100 samples/cycle is on the low end. 1000 samples/cycle is much better. Mar 25, 2014 at 15:13
• Given a repeating signal that's much faster than 60Hz (e.g. in the multi-kHz or MHz range), is it necessary to have dozens or hundreds of samples from one cycle, or could one simply take a thousand randomly-timed samples and figure that they'll probably be more-or-less distributed over the waveform? One would end up with a 1/sqrt(N) noise component, but if one wants to update the display four times per second, getting N high enough for clean readings might be easier than having a sample rate that was many times higher than the input frequency. Mar 25, 2014 at 15:28
• @supe: Yes, but only if two conditions are met: 1 - The samples must not be correlated to the signal being measured, else you get aliases instead of random noise. 2 - The input signal must be regularly repeating. Mar 25, 2014 at 15:39

All this is with reference to periodic waveforms.

Here is a list of various waveforms and their crest factors.

For "low duty cycle", consider a PWM signal with a low "on" time in relation to the period.

A PWM signal has a crest factor of $\sqrt{T\over t_{ON}}$, so if you have a periodic PWM at 5kHz (T= 200$\mu$sec) with a 5$\mu$sec $t_{ON}$ (2.5% on time), the crest factor is 6.3.

You can calculate that from the RMS value and the peak value. The crest factor stays the same regardless of the amplitude, so say the amplitude is 1. Then the peak value is also 1, and the RMS value is $\sqrt {t_{ON} \over T}$, so the crest factor is just the inverse of the RMS value.