Make Better AC RMS Measurements with Your Digital Multimeter
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Introduction
If you use a digital multimeter (DMM) for AC voltage measurements, it is important to know what type of reading your meter is giving you so that you can properly interpret the results. Is your meter is giving you peak value, average value, root-mean-square (RMS) value, or something else? If the answer is “something else,” you may be in trouble, and the trouble usually happens with AC rms measurements. This application note will help you understand the different techniques DMMs use to measure rms values, how the signal affects the quality of your measurements, and how to avoid common measurement mistakes.
Measuring AC RMS
Measuring AC rms values is more complicated than it appears at first glance. If it is complicated, why do we bother? Because true rms is the only AC voltage reading that does not depend on the shape of the signal. It often is the most useful measurement for real-world waveforms. Often, rms is described as a measure of equivalent heating value, with a relationship to the amount of power dissipated by a resistive load driven by the equivalent DC value. For example, a 1Vpk sine wave will deliver the same power to a resistive load as a 0.707Vdc signal. A reliable rms reading on a signal will give you a better idea of the effect the signal will have in your circuit. Figure 1 shows four common voltage parameters. Peak voltage (Vpk) and peakto-peak voltage (Vpk-pk) are simple. Vavg is the average of all the instantaneous values in one complete cycle of the waveform. You will learn how we calculate Vrms below. For sine waves, the negative half of the waveform cancels out the positive half and averages to zero over one cycle. This type of average would not provide much insight into the signal’s effective amplitude, so most meters compute Vavg based on the absolute value of the waveform. For a sine wave, this works out to Vpk x 0.637 (Figure 2). You can derive Vrms by squaring every point in the waveform, finding the average (mean) value of the squares, then finding the square root of the average. With pure sine waves, you can take a couple of shortcuts: just multiply Vpk x 0.707 or Vavg x 1.11. Inexpensive peak-responding or average-responding meters rely on these scaling factors.
The scaling factors apply only to pure sine waves. For every other type of signal, using this approach produces misleading answers. If you are using a meter that is not really designed for the task, you easily can end up with significant error—as high as 40 percent or more—depending on the meter and the signal. The ratio of Vpk to Vrms known as the crest factor, is important to measurement accuracy. The crest factor is a measure of how high the waveform peaks, relative to its RMS value. The higher the crest factor, the more difficult it is to make an accurate AC measurement. Two measurement challenges are associated with high crest factors. The first involves input range. Imagine a pulse train with a very low duty cycle but a relatively high peak amplitude. Signals like this force the meter to simultaneously measure a high peak value and a much lower rms value, possibly creating overload problems on the high end and resolution problems on the low end. The second challenge is the amount of higher-frequency energy in the signal. In general, high crest factors indicate more harmonics, which can cause trouble for all meters. Peak- and average-responding meters that are trying to measure rms have a particularly hard time.
Tips for Making Better AC RMS Measurements
Given the importance—and difficulty—of measuring rms, what is the best way to proceed with your day-to-day measurement tasks? The following tips will help you achieve better results.
