Electronic – How to tell if a particular multimeter measures AC with RMS or Average

Simple: the average of a sine is zero.

Power is proportional to voltage squared:

\$ P = \dfrac{V^2}{R} \$

so to get average power you calculate average voltage squared. That's what the RMS refers to: Root Mean Square: take the square root of the average (mean) of the squared voltage. You have to take the square root to get the dimension of a voltage again, since you first squared it.

This graph shows the difference between the two. The purple curve is the sine squared, the yellowish line the absolute value. The RMS value is \$\sqrt{2}/2\$, or about 0.71, the average value is \$2/\pi\$, or about 0.64, a difference of 10 %.

RMS gives you the equivalent DC voltage for the same power. If you would measure the resistor's temperature as a measure of dissipated energy you'll see that it's the same as for a DC voltage of 0.71 V, not 0.64 V.

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Measuring average voltage is cheaper than measuring RMS voltage however, and that's what cheaper DMMs do. They presume the signal is a sine wave, measure the rectified average and multiply the result by 1.11 (0.71/0.64) to get the RMS value. But the factor 1.11 is only valid for sinewaves. For other signals the ratio will be different. That ratio got a name: it's called the signal's form factor. For a 10 % duty cycle PWM signal the form factor will be \$1/\sqrt{10}\$, or about 0.316. That's a lot less than the sine's 1.11. DMMs which are not "True RMS" will give large errors for non-sinusoidal waveforms.

The answer to this is a solid "it depends". More specifically, it depends what kind of signals you are going to apply the meter to.

If every AC signal that you wish to measure the RMS value of is a pure sine wave, then you don't need a true RMS meter. If, however, you want to measure the RMS value of a square wave, the output of a half-wave rectifier or something else more complex, then a true RMS meter will be advantageous. An example of where this might be relevant is if you are trying to calculate the power dissipation of a resistive load in an AC power system where the mains has been through some sort of processing, or perhaps if it is being driven with a PWM signal.

Although it is a load of marketing, Fluke's website has a good article on the matter here. One nice figure it gives is that for a square wave, a non-true RMS meter will read 10% high when measuring the RMS value of a square wave (and this will vary by pulse width for a PWM signal).

By the way, Dave Jones over at EEVBlog did a $50 multimeter shootout a few years back. A bit outdated, but still useful for reasons to choose a particular meter without tRMS and then the $100 multimeter shootout covering tRMS meters.