Understanding crest factors, temperature-sensing circuits, and more.

In several previous columns, we have seen how excruciatingly hard it is to accurately measure ac power, especially if phase shifts, reactive energy, nonlinearities, strange waveforms, sparking, strong harmonics, or low duty cycles are in any way involved. More often than not, a casual or improper power measurement tends to end up wildly low, leading to dead wrong conclusions concerning real efficiency. Sometimes such wrong measurements are what's behind those "overunity" pseudoscience fantasies seen on the web.

This month, we'll look at yet another power-measurement "gotcha."

Crest Factors

Figure 1 shows us a property of any repeating waveform that's known as its Crest Factor. We have already seen that the peak value of a waveform is its maximum height, the average value is like any other average, and that effective or rms value is the equivalent DC heating power. Because power involves either the square of current or voltage or else the product of these two, rms values are always equal or greater than average. Except for a pure DC current, rms is always greater than average. Sometimes it is even ridiculously greater.

The crest factor of any current or voltage waveform can be defined as the ratio of peak to rms. For instance, a DC voltage has a peak value of 1.0, an average value of 1.0, arms value of 1.0, and thus a crest factor of 1.0. One cycle of a pure sinewave might offer a peak value of 1.00, an average value of 0.634, arms value of 0.707, and a crest factor of 1.00/0.707 = 1.414.

A low brightness setting on a half-wave lamp dimmer may give you a peak value of 1.28, arms value of 0.32, an average value of 0.11, and a crest factor of 4.0. Values for the narrow impulse current waveform of a capacitance-input diode rectifier will end up waveform dependent, but you can have a peak value of 1.414, an average value of 0.04, and arms value of 0.22, and a crest factor of 6.42.

There are two key points here: First, the ratio of rms to average current will change wildly from waveform to waveform! That is always highly duty-cycle dependent. Thus, most average-responding meters lie like a rug when fed anything but whole cycles of pure AC sinewaves.

A figure of "1.11" rms-to-average seems to be widely bandied about. In reality, that figure is not a constant; its value can (and will) be anything from one to a million. In fact, nearly all real-world waveforms will have rms to average readings far above unity, leading you to wildly wrong underreporting on cheap meters.

The second point is that every wattmeter design has its specific maximum allowable crest factor. Crest factors above that critical value will usually read low, and possibly severely so. Most ordinary wattmeters are totally unsuited to accurately measure lower duty-cycle waveforms with high crest factors. Always check on your crest factor limit to be sure.

Why is there a crest-factor limit? Because the product of any two big numbers will end up as a very big number, meaning that a tremendous dynamic range …