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The buzz about crest factor in power supply design and test

Among the several measurement parameters used to assess power quality, crest factor (not to be confused with power factor) often garners attention. Crest factor is the ratio of the peak amplitude (current, voltage etc.) to the RMS (root mean square) value of the amplitude of a waveform.

C = |A|PEAK / ARMS

So how exactly does crest factor manifest itself in real life?

Have you ever heard a slow soothing song that intermittently bursts into a loud sound and then retreats into the soothing melody (much like the 1812 Overture)? Those short bursts of sound represent signals that have crest factors larger than those of the melody.

Now if you are using an AC power supply in your system design, you will always want to test the power quality of your supply so that it meets the maximum current specifications of the equipment under test (EUT). Switch mode power supplies form the core of power conversion systems today, so designing and testing for power quality on an AC input or output of your system (AC-DC converters or inverters) is imperative.

In a switching power supply, current waveforms often look distorted, as follows in Fig. 1:

Fig. 1 – AC current at the output of a switch mode power supply, measured using the MSO5204B oscilloscope

Here’s a near perfect sine wave in Fig. 2 (generated by the AFG in Tektronix’s new 6-in-1 oscilloscope), to compare Fig. 1 to:

Fig. 2 – A typical sine wave (generated by an Arbitrary Function Generator)

For an ideal sine wave, Vpeak = VRMS / 1.414. By definition, therefore, a sine wave should have a crest factor of 1.414. Can you guess whether the crest factor in Fig. 1 is higher or lower than 1.414?

Ok, I’ve told you what it looks and sounds like, and should probably tell you what it means. In power supplies, interactions between an AC source and a DUT/EUT cause fluctuations and distortions in signals that alter the relationship between peak and RMS values of these signals. Crest factor is essentially a measure of this distortion. The distortions generate harmonics of the line frequency, which can also be measured by oscilloscopes and power analyzers. This is a critical spec when connecting a power supply to a power grid. For example, an “ideal” sine wave would look as follows, in the frequency domain:

In contrast, a distorted sine wave (like Fig.1) would clearly indicate the presence of harmonic content:

In the context of test and measurement, if a power analyzer or power meter can measure up to a certain crest factor, it means that it is powerful enough to provide an accurate estimate of the distortion in AC currents/voltages up to a certain level.

If you’ve worked with oscilloscopes before, you may have encountered dynamic range as an important figure of merit. A crest factor specification on a power analyzer or power meter is analogous to the dynamic range of an oscilloscope. While an oscilloscope is a powerful tool for making such measurements automatically, high precision power analyzers or power meters provide a more accurate view. Crest factor measurement precision depends on the test instrument used, which is dictated by the application. For instance, a typical oscilloscope will provide a 3% measurement accuracy with voltage and current, and hence a higher level of uncertainty with power measurements (since P = V*I). On the other hand a power analyzer can provide measurement accuracy on the order of 0.01%. However, it is essential to know the maximum crest factor to still maintain  this accuracy level. For instance, the Tektronix power analyzers are capable of handling crest factors of up to 10 at an accuracy of 0.01% - this would be ideal for a design engineer who is concerned about a large inrush current to a device when it is powered on.

This was a quick overview of one of the important considerations in power supply design and test, and there will be more to come on Bandwidth Banter. You can also download our Power Supply Measurement and Analysis Primer for more information on switch mode power supplies. For a quick overview of the types of measurements, refer to our Fundamentals of AC Power Measurements App Note. And please be sure post up any questions or feedback in the comments section below.