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Douglas C. Smith

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Technical Tidbit - September 2003
Sin(x)/x, the Forgotten Setting - Part Two
An EMI Example

Accumulated Waveforms - undersampled
Figure 1. Accumulated Waveform Sampled at 250 MSa/sec (Sin(x)/x On)

Abstract: The August, 2003 Technical Tidbit, Sin(x)/x, the Forgotten Setting - Part One, is carried further to present an example resulting from electromagnetic interference, EMI. The example illustrates how significant error can result when use of the Sin(x)/x function in a digitizing scope results in hiding the possibility that a waveform is undersampled. The presented results are dramatic as well as possible in real measurements. External EMI getting into a measurement is a common source of undersampling problems.

Discussion: Figure 1 shows an accumulated waveform purposely undersampled at 250 MSa/sec. Each waveform is a nice looking smooth damped sinusoid. But, because the signal is undersampled, the accumulated plot in Figure 1 shows that the captured waveforms vary considerably from each other. If only one "glitch" were captured, it would not be apparent that this measurement is not repeatable.

Figure 2 shows the test setup used to generate the waveforms of Figure 1. A Fischer Custom Communications PEG-1 Pulsed Field ESD Simulator (click here for 436 kB data sheet) was used to generate a series of nearly identical impulsive fields. These pulsed fields were picked up by a shielded magnetic loop and displayed on an oscilloscope. Even though the pulses are nearly uniform, the accumulated waveforms in Figure 1 are not due to undersampling.

  Test setup
Figure 2. Test Setup

Figure 3 shows an accumulated set of waveforms generated by the same test setup, but sampled at 8 GSa/sec. The waveforms now are nearly identical and the resulting waveshape looks nothing like the waveforms in Figure 1 even though the pulses are the same as those that generated the plots in Figure 1 and the scope settings are otherwise the same.

   Accumulated Waveform - 8 GSa/sec
Figure 3. Accumulated Waveform Sampled at 8 GSa/sec

In general, we really don't know as much as we think about measured signals, because of many factors. If one knew the properties of the signals to measured, then the right sampling rate could be used and problems avoided. One issue, for example, arises in that oscilloscope probes are in general very sensitive to external EMI, such as ESD, in the vicinity of the measurement. I have observed that normal human activity generates tens to hundreds of ESD pulses per hour in typical lab and office settings and these pulses get into measurements. Even in highly controlled environments where ESD is suppressed, there is still significant EMI generated by sparking contacts (light switches, motors, anything that makes a spark) and even other electronic devices like mobile phones. The pulses can have very fast risetimes, much faster than the signals being measured. But with Sin(x)/x interpolation hiding undersampling of these pulses, the result can look like a part of the signal being measured. That can lead to wasted time in the lab tracking down a problem that does not exist in the equipment.

Summary and Conclusion: Use of Sin(x)/x interpolation can hide the fact that the sampling rate used is not fast enough to display a waveform. Because of unavoidable EMI getting into measurements, I believe Sin(x)/x interpolation should be at least initially disabled to insure an accurate measurement. Once measurement accuracy is determined, Sin(x)/x can be enabled if desired but with some risk.

Other papers and articles on this site with more information relating to EMI and measurements include:

Equipment used in this article include:

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Copyright © 2003 Douglas C. Smith