Anti-aliasing in high performance DSOs. (Special Section: Test Equipment).
The Basics of Signal Aliasing
Aliasing is caused when a signal is undersampled. Specifically, Nyquist's Theorem tells us a digital sampling system must capture more than two samples per cycle in order for the instrument to be able to reconstruct the proper signal frequency. When less than two samples per cycle are captured, the instrument still has data and an unwary user may think the signal being observed is the actual signal from the circuit; instead it is an "alias." The word alias denotes that the actual signal frequency and real signal shape are not seen; rather, the digitized points show a "fake" signal, which can be very misleading.
Figure 1 shows the results of capturing a 5.5 GHz signal using a 20 CS/s sampling rate versus using 10 CS/s. In the first case, the correct signal shape is captured and the proper frequency is measured. In the second case, though the signal looks very real, it is undersampled. The measured frequency, 4.5 GHz, is the difference between the sample rate (10 GS/s) and the real signal frequency (5.5 GHz).
An unwary oscilloscope user may look at the second oscilloscope screen in Figure 1 and think the real signal frequency is 4.5 GHz. Or suppose the primary signal was a 2.5 Gbit communications signal, but there was some 5.5 GHz noise on it. The user may believe the noise is at 4.5 GHz and waste time looking for a noise source at that frequency.
Preventing Aliasing Using Long Memory
Once an alias has been digitized as part of a signal acquisition, it is not possible to distinguish the alias from a real signal that occurred at the alias frequency. There may even be a real component to the signal at a certain frequency as well as an aliased component. How does one avoid this problem? The first defense is a good understanding of the digitizing instrument being used. Figure 2 shows a graph of sampling rate versus timebase. Even though the maximum sampling rate of a digitizer might be 20 CS/s, if the samples must be stretched across a wide time range, the spacing between samples will become larger than 50 picoseconds. This means information is lost, and signal components above the Nyquist limit will be aliased.
The first level of protection against aliasing is to have a memory system that preserves high sampling rate on as many timebases as possible. The timebase at which aliasing occurs can be easily calculated. Check the digitizer's technical data sheet to see how much memory can be used at the maximum sampling rate. A digitizer might have 32 million points of total memory but only be able to capture a maximum of one million at the fastest sampling rate. That equates to a signal length of 50 ps (50 ps per sample X one million samples) or a timebase of 5 [micro]s per division. A digitizer with 100 million points of memory could maintain 20 GS/s for S ins. At each timebase longer than that, it will sample 100X faster than the DSO that has only one million points.
For any digitizer, beyond a certain point, each click of the timebase decreases the sampling rate and increases the span of aliased signals. It is easy to compute which components of a signal will be aliased. The front end amplifier of a DSO acts as a filter, limiting the amplitude of incoming signals beyond the bandwidth of the amplifier. The signal components that will be aliased are those that are passed through the amplifier and which are above the Nyquist frequency. Older oscilloscope architectures that have wide band amplifiers and weak signal processing capabilities will pass the full amplitude of an alias into the digitized signal. New signal processing techniques, however, make it possible to squelch aliasing using DSP filters.
For example, suppose you are capturing a long, complex 1 Cbit data signal using a 10 GS/s sampling rate. The Nyquist frequency is 5 CHz, so choose a filter that suppresses signal components above that point. At 5 CS/s, use a filter at 2.5 CHz. In the "old days," a careful engineer might keep a whole set of hardware filters in a drawer. With the advent of powerful microprocessors and data handling techniques, however, real time oscilloscopes can apply a flexible set of analog and DSP filters to prevent aliasing and still have throughput rates faster than oscilloscopes built on previous generations of technology.
Maybe you have a high-speed oscilloscope on your bench to work on fast signals, but occasionally you need to look at slower, longer signals. Perhaps you would like to analyze the coupling between a microprocessor clock and power supply over one full AG line period (16 ms for 60 Hz), or maybe you just need to help a colleague who is debugging problems in a long, complex data stream. When pushing the limits of the oscilloscope's memory, keep an eye on the sampling rate. Nearly every oscilloscope will show its sampling rate on the screen. Keep in mind the Nyquist limit. If you think the signal has harmonics or wideband noise that are above Nyquist, use a hardware filter or a DSP filter to kill those aliases. Keep in mind that a wideband amplifier with a short memory is a risky combination. You will get maximum amplitude aliasing if signals pass through the amplifier and are undersampled by the digitizer.
[FIGURE 2 OMITTED]
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Dr. Michael Lauterbach is Director, Product Development at LeCroy Corp., 700 Chestnut Ridge Rd., Chestnut Ridge, NY 10977-6499; (800) 453-2769; Fax: (845) 425-8967; www.lecroy.com.
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|Author:||Michael, Dr. Lauterbach|
|Publication:||ECN-Electronic Component News|
|Date:||Mar 1, 2003|
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