Aliasing: A tutorial

Rather than rewriting content about aliasing that is prevalent in many texts and website, please refer to available free tutorials on digital reconstruction and aliasing currently available.

Now that you understand the math/physics/ background, here's how it specifically applies to jitter measurements.

Basically, sub-sampled acquisition means that your measurement system is subject to aliasing errors if there is any non-stationary jitter in the waveform. Additionally, the user gets less confidence of capturing rare timing events. And, as a result, these systems will tend to under-predict worst-case jitter; especially when trying to predict low BER jitter with only short pseudo-random bit sequence (PRBS) patterns.

Sub-sampled systems can miss important rare timing events, like runt pulses, Bit Error Rate Bursts, ground bounce, etc. Because their sample rate is far below the frequency content of the signals they test, unless the signal is repetitive, they will almost always miss any transient events. This is worsened as their sample rate is lowered. For example, a 10 kSa/sec sampling system has less of a chance of capturing transient timing errors than a 40 kSa/sec sampling system.

And even if the rare event events are repetitive, sometimes sub-sampled systems can take a very long time to see the errors. At a mere 40 kSa/sec and taking only one sample point, it takes a long time to capture when the samples are 25 usec apart. And in some cases, they can miss repetitive errors all together. For example, short-length PRBS testing (say 2^7 patterns) can completely miss repetitive power-supply-induced jitter.

Even when they do see what appears to be errors, the user is never quite sure if the error is really present in the signal or instead it is an artifact of the aliasing; created by under-sampling.

Fully adjacent cycle capture, like what M1 provides, sees everything. Most importantly, it is not blind to important timing pathologies (e.g. large-displacement failures) like sub-sampled systems are.

Additionally, one of the biggest problems with sub-sampled systems is that systems designed around them are not very good general purpose debug solutions. They usually have many trade-offs that make them very difficult to use and sometimes even very expensive. For example, many don't have trigger pick-offs; making probing a device under test (DUT) very hard. Instead you have to synchronize your DUT to their tool. Another example is the need to model transition times in order to obtain threshold crossings. This edge modeling adds significant error to jitter measurements because rare timing events are assumed to look like typical timing events. This can vastly under-predict the significance of rare timing events.

The core for why they become hard to use, for simple daily tasks like debug, lies at the root of their acquisition system. Sub-sampled systems do not look at DUTs in real-time; they look at them in equivalent-time. Hence sub-sampled systems do not see what the DUT sees, they see the limited view that the sub-sampled system can see. And oftentimes, in an attempt to accommodate what these systems cannot see, the designers of these tools must add things that create error or create user complexity in understanding the result.

Part of what is important in an excellent general-purpose instrument is that they are generally prevalent today. Most system designers and many component designers have a precision real-time scope in their lab. Because of this, M1 adds very little incremental cost, yet offers dramatically more diagnostic capabilities to debug to root cause rare timing events. Few engineers use a sub-sampled system to diagnose a digital error to root cause. Acquiring a sub-sampled system is expensive and generally most engineers do not even consider it.

Click here to learn more about the specifics of equivalent-time sub-sampling vs real-time jitter analysis.

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