Look for jitter in a bathtub

Imagine you're under pressure to move a hypothetical multi-gigabit-per-second communications design to production. One problem remains elusive—the high-speed communication between chips suffers occasional bit errors that you just can't track down. Could there be a jitter problem lurking below the surface?

An eye diagram provides a good way to visualize jitter. If you were to focus on the center of the eye, you would see an occasional signal edge move toward it. If you were to wait long enough (or if the jitter were bad enough), you would eventually see edges that slipped rightward from the left past the center of the eye (late edge case) or that slipped leftward from the right past the center (early edge case). For your hypothetical design, the eye diagram might look as healthy as ones you've seen for fully functional systems. So what's going on?

The eye diagram for your problematic design may resemble that for a functional system, because even good transceivers exhibit jitter—the trick is to ensure that resulting bit errors don't happen very often. The target bit error ratio (BER), typically 1x10^–12 for communications applications, determines how often is too often, and your hypothetical design might exceed its target level. You need a way to quantify your design's BER.

To quantify bit errors, you could employ a bit-error-ratio tester (BERT)—an instrument specifically designed to count them. BERTs make decisions the same way receivers do—they set a decision point (usually halfway through a bit period) and determine whether each incoming bit signal is above or below a preset voltage threshold. An edge that occurs early or late with respect to the decision point registers as an error. A BERT keeps track of the proportion of bits that exhibit such errors.

A key advantage of a BERT is efficiency. Unlike under-sampled instruments such as time-interval analyzers (TIAs) or oscilloscopes (see "BERTs vs. under-sampling instruments ,"), a BERT samples every incoming bit—an approach typically used in SONET/SDH measurements. Because BERTs look for something that doesn't happen often, however, a measurement can take a very long time. For example, in a 1-Gbit/s system, errors would occur on average once every 1000 s (about 17 min) for 1x10^–12 BER, and you need to detect from 10 to 100 errors before you can have confidence in your measurement.

Figure 1. The crossing point of an example eye diagram shows multiple bit paths (caused by deterministic jitter) and the fuzziness on each (caused by random jitter).

Because the variation is entirely repeatable, it's called deterministic jitter (DJ). But in addition, each of the distinct deterministic paths has a fuzziness about it—even for a single repeated pattern sequence, edge arrival times vary, resulting in a jitter component called random jitter (RJ).

To measure the RJ and DJ components, you can apply a relatively short test pattern, such as the PRBS-7 pattern, which is 2⁷–1, or 127, bits long. Repeated applications ensure that the parts of the pattern that the DUT handles easily and the parts the DUT struggles with (and which cause DJ) occur frequently.

With a BERT, you can easily vary the decision point (with respect to time and voltage threshold) at which the BERT evaluates each bit in the short pattern. Instead of parking the decision point in the center of the eye, you can start to move it in time (horizontally on the eye diagram) in either direction to see what happens.

Assuming a relatively good eye, you'll see very few errors at the center of the eye opening. Moving away from the center but remaining within the opening, you'll continue seeing few errors.

You will begin to see more frequent errors, though, in the region where the eye opening gives way to the randomly varying edges of the most extreme deterministic path. If you plot probability of error vs. position within this region, you'll observe a well-behaved probability distribution. You could fit a curve to your measured BER data points and extrapolate down to 10^–12, a process that's much quicker than making the bit-by-bit measurements of the traditional SONET-style approach.

From the position of the most extreme deterministic edge, you can work out how far it is offset from the ideal edge arrival time, thereby deducing the deterministic portion of the jitter. Combining these two pieces of information, the total jitter (TJ) at 10^–12 is the sum of the RJ and DJ portions.

Figure 2. a) A bathtub curve shows measurements taken down to about a 10-7 bit error ratio, with extrapolation to jitter performance at lower BER. b) Additional measurements may indicate an underlying error floor.

You now have a good, fast shortcut to making an accurate jitter measurement. So where might things fall apart, and how can you avoid problems? First, when doing curve fitting for the random portion of the jitter, avoid any effects that the deterministic portion might contribute; otherwise the extrapolation may be poor.

Also, keep in mind that for a quick measurement, you need patterns to repeat frequently. A PRBS-7 sequence (127 bits) repeats many, many times a second at a 1-Gbit/s rate. A PRBS-31 pattern, with 2 billion bits, repeats every 2 s at 1 Gbit/s.

Long PRBS patterns contain long runs of zeros and other sequences that are particularly likely to induce deterministic jitter in a test device that is prone to it, but the worst offending sequences may appear only once in each pattern repetition—a few bits in a billion, resulting in an infrequently occurring outlier in the eye that has its own RJ tails. To accurately describe the jitter, your measurement technique must catch this outlier, making sure that you measure enough data along the bathtub curve to catch all of the deterministic activity while ensuring that RJ extrapolation is clear of its effects.

You should choose a PRBS that is closest to the aggressiveness of the data you will be passing through your component or system. Patterns between 2⁷–1 and 2²³–1 (such as 2⁹–1, 2¹¹–1, 2¹⁵–1) are good gradual steps up in difficulty that let you see where designs start to fail, or how much margin you have beyond pass/fail.

The situation for instruments other than BERTs is a little different. For an effect that occurs only once every billion bits, instruments that effectively sample at kilohertz or megahertz rates would have to sample for a very long time in order to catch all effects needed to make an accurate jitter measurement. This poses a problem for such instruments, and typically they will rely on other clues to try to make an accurate extrapolation.

Another situation that would impede a quick measurement is an error floor, as shown in Figure 2b. The DUT represented in this figure is the same as that for Figure 2a. In Figure 2a, however, the measurement was not carried out for a sufficiently long period to see an infrequently occurring interference effect (breakthrough emanating from a nearby circuit and getting into the DUT's sensitive receiver electronics) that was causing an error floor at around 10^–8.

Any extrapolation of Figure 2a's jitter down to 10^–12 would not be valid because of this error floor, and results for DJ and RJ would be meaningless. Good practice is to check the center of the eye for indication of an error floor before initiating a bathtub plot, an automatic step taken by some BERTs.

An under-sampling instrument would struggle to detect an error floor such as this simply because the measurement time would be so long. Error floors can occur for reasons other than jitter, such as low-probability amplitude variation. A BERT cannot distinguish between edges straying too far in time and logic levels straying too far the wrong way in amplitude. Sometimes, there may be clues in the eye diagram, so it is worth checking with a scope.

As a test strategy, many instruments give good extrapolated results. TIAs and real-time scopes perform well for applications at 3 Gbits/s and below, but for higher bit rates, the BERT and a communications analyzer are the instruments of choice.

While BERTs can make quick measurements, taking only the higher points in the bathtub curve and extrapolating, they have the distinct advantage of being able to make a direct measurement when needed. For R&D, the full bathtub measurement with points taken down to, or near to, the region specified can be revealing and ensures that there are no lurking design problems that could cause problems later.

Taking the extra time to perform the full measurement is the only way to learn for sure what a device is really doing. You should also perform the full bathtub measurement periodically during manufacturing to remain confident that problems haven't crept in over time.

"Using Bathtub Jitter Software with the Agilent 86130A and 71612C Error Performance Analyzers," Application Note 1550-12, December 2002.

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