Jitter Characterization

High-Speed Digital Design Online Newsletter: Vol. 11 Issue 06

I'll be in San Jose Oct. 27-Nov. 4, teaching all three of my public seminars together for the first time. My new Noise and Grounding class may interest those of you doing mixed-signal designs.

I am receiving so many requests for private showings of the Noise and Grounding course in other cities that I will likely not return again to do public courses in San Jose for some time; perhaps not at all in 2009. Don't miss this chance.

Today's topic concerns the characterization of jitter.

I wish I could begin by stating the definition of jitter. Wouldn't it be great if there was only one definition? Unfortunately, the subject isn't that simple. Here's a sampling of definitions from various sources:

Jitter:"Abrupt, spurious variations in… [time, amplitude, frequency, or phase]." IEEE Standard Dictionary of Electrical and Electronics Terms.

This IEEE definition seems to me very general and somewhat obtuse, like it was written by a committee. Not surprising. The IEEE Standard Dictionary is an unedited collection of definitions from all the IEEE standards developed over the years. In an open standard, anybody can join the process, and anybody can propose a definition. No matter how poorly worded a definition may be, if it doesn’t break anything it will get voted into the standard, the theory being, "Why fix something that isn’t broken?"

The next is a definition more relevant to my cause today:

Jitter: "Unwanted pulse position modulation." Patrick Trischitta and Eve Varma, Jitter (in Digital Transmission Systems), Artech House, 1989. Their book is extremely relevant to SONET and similar systems with multiple stages of signal propagation. It is very mathematical.

I prefer the term "unwanted" rather than "abrupt", because "unwanted" implies that the definition of jitter depends on you and what you expect from your circuit, which is precisely the case. The term "abrupt" implies an absolute delineation between "fast" and "slow" events. Such a delineation does not exist. What's fast in one application is slow in another, and vice-versa.

OK, now let’s get down to a definition written by people who have actually made lots of high-speed digital system measurements: the Fibre Channel committee. That group was among the first to write an explicit procedure for measuring jitter.

Jitter: "Deviation from the ideal timing of an event." Methodology of Jitter Specification, NCITS (National Committee for Information Technology Standards), T11.2. This document is informally referred to as the "MJS".

The MJS report was produced as part of the Fibre Channel effort. In that process numerous companies involved in producing, using, and measuring serial data communications hardware battled out the details of how jitter should be defined and characterized. If you haven’t read this piece of work, I highly recommend it. Steve Joiner of HP did a beautiful job of technical editing for the document. It forms the basis of most high-speed jitter analysis used today.

I like this definition because it highlights the relative nature of the problem. The definition suggests a comparison between actual events and ideal events. That's not quite what we measure in real life, though. In actual practice jitter is always measured as deviations between one signal and another. The other is never ideal.

Jitter Characterization

Imagine in front of you a jittery data stream. Think of jitter as a second signal, separate from the data stream, that encodes only information about timing variations in the data. When a data edge arrives early, the jitter swings negative. When the data is late, the jitter goes positive. In a system with slowly-wobbling timing variations, the jitter signal may undulate from one extreme to the other over a period of thousands or millions of bits. In a system with sudden, quick variations the jitter signal might jump around like a drop of water sizzling on a hot stove. Either way, the jitter signal constitutes a random process.

Many random processes, jitter included, can be characterized by two types of statistics: an auto-correlation function and an amplitude histogram. These two dimensions of specification are independent. Both types of information must be stipulated to completely represent a random process.

The auto-correlation function speaks to the time-domain predictability of a waveform, while the histogram speaks only to the distribution of amplitude values, independent of time. Both specifications play an important role in jitter analysis.

For example, consider the familiar term "white Gaussian noise" (WGN). When used to describe a random process, the word "white" implies no auto-correlation between the value at any one point of time and the value at any other time. In other words, the signal is not predictable. In frequency-domain terms, the power in a white signal distributes itself evenly throughout the spectrum.

The hiss of escaping steam, or the sound you hear on an FM radio when tuned between stations, are both white audio processes.

The term "Gaussian" refers to the shape of the amplitude histogram, independent of time. A Gaussian histogram is shaped like a bell. It has one central blob surrounded on either side by long lingering tails. Any random process built from a large number of tiny, independent, superimposed events tends to have a Gaussian histogram.

The distribution of SAT math scores forms a Gaussian curve (truncated at 0 and 800).

No physical random process can ever be truly white, because a truly white process implies spectral content (and thus power) extending from DC to infinite frequency. That's not possible. All physical processes that we know of have limited bandwidth. In practical terms a random processes is "white" (i.e., the power density spectrum is flat) only over a limited range of frequencies.

Similarly, no physical random process can ever be truly Gaussian, because a truly Gaussian histogram includes values extending to plus and minus infinity. All physical processes that we know have upper limits to their extreme values. What we call Gaussian is usually a distribution that looks Gaussian over the range of several standard deviations to either side of the mean. Beyond that limit the distribution falters.

Let's look at an example of jitter using three different tools: amplitude histogram, spectral plot, and time-domain jitter waveform.

Amplitude histogram

Figure 1 illustrates a decidedly non-Gaussian histogram obtained using the Serial Data Analysis feature on my LeCroy SDA6020 scope.