Jitter analysis under the hood: Rj/Dj decomposition

From guest blogger Randy White: In my last post, we took a look under the hood at how jitter-analysis packages handle clock recovery. In this post, I explore the task of separating total jitter (Tj) into individual components, focusing on separating out random jitter (Rj) and deterministic jitter (Dj). Let’s start by taking a look at some advantages of oscilloscope-based jitter analysis:

Speed: Directly measuring error performance at 1e-12 requires directly observing many bits (1e14 or more). This task is time consuming! Extrapolation from a smaller population can be done in seconds instead of hours. This is the point of modeling, whether you’re an EE, ME, or other engineering discipline.

Knowledge: Jitter decomposition gives great insight into the root causes of eye closure and bit errors, and is therefore invaluable for analysis and debug. In fact, through a few simple transforms you ultimately end up with Tj at various BER levels, which is more important than almost anything else.

Flexibility: Already have a scope on your bench? You can do Tj@BER measurements without acquiring more, perhaps somewhat specialized equipment. Fortunately, there has been extensive work done to correlate scope-based measurements to other instrumentation that relies on direction measurement observation.

There are primarily two techniques for Rj/Dj seperation: the repeating-pattern method and the arbitrary-pattern method. It’s helpful to understand how the tools actually perform decomposition.

Repeating-pattern method

This method of Rj/Dj analysis uses a Fourier transform of the TIE (time-interval-error) signal to identify and separate jitter components. It is described in the Fibre Channel MJSQ (Methodologies for Jitter and Signal Quality) Specification and has wide industry acceptance. This method requires that the data signal be composed of a pattern of N bits that are repeated over and over. The pattern length (N) must be known, although it is not necessary to know the specific bits that make up the pattern.

The process for generating specific jitter components is as follows:

1. Start with TIE values (error versus time)
2. Take FFT of TIE
3. Sum pattern related bins => DDJ, DCD
4. Sum unrelated periodic bins => PJ
5. Measure RMS of remaining bins => RJ

Arbitrary-pattern method

When the data pattern is not repeating, or is unknown (live traffic, for example), a second method of Rj/Dj analysis may be used. (It may also be used if the pattern is repeating, and correlates well with the spectral method in this case.) This method assumes that the effects of ISI (intersymbol interference) last for only a few bits. For example, in a band-limited link where a string of ones follows a string of zeros, the signal may require three or four bit periods to fully settle to the “high” state.

In this method, an analysis window with a width of K bits is slid along the waveform. For each position of the window, the TIE of the rightmost bit in the window is stored, along with the K-1 bit pattern that preceded it. After the window has been slid across all positions, it is possible to calculate the component of the jitter that is correlated with each observed K-1 bit pattern by averaging together all the observed errors associated with that specific pattern.

The sliding window should include enough bits to encompass the impulse response of the system under test−usually 5 to 10 bits. A good practical test is to check whether increasing the window length causes any appreciable change in the jitter results; if not, the window length is effectively capturing all of the ISI effects. The disadvantage of increasing the window length is that it uses more memory and requires additional processing time.

Another adjustment is the population of each K-1 bit pattern that must be accumulated before the TIE associated with that pattern is considered accurate. Using a larger population means that more observations are averaged together, so the variance of the measurement is reduced. Specifying a larger population has the disadvantage of requiring a longer measurement period before results can be calculated, and it may be necessary to sequence the instrument several times before enough statistics are accumulated to provide results.

The arbitrary-pattern approach for measuring jitter may not be appropriate if there are very-long duration memory effects in your data link. An example would be if there are impedance mismatch reflections that arrive long enough after the initial edge to fall outside the analysis window. With a better sense of how jitter-analysis packages work under the covers, you’re ahead of the game when it comes to tracking down unwanted sources of noise in your designs.

Randy White is the Serial Applications Technical Marketing Manager at Tektronix. Randy has worked with various aspects of test and measurement solutions at Tektronix over the past few years. He has given seminars on high-speed serial measurements and is actively involved in many working groups for high-speed serial standards. He holds a BSEE from Oregon State University in Corvallis.