# The many faces of jitter

-October 23, 2013

In high-speed data communications, jitter can be a surprisingly abstract concept. Experts spend years working to develop an intuitive understanding of its behavior. For novices, the sheer amount of information can be intimidating.

Whenever I need to explain jitter issues to engineers new to the field, I use Figure 1 to convey the relationships between various models/methods for test and measurement as well as simulation.

Figure 1. An FFT produces a frequency plot of a signal or of a jitter time-interval error. An integration of a histogram produces a bathtub curve for extrapolating BER.

Intuitively, it makes sense to start our discussion with the waveform because that's how most people visualize data signals. The waveform has time as the x-axis and voltage as the y-axis – what a typical oscilloscope measures. A Fourier analysis of the waveform gives us a spectrum of the waveform. This spectrum has frequency as the x-axis and voltage as the y-axis. The waveform spectrum is what a typical spectrum analyzer measures (although the y-axis may sometimes be in units of power such as dBm). Note that, in the figure, the arrow points in one direction. That's because a waveform measurement can easily derive the spectrum, but a spectrum measured by a typical spectrum analyzer cannot derive a waveform.

If you think of jitter as timing modulation, then demodulating the waveform with an appropriate reference clock (ideal or recovered) gives us a jitter-time series, a.k.a. time interval error (TIE). A TIE is usually displayed with time as the x-axis and jitter on the y-axis. A Fourier analysis of TIE produces jitter spectrum with jitter frequency on the x-axis and jitter on the y-axis. Remember that a jitter spectrum isn't the same as a waveform spectrum.

This is particularly confusing in many situations, such as when a waveform suffers attenuation of high frequencies caused by channel loss, which increases pulse width jitter (generally considered to be high-frequency jitter). It's not easy to directly measure a jitter spectrum. A phase noise measurement on a “1010” pattern is as close to a direct measurement as we can get. Again, the direction of the arrows shows the derivations.

The TIE can also be binned into a histogram. If the histogram is normalized, then it is a probability density function (PDF) with jitter on the x-axis and probability density as the y-axis. You can directly measure the PDF with a time-interval analyzer or a sampling oscilloscope. Just as before, the direction of the arrow indicates that a measured PDF cannot always derive a TIE.

Lastly, an integration of the PDF gives us the cumulative density function (CDF). A CDF is the same as a bathtub curve measured by a bit error rate tester (BERT), with jitter on the x-axis and probability of bit errors as the y-axis.

This simple flow chart effectively shows how the various representations (or “faces”) of jitter relate to each other as well as the signal waveform. Each representation can be measured directly with specialized test equipment. Conversion from one face to another face, however, can sometimes be difficult.