Resolving jitter measurement variations

As digital communications push data rates to 40 GHz and beyond, precise signal timing becomes critical. A key parameter that designers must control is the variability, or jitter, of clock and data edge placement. A variety of tools and methods are available for measuring jitter, but they do not always arrive at the same value. To get the most out of jitter measurements, test engineers need to understand how these differences arise.

Three types of instruments are available to help test engineers measure jitter: bit-error-rate testers (BERTs), timing interval analyzers (TIAs), and oscilloscopes. Design engineers typically use more than one type to measure and analyze jitter because each instrument offers different advantages (Ref. 1). Unfortunately, the instruments can also produce different values for the jitter they measure, complicating characterization and qualification testing.

Much of the variability arises because jitter has both deterministic and random components. Deterministic jitter comes from system sources such as crosstalk, inter-symbol interference, and power-supply feedthrough. It is bounded, so it can be characterized by its peak-to-peak value.

Random jitter comes from physical sources such as thermal noise, shot noise, and scattering in optical media. The only way to characterize random jitter is through its probability density function, which is typically Gaussian in shape. Gaussian functions are infinite in extent, so the random component of total jitter is unbounded.

The unbounded nature of total jitter gives rise to two forms of measurement variability: measurement period and measurement bandwidth. The period variability stems from the random jitter component. The longer the interval during which jitter is measured, the greater the chance of capturing a high-amplitude error event. So, longer measurements yield larger jitter values.

The bandwidth variability stems from both random and some deterministic jitter sources. Shot noise, for instance, is essentially white noise. The wider the measurement bandwidth, the more noise energy will be included in the total jitter.

The key to controlling variability in these instances is to use a consistent procedure for measuring jitter. Controlling the measurement period, or total number of measurements taken, will limit one source of variability. Controlling the measurement bandwidth through careful selection and connection of probes and cables as well as the use of band-limiting filters will help control the other source.

But these are not the only sources of measurement variability among the three types of instruments. All instruments suffer from systematic error. Because the three instruments use different measurement methods, they have different systematic errors. Resolving these requires an understanding of how the instruments operate.

The familiar eye diagram (Figure 1) helps illustrate the different techniques. Oscilloscopes build the eye diagram by sampling a repetitive signal over time using an internal sampling clock and an external trigger event. They measure jitter by forming a histogram of the signal's threshold crossing time. This histogram is, in essence, an approximation of the jitter's probability density function (PDF), which can be analyzed to extract jitter measurements.

The TIA also forms a histogram, but works by measuring the interval between threshold crossings or from a reference clock to a signal edge. Both instruments build the histograms by collecting a large number of data points.

BERTs work on an entirely different principle. They use signals with known data patterns and count the number of errors that occur within a given time period. From this measurement, they calculate the signal's bit-error rate.

Typically, a BERT will sample the data stream at a point corresponding to the middle of the eye opening. To measure jitter, the instrument will adjust the sampling clock's timing, scanning it across one data period, or unit interval (UI), and measuring the error rate at each position. The result (Figure 2) is known as a bathtub curve and gives the bit-error rate as a function of sampling position. Jitter causes increases in error rate as the scan approaches the threshold crossings, so the bathtub curve provides a means of calculating the jitter PDF.

Because the three methods are subject to different systematic errors, a direct comparison of their results would be ambiguous at best. The oscilloscopes and TIAs, for instance, are subject to jitter in their internal sampling clocks, which adds to the measurement of data jitter. They also use sampling to gather data so they may miss transient events, resulting in an underestimate.

All three instruments are subject to noise in their internal signal amplifiers and threshold-crossing detectors. This noise can advance or retard the recognition of a crossing event, effectively adding to the jitter measurement. Thus, a comparison of the results from these instruments must account for these errors that are inherent to the instruments themselves.

The threshold-crossing level itself may also differ between instrument types. If the BERT's internal logic threshold is above or below the actual signal crossing point, sweeping the sample point across the unit interval will encounter errors at a different point than they actually occur. This results in a jitter measurement bias that increases the measured value of deterministic jitter. Because these thresholds are not subject to user adjustment, there is no way to calibrate out the bias.

Another source of measurement variations comes from the calculation of random jitter values. For TIAs and oscilloscopes, the PDF of total jitter comes directly from the jitter histograms and typically has a shape similar to Figure 3. This shape is the convolution of both deterministic and random jitter PDFs, and separating them out as independent measurements requires considerable analysis.

The random jitter can be assumed to be Gaussian, but the presence of deterministic jitter spreads out the Gaussian distribution into right and left halves. Measuring the peak-to-peak deterministic jitter is relatively easy; it is the difference in the means of the right and left Gaussian peaks. Determining the width of the Gaussian functions, however, is more complicated. It involves fitting a Gaussian curve with six degrees of freedom to the right and left tails of the PDF histogram. The quality of this fit depends on the analysis software algorithms and the absence of spikes in the tails of the PDF. The results may thus vary from instrument to instrument as well as from measurement to measurement.

In the case of the BERT, calculating the random jitter component requires fitting a Gaussian to the interior of the bathtub curve. That fit requires some simplifying assumptions about the deterministic jitter's PDF and about the transition point on the curve where random jitter becomes the dominant factor. As with the other instruments, the results depend on the analysis software.

This inconsistency among instruments may not impact the designer trying to track down error sources, but it can have a considerable impact on qualification and manufacturing test. The best defense is to have a well-specified procedure and consistent test setup for measuring jitter, making sure that engineering specifications and manufacturing test use the same instrument. Most often this will involve using a BERT because, ultimately, the reason for measuring jitter is to ensure reliable communications, and the BERT measures reliability directly. All three instrument types have their value, however, and knowing their differences will help you accurately interpret their measurements.