Random or Deterministic: Understanding jitter is key to serial data comm success

As data rates increase, the adverse effects of jitter become more critical. So jitter budgets understandably become tighter. Consequently, it is not surprising that jitter measurements are becoming increasingly important in the characterization and qualification of high-speed computing and communication systems. This is especially true with the recent proliferation of embedded-clock serial buses.

This article introduces jitter, its measurement techniques and some issues relating to the accuracy of measurement. Though jitter, more generally, is of importance in a wide variety of diverse applications ” ranging from oscillator design to telecommunication network synchronization ” most of what follows applies primarily to serial data communication applications.

Understanding Jitter

Jitter is the deviation of a timing event of a signal from its ideal position. One of the factors contributing to the complexity of jitter is that it comprises both random and deterministic jitter components. Random Jitter (RJ) is theoretically unbounded and Gaussian in distribution. “Unbounded” simply means that if you wait long enough, the peak-to-peak jitter will increase indefinitely ” at least theoretically. This means that an eye-diagram may never show the worst-case condition. If the jitter in your system consisted of just random jitter, then each edge of the data signal would have the same probability of timing error.

Deterministic Jitter (DJ) is bounded in distribution. It may be comprised of several different sub-components and is usually caused by systematic problems in a high-speed digital design. For this reason, DJ is sometimes referred to as systematic jitter. If you were to view each individual edge of the data signal, you would probably see that particular data edges contribute different amounts of timing error. Depending on the data pattern, some edges in the serial pattern will always be shifted to the right (positive timing error), while other edges will always be shifted to the left (negative timing error) ” relative to their ideal timing locations. Complicating matters, the random jitter component present causes these individual data bit edges to randomly bounce around the shifted/offset deterministic amplitude of jitter.

One technique to determine the existence of random versus deterministic jitter is to use a scope's histogram feature. By taking a look at a slice of data across the center of the screen, we can see, in Figure 1 that the distribution of edge placements is a combination of random and deterministic jitter.

Measuring Jitter

The traditional way to measure jitter is with an eye-diagram using repetitive acquisitions on an oscilloscope, as shown in Figure 1. Measuring the total jitter in your system with a Bit Error Ratio Tester (BERT) or real-time RJ/DJ separation techniques will tell you whether or not your system meets a jitter/timing budget specification. And viewing an eye-diagram along with a histogram can give you a good intuitive feel concerning the type of jitter in your system and a rough feel for the amount of total jitter. But neither of these two types of measurements can provide you with much insight into how to identify, view and then reduce specific components of jitter. This is where real-time jitter analysis steps in.

Figure 1. An eye diagram displaying the repetitive acquisitions. The well-defined paths of brightness are a clear indication of deterministic jitter.

The primary contribution of jitter analysis using a real-time oscilloscope is its inherent ability to capture data or clock pulses in a single acquisition with timing measurements on each and every pulse in a long stream of data. The real-time scope and jitter analysis can then be used to time-correlate specific jitter error measurements to specific data bits or other signals in your system that might be contributing to the total system jitter.

Using the oscilloscope's variable intensity or color-graded display capability, you can visually look for the existence of “bright” trace paths within the infinite-persistence display. Referring to the traces in Figure 1, we can see several well-defined paths of brightness. This is a clear indication of deterministic jitter. Some of the data edges consistently occur in some locations while other edges occur in other locations of the eye-diagram. The power of a real-time scope is the ability to view these particular data edges individually.

The key to finding sources of jitter lies in the ability to time-correlate jitter measurement results with high-speed serial data signals, as well as other possible sources of uncorrelated periodic jitter. A real-time oscilloscope with jitter analysis along with the appropriate stimulus meet that critical time-correlation requirement to relate jitter trend measurement results to measured signals. Once you are able to time-correlate particular real-time timing error measurements to particular bits within a serial data pattern, it usually becomes a routine troubleshooting task to solve your deterministic jitter problems.

Figure 2 illustrates the technique that real-time jitter analysis uses to measure jitter on a non-return-to-zero (NRZ) data signal. This type of real-time jitter measurement is typically referred to as a Time Interval Error (TIE) or phase jitter measurement. The real-time scope first captures a deep record of the NRZ data signal and then creates an ideal software-recovered clock based on the captured data. Depending on the user's selection, this software-generated clock can be either of a fixed-frequency or a PLL-type clock with a specified loop bandwidth. The jitter software then performs a best-fit algorithm to align the NRZ data edges with the “virtual” clock edges.

Jitter measurement is discussed in more detail in the application note listed in the Bibliography.

Figure 2. Real-time jitter analysis. The jitter “trend” diagram is a plot of absolute timing errors plotted on the vertical axis with the horizontal axis corresponding to the oscilloscope's timebase.

Characteristics of Individual Jitter Components

In order to interpret measurement results and waveform views performed by real-time jitter analysis, you must first understand the characteristics and likely causes of individual jitter components.

As explained earlier, Total Jitter (TJ) is composed of a Random Jitter (RJ) component and a Deterministic Jitter (DJ) component. Random jitter is unbounded, and for this reason (unlimited peak-to-peak) RJ is usually measured in terms of an RMS value. In addition, random jitter is very predictable in terms of distribution. The Probability Distribution Function (PDF) is always Gaussian in distribution. Unfortunately, predicting the cause of RJ is a more difficult task. RJ is often caused by thermal noise of semiconductors and requires a deeper understand of physics. However, one piece of advice is to pay close attention to the amount of vertical noise in your system. Random vertical noise will directly translate into random timing jitter.

On the other hand, deterministic jitter is bounded and is always measured in terms of a peak-to-peak value. Although the distribution of deterministic jitter can be very unpredictable, the likely causes and characteristics of the individual sub-components of measured deterministic jitter are very predictable. The sub-components of Deterministic Jitter (DJ) consist of Duty Cycle Distortion (DCD), Inter-Symbol

Interference (ISI), and Periodic Jitter (DJ) as shown in Figure 3.

For a detailed discussion of isolation techniques and the causes of jitter refer to the application note identified in the Bibliography.

Figure 3. Deterministic jitter is bounded and is always measured in terms of a peak-to-peak value. The sub-components of Deterministic Jitter (DJ) depicted here, schematically are Duty Cycle Distortion (DCD), Inter-Symbol Interference (ISI), and Periodic Jitter (DJ).


The accuracy of jitter measurements depends not only on the characteristics of the measurement system, but also on the characteristics of the measured signal and the type of jitter being measured. This means that the same measurement system, measuring the same signal will have a different accuracy when measuring period deterministic jitter than it does when measuring random jitter. It also means that a given measurement system will have a different accuracy measuring the same type of jitter on two different signals.

For example, voltage noise is typically the dominant source of error in jitter measurements. Since the voltage noise is converted to time jitter by the slope of the signal's transitions, a jitter measurement's accuracy depends on the slew rate of the signal being measured.

So, the trick to characterizing the accuracy of jitter measurements is to match the target measurement system and target signal characteristics, while measuring a known ideal source.. Use care in choosing a signal source that has sufficiently low jitter for your application. In addition, ensure that your connection to the target measurement system has sufficient fidelity not to add significant data-dependent jitter.

Determining the Jitter Measurement Floor

Although some jitter measurements underestimate the true jitter value, many measurements overestimate it. This is because the dominant jitter measurement errors tend to be uncorrelated additive random processes. Specifying jitter measurement floor is one easy way to quantify the amount that a jitter measurement overestimates the true jitter value.

Jitter measurement floor (JMF) refers to the lowest value a jitter measurement would produce if it were applied to a perfect source that had zero jitter.

Here are steps in determining the measurement floor in a period jitter measurement:

1. Configure the measurement system to match that of the target measurement system.
2. Determine the slew rate of the target signal. Note that an oscilloscope's built-in differentiate function can be useful for measuring slew rate.
3. Determine the nominal period of the target signal.
4. Connect a low-jitter signal source to your oscilloscope. Duplicate the target jitter measurement setup as much as possible. If the target jitter measurement will be made through a probe, then connect the sinewave source through the same probe.
5. Set the signal source frequency, amplitude, and slew rate so that they match those of the target signal as much as possible.
6. Measure the jitter of the low-jitter source.

In Figure 4 is shown an example of a period jitter measurement floor measurement for a PCI Express application. The target signal to be measured is a 1.0-Vp-p, 2.5-GHz clock signal with a nominal slew rate of 10 V/ns. In this example, two cycles of a 0.6-Vp-p, 5.0-GHz sinewave are used to mimic the period and slew rate of the target PCI Express signal. The oscilloscope is configured to measure the time interval between two clock transitions that are two cycles apart. Measurement statistics are then used to calculate the standard deviation of a large number of these two-cycle time interval measurements.

Figure 4. An example of a period jitter measurement floor measurement for a PCI Express application. The target signal to be measured is a 1.0-Vp-p, 2.5-GHz clock signal with a nominal slew rate of 10 V/ns. In this example, two cycles of a 0.6-Vp-p, 5.0-GHz sinewave are used to mimic the period and the slew rate of the target PCI Express signal. The measured jitter measurement floor is 900 femotseconds rms.

Subtracting-Out Jitter Measurement Floor

Subtracting the jitter measurement floor from raw jitter measurements is always tempting, and often effective, but be careful. Subtracting the variance of the measurement floor from the variance of the measured value, as shown in equation 1, only applies if the measurement errors are completely uncorrelated to the true jitter.


Also, as the magnitude of the measured value becomes closer to the measurement floor, the relative uncertainty of the reported value grows. This technique may allow you to report a smaller jitter value, but the relative uncertainty of this value may be greatly increased.


Finding Sources of Jitter with Real-Time Jitter Analysis, Agilent Technologies Application Note AN1464,

How Accurate Are Your Jitter Measurements?, Steven D. Draving, Proceedings of DesignCon East 2003

Author Biographies

Steve Draving received his BSEE in 1985 and a MSEE in 1987 from Kansas State University. He has designed oscilloscopes and logic analyzers for Agilent Technologies (Hewlett-Packard) since joining the company in 1987. He holds nine patents for time base, trigger, and probe design.

Johnnie Hancock graduated from the University of South Florida with a degree in electrical engineering and is an Applications Engineer with Agilent Technologies' Design Validation Division in Colorado. He began his career with Hewlett-Packard in 1979 as an analog and digital hardware designer, and holds a patent for digital oscilloscope amplifier calibration. Johnnie is currently responsible for worldwide measurement applications training supporting Agilent's high-performance, real-time oscilloscopes. In his spare time, he enjoys cross-country running and restoring his 109 year-old Victorian home in Colorado Springs.

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