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High Design From April 2004 High Frequency FUNDAMENTALS Copyright © 2004 Summit Technical Media, LLC Jitter—Understanding it, Measuring It, Eliminating It Part 1: Jitter Fundamentals

By Johnnie Hancock Agilent Technologies

n data communica- Jitter is a key performance tions, once bit trans- factor in high-speed data Ifer rates exceed one communications. This gigabit-per-second, sim- three-part series discusses ply dealing with 1s and methods for measuring 0s is no longer sufficient. jitter and presents tech- This situation is clearly niques for its elimination the case with many of the new data transfer stan- dards—InfiniBand, PCI Express, 10-Gigabit Figure 1 · Jitter can cause a receiver to mis- , Fibre-Channel, HyperTransport, interpret transmitted digital data. RapidIO, and the like. Now, designers must concern themselves with the true nature of a circuit carrying binary information, realizing ently than the transmitter intended, causing a that it is, in fact, an analog circuit. This bit error, as depicted in Figure 1. that many parametric issues have become Furthermore, as we will discuss in this and more important than ever. future articles, jitter measurements can aid in Among the parametric issues, jitter has discerning the various kinds of jitter which, in risen to the top as one of the most significant turn, leads to their causes and to effectively and is therefore having a huge impact on the diminishing their deleterious effect on circuit design, operation, and proof of many of today’s performance. products. Jitter can be defined as “the deviation of This series of three articles is intended for the significant instances of a from their engineers who design data transfer systems ideal location in time.” To put it more simply, and components operating at over one gigabit- jitter is how early or late a signal transition is per-second and so must be concerned with the with reference to when it should transition. In effects of jitter on their system’s a the significant instances are (BER). This first article covers the fundamen- the transition (crossover) points. This applies tal of jitter, the kinds of jitter, its causes, the whether the time reference is generated from characteristics of individual jitter components the sampled data or is externally provided. and some measurement vantage points. These definitions allow for a number of ways of quantifying jitter, as noted next. Why Measure Jitter? Jitter isn’t measured simply to create Quantifying Jitter , it is measured because jitter can Cycle-To-Cycle Jitter—The time differ- cause transmission errors. For if jitter results ences between successive periods of a signal. in a signal being on the “wrong side” of the Period Jitter—An RMS calculation of the transition threshold at the sampling point, the difference of each period from a waveform receiving circuit will interpret that bit differ- average.

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Figure 2 · An idealized eye diagram. Figure 3 · An eye diagram with an irregular shape pro- vides a wealth of information

Time Interval Error (TIE)—The fundamental, intuitive view of jitter. It tled to its high or low value and, if difference in time between the actual is a composite view of all the bit peri- sampled here, is least likely to result threshold crossing and the expected ods of a captured waveform superim- in a bit error. transition point (or derived clock posed upon each other. In other words, edge). The deviations in time use the waveform trajectory from the start Sources of Jitter either the actual transmitter clock or of period 2 to the start of period 3 is Before examining the eye diagram a reconstruction of it from the sam- overlaid on the trajectory from the with jitter effects, let’s review the pled data set and take the form of start of period 1 to the start of period sources of jitter. Jitter on a signal will instantaneous phase variations for 2, and so on, for all bit periods. exhibit different characteristics each bit period of the waveform cap- Shown in Figure 2 is an idealized depending on its causes. Thus, cate- tured. Incidentally, this representa- eye diagram, with very smooth and gorizing the sources of jitter is impor- tion of jitter is of most interest for symmetrical transitions at the left tant. The primary phenomena that current standards. and right crossing points. A large, cause jitter are listed below: wide-open “eye” in the center shows How an Eye Diagram Portrays the ideal location (marked by an “x”) 1. System phenomena Jitter Intuitively for sampling each bit. At this sample These are effects on a signal that An eye diagram provides the most point the waveform should have set- result from the characteristics of its being a digital system in an analog environment. Examples of these sys- tem-related sources include:

• from radiated or con- ducted • Dispersion effects • Impedance mismatch

2. Data-dependent phenomena These are patterns or other char- acteristics of the data being trans- ferred that affect the net jitter arriv- ing in the receiver. Data-dependent jitter sources include:

• • Duty-cycle • Pseudorandom, bit-sequence peri- odicity ϕ 3. Random phenomena fied by the phase error function j(t), These are phenomena that ran- is the sum of the deterministic and domly introduce noise in a system. random jitter components affecting These sources include: the signal:

ϕ ϕ D ϕ R • Thermal noise—kTB noise, which j(t) = j(t) + j(t) is associated with electron flow in ϕ D conductors and increases with where j(t) , the deterministic jitter bandwidth, temperature, and component, quantified as a peak-to- D noise resistance peak value, Jpp , is determined by • —electron and hole adding the maximum phase (or time) noise in in which advance and phase (or time) delay the magnitude is governed by bias produced by the deterministic current and measurement band- (bounded) jitter sources. ϕ R width j(t) , the random jitter compo- • “Pink” noise—noise that is spec- nent, quantified as a standard devia- R trally related to 1/f tion value, Jrms , is the aggregate of all the random noise sources affect- These phenomena occur in all ing the signal. Random jitter is semiconductors and components, and assumed to follow a Gaussian distri- therefore are encountered in phase- bution and is defined by the locked-loop designs, oscillator topolo- and sigma of that Gaussian distribu- gies and designs, and crystal perfor- tion. To determine the jitter produced mance. by the random noise sources, the Further discussion of jitter Gaussian function representing this sources can be found in the section random jitter must be determined “Jitter reduction requires a multi- and its sigma evaluated. faceted view” in Reference [1]. What’s How to calculate total jitter is more, isolating and measuring these explained in the section “Calculating jitter sources will be discussed in the total jitter” in Reference [1]. third article in this series. Why an Eye Diagram Contains a 4. Bounded and Unbounded Jitter Wealth of Information The sources of jitter are often cat- Shown in Figure 3 is an eye dia- egorized as “bounded” and “unbound- gram of a waveform that is even less ed”: ideal. But the characteristics of its Bounded jitter sources reach max- irregular shape enables the viewer to imum and minimum phase deviation learn much about it—without having values within an identifiable time to resort to far more complex mea- interval. This type of jitter is also surements. called deterministic, and results from The bottom appears to have a systematic and data-dependent jit- smaller variation than the ter-producing phenomena (the first top, so the signal seems to carry more and second groups identified above). 0s than 1s. There are four different Unbounded jitter sources do not trajectories in the bottom, so at least achieve a maximum or minimum four 0s in a row are possible. Whereas phase deviation within any time on top there appears to be no more interval, and jitter amplitude from than two trajectories, indicating the these sources approaches infinity, at waveform contains at most only two least theoretically. This type of jitter 1s in a row. The waveform has two is also referred to as random and different rising and falling edges, results from random noise sources denoting the presence of determinis- identified in the third group above. tic jitter. The rising edges have a The total jitter on a signal, speci- greater spread than the falling edges, High Frequency Design JITTER FUNDAMENTALS

Figure 4 · Histogram of period jitter.

Figure 5 · Bathtub plot. and some of the crossover points intersect below the threshold level, denoting duty-cycle distortion, with 0s having a longer cycle or on-time than 1s. bit transitions in a waveform capture. Additional discussion of this eye diagram is given in “A The TIE histogram is also of particular value in sepa- case study: jitter evaluation on an eye diagram” in rating random from deterministic jitter, as described in Reference [1]. Reference [1]. Now that jitter has been briefly described and explained, let’s examine some additional ways to measure The Bathtub Plot and view jitter. Each of these various jitter measurement Another viewpoint of jitter is provided by the “bathtub vantage points can each provide insight into the nature of plot,” depicted in Figure 5. It is so named because its char- the jitter affecting a system or device. Then by mentally acteristic curve looks like the cross-section of a bathtub. A ‘integrating’ the different viewpoints you can acquire a bathtub curve is a graph of BER versus sampling point more complete picture of the jitter, that will assist you in throughout the Unit Interval. (See the Note at the end of identifying the jitter sources and in choosing ways to this article for a discussion of Unit Interval.) reduce or eliminate it. A bathtub plot is typically shown with a log scale that illustrates the functional relationship between sampling- The Histogram time and BER. A histogram is a plot of the range of values exhibited When the sampling point is at or near the transition by a chosen parameter—often time or magnitude —along points, the BER is 0.5—equal probability for success or the x-axis versus the frequency of occurrence on the y- failure of a bit transmission. The curve is fairly flat in axis. The histogram provides a level of insight that the these regions, which are dominated by deterministic jitter eye diagram cannot, and so is very useful in understand- phenomena. ing a circuit and for diagnosing problems. In addition, his- As the sampling point moves inward from both ends of tograms, particularly TIE histograms, are essential data the unit interval, the BER drops off precipitously. These sets for jitter-separation routines required by various dig- regions are dominated by random-jitter phenomena and ital bus standards. the BER is determined by the sigma of the Gaussian pro- For troubleshooting, waveform parameters such as cesses producing the random jitter. As one would expect, rise time, fall time, period, and duty cycle can be his- the center of the unit interval provides the optimum sam- togrammed. These histograms clearly illustrate condi- pling point. tions such as multi-modal performance distributions, Note that there is BER measured for the middle sam- which can then be correlated to circuit conditions such as pling times. Again with an “eyeball” extrapolation we can transmitted patterns. estimate that the curves would likely exceed 10–18 BER at Shown in Figure 4 is a histogram of period jitter. The the 0.5 point of the unit interval. In this case, even for a left hump appears to have a normal Gaussian shape but 10 Gb/s system it would take over 3×108 seconds to obtain the right side has two peaks. Further analysis discloses that value. that this signal, a clock reference, has a second and fourth The curves of the bathtub plot readily show the trans- harmonic that are a source of jitter. mission-error margins at the BER level of interest. The An invaluable application of the histogram is to dis- further the left edge is from the right edge at a specified play the frequency of occurrence of the TIE values for all BER—10–12 is commonly used—the more margin the

48 High Frequency Electronics High Frequency Design JITTER FUNDAMENTALS

(FFT) of the TIE data. The FFT has much less resolution than the low-level phase-noise view, but is an excellent method of viewing high-level phenomena quickly and easily. Part 2 of this series will cover the selection of instru- ments for jitter measurements, jitter measurements at high data rates, and issues that are essential in assuring the accuracy of jitter measurements.

References 1. Measuring Jitter in Digital Systems, Application Note 1448-1, available at www.agilent.com 2. Jitter Solutions for Telecom, Enterprise, and Digital Designs, Product Note 5988-9592EN, available at www.agilent.com Figure 6. · Intrinsic jitter spectrum. Note Unit Interval—By representing jitter in terms of design has to jitter. And of course, the closer these edges phase perturbation only, it is possible to consider different become, the less margin is available. These edges are domains for analysis. In mathematical terms, the phase directly related to the tails of the Gaussian functions error (advance or delay) is generalized with the function ϕ derived from TIE histograms. The bathtub plot can also j(t), so the equation for a pulsed signal affected by jitter be used to separate random and deterministic jitter and becomes: determine the sigma of the random component, as π ϕ described in Reference [1]. S(t) = P[2 fdt + j(t)]

Frequency-Domain Jitter Vantage Points where P denotes a sequence of periodic pulses and fd is Viewing jitter in the frequency domain is yet another the data-rate frequency. way to analyze its sources. Deterministic jitter sources This leads to mathematically-equivalent expressions appear as line spectra in the frequency domain. This fre- for jitter. Since the argument of the function is in radians, quency-domain view is provided by or jitter dividing ∆ϕ (peak or rms phase) by 2π expresses jitter in spectrum analysis and relates phase noise or jitter-ver- terms of either the unit interval (UI), or bit period (for the sus-frequency offset from a carrier or clock. pulses): Phase-noise measurements yield the most accurate appraisals of jitter due to effective oversampling and J(UI) = ∆ϕ/2π bandwidth control in measurement. They provide invalu- able insights into a design—particularly for phase-locked- The Unit Interval expression J(UI) is useful because it loop or crystal oscillator designs—and readily identify provides an immediate comparison with the bit period deterministic jitter due to spurs. Such measurements are and a consistent comparison of jitter between one data helpful for optimizing clock recovery circuits and discov- rate or standard and another. Dividing the jitter in unit ering internal generators of spurs and noise. intervals by the frequency of the pulse (or multiplying by Phase-noise measurements can also be integrated the bit period) yields the jitter in units of time: over a specific bandwidth to yield total integrated jitter, ∆ϕ π although this is not directly convertible to peak-to-peak J(t) = /2 fd jitter as specified for data communications standards. Shown in Figure 6 is an intrinsic jitter spectrum of a Author Information phase-locked loop. Noise peaking occurs at a 2 kHz offset. Johnnie Hancock is a Signal Integrity Applications There are also frequency lines that identify deterministic Engineer within Agilent Technologies Electronic Products jitter sources. These lines, ranging from 60 Hz to approx- Group. He is resposible for worldwide application support imately 800 Hz, are power-line spurs. Frequency lines evi- activities for Agilent’s high-performance digitizing oscillo- dent in the range of 2 to 7 MHz are most likely to be clock- scopes. He has a degree in Electrical Engineering from reference-induced spurs, causing deterministic jitter. the University of South Florida and he holds a patent on Another method of obtaining a frequency-domain digital oscilloscope amplifier calibration. He can be viewpoint of jitter is to take a reached at [email protected]

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