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Testing at MultiGbps Rates Jitter Models for the Design and Test of Gbps-Speed Serial Interconnects Nelson Ou, Touraj Farahmand, Andy Kuo, Sassan Tabatabaei, and André Ivanov University of British Columbia valid for describing a Gaussian distribution such as RJ. Moreover, a simple RMS or peak-to-peak number cannot sufﬁciently describe the characteristics of different types of jitter. Overall, we need more-accurate jitter and noise models to allow better predictions and characterizations of devices subject to jitter effects. One difﬁculty with jitter analysis is identifying the different jitter components contributing to TJ. Deconvolution algorithms such as the TailFit algorithm can separate TJ into its random and deterministic components.2-4 Another method uses a real-time sampling oscilloscope to capture the timing information of each edge transition in a data stream. Proper techniques can then extract jitter parameters directly from the acquired data set. We can further decompose DJ to model the different impacts of its subcomponents on link performance. This article presents models that allow for such further jitter decomposition. Editor’s note: Gigabit data rates in high-speed interconnects require careful modeling of jitter and its effect on the bit error rates. This article presents a comprehensive analysis of jitter causes and types, and develops accurate jitter models for design and test of high-speed interconnects. —Dimitris Gizopoulos, University of Piraeus THE RECENT DEPLOYMENT of gigabit-per-second (Gbps) serial I/O interconnects aims at overcoming data transfer bottlenecks resulting from the limited ability to increase chip pin counts in parallel bus architectures. Gigabit-per-second data rates in today’s asynchronous I/O interconnects introduce new signal integrity issues. The traditional measure of a communication link’s performance has been its associated bit error rate (BER), which is the ratio of the number of bits received in error to the total number of bits transmitted. When data rates increase, jitter magnitude and signal amplitude noise must decrease to maintain the same BER. As data rates exceed 1 Gbps, a slight increase in jitter or amplitude noise has a far greater effect on the BER. Specifying jitter and noise simply through peak-to-peak or root-mean-square (RMS) values is inadequate and insufﬁciently accurate.1 Peak-to-peak value is sample-size dependent and is inaccurate in the presence of random noise because, by deﬁnition, random noise is unbounded. A peak-to-peak random jitter (RJ) measurement is ambiguous without an established boundary condition. Conversely, describing total jitter (TJ) simply by an RMS value is inaccurate in the presence of nonrandom noise. This is because a deterministic jitter (DJ) probability density function (PDF) can take any form and might have little correlation with a DJ RMS value. An RMS value is only 302 0740-7475/04/$20.00 © 2004 IEEE Jitter definition Jitter is the deviation of a signal’s timing event from its intended (ideal) occurrence in time, as shown in Figure 1a. Traditionally, an eye diagram, like that shown in Figure 1b, has served to specify signal integrity limits, including jitter. It’s possible to express jitter in absolute time or normalized to a unit interval (UI). A UI is the ideal or average time duration of a single bit or the reciprocal of the average data rate. An eye diagram is a composite of all the bit periods of the captured bits superimposed on each other relative to a bit clock (recovered or available from the source). We call the area within the eye the eye opening. Copublished by the IEEE CS and the IEEE CASS IEEE Design & Test of Computers Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. Ideal timing event Total jitter (TJ) Deterministic jitter (DJ) Periodic jitter (PJ) (a) Random jitter (RJ) Data-dependent jitter (DDJ) Bounded uncorrelated jitter (BUJ) Jitter Left eye crossing Right eye crossing Duty-cycle distortion (DCD) Intersymbol interference (ISI) Figure 2. Subcomponents of total jitter. Eye opening crossing the eye mask is violating the speciﬁcation. A transmitter and receiver would normally have different speciﬁca1 unit interval tions, and thus different eye masks. tUI = 0 tUI = 1 Figure 1c shows combined transmitter (b) and receiver eye diagrams with corresponding eye masks fitted over the eye openings. Overlapping the transmitter and receiver eye masks, as Figure 1d shows, gives a measure of signal amplitude attenuation budget and jitter budget 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 for the interconnect.5 TJ’s two subcategories are DJ and RJ.3,6-8 Figure 2 shows TJ’s various subcomponents.3 A serial communication link’s jitter 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 specifications normally indicate TJ and (c) either RJ or DJ—or both. When RJ Attenuation appears as a peak-to-peak value, some Transmitter budget I/O standards define TJ as equal to the eye mask sum of RJ and DJ when these are expressed in time units.2 When jitter is Receiver eye mask expressed through a PDF, the TJ’s PDF is Jitter budget equal to the convolution of its RJ and DJ (d) components.9 Figure 1. Jitter (a) and eye diagram (b). Examples of DJ in turn comprises several subcomponents. Sinusoidal jitter/periodic jitter transmitter (top) and receiver (bottom) eye diagrams with (PJ) refers to periodic variations of signal masks (c) specify signal integrity limits. Overlapping the edge positions over time. Possible causmasks gives an indication of attenuation and jitter budgets (d). es of PJ are electromagnetic interference sources such as power supplies. Bounded Speciﬁc protocol AC and DC speciﬁcations can con- uncorrelated jitter (BUJ) is typically due to coupling— struct so-called eye masks. Such eye masks can repre- for example, from adjacent data-carrying links or onsent the minimum signal requirements at the transmitter chip random logic switching.8 BUJ is bounded owing to output or at the receiver input. In device characteriza- the finite coupling strength, and the exact model tion stages, fitting an eye mask over an eye opening depends on the data pattern, coupling signal, and coushows signal compliance with a protocol. Any signal pling mechanism. Because generally applicable mod- July–August 2004 Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. 303 Testing at MultiGbps Rates xs PDFleft PDFright 0.5 0.5 0 1 xs Bit error rate (cumulative distribution function) Figure 3. Obtaining the bit error rate from the total jitter probability density function. els aren’t available, we do not further discuss BUJ in this article. Data-dependent jitter (DDJ) corresponds to a variable jitter that depends on the bit pattern transmitted on the link under test. DDJ does not describe jitter induced by crosstalk resulting from coupling with other signal paths. DDJ in turn has two subcomponents. The first DDJ subcomponent, duty-cycle distortion (DCD), describes a jitter amounting to a signal having unequal pulse widths for high and low logic values. Causes of DCD can be voltage offsets between the differential inputs, and differences between the system’s rise and fall times.8 The second DDJ subcomponent, intersymbol interference (ISI), is jitter that depends on the transmitted patterns. ISI has three main causes: DJ components is a deconvolution process.9 Convolution and deconvolution processes both require the description of RJ and DJ components by mathematical functions rather than through simple peak-topeak values. Because jitter is generally a stochastic process, PDFs can effectively characterize it. In most practical cases, a Gaussian distribution can characterize RJ.3,7-9 We assume DJ is bounded; it can have a variety of PDFs describing its subcomponents. Engineers can use the TJ PDF to estimate the BER.1 That is, the BER is essentially the cumulative distribution function (CDF) of the TJ PDFs of the left and right eye crossings over the time interval in which a bit error occurs. In Figure 3, the time interval of interest is that to the right of sampling instant xs for the left eye crossing and that to the left of xs for the right eye crossing. Integrating the PDFs of both eye crossings over their respective time intervals produces the BER function:1 xs 1− PDFLeft ( ∆x )d ( ∆x ) + 1 BER( x s ) = CDF ( x s ) = x s − ∞ 2 PDFRight ( ∆x )d ( ∆x ) − ∞ ∫ ∫ Figure 3 illustrates the relationships between the TJ PDF and the BER function. The BER at the bottom of the ﬁgure is also known as a bathtub curve. Random jitter The following subsections discuss the types of noise that cause RJ and how engineers model RJ. Causes ■ ■ ■ 304 Bandwidth limitation of the transmission medium can result in effects on a single bit that come from the sequence of preceding bits. The nonlinear phase response of the transmission media can cause frequency-dependent group delay. This nonlinear response causes edge shifts that depend on the transition density within the data stream. Reflections can arise from imperfect transmission line terminations, resulting in effects on a single bit that come from the sequence of preceding bits. RJ comes from device noise sources—for example, thermal effects and flicker.3,4 An example of device noise is shot noise, which is related to a transistor’s ﬂuctuation in current ﬂow. Thermal noise is a component of device noise. Electron scattering causes thermal noise when electrons move through a conducting medium and collide with silicon atoms or impurities in the lattice. Higher temperatures result in greater atom vibration and increased chances of collisions. Flicker noise, or 1/frequency noise, results from the random capture and emission of carriers from oxide interface traps, which affects carrier density in a transistor.3 Jitter probability density functions and bit error rate Modeling random jitter As mentioned earlier, TJ’s PDF is the convolution of its RJ and DJ components. Separating TJ into its RJ and Engineers commonly model RJ by the Gaussian distribution function IEEE Design & Test of Computers Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. J RJ ( x ) = 1 σ 2π e ( x )2 − 2 2σ where JRJ(x) denotes the RJ PDF, σ is the standard deviation of the Gaussian distribution, and x is the time displacement relative to the ideal time position. Hence, a Gaussian RJ is completely specified by a single parameter—its standard deviation. Deterministic jitter The next subsection discusses how system component interaction causes DJ, and the subsequent ones present a model for each DJ subclass. Causes DJ arises from the interaction of different system components. Its major causes include electromagnetic interference, crosstalk, signal reﬂection, driver slew rate, skin effects, and dielectric loss.3,10 Electromagnetic interference is the interference from radiated or conducted energy that comes from other devices or systems. Such radiation can induce currents on signal wires and power rails, and alter the signal voltage biases or the reference voltages. Impedance mismatch between the cables or traces and a terminating resistor contributes to signal reflections. As a signal propagates and reaches the receiver, part of the signal energy reﬂects back toward the transmitter. It’s possible to estimate the percentage of reﬂected energy relative to signal energy.11 %reflect = Z L (ω ) − Z ο (ω ) ×100% Z L (ω ) + Z ο (ω ) nal’s impact depends on the transmitted data pattern, we can assume signal reﬂection is a cause of DDJ. Above a certain frequency, transmitting conductors experience a skin effect. This is a phenomenon whereby at high frequencies conductor self-inductance causes the current flow to concentrate on the surface of a conducting medium. The onset frequency is a function of the conductor’s cross-sectional area, impedance, and other material physical parameters.10,11 The skin effect increases the conductor’s resistance because of the reduction in effective cross-sectional area and leads to increased attenuation of a signal’s high-frequency contents. The results are longer rise and fall times, and degraded signal amplitudes. Dielectric loss results from the delay of polarization in the dielectric material when it is subject to a changing electric ﬁeld. In an ideal lossless material, the current leads the voltage by 90 degrees. But in real material, the delay in polarization creates a phase lag between the external electric ﬁeld and the resonating molecules, which leads to a phase difference in current, thus amounting to power loss. Above some frequencies, dielectric losses dominate skin effect losses because dielectric losses are proportional to the frequency, while skin effect losses are proportional to the frequency’s square root.10 The frequency dependency of skin effect and dielectric losses makes them causes of DDJ. Attenuations due to skin effect and dielectric losses contribute to the vertical closure of the signal eye. The attenuations also contribute to slower rise and fall rates, which reduce the horizontal eye opening. The signal slew rate depends on the signal driver’s ability to drive its load. A strong driver can provide a fast slew rate and drive higher-frequency signals. When a high-frequency signal’s driver is weak, the signal at the opposite end of the wire might not have enough time to rise or fall to the desired signal high or low value. Using a linear phase ﬁnite-length impulse response ﬁlter with a cut-off frequency of 1 GHz to emulate a driver, Figure 4 illustrates the slew rate limitation when transmitting a data pattern at 3 GHz. Signal value (V) where ZL is the load impedance, Zo is the wire impedance, and ω is the angular frequency of the transmitter signal. Mismatches in the terminating resistance cause electrons to literally bounce back to the transmitter. This corrupts the succeeding bits and reduces the signal-to-noise ratio. The reﬂected signal energy bounces back and forth until it dissipates completely. As it bounces, it adds to the original signal out of the phase, resulting in jitter. If a source 1 side termination resistor is 0 used at the receiving end and has matching resis−1 tance, it will absorb the 0 1 2 3 4 5 Time (ns) reﬂected signal, and no data corruption will occur. Because a reﬂected sig- Figure 4. Signal driver slew rate limitation. 6 7 July–August 2004 Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. 8 9 10 305 Testing at MultiGbps Rates Duty-cycle distortion model. The sum of two δ functions can represent the jitter due to DCD.2 Modeling deterministic jitter PDF We assume that DJ magnitude is bounded. The following subsections x δ (x − W/2) δ (x − W/2) present a jitter model for each DJ subclass. We have written a MatLab Figure 5. Probability density program that simulates function for duty-cycle distortion. signal behavior through a hypothetical transmission medium modeled by a linear filter with a nonlinear phase response. For our study, the filter contributes a signal amplitude distortion, thereby simulating the amplitude noise and frequency-dependent phase delay generally encountered in a transmission system. For this reason, the speciﬁc accuracy of the ﬁlter model and the model’s effects on the transmission medium are not critical. The filter we used in our study has a cut-off frequency of 2.1 GHz and rise and fall times of 0.25 ns. Signal value (V) 0.5 1 0 −1 0 1 2 3 4 5 Time (ns) 6 7 0 1 2 3 4 5 Time (ns) 6 7 0 0.1 0.2 0.3 0.4 0.5 Time (ns) 0.6 0.7 Signal value (V) (a) 1 0 −1 Signal value (V) (b) 1 0 −1 No. of occurrences (c) 0.15 0.20 (d) 0.25 0.30 0.35 0.40 Time (ns) 0.45 J DCD ( x ) = W W ) δ(x + ) 2 + 2 2 2 δ(x − where JDCD(x) is the DCD PDF, W is the peak-to-peak DCD magnitude, and x is the time displacement relative to the ideal time position. The two δ functions represent the rising and falling edges of the signal. The magnitude of each δ function is 1/2 because the equation assumes that there are equal numbers of rising and falling transitions in the transmitted signal. This is the typical case, for example, with DC-balanced encoding schemes such as 8b/10b encoding. This characteristic also holds for non8b/10b encoding schemes, as long as the data pattern has sufﬁcient transitions—that is, no long sequences of ones or zeros. Figure 5 shows the DCD PDF. Figure 6 illustrates the simulation of a 2-Gbps clocklike data signal (Figure 6a) passed through our transmission path model. The data signal has a 60% duty cycle in this case. Figure 6b shows the signal 8 9 10 at the output of the transmission path model, displaying the effect of that model on the transmitted data pattern. Figure 6c displays the eye. The his8 9 10 togram, shown in Figure 6d, clearly shows the jitter distribution as two delta functions. This observation validates our assumption for a DCD model. 0.8 0.50 0.9 0.55 1.0 0.60 Figure 6. Example duty-cycle distortion simulation: transmitted bit pattern (a), transmitted pattern at the output of the transmission path model (b), eye diagram (c), and jitter histogram (d). 306 Intersymbol interference model. ISI depends on the transmitted bit pattern. With ISI, the timing of each edge of the transmitted signal depends on the bit pattern preceding this edge, which in this article we refer to as the edge pattern. Different edge patterns have different IEEE Design & Test of Computers Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. PDF a b c Repeat pattern d P3 P2 P1 P4 x x2 t0 t2 t4 t6 t8 Bit time x1 Figure 8. Four distinct edge patterns in a 7-bit pattern. Figure 7. Intersymbol interference model probability density function. frequency components. Fast-changing edge patterns behave as high-frequency signals; slow-changing edge patterns behave as low-frequency signals. Because of the conductors’ ﬁltering effects, different edge patterns propagate at different speeds through the conductors. This difference in propagation speeds causes bits to smear into adjacent bits, resulting in ISI. To calculate total ISI, we must know the probability of occurrence of each edge pattern and the corresponding jitter magnitude. We use Pi to denote the probability that given bit pattern i will occur; xi is the magnitude of the bit pattern, as illustrated in Figure 7. Assuming that the jitter magnitude of each distinct edge pattern remains constant over time (it is time invariant2), then a weighted sum of δ functions can represent the PDF for each edge, with the weights corresponding to the edge pattern probabilities. Thus, the following equation can express the jitter due to ISI: N J ISI ( x ) = ∑P × δ ( x − x ) i i This information lets us calculate the occurrence probability of all edge patterns, which in this case is 1/4. Figure 9 is the simulation result for transmitting the bit pattern in Figure 8 over the same transmission path model as in the previous cases. Figure 9a shows the transmitted signal, and Figure 9b shows the signal at the output of the transmission channel. Figure 9b shows the distortion introduced by the transmission path model onto the transmitted data pattern, where the amount of distortion is frequency dependent—that is, dependent on the data pattern. The eye diagram in Figure 9c displays ISI jitter. The simulation results illustrate four δ lines in Figure 9d, derived from the results shown in Figure 9b, thereby supporting our assumptions about adequately modeling ISI through a summation of δ functions. Periodic jitter model. PJ causes periodic deviation of transitions from their ideal values over time, as shown in Figure 10a. The square wave represents a transmitted signal, and the sine wave represents the periodic edge deviations. A summation of cosine functions with different phases and amplitudes provides a model for PJ: i =1 where JISI(x) is the ISI jitter PDF, N is the number of distinct edge patterns, Pi is the probability of occurrence of edge pattern i, xi is the jitter magnitude for the ith edge pattern, and x is the time displacement relative to the ideal time position. Measurements can provide the jitter magnitude xi of edge pattern i. Figure 8 shows a repeating 7-bit pattern with four distinct edge patterns, labeled a, b, c, and d. The bit-time axis labels t0 through t8 designate the beginning of each bit period. To calculate Pi, it’s necessary to ﬁnd the total number of occurrences of each edge pattern i over a given time period. Our simulation repeatedly transmits the 7-bit pattern in Figure 8 and records edge shifts for each pattern edge. In practice, the number of sampled repetitions depends on the per-edge-shift averaging required to reduce RJ and PJ effects to negligible levels. N PJ Total (t ) = ∑ A cos(ω t +θ ) i i i i =0 where PJTotal(t) denotes the total periodic jitter, N is the number of cosine components (tones), Ai is the corresponding amplitude, ωi is the corresponding angular frequency, t is the time, and θi is the corresponding phase. The following equation describes the PDF of a singletone PJ:12 1 2 2 π A − x J PJ ( x )= ∞ 0 July–August 2004 Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. 307 Testing at MultiGbps Rates No. of occurrences Signal value (V) Signal value (V) Signal value (V) where A is the amplitude of the PJ sinusoidal component and x is the time dis0 placement relative to the −1 ideal position. Let’s assume 0 1 2 3 4 5 6 7 8 9 10 there is only PJ in the sigTime (ns) (a) nal. The resulting jitter PDF will then have a concave 1 shape because there will 0 be a higher proportion of −1 samples having jitter mag0 1 2 3 4 5 6 7 8 9 10 nitudes closer to the sinuTime (ns) (b) soidal peaks than those with smaller jitter magni1 tudes. Measurements can 0 determine the jitter fre−1 quencies and phases—for example, from Fourier 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Time (ns) (c) transformation with peak detection on edge data acquired using a fast realtime oscilloscope.13 The PDF in Figure 10b is for a 0 single-tone PJ. If the fre0.245 0.250 0.255 0.260 0.265 0.270 0.275 0.280 quencies of the cosine Time (ns) (d) components for a multitone PJ are not harmonically related to each other, Figure 9. Example intersymbol interference simulation: transmitted bit pattern (a), it’s possible to estimate the transmitted pattern at the output of the transmission path model (b), eye diagram (c), total PJ PDF by convolving and jitter histogram (d). the PDFs of individual components. Figure 11 illustrates PJ’s effect on an eye diagram. Figure 11a shows a clocklike data pattern with a 50% duty cycle, assumed to be transmitted at 2 Gbps over the same transmission path model used in previous simTransmitted signal t ulations. Figure 11b shows the signal at the transmission PJ(t ) path model’s output. We set the PJ peak amplitude to 100 ps. Figure 11c clearly shows the eye closure caused A −A by PJ. Figure 11d illustrates that the histogram corre(a) sponds to the PJ PDF, which is as expected from the PDF model, as in Figure 10. Thus, our simulation results reinforce our PJ model assumptions. 1 1/πA (b) −A t A Figure 10. Illustration of periodic jitter (a) and the periodic jitter probability density function (b). 308 Total jitter We presented RJ and DJ as separate jitter components. In actuality, however, jitter doesn’t exist as separate entities but rather as a combination of different jitter components resulting in TJ. In the time domain, TJ is simply the sum of its RJ and DJ components. However, IEEE Design & Test of Computers Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. Signal value (V) TJPDF = RJPDF * DJPDF (a) where * denotes convolution. Signal value (V) when a PDF describes TJ, the TJ PDF is the convolution of its RJ and DJ components’ PDFs. 1 0 −1 0 1 2 3 4 5 Time (ns) 6 7 8 9 10 1 0 −1 No. of occurrences Signal value (V) Figure 12 shows simula1 2 3 4 5 6 7 8 9 10 0 Time (ns) tion results from various (b) combinations of jitter com1 ponents. We assume a transmission rate of 2 Gbps 0 as well as the same trans−1 mission path model used 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 in the previous simulations. Time (ns) (c) Figure 12a shows the combined result of PJ and DCD. The injected PJ has an amplitude of 40 ps and a frequency of 5 MHz, while 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 the DCD component has a Time (ns) (d) 70% duty cycle. A clocklike signal inhibits ISI jitter and RJ. The histogram Figure Figure 11. Example periodic jitter simulation: transmitted bit pattern (a), transmitted 12a exhibits two apparent pattern at the output of the transmission path model (b), eye diagram (c), and jitter concave curves that indi- histogram (d). cate the convolution of the PJ PDF and the DCD PDF. The 40-ps PJ amplitude is obvious from the ﬁgure as well. Jitter model design implications We derive Figure 12b by injecting RJ and PJ onto a Jitter models break down jitter to its subcomponents clocklike data pattern with no DCD and assuming the for better estimation of jitter impact on an I/O link’s BER same transmission channel as in all other cases. In this performance. These models also have design implicacase, RJ has an amplitude of 10 ps, and we set the PJ tions because different jitter components correlate with magnitude to 100 ps. The RJ PDF convoluted with the different sources in devices and systems. For example, PJ PDF will theoretically result in a double-peaked TJ device noise arises when active devices in the transmitPDF. This histogram clearly illustrates the RJ curves at ter or receiver impact the unbounded RJ. Design techits outlying portions and the concave curve character- niques to limit RJ include increasing output stage istic of the PJ PDF in its center portion. currents, reducing the number of stages from sampling Figure 12c is the histogram that results from com- or source clocks to samplers, and using narrow-band bining RJ and DCD only. RJ, in this case, has an RMS phase-locked loops (PLLs) to reduce power supply noise. value of 20 ps, and DCD has a 70% duty cycle. The ﬁgPJ also has model design implications. PJ typically ure also shows the convolution of the RJ PDF with the results from coupling different clock sources to the DCD PDF. Figure 12d is the combined result of RJ, PJ, main transmitting or receiving block. One way to deal and DCD. The transmitted pattern in this case is a clock- with PJ is to route or move clock sources away from senlike signal. The histograms in Figure 12 demonstrate the sitive circuit parts. Shielding and power-supply bypass capabilities of our jitter models in capturing the char- are extremely important for combating PJ. acteristics of TJ PDFs. Not all PJ components affect link performance in the July–August 2004 Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. 309 No. of occurrences Testing at MultiGbps Rates 0.15 0.20 0.25 0.30 0.35 Time (ns) 0.40 0.45 0.50 0.55 No. of occurrences (a) quency range that cannot be tracked by the receiver PLL. There are multiple strategies for reducing DDJ: ■ No. of occurrences No. of occurrences Use proper terminations and avoid discontinuities to reduce reﬂections. ■ Balance the rise and 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 (b) fall time of the drivers Time (ns) to reduce DCD. Some devices have programmable rise and fall times, thereby allowing adjustments to make these times match 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 (c) Time (ns) each other. ■ Use transmission paths with very high bandwidth and highly linear phase response. However, such paths are a 0.2 0.3 0.4 0.5 0.6 major constraint in (d) 0.1 Time (ns) many systems; therefore, using preFigure 12. Example total jitter simulations: duty-cycle distortion and periodic jitter (a), emphasis in transmitrandom jitter and periodic jitter (b), random jitter and duty-cycle distortion (c), and ters and equalization random jitter, periodic jitter, and duty-cycle distortion (d). in receivers can compensate for the transmission paths’ nonideal frequency response. These same way. Therefore, a golden PLL can replace the techniques in particular can drastically reduce DDJ receiver clock recovery circuit. This permits synthesis and improve link performance. of the jitter timing reference from the data stream, as Figure 13 shows, and the PLL can serve as the timing reference for the measurement instrument. Jitter measurement methods and Because the golden PLL extracts, or rejects, the low- applications frequency PJ, its effect on jitter modeling is to reduce Although designers can ignore certain jitter compothe importance of the low-frequency PJ components in nents in some applications, they cannot ignore most jitjitter characterization. Failure to implement the low-fre- ter components, which therefore require careful quency tracking function in the golden PLL results in measurement and characterization. Many jitter meagreater signal degradation because of the otherwise surement methodologies are in use or have been protrackable low-frequency jitters in the data stream.2 posed in the literature. The various methods use time Two additional design implications for jitter models interval analyzers (TIAs), oscilloscopes, and bit-errorconcern BUJ and DDJ. BUJ comes from crosstalk. Good rate testers (BERTs). Describing all such methods is isolation techniques, such as shielding and power-sup- beyond the scope of this article. Table 1, however, lists ply bypass, can reduce this type of jitter. DDJ is a main some key jitter model characteristics that help in measource of jitter in systems and must be minimized suring jitter components, thereby illustrating the applibecause its frequency contents often lie in the high-fre- cation of jitter models in test and measurement. We 310 IEEE Design & Test of Computers Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. present these jitter measurement methods to show how they use jitter models in general. Interested readers can seek out the relevant references for more information. There are several RJ measurement methods. Assuming the signal is a simple clocklike pattern and there are no DJ components, engineers can estimate RJ from captured histograms. In the presence of other jitter components or when the transmission is a non-clocklike data pattern, engineers need other methods for measuring RJ. One such method entails curve-ﬁtting algorithms. Because a jitter histogram’s tails contain Gaussian RJ components even when in the presence of DJ, curve-ﬁtting algorithms try to ﬁnd the best Gaussian ﬁt to the tail regions. The standard deviation of the matched Gaussian distribution provides the RJ estimate.2 Another method for measuring RJ requires a spectral analysis, which uses a Fourier transform of the captured data to reveal the spectral content of the jitter signal. Because RJ is stochastic, it appears on the spectral graph as a small-amplitude noise floor across all frequencies. The noise floor’s RMS value is the RJ RMS value.13 With BERT measurements, RJ can be calculated using the slope of the BER bathtub curves; these Data Data in Trigger Golden PLL Measurement instrument Figure 13. Golden phase-locked loop in the jitter measurement setup. Possible measurement instruments include bit-error-rate testers and oscilloscopes. curves represent the jitter’s cumulative distribution function. However, such jitter estimates based on BERT measurements tend to overstate RJ.6 Transmission of a clocklike data pattern permits direct measurement of DCD by measuring the periods of logic high and logic low. ISI doesn’t exist in this case, and RJ can be averaged out with a large number of samples. Using the same clocklike data pattern lets us estimate the peak-to-peak PJ on the histogram. The histogram, captured by an oscilloscope or a TIA, contains both RJ and PJ components. Because the tail portions are the RJ Table 1. Measurement methods and equipment. Jitter type Model properties Measurement methods Equipment Random jitter Gaussian distribution Time interval error (TIE) Real-time sampling measurement and PDF or oscilloscope, TIA histogram tail ﬁt BER bathtub curve BERT Random nature Frequency domain Spectrum analyzer (any distribution) TIE measurement and Real-time sampling frequency domain analysis Undersampled TIE oscilloscope, TIA Oscilloscope, TIA measurement and frequency domain analysis Data-dependent jitter Discrete δ lines in PDF TIE measurement, histogram Real-time sampling oscilloscope, BERT Deterministic TIE variation from edge to edge TIE measurement with edge lock method and averaging in Real-time sampling oscilloscope, TIA the time domain Repetitive nature when the pattern is repeated TIE measurement and Real-time sampling oscilloscope frequency domain analysis Periodic jitter PDF or histogram shape TIE or time interval histogram Real-time sampling oscilloscope Periodic nature TIE measurement and Oscilloscope, TIA autocorrelation estimation method July–August 2004 Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. 311 Testing at MultiGbps Rates components, simply measuring the peak-to-peak separation in the histogram provides a PJ estimate.6 It’s possible to measure ISI jitter by transmitting a data pattern containing both long and short bit runs. The ideal timing event for the ith edge in the pattern relative to a reference edge would occur at n × UI, while an actual timing event can contain deviations expressed as n × UI + Xi, where Xi denotes the displacement of the ith edge. Devices such as a TIA, which can accurately measure the time between two timing events, let us measure Xi for each edge. The measured Xi values contain random and periodic components, which averaging can remove. The distribution of averaged Xi is the ISI PDF. The need for a repeating pattern limits the use of this method. Spectral analysis offers another way to measure PJ, DCD, and ISI. Because a PJ component has ﬁxed-frequency components, it will appear in the spectral graph as a large-magnitude peak. An inverse Fourier transform lets us compute the PJ magnitude after isolating it from all other jitter components in the spectral graph. Because DCD and ISI are pattern dependent, they must appear in the spectral graph at multiples of 0.5/N, where N is the data pattern length.13 The application note in the previous citation describes a method that amounts to ﬁrst performing an inverse transform of the combined components, then constructing one histogram for each of the rising and falling edges. The difference between the two histograms’ mean values is the DCD, while the difference between the histogram’s peak-to-peak values corresponds to the ISI. These measurement methods let us specify jitter PDFs according to the models we presented earlier. TJ for the serial communication system under measurement is then a convolution of all the jitter PDFs. Jitter measurement instruments have characteristics that make some instruments better for certain types of applications. A fast real-time sampling oscilloscope acquires as many samples of a signal as possible in one pass and interpolates to reconstruct the signal waveform for display. In such cases, we can recover the clock using a golden clock data recovery (CDR) circuit, working on the signal bitstream. Comparing the recovered clock with the acquired data determines each edge’s timing error. Spectral analysis then uses the resulting set of error values.2 A real-time oscilloscope can also construct a waveform eye diagram and ﬁt waveform eye masks. Another type of oscilloscope, the equivalent-time sampling oscilloscope, acquires signal samples in many passes and reconstructs the signal waveform by overlaying different samples captured over the multiple passes.2 This 312 type of oscilloscope provides very low intrinsic jitter, which is helpful for measuring RJ accurately. It also provides the highest front-end bandwidth available in today’s instruments, which minimizes the instrument impact on DDJ measurement accuracy. The equivalenttime sampling oscilloscope, however, requires a repeating signal pattern and a triggering signal to control the sampling process. This oscilloscope can measure signals running at frequencies higher than its sample rate but has the disadvantage of low acquisition speed and difﬁculty in acquiring noncoherent noises. An equivalent-time oscilloscope can also construct waveform eye diagrams. Unlike real-time oscilloscopes, equivalenttime oscilloscopes suffer from trigger jitter because they use multiple triggers.2 A TIA can operate with or without a clock (generated from a golden PLL) or a pattern marker. Rather than extrapolating acquired signal samples to get the timing information, a TIA uses many single-shot edge-to-edge time measurements. Engineers can perform spectral analysis on the TIA-acquired data set. Using a TIA is fast because it collects only edge-timing data that carries jitter information. A BERT measures a signal’s BER at a certain point in the transmission link, and it should be clocked by a golden CDR circuit driven by the signal under test. A BERT varies the sampling instant with respect to the clock edges over the entire bit time and measures the BER. The resulting plot of BER versus time (a bathtub plot) provides a direct measurement of TJ. A longer measurement time yields a lower BER. However, the apparent constraint on test time limits the BERs achievable in practice. Some curve extrapolation techniques use statistical jitter models to extend the measured BER to lower values without incurring unfeasible test times. There are methods that use jitter models to separate the RJ and DJ components from the bathtub curve.6 THE RAPIDLY GROWING POPULARITY of Gbps-speed serial I/O interconnects such as PCI-Express in electronic devices and systems makes jitter analysis and jitter modeling increasingly important in reducing test time and cost. The University of British Columbia’s SoC Lab is using the jitter models presented here in ongoing research on jitter—in particular for building jitter decomposition algorithms. Further research will help us understand the behavior of BUJ and develop models that can represent its behavior and impact on system performance. ■ IEEE Design & Test of Computers Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. Acknowledgments We thank the reviewers for their valuable comments and suggestions and extend our very special thanks to Reviewer 2 and Reviewer 4 for the extremely detailed and constructive review. We also acknowledge University of British Columbia SoC Lab members A.K.M. Kamruzzaman Mollah and Roberto Rosales for their valuable discussions and suggestions. References Nelson Ou is an ASIC design engineer with VIA Optical Solutions in Taiwan and a former member of the SoC research group at the University of British Columbia. His research interests include jitter measurement, SoC design methodologies, and DFT. He has a BS in applied science and an ME in electrical and computer engineering from the University of British Columbia. 1. M. Li and J. Wilstrup, “Paradigm Shift for Jitter and Noise in Design and Test > 1Gb/s Communication Systems,” Proc. Int’l Conf. Computer Design (ICCD 03), IEEE CS Press, 2003, pp. 467-472. 2. Secretariat Int’l Committee for Information Technology Standardization (INCITS), T11.2/Project 1316 DT/Rev 10.0, “Fiber Channel—Methodology for Jitter and Signal Quality Speciﬁcation-MJSQ,” Mar. 2003. 3. J. Patrin and M. Li, “Comparison and Correlation of Signal Integrity Measurement Techniques,” DesignCon 2002; http://www.wavecrest.com/technical/pdf/ Touraj Farahmand is a research engineer at the University of British Columbia’s SoC Lab. His research interests include high-speed signal timing measurement, signal processing, jitter measurement, and serial communication and control. Farahmand has a BS in electrical engineering from Esfahan University of Technology, Esfahan, Iran, and an MS in control engineering from Sharif University of Technology, Tehran, Iran. Designcon2002.PDF. 4. “Jitter Analysis Techniques for High Data Rates,” Agilent Technology, application note 1432, Feb. 2003. 5. Y. Cai, B. Laquai, and K. Luehman, “Jitter Testing for Gigabit Serial Communication Transceivers,” IEEE Design & Test of Computers, vol. 9, no. 1, Jan. 2002, pp. 66-74. 6. Y. Cai et al., “Jitter Testing for Multi-Gigabit Backplane SerDes,” Proc. Int’l Test Conf. (ITC 02), IEEE CS Press, Andy Kuo is a master of applied science student at the University of British Columbia’s SoC Lab. His research interests include high-speed signal integrity issues, jitter measurement, serial communications, and design for testability. Kuo has a BA in computer engineering from the University of Toronto. 2002, pp. 700-710. 7. “Understanding Jitter,” Wavecrest Corp., application note, 2001; http://www.wavecrest.com/technical/ VISI_6_Getting_Started_Guides/6understanding.PDF. 8. “Jitter in Digital Communication Systems, Part 1,” Maxim Integrated Products, application note HFAN04.0.3, Rev0, Sept. 2001. 9. J. Sun, M. Lee, and J. Wilstrup, “A Demonstration of Deterministic Jitter (DJ) Deconvolution,” Proc. 19th IEEE Instrumentation and Measurement Technology Conf. Sassan Tabatabaei is the chief scientist at Guide Technology and cofounder of Vector12 Corp., where he was chief technical officer. His professional and research interests involve mixed-signal design and test, including signal integrity and jitter measurement and test methodologies for serial interfaces. Tabatabaei has a PhD in electrical engineering from the University of British Columbia. (IMTC 02), IEEE Press, 2002, pp. 293-298. 10. H.W. Johnson and M. Graham, High-Speed Signal Propagation: Advanced Black Magic, Prentice Hall, 2003. The biography of André Ivanov appears on p. 276 of this issue. 11. H.W. Johnson and M. Graham, High-Speed Digital Design: A Handbook of Black Magic, Prentice Hall, 1993. 12. A. Papoulis and S.U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, 2002. 13. “Understanding and Characterizing Timing Jitter,” Tektronix application note 55W-16146-0, Sept. 2002. Direct questions and comments about this article to Andy Kuo, SoC Research Group, University of British Columbia, 2356 Main Mall, Vancouver, BC, V6T 1Z4, Canada; [email protected] July–August 2004 Authorized licensed use limited to: University of Illinois. Downloaded on January 16, 2009 at 10:49 from IEEE Xplore. Restrictions apply. 313