the instrument bandwidth effect in jitter and ber test for high-speed serial interconnection

256 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 61, NO. 1, JANUARY 2013

The Instrument Bandwidth Effect in Jitter and BERTest for High-Speed Serial InterconnectionYang Jun-Feng, Member, IEEE, Song Ke-Zhu, Member, IEEE, and Cao Ping, Member, IEEE

Abstract—Different from other electronics measurement, thebandwidth of the instrument can affect the test results more seri-ously in jitter and bit-error rate (BER) test. This paper analyzesthe effect on the jitter and BER test results caused by instrumentbandwidth in high-speed serial interconnection. An algorithmis presented to measure and estimate the equivalent frequencyresponse of instruments. Computed data-dependent jitter (DDJ)results are produced based on the -parameter of the serialinterconnected channels and the equivalent frequency response ofinstruments, which are perfectly consistent with actual DDJ mea-sure results. These methods can be used to measure and calibratethe instrument bandwidth effect precisely in jitter and BER test.At last, the paper gives the results of the instrument bandwidtheffect for three channels and a set of instruments according tosimulation, and presents a new concept “equivalent bandwidth”to roughly estimate the test error of DDJ caused by instrumentbandwidth.

Index Terms—Bit-error rate (BER), data-dependent jitter(DDJ), Inter Symbol Interference (ISI), jitter, serial interconnect.

I. INTRODUCTION

T HE bit rate of serial links has been pushed to over 10Gb/s [1]–[3], where more serious signal integrity prob-

lems have been met. In such situation, precise measuring resultswill be helpful for engineers in high-speed digital design.In most of system and test, quite accurate measurement re-

sults can be obtained if using test instruments only a little fasterthan the rise time of the system to be tested [4]. Therefore weseldom consider the instrument bandwidth in high-speed elec-tronic measurement when we use “fast-enough” instruments.However for jitter and bit-error rate (BER) test in high-speed se-rial interconnection, the bandwidth of the instruments, includingboth the transmitter, such as a BERT, and the receiver, such asan oscilloscope, can affect the test results more seriously thanother tests.Jitter is timing deviations of the data transitions compared

to a reference clock, which reduces the horizontal opening ofthe data eye, closes the data eye, and increases the bit-errorrate (BER). The category and the relation of jitter and BER can

Manuscript received May 06, 2012; revised November 04, 2012; acceptedNovember 07, 2012. Date of publication December 20, 2012; date of currentversion January 17, 2013.Y. Jun-Feng is with the State Key Laboratory of Particle Detection and

Electronics and Anhui Key Laboratory of Physical Electronics, Department ofModern Physics, University of Science and Technology of China, Hefei, Anhui230026, China (e-mail: [email protected]).S. Ke-Zhu and C. Ping are with the State Key Laboratory of Particle Detec-

tion and Electronics and Anhui Key Laboratory of Physical Electronics, De-partment of Modern Physics, University of Science and Technology of China,Hefei, Anhui 230026, China (e-mail: [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMTT.2012.2228666

be found in [5], and studies on various deterministic jitter (DJ)properties are presented in [6]–[10]. Among these jitter sources,data-dependent jitter (DDJ) is a prominent form of DJ that iscorrelated to limited bandwidth [7]. As part of the channel re-sponse, the bandwidth of the test instrument can superpose onthe channel response, increase the DDJ component, and aggra-vate the BER performance in jitter and BER test.We use the peak–peak value of DDJ to evaluate the effect of

the instruments. The generation of DDJ and the algorithms tocompute the precise DDJ peak–peak value for various kinds ofchannel with distinct channel response can be found in [7] and[10]. These algorithms and conclusions Appendix I will be usedin this paper.In this paper, the effect of instrument bandwidth in jitter

and BER measurement of high-speed serial interconnectionwill be quantitatively discussed. At first, the theoretical resultson the effect of instrument bandwidth in jitter and BER testare computed based on first-order linear time-invariant (LTI)system, then simulations are made based on the -parameter ofreal channels without considering transmitter (a BERT) band-width, and the simulation results are compared with an actualDDJ measurement result to show the effect of test instrumentbandwidth in jitter and BER measurement. In Section III analgorithm to measure and estimate the equivalent frequencyresponse of the instrument will be discussed, and the simulationresults after calibration will be given. Then, as the conclusion,the concept of “equivalent bandwidth” of the instrument isgiven to provide a convenient method to estimate a jitter andBER test result when considering the transmitter bandwidthaccording to the simulation results.

II. THEORETICAL COMPUTING FOR FIRST-ORDER SYSTEM

A typical jitter and BER test system is constructed with atransmitter (or an instrument acting as a transmitter), a channeland a receiver (or an instrument acting as a receiver). The trans-mitter (BERT or a real SERDES) can generate test codes, suchas pseudorandom bit sequence (PRBS), to send into the se-rial communication channel, while kinds of jitter componentsare often modulated into the test code flow for BERT. Instru-ments, such as time interval analyzer (TIA), oscilloscopes withjitter-analyzing function, or BERT itself, are connected at theend of the channel, which can plot eye wave, jitter distributionhistogram, or BER bathtub curve, through which jitter and BERperformance can be observed directly and precise jitter and BERresults can be printed.The DDJ peak–peak value of a first-order low-pass system

has an explicit function expression as follows [7], [9]:

(1)

0018-9480/$31.00 © 2012 IEEE

JUN-FENG et al.: INSTRUMENT BANDWIDTH EFFECT IN JITTER AND BER TEST FOR HIGH-SPEED SERIAL INTERCONNECTION 257

Fig. 1. System model of first-order system.

where is the time constant, and is the unit interval (UI) ofa bit. Most real channels have frequency responses similar to afirst-order system, so we can use first-order low-pass system asa simple model to compute the effect of transmitter in jitter test.Assuming that the instruments and the channel both have

impulse response as first-order LTI systems with different timeconstant and , we can set up the wholesystem as Fig.1 when defining bandwidth of the instrument andthe channel as and :Mostly, , and we define .

The DDJ peak–peak value result (using UI as the unit of DDJ)without considering test instruments can be expressed as fol-lows through (1):

(2)

and we use as the index to evaluate the effect ofthe instrument bandwidth, where is the DDJ peak–peakvalue when considering the instrument bandwidth. reflectsthe aggravation of DDJ when considering the instrument band-width, which can be computed through (3) and (4) using thesimilar method described in [7] and [9]

(3)

(4)

Different from the (2), only numerical solution of (3) and (4)can be obtained, as shown in Figs. 2–4.From Fig. 3, we can see that the DDJ peak–peak value of the

whole system is more sensitive to than to the data rate, whichmeans that the BER and jitter test often generates large errorwhen the channel to be tested has a relatively “high” band-width even when the data rate is slow. From Fig. 4, it can beinferred that only when the instrument bandwidth far outweighsthe channel bandwidth can the instrument bandwidthbe neglected ( , test error )in jitter and BER test. We can also observe that when test instru-ment bandwidth is close to the channel bandwidth , thejitter test result is apparently affected by the instrument band-width, which leads to different jitter and BER test results whenusing different test instruments, as we often meet in jitter andBER test of high-speed serial interconnect. The test and simula-tion result based on three different real channels will be shownto illustrate this conclusion in the next part.

Fig. 2. DDJ peak–peak value versus data rate curve for the first-order LTIsystem.

Fig. 3. -data rate curve for the first-order LTI system.

Fig. 4. – curve for the first-order LTI system model.

III. TEST AND SIMULATION OF THE EFFECT OFINSTRUMENT BANDWIDTH

The system to test and simulate the amplitude of all kinds ofjitter components transferred in channel is constructed as Fig. 5.


Fig. 5. Block diagram of jitter test and simulation system.

Compared with the typical jitter and BER test systemmentioned before, a network analyzer is used to measure thechannel response, while a simulation platform is made up usingMATLAB to calculate the amplitude of jitter components.The simulation uses the peak–peak value of DDJ as the indexto evaluate the jitter performance, and uses the algorithmdescribed in Appendix I.In this test system, the results measured on the oscilloscope

include the effects of BERT, channel, and oscilloscope, whilethe results obtained through simulation based on channel -pa-rameter only reflect the effect of channel. The effect of instru-ments on jitter can be illuminated by comparing two sets of re-sults. The BERT we use is Agilent J-BERT N4903A, which cangenerate PRBS codes from 150 Mbps to 12.5 Gbps modulatedwith appointed jitter components. We used Agilent 86100 C, awideband (80 GHz) oscilloscope with jitter-analyzing function,to generate DDJ test results.Three channels are tested and simulated in the system: a

5-in FR4 channel, a 10-in FR4 channel, and a 15-in ROGERSchannel. Their channel frequency responses are describedas Fig. 6.Using the algorithm described in Appendix I, DDJ peak–peak

values of different channels in different bit-rate can be calcu-lated in Tables I and II, where test results, the error and the(defined as the radio of the test result and the simulation resultto match the previous definition in part II) are shown together.The results show that the test results significant error com-

pared to the simulation results. The error comes from the closebandwidth between the channels to be test and the instrumentsas we analyzed in Section II. In fact, because of different test in-struments and SERDES with different bandwidths, even whentesting or simulating a same channel, different test result will bemeasured, and simulation results divert from the measurementresult, especially to a channel with relatively “high” bandwidth,which makes it necessary to measure and evaluate the effect ofinstruments, and calibrate it.

IV. MEASURE AND CALIBRATION OF THE EFFECT OFINSTRUMENT

Compared with the frequency response of the channel thatcan be tested easily using a network analyzer, it is hard to find adirect method to test the frequency response of instruments. Tomeasure the effect of instruments, we make up a test system asFig. 7.The effect of instruments can be equivalent to an ideal square

wave generator adding a filter, and the unit impulse response

Fig. 6. Channel frequency responses for three channels. (a) 5-in FR4channel. (b) 10-in FR4 channel. (c) 15-in ROGERS channel.

TABLE ITEST AND SIMULATION RESULTS OF DDJ PEAK–PEAK

VALUE (6.25 GBPS)

TABLE IITEST AND SIMULATION RESULTS OF DDJ PEAK–PEAK

VALUE (9.95328 GBPS)

of the filter can be tested by connecting the oscilloscopeand transmitter (BERT) directly. The BERT generates thePRBS10 sequence repetitively without modulating any jittercomponents, and the oscilloscope acquires the average wave-forms of every bit in PRBS sequence.


Fig. 7. Block diagram of jitter test and simulation system with calibration ofinstruments.

If there is no jitter injected in the clock path, the derivative ofthe output when an ideal data sequence with bit period passesthrough the filter can be represented as

(5)

in which . If the filter is a causal LTI system,. If the time region of in consideration is

, which means , then in time region, the derivative of the output will

be

(6)

If is sampled with the period of , the th value ofin the time region can be represented as

(7)

where , , and can be obtainedfrom the interpolation of tested waveform.

Fig. 8. Frequency response of equivalent filter.

For a given , if the period of input bit sequence is (1024for PRBS-10), in all time intervals can be described asfollows:

(8)

By removing the equations in which the label of is nega-tive, we will get

(9)

In (9), there are unknownsand the total number of equations is . If

, we can only get a least squares solution.For an equation , the least squares solution of is

, where is a toeplitz matrix. For each, can be calculated. Sorting the results by time, we will

get the impulse response of the equivalent filter.For the conditions of bit rate equaling to 6.25 and 9.95328

Gbps, two results for the impulse response of instruments(mainly of Agilent J-BERT N4903A) can be determined, andthe frequency response of instruments can be shown asFig. 8.As expected, the two results for 6.25 and 9.95328 Gbps are

very close. These results reflect the reasonableness of the hy-pothesis of equivalent filter and the correctness of the algorithm.Then the impulse response of the total interconnect, includingthe channel and the test instruments, can be computed by

(10)


TABLE IIITEST AND SIMULATION RESULTS OF DDJ PEAK-PEAK VALUE AFTER

CALIBRATION (6.25 GBPS)

TABLE IVTEST AND SIMULATION RESULTS OF DDJ PEAK-PEAK VALUE AFTER

CALIBRATION ( 9.95328 GBPS)

Using , the simulation results of DDJ peak–peakvalue can be calibrated after considering the bandwidth ofinstruments as Tables III and IV.Shown as the table, for all conditions tested, the errors be-

tween the simulation results and the measured results are below8%, which is very coincident considering of the precision ofjitter test. These results enable us to use the simulation methodsto analyze the calibration of instruments in jitter and BER test.For the three channels and the instruments mentioned above,

the simulated DDJ results with different data rate are shown asthe following figure.As shown from the figure with log–log coordinate, the curves

for all condition appears a set of parallel lines, which means theDDJ can be approximately expressed as: ,where is the data rate, is related to the bandwidthof the channels and the instruments, and is nearly a constant

. So is approximately indepen-dent of and only related to . Similarly, it can be observedfrom Fig. 3 that the aggravation of DDJ when considering theinstrument bandwidth changes slowly with data rate in a widerange and vary distinctly with . Promoting this conclusion toa real jitter test condition, if we can give reasonable definitionsfor the “bandwidth” and , a rough estimation on the instrumenteffect can be made conveniently.

V. A ROUGH ESTIMATION ON THE INSTRUMENT EFFECT

According to Part IV, it still needs complicated measurementand compute to precisely calibrate the effect of instrument band-width in jitter and BER test. But in many cases, only a rough es-timate of the range of the instrument effect is sufficient in jitterand BER test. A rough estimation on the instrument effect injitter and BER test will be discussed in this part.To conveniently estimate the effect of the jitter and BER test

caused by instruments, a concept of “equivalent bandwidth”is presented. The definition of “equivalent bandwidth” comesfrom the 3-dB bandwidth for a first-order LTI system.In a first-order LTI system, when a rectangle pulse with thewidth (stream “ ”) is inputted, the shape of theoutput signal , which is defined as the “unit pulse response”

Fig. 9. Simulated DDJ result for three channels with and without consideringinstrument. (a) Linear coordinate. (b) Log–log coordinate.

as we used in [7], is closely related to the jitter of the signal.For a first-order LTI system, when is normalized by thecondition of the unit step response (stream “ ”)

, the bandwidth can be expressed as follows:

(11)

where is the data rate of input stream.Similarly, we use expression (11) as the definition of the

“equivalent bandwidth” of a system, which can be easilyobtained from the -parameter test result for a real channel,or from the wave information obtained by a wideband oscillo-scope for instruments.Generally, is a function of , but for first-order LTI

system is a constant which is independent of . The fol-lowing figure shows the simulated equivalent bandwidth forthree different channels and the test instrument.A system has similar unit pulse response with a first-order LTI

system when the two systems have the same equivalent band-width, which can be shown as the following figures:Because the jitter is sensitive with the time domainwaveform,

the systems with similar unit pulse response often have the sim-ilar jitter character. So the effect of the instrument bandwidth injitter and BER test can be estimated roughly from the solutionof (3), (4) when is defined by the equivalent bandwidth. At the


Fig. 10. Simulated equivalent bandwidth for three different channels and thetest instrument.

Fig. 11. Unit pulse response curves of two systems with same equivalent band-width.

same time, simulation results can be obtained using the methoddescribed in Part IV. The following figures show the simulatedand with different date rate.

VI. CONCLUSION

Although in most of system and test we can make quite accu-rate measurement if using test instrument only a little faster thanthe rise time of the system to be tested [4], this conclusion is nottenable in jitter and BER test. The results obtained in this papershows that in jitter and BER test, a quite high bandwidth (times the channel bandwidth) is needed to reduce the test error.Because of the difficulty to improve instrument bandwidth, the

Fig. 12. Simulated curves. (a) (defined by equivalent bandwidth). (b) .

measure, calibration and estimation of the effect of instrumentin jitter and BER test is important to the accuracy and consis-tency of the results when using different instruments.In this paper, a set of test methods and algorithms are pre-

sented to predict the DDJ amplitude, measure, calibrate andestimate the effect of instrument in jitter and BER test. Thesemethods and algorithms will be helpful for current jitter andBER test standard.

APPENDIXANALYSIS OF PEAK-PEAK VALUE OF DDJ

When there is no noise, a received NRZ data signal andits threshold crossing time can be described [2], [7], and [10]as

(A1)

where is data symbols, is the re-ceived pulse response with pulse width , is the width of onebit, is the step response of the channel, and is the deci-sion voltage threshold. The characters of the solutions for for-mula (A1) with different reflect the distribution of DDJ. Tocomputer the peak–peak value of DDJ, we use the iterative algo-rithm shown in [10]. The principle of the algorithm is finding thesymbols that results in the maximum and minimum valueof DDJ, then computing the DDJ peak–peak value through nu-merical evaluation. The algorithm can be described as follows.


Fig. 13. Illustration of DDJ peak–peak value calculation.

1) Calculate the “ideal” threshold crossing time using, is the time reference when

computing DDJ;2) Sort with the weight of , the with higher

placing in the front of the queue. Generally(suchas in an LF channel), the queue is ;

3) Set the initial value of , , this isthe edge position to be test. For other symbols ,set (or other values, it doesn’t matter); set thetemporary symbols with the initial value ;

4) For every with the order of the queue, calculate the DDJvalue with the current input , thencalculate

(A2)

If , in the symbols which result in Max. DDJ, ,while the symbols which result in Min. DDJ, . If

, equals the reverse value of the value when .5) When every have been computed, we got a new .If , the iterative algorithm completes. If

, we should set , and compute anew based on the new , then perform Step 2 Step5 until .

Through the algorithm, we can get a set of symbols, whichleads to the max (or min) DDJ value, the peak–peak value ofDDJ can be calculated through these symbols. The formula (A2)can be illustrated as Fig. 13. Related paper, such as [11], cannotprocess the situation of closing to 0 correctly.

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Yang Jun-Feng (M’11) received the M.S. and Ph.D.degrees in electronic science and technology from theUniversity of Science and Technology University ofChina (USTC), Anhui, China, in 2002 and 2005, re-spectively.He is currently a Lecturer in the Department of

Modern Physics, USTC. He is also a Researcher inthe State Key Laboratory of Particle Detection andElectronics at the same university. His research in-terests include the jitter in high-speed serial intercon-nect and data acquisition system design in high-en-

ergy physics and oil exploration.

Song Ke-Zhu (M’11) received the M.S. degree inmarine ship automation from Dalian Maritime Uni-versity, Liaoning, China, in 1992, and the Ph.D. de-gree in nuclear and particle physics from the Uni-versity of Science and Technology of China (USTC),Anhui, China, in 2001.He is currently an Associate Professor in the De-

partment of Modern Physics, USTC. He is also a Re-searcher in the State Key Laboratory of Particle De-tection and Electronics at the same university. His re-search interests include high precise, mass and real-

time data acquisition and signal processing.

Cao Ping (M’11) received the B.S. degree in appliedphysics and the Ph.D. degree in electronic scienceand technology from the University of Science andTechnology of China (USTC), Anhui, China, in 2002and 2007, respectivelyHe is currently a Postdoctor with the Department

of Modern Physics, USTC. His research interests in-clude signal processing, large-scale data acquisition,and their applications for geophysical exploration in-struments.

the instrument bandwidth effect in jitter and ber test for high-speed serial interconnection

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