Jitter Fundamentals: Agilent 81250 ParBERT Jitter Injection andAnalysis Capabilities

Application Note

Introduction

In digital communications, asequence of 0’s and 1’s flowsfrom a transmitter to a receiv-er. The transmission media iscopper, fiber or air.Communication systems aremaximized for bandwidth andminimized for errors. Theseerrors are counted as BitError Ratio (BER).

Digital communication systemstransmit the pure bit streamin terms of a NRZ data streamonly, and then regenerate thebit clock at the receiverthrough the use of a clock anddata recovery (CDR) circuit.Timing aberrations of theincoming signal causes mal-function of the CDR circuitresulting in bad sampling ofthe data causing bit errors.These timing aberrations arecalled jitter.

Jitter Fundamentals• What is Jitter?

• Jitter Components

• Jitter Challenges

• Jitter in SONET and Ethernet

• Stressed Eye

• Jitter Measurement in Time/Frequency Domain

81250 ParBERT Jitter Capabilities

• Delay Control / Clock Modulation

• Bandwidth Control

• Bath Tub Measurement with RJ / DJ Separation

• Spectral Decomposition of Jitter

Figure 1: Jitter Fundamentals

2

It causes bit errors!

Data Cycle, Bit Period

Figure 2: Why Jitter is an important issue

Jitter is significant because itis one of the major potentialcauses for data being receivedin error. For example, if a longstring of bits is on the shortside, eventually a receiver willmake a decision at the edge ofthe bit rather than the center(if the clock rate is held con-stant). This will result inerrored bits. Another perspec-tive is to view the eye dia-gram. As the jitter increases,eventually the eye will closehorizontally. In the eye open-ing display, one can see howthe eye closes the higher theBER figure gets. The represen-tation here defines so calledISO-BERs. In the originalGraphical User Interface (GUI),this diagram would be incolor, and the color coding onthe right defines the BER fig-ure for each line. If the clockis derived from the data(CDR), the sampling point canthen follow the jitter and allowthe system to tolerate jitter. Aclock recovery process is limit-ed by the loop bandwidth ofthe clock recovery circuitry.

There are many challenges totoday’s jitter measurements:

- Huge problems on complexASICs to avoid ground bounceand clock crosstalk inducedjitter.

- New high speed IO standardsrequire DJ, RJ specified sepa-rately.

- SONET based jitter transferspecs only make sense whenthere is no other (intrinsic)jitter source than the artificial-ly injected jitter.

- New defect types in produc-tion: process variation affectsgross yield through differentinfluences on DJ and RJ.

- Design goal for maturinghigh speed interfaces: Generaterobustness with circuits thatshow more margin againstprocess influence on DJ andRJ.

- Increasing difficulties fordesign validation and debug-ging.

- A better analysis of jittermechanisms is required.

- Probabilistic view (histogram)is no longer sufficient.

Why is jitter an important issue?

3

By examining the edges of adigital communications bitstream, we can better illustrateour definition. Figure 3 showsan oscilloscope display of adata stream with the systemclock waveform. If the timingof this bit stream is jitter free,the period for all of the bitswill always be precisely identi-cal. Thus the time between anytwo rising or two falling edgeswill always be a precise inte-ger multiple of the nominal bitperiod.

Another way to look at this isto look at the data stream rel-ative to an ideal clock source.The time between a data edgeand the closest clock edgeshould always be the same. Ifthe data signal is jitter free,then the 50% amplitude pointson the data waveform shouldconsistently align with pointson the clock waveform. However, if the bit period fluc-tuates for any reason, the bitstream will no longer be jitterfree.

Although there are differencesin the many definitions of jit-ter, the fundamental similarityis that jitter has to do withthe time difference betweenthe ideal and actual occur-rence of an event. A simpledefinition is:

“Jitter is the time differencebetween when a pre-definedevent should have occurredand when it actually didoccur. The time difference isexpressed in unit interval(UI), 1 UI is the value of thebit period of the ideal clocksignal. This time differencecan be treated as phase mod-ulation, there are one (ormore) signals modulating theideal position of the data sig-nal.”

• Significant instants can usually be defined as edges

• The system clock can be used to define what the ideal positions in time are

• Edge position of the data should consistently align with the same relative points on the reference clock waveform

Figure 3: Ideal signal = constant bit period

A more sophisticated definitionfrom the viewpoint of theSONET standard [1] is: “Jitteris the short term phase vari-ation of the significantinstants of a digital signalfrom their ideal positions intime. It is primarily con-cerned with non-cumulativevariations above 10 Hz.Cumulative phase variationsbelow 10 Hz are referred toas wander.”

The Fibre Channel communitydefined it thus: “Jitter is thedeviation from the ideal tim-ing of an event. The referenceis the differential zero cross-ing for electrical signals andthe nominal receiver thresholdpower level for optical sys-tems.” [2]

4

Jitter Components (1)

Jitter consists of two funda-mental components calledRandom Jitter (RJ) andDeterministic Jitter (DJ).Figure 4 illustrates an exampleof a signal with an extremelylarge amount of DJ. RandomJitter is unbounded and isusually best described by aGaussian probability densityfunction. Deterministic jitter isbounded, ie it has definiteamplitude limits from an earli-est to a latest trace. TheRandom Jitter (RJ) is definedby an rms value which in thiscase equals the ‘s’ (sigma) ofthe Gaussian distribution. Thetotal jitter is a function of ‘n’times the rms value, dependingon what BER limit a system isspecified, plus theDeterministic Jitter (DJ) whichis by nature a peak- to-peakvalue.

Deterministic Jitter (DJ):spacing between mean values of“earliest” and “latest” trace

Random Jitter (RJ):Defined by RMS value which equals s (sigma) of the Gaussian distribution

Total Jitter (pp) :Data jitter

plus n(BER) xs

s :sigma

BER n-------------------10-6 9.810-9 12.210-10 12.710-12 14.110-14 15.3

Figure 4: A real signal

5

Jitter Components (2)

This is the whole picture ofthe jitter components: The Deterministic Jitter (DJ)has several faces, e.g. it iscaused by bandwidth limita-tions and component interac-tion (crosstalk). The diagramshown here separates the indi-vidual components and pinsthe nature of the origin.The first layer separates theDJ into:

- Periodic Jitter (PJ), whichdisplaces the timing of risingand falling edges with a peri-odic pattern (or as the originof this type of jitter is sinu-soidal modulation, it is alsocalled SJ).

- Data Dependent Jitter (DDJ)(which is a function of bitpatterns).

- Bounded Uncorrelated Jitter(BUJ) which is caused byinterference with asynchronoussignals: cross-talk betweensub-circuits, power supplynoise and electro-magneticinterference (EMI).

In the next layer the DataDependent Jitter can be sepa-rated into:

- Duty Cycle Distortion (DCD),which is caused by voltage off-sets between differential inputsand differences between transi-tion times within a system.

- Inter-Symbol Interference(ISI), which is caused by thedifferent symbols (long andshort bit cycles).

Total Jitter

RandomJitter

Data DependentJitter

PeriodicJitter

DeterministicJitter

Duty CycleDistortion

Inter SymbolInterference

pk-pk

Unbounded, rms Bounded, pk-pk

Sinusoidal Data smearing

Lead/trail edge

Long/Short bits

BoundedUncorrelated

Crosstalk

Figure 5: Jitter Component Segmentation

This can also be explaind fromBandwidth limitations whichoccur from AC coupling (lowfrequency cut-off) or from highfrequency roll-off. However,this is from filters with non-linear phase characteristiconly. Linear filters, such asBessel filters, do not cause jit-ter. DCD and ISI jitter are afunction of the pattern. Thejitter appears when changingthe pattern from a clock-likepattern to real data. PRBStype patterns are good fortesting as they contain manyvariants of frequency compo-nent.

6

Random Jitter (RJ)

RJ is caused by thermal andnoise effects. These effects arestatistical by nature. So theRandom Jitter (RJ) isunbounded and is modeled bya probability density functionand is quantified by the rmsvalue of the density function.In most cases the Gaussiandistribution is used for thecharacterization of RandomJitter. In this case the rmsvalue equals the ‘s’ (sigma) ofthe Gaussian distribution.There is a fixed relationbetween ‘s’ (sigma) and thenumber of events. While arange of 6 sigma alreadydefines a high number ofevents (99.7%), this is a smallnumber for BER. Typically aBER is required to be as lowas 10-12, this needs a range of14.1 sigma to be included forthe total jitter budget.

In the past the common modelwas to fit the actual jitter his-togram into the Gaussian curveand the rms value wasextracted. For a signal withsignificant DJ this resulted ina value way too high for therms figure. This led to theRJ/DJ separation model. Sofirst any DJ jitter componentis isolated and only the‘remaining’ jitter is then treat-ed as RJ. DJ would broadenthe Gaussian curve, while thetail portions of the histogramrepresent the RJ jitter compo-nent [3]. However, it is notnecessary to perform his-togram measurements to iso-late RJ/DJ components. Laterin this Note it will be shownthat the BERT ScanMeasurement allowsRandom/Deterministic Jitter tobe separated directly. Thiseliminates the need for specificjitter test sets, because the jit-ter measurements can beobtained from BER test equip-ment.

time

mean value

sigmaNormalized Events sigma

General: # events = n x s (sigma)

Random Jitter: n(BER) xs

N # events BER

---------------------------

2 67% 0.33

4 97% 0.03

6 99.7% 0.003

9.8 106 10-6

12.2 109 10-9

14.1 1012 10-12

sigmasigma

Figure 6: Random Jitter: The Gaussian Distribution

7

Inter-Symbol Interference

Inter-Symbol Interferencedescribes the amount of jitteroccuring through data content.Here the issue is the transmis-sion of long and short bits.Within the data stream thedata cycles most affected arethose which contain a singlebit state which is opposite tothe surrounding bits. In Figure7 this is represented by thetrace which shows a data bitbeing one cycle a ‘1’ while itis surrounded by ‘0’s.

This type of jitter results frombandwidth limitations whichare low/high pass filters withnon-linear phase characteristic,or from loss within transmis-sion lines. Loss incables/microstrips causes droopwhich again limits signal set-tling before the next transitionoccurs. Both bandwidth limita-tion and cable loss lead to ashortening of this bit as this isinsufficient time to settle thesignal to 100% before theopposite state starts. Thisleads to an early start of thetransition with the disadvan-tage that 50% is too early andwithin random data, the eyewill start to close.

A lot of jitter tests use specif-ic filters which incorporate jit-ter as inter-symbol interfer-ence. These filters are calledJIMs (Jitter Injection Modules),and are built as L-C chains,which resulting in a higherorder. Here, Phase Shift occursnot only for a single bit butalso for 2,3 or more consecu-tive bits. This is applied in theso called “Stressed Eye Tests”,which will be covered later inthis Note. [4]

caused by bandwidth limitation / loss

• low/(high) pass filter

• cable droop

C

R

Zl

1 2 2

2: 0 -> 1 transition1: 1-> 0 transition

1

33

3: 1 UI pulse

Figure 7: ISI: Inter-Symbol Interference

8

Periodic Jitter (PJ)

Periodic Jitter provides sinu-soidal varying jitter, where asinusoidal signal modulates thephase of the ideal clock ordata signal. The sinusoidal sig-nal may be asynchronous orsynchronous to the clock /data signal. Synchronous clocksub-rates cause every ‘n’thcycle to be shorter/longer thanthe others.

Often this type of jitter isused in jitter testing. In thiscase a sinusoidal signal isused to displace the dataedges. This helps to character-ize the bandwidth of CDR cir-cuits. SONET Jitter testing isstandardized for all jitter com-ponents to be sinusoidal.

Figure 9 shows the traditionaleye measurement taken from asampling scope. This allowsthe jitter to be viewed as rmsand peak- to-peak values and ahistogram is generated. Thehistogram can tell us somedetails about the jitter distri-bution. But the histogram isnot able to get insight on whatlies beneath this. In this casethere is a mix of Random andSinusoidal jitter. As mentionedearlier, with help of some DSP(Digital Signal Processing) toolsit would be possible to do aRJ/DJ separation from theHistogram for gaining therms/peak- to-peak value of thejitter components. But it isimpossible from the histogramto gain the bandwidth of thenoise or the frequency of thesinusoidal interference. Thisrequires another approach.

Ideal clock:

Jittered clock:

)2sin( tfcp

( ))2sin(2sin101

34 tftf cc ppp +

)2sin(101

34 tfcppJitter:

UI32

Figure 8: Periodic Jitter

What you see today...

...What is behind(RJ=0.2UIrms 80MHz bandwidth

, DJ=0.05UIpkpk, 10MHz)

Figure 9: Jitter Measurement Situation

9

Clock with 1MHz Sinusoidal Jitter

Jitter 25ps (0.08UI pp)

Clk with 80MHz Broadband Gaussian Jitter

Jitter 13ps rms (0.04UI rms)

Jitter Spectrum, Peak at 1MHz

Figure 10: Spectral Decomposition of Jitter

Jitter in the Frequency Domain

Figure 10 introduces jitter inthe frequency domain. Thisshows a diagram with frequen-cy on the x-axis and power(or power factor) on the y-axis. The graphs show the twojitter components separated forsinusoidal and random. In thehistogram there is only aslight difference between theSinusoidal (DJ) and theGaussian (RJ) jitter. In the fre-quency decomposition thesinusoidal jitter is representedas a single line occurring at asingle frequency. The randomnoise shows a wide frequencyspectrum up to the bandwidthof the random spectrum (inthis case 80 MHz). Above thisvalue, the power decreasesdown to the noise floor.This kind of representation ispossible using a SpectrumAnalyzer with a PhaseDiscriminator. The PhaseDiscriminator (or Demodulator)de-modulates the signal toobtain the phase modulationsignal which is what we see inthe figures above. This type ofmeasurement is very commonto jitter measurements onSONET devices. However, onehas to be aware that this ispractical for jitter on a clocksignal, but cannot be used fortrue data signals.

There is a new tool usable onBER test equipment, which canperform these SpectralDecomposition Measurementseliminating the need ofSpectrum Analyzer equipmentand the capability to do thesemeasurements on true datasignals. This will be explainedlater in this Note.

10

The BERT Scan Measurement

The Gigabit Ethernet approachto measuring something that isunbounded is through a Bit-Error-Ratio measurement,specifically through a “BathTub plot”:

Data Jitter will result in thesignal edges moving toward thecenter of the eye diagram.Extreme excursions will occurless frequently than minorexcursions. If the transmit sig-nal is fed to an error detectorand the sampling point is opti-mized in both time and ampli-tude, the error rate should bewell below 10E-12 (as close tozero as can be measured). As the sampling point is con-tinually moved into the edgesof the eye, the BER will getsteadily worse.

The important element fordoing characterization is theability to move timing edgesaround. On an analyzer thisallows to move the samplingpoint around.

It is important to state: thismeasurement can be performedon differential signals!Moving the sampling point overone cycle and plotting theerror rate, results in a graphcalled ‘Bath Tub’. The x-axisof this graph is time, the y-axis is the BER figure. Thename ‘Bath Tub’ results fromthe specific shape of the curve.This specific shape resultsfrom the fact that the lowerthe BER figure gets, the moretest vectors have to beprocessed. The longer the testruns, the wider the jitter bandof a real world signal will be.So the lower the BER thresh-old is specified, the less theresulting phase margin will be.

The IEEE 802.3ae standardsets the allowable jitter magni-tude at the 10E-12 BER level.Thus the “eye” must have aspecified opening at this BER.

Bath Tub measurements arethe basis for all measurementslisted above including jittermeasurements. For the jittermeasurement (especially theRJ/DJ separation) the transi-tional behavior of the left andthe right slope between twopoints specified as BER figureswill be extrapolated.

Data OUT Vector n

Bit Error Ratio

Range forAnalyzer sampling delay

Timing Measurements:-> Bath Tube

Time

Bit ErrorThreshold

Jitter Measurements:

Measurements:-> Optimum Sampling Point-> Skew-> Phase Margin-> Setup/Hold Time-> Jitter

Eye Opening

at BER 10-12

Figure 11: BERT Scan

11

Jitter within the Standards

Jitter is described differentlywithin the various standardswithin the communicationindustry. The SONET as a syn-chronous architecture dealswith Jitter Generation, JitterTolerance and Jitter Transfer.Jitter Generation is the jittercoming from the device, JitterTolerance is the jitter whichthe device can handle, andJitter Transfer is the jitterwhich moves through thedevice from input to output.The jitter used for the meas-urements is sinusoidal only.

The more modern standardsare dominated by the Ethernetcommunity dealing with asyn-chronous architecture. Here thejitter is a mixture of randomand deterministic content. Andthe 10GbE community hasestablished new concepts ofmeasuring: TransmitterDispersion Penalty (TDP) andStressed Eye Test.

The difference between SONETand Ethernet is the clockingsystem:

SONET/SDH uses a commonsystem frequency which isrecovered by CDR within eachreceiver, and then used withinthe whole circuity. Therefore itis called synchronous or a-synchronous clocking. The out-going signal is retimed withthe recovered clock of theincoming signal so that theclock propagates through thesystem. An important specifi-cation therefore is JitterTransfer. A disadvantage isthat the imparities can accu-mulate, as from sub-system tosub-system jitter can add upuntil a very specific clean-upPLL is used. An advantage(especially for testing) is thatthe data rate is identicaleverywhere in the system, andthe number of data bits on

SONET/SDH – ITU-T0.172, GR-253-CORE

Synchronous Architecture

Transceiver timing derived from received signal therefore jitter propagation critical

• Jitter Generation

Characterizes transmitter jitter performance

• Jitter Transfer

Characterizes clock recovery performance against jitter

• Jitter Tolerance

Characterizes receiver’s tolerance to jitter

Gigabit Ethernet and 10 Gigabit Ethernet – IEEE 802.3z and 802.3ae

Asynchronous Architecture

Transceiver timing not derived from received signal therefore jitter propagation less critical

• 1 Gb En

Bathtub plots to measure jitter generation

• 10 Gb En: Serial TDP(Transmitter dispersion Penalty) for transmitters Stressed Eye receiver test

– similar to Jitter Tolerance

XAUI Bathtub, Stressed Eye

Gene

ratio

n

Tole

ranc

e Transfer

Figure 12: Jitter: the Standards

Figure 13: The difference in clocking of SONET/SDH and Ethernet

SONET/SDH = Synchronous clocking

• Important spec is Jitter Transfer

• Outgoing signal is retimed with recovered clock of incoming signal so that clock propagates through the system

• Disadvantage: imparities can accumulate until clean-up PLL is used

• Advantage: as data rate is identical everywhere number of data bits on both sides of DUT is identical, too

(10Gb)Ethernet

• No such spec as Jitter Transfer

• Outgoing signal is retimed with independent DUT clock which may have a slightly different rate (+/- 100ppm)

• Advantage: no accumulation of clock disparities / jitter

• Disadvantage: as number of data bits on both sides of DUT is not identical, bit-stuffing/discarding scheme is required

CDR

Signal processing

CDR

Signal processing

CDRindep.

clk

FIFOSignal

processing

each sides of the DUT is iden-tical, too.

For (10Gb) Ethernet there isno such specification as JitterTransfer. The reason for this isthat the outgoing signal isretimed with an independentReference Clock within theReceiver. This new ReferenceClock is allowed for a slightlydifferent rate (typically +/-100ppm). The resulting disadvan-tage is that the number ofdata bits on each side of DUTis not identical. So an Idlescheme with bit-stuffing/dis-carding is required. The major

advantage is that no accumula-tion of clock disparities/jitteroccur throughout the device,so no jitter transfer happensand therefore no such specifi-cation or measurement is nec-essary.

12

0 to 40MHz

10.3125GHz

Clock

PatternGenerator

~1-2 GHzsine

7.5 GHzLPF

Laser

0 to 40MHz

10.3125GHz

Clock

PatternGenerator

~1-2 GHzsine

7.5 GHzLPF

Laser

• Sinusoidal jitter modulates the clock timing the pattern generator

• Sinusoidal interference signal summed with jittered data pattern

• Summed signal low-pass filtered

Figure 14: Stressed Eye Example

Stressed Eye

Stressed Eye for Ethernet [5]is similar to Jitter Tolerancefor SONET/SDH. WhileSONET/SDH deals with sinu-soidal jitter only, here thestressed eye is a well definedmix of periodic jitter in timeand amplitude.

An arbitrary WaveformGenerator is used to modulatea Signal Generator whichsends the jitter modulatedclock into the PatternGenerator. The data stream isadded with a sinousoidalinterference signal and finallyis low-pass filtered for a spe-cific shape supplied to opticalconverters. Often there areadditional filters to the PatternGenerator output to includeData Dependent Jitter (ISI)with the data pattern.

13

The 81250 ParBERT can emu-late (1) and measure (2+3) jit-ter. For Jitter Tolerance typetesting, the ParBERT allowseither a modulated clock to beworked with and/or the delayof the generator output to becontrolled (by 3.3 Gb/s genera-tor E4862B and 13.5 Gb/s gen-erator N4872A).

The modulation of the externalclock can be done to achievemultiple Unit Intervals (UI’s)as jitter, but this is limited toa certain bandwidth as thereare PLLs within the internalclock distribution path. ThePLLs will filter the higher fre-quency contents of the modu-lation signal. With the delaycontrol input each generatorcan be controlled individuallyup to a modulation frequencyof 200 MHz and a peak- to -peak modulation of 500 ps. At3 Gb/s speed this allows a jit-ter budget exceeding the eyetotally. The modulation signaltype controls the distributionof the jitter. With a mix ofrandom and square wave sig-nal one can emulate a mix ofRJ and DJ.

The measure capability of the81250 ParBERT is BER, BathTub, Eye Opening and FastEye Mask. With the Bath Tubit is possible to read the jitterseparated for RJ and DJ.

The ParBERT generators (3.3Gb/s E4862B & 13.5 Gb/sN4872A) provide a ControlInput for modulating the Delaywith help of an external sig-nal. This modulation can beused to emulate jitter. Figure16 shows this jitter emulationas a scope view for three dif-ferent types of control voltage:sinusoidal, rectangle and ran-dom. This Jitter Modulationcan be used to test a DUT forJitter Tolerance or to built a

Figure 15: 81250 ParBERT Jitter Capabilities

Figure 16: Jitter Injection

Modulated Clock (<10 kHz)

Delay Control

DUT

Data In Data OutClock

BER

Jitter Decomposition

Bath Tub RJ/ DJ

Generators 3.3G only

1st 2nd

3rd

“Clean Eye” Jitter modulated with Sine - Wave

Jitter modulated with Rectangle -Wave

Jitter modulated with Noise

As a source for these modula-tion voltages Agilent offers the3325A Function/ArbitraryWaveform Generator. This typeof instrument can generate anymentioned type of signal, butone at a time. By combiningtwo of them with help of apower splitter (11667B), a mixof two signals is possible. Somixing random and Sine/rec-tangle emulates jitter with RJand DJ components.

The control inputs of the dif-ferent ParBERT generatorswork similarly but differ inparameters: the 3.3 Gb/s gen-erator (E4862B) allows a delaymodulation of +/- 250 ps upto 200 MHz modulation band-width, the 13.5 Gb/s generator(N4872A) allows a range of +/-100 ps up to 1 GHz band-width.

ParBERT 81250 Jitter Capabilities

14

The ParBERT can run on anexternal Clock. For JitterEmulation where multiple UIjitter is required (what thedelay control cannot offer) anexternally modulated Clock canbe fed to the ext. Clk Input ofthe clock module. But thereare PLLs in the clock pathbetween the ext. Clk input andthe channels. There are somespecific restriction dependingon the specific speed class ofParBERT data clock and datamodules.

- 675 MHz data modules usedwith E4805 /E4808A clockmodule: In regular operationthere is a PLL inside the clockmodule with a cut-off frequen-cy of around 10 kHz. So onecan generate a modulated jittercovering multiple UIs (lineartransfer range) only up to thiscut-off frequency. There is aspecific procedure to bypassthe PLL, in this case the cut-off can be avoided. For detailsof operation contact ParBERTtechnical support.

- 1.65 Gb/s, 2.7 Gb/s, 3.3 Gb/sand 10.8 Gb/s with any clockmodule: There are always mul-tiplying PLL‘s in the clockpath inside the data moduleswhich cannot be bypassed.These have a bandwidth limitof 10 kHz.

- 13.5 Gb/s data modulestogether with E4809A clock:This module offer a clock pathat speed, so there are no mul-tiplying PLL‘s. This achieves anunlimited bandwidth of theclock path, so a modulation ofmultiple UIs is possible up toclock speed.

Figure 17: ParBERT 81250 Jitter Emulation with a modulated Ext. Clock

Transfer

Frequency

1: linear transfer

2: max. bandwidth

3: suppression

1

2

31

2

3

Cutoff~5kHz

UI

Clock & Data Modules

Ext. Clock Input

Clock Distribution to Modules

A modulated clock is achievedby modulation of a signal gen-erator. Agilent offers varioussignal generators. A signalgenerator provides a sinusoidalsignal, which is fine for theext. Clk input of the ParBERTclock module. The power levelis also sufficient. To establisha modulation, the signal gener-ator again needs a functiongenerator or another signalgenerator as its modulationinput.

15

BER

Time

High RJ

Low RJ

RJ + DJ

Range for Extra-

polation

RJ, Random Jitter, rms

Quality of Fit

DJ, Deterministic Jitter

Extraplolated Total Jitter (for BER 10^-6 to 10^-15)

BER Threshold

Min. BER

Figure 18: 81250 Bath Tub with RJ / DJ

Figure 18 shows three meas-urements of a Bath Tub curvewith three signals of differentjitter content. As a stimulus tothe ParBERT analyzer aParBERT generator is used:

Low RJ: This is the most idealsignal (clean data signal, nomodulation) from a ParBERT3.3 Gb/s generator.

High RJ: This is the modulatedsignal using noise applied tothe control input. As the noisecloses the eye, it reduces thephase margin. The slopes ofthe Bath Tub curves get lesssteep as in the case of nomodulation.

RJ + DJ: This is a modulatedsignal using noise and sinu-soidal modulation. The amountof modulation is set forobtaining the same phase mar-gin as the High RJ signalat theBER threshold of 10- 3. But theshape is different especially forthe ‘shoulder‘ at BER = .25,which is characteristic for theDJ jitter component.

The visualisation of the BathTub Measurement includes atabular format under thegraph, which represents themeasured values. Each signalreads for Phase Margin (out ofthe viewable range), JitterMean, Random Jitter (RMS) =RJ, Deterministic Jitter = DJ,Estimated Total Jitter (whichis an extrapolation value fortotal jitter at a very low BERthreshold, much lower thanmeasured), and finally thereare 4 colums for representingthe quality of fit for the RJ/DJseparation.

All the values can be readeither in time (ps) or in UI(Unit Interval) by configuratingthe Window View.

The RJ extrapolation is donewithin the Bath Tub from arange specified by two pointsfor BER: one is the BERthreshold, the other as a MinBER figure (see Figure 18). Inthe table below the graph,there a 4 colums dealing withthe quality of fit obtained, theR*2 value is the appropriateindicator, this value should bebetween .75 and 1 for goodextrapolation.

16

Figure 19 shows the so calledProperty Window for theparameters defining of theRJ/DJ separation.

Two values of the Bath Tubproperties define the range forthe RJ extrapolation: the BERThreshold defines the uppervalue, the Min BER for RJ/DJseperation defines the lowervalue. In practice, the valuesshould be set to the lowerregion of the Bath Tub curvewhere the slope of the curvesis defined by the random jitteronly. However, the range needsbe wide enough for a coupleof measurement points to beincluded. Otherwise the fit willbe marginal due to insufficientnumber of points.

The Residual BER forEstimated Total Jitter definesthe BER value at which theextrapolated Total Jitter is cal-culated and displayed. Thisextrapolation method savesmeasurement time, as it elimi-nates the need for measure-ments, which at a BER thresh-old of 10-12 or lower themeasurement time is verylarge. So the extrapolationmethod is as fast as the meas-urement for a BER down to10- 6 which can be done withina few seconds of measurementtime.

With help of the Bath Tubmeasurement and the propertysettings, it is also possible toextract the value for the DutyCycle Distortion (DCD) JitterComponent. The duty cycledistortion is the difference ofthe phase margin (horizontaleye opening) for the Bath Tubcurves of separating betweenErrors on ‘0‘s only and Errorson ‘1‘s only. The parametersetup allows the selection forthis settings, indicated inFigure 20. It is not necessaryto take the measurement twice.

Two values defining the range for RJ extrapolation

This value defines the BER value at which the ‚extrapolated‘ Total Jitter is displayed

Figure 19: Bath Tub Properties for RJ / DJ

•DCD is

•Difference of horizontal eye opening for ‘Errors if 0’s Expected and Errors if 1’s Expected

Figure 20: Jitter Measurement, DCD extraction

Simply perform the measure-ment once for ‘All Errors’ andafter the measurement, checkthe values for the phase mar-gin once for ‘Errors if ‘0‘sExpected’, and once for ‘Errorsif ‘1‘s Expected’. The differenceof the two phase margin val-ues is the DCD value.

17

Incoming Data

ExpectedData

Jitter Power

DeterministicJitter

Unlimited Frequency

Post-Processing

Error Function,DSP

Deterministic Jitter can beanalysed for its spectral con-tents. This is a complimentaryview in the frequency domain,while the BERT Scan methodanalyses jitter in the timedomain.

The Jitter Decomposition isgained from a specific meas-urement, which uses an ErrorFunction obtained from thereal-time compare of incomingdata against expected data.The error function is the pass-fail information over a certainnumber of data bits. The con-tent of the error function isprocessed with Digital SignalProcessing Tools (DSP) to visu-alize the spectral information.The DSP tools used are theAutocorrelation, the FurrierTransformation and the powerdensity calculation. The DSPprocessing delivers a powerfactor as a function of fre-quency which is visualized inan x-y graph. The algorithmworks in a wide frequencyrange: from DC up to half ofthe signal’s data rate.

There are two principles togain Spectral Jitter informa-tion:

Firstly, there is the PhaseNoise Measurement.SONET/SDH does all jittertesting according this principle.This uses a Spectrum Analyzertogether with a phase discrim-inator. A discriminator or de-modulator extracts a signalwhich is proportional to thephase deviation in the runningsignal, and the SpectrumAnalyser visualizes the powerfactor versus frequency. Thistype of measurement is possi-ble on clock signals only. Sofor a data signal a CDR (ClockData Recovery) is needed toconvert it into a clock signal.

SpectrumAnalyzer

Phase Noise Measurement:

• Clock only, no Data Jitter

• CDR, Bandwidth limitted

clock

clockdataCDR

Scope

Real Time Scope Measurement (EZJIT):

• Histogram

• Software CDR

• Jitter Trend/Spectrum

• Spectrum is without Bandwidth limitting/rating

data

Similar to ParBERT

Different to ParBERT

Any CDR has its characteristicin terms of bandwidth, so partof the jitter is removed, espe-cially the high frequency part.So SONET/SDH looks at thejitter only within a specifiedbandwidth range. The phasenoise measurement is differentfrom the SpectralDecomposition offered on theParBERT.

Another solution is the JitterMeasurement Software (EZJIT)on the Agilent Infiniium 54850series oscilloscopes. This solu-tion samples a portion of the

data stream. Out of this itruns a software based CDR,and with further help of DSPtechnology, it gains the spec-tral information. This is a sim-ilar methodology to theParBERT implementation.

Figure 21: Jitter Decomposition by Spectrum Analysis

Figure 22: Existing Spectral Jitter Solutions

Spectral Decomposition of Jitter

18

Use of Jitter DecompositionMeasurement:

This type of measurement isembedded within the ParBERTmeasurement suite, as a newmeasurement in the softwaremeasurement package. As it isproviding qualitative informa-tion on the frequencies withinthe Deterministic Jitter budget,it is a DEBUG Tool. So forany kind of design verifica-tion/characterization it canhelp the designer to identifythe root cause of JitterInjection and sources, whichare impossible to simulateeven with todays sophisticatedtools. The final implementationof high integrated ASICS withall kind of analog circuitry(PLL, CDR, ...) within largedigital cores will always giveunexpected results

Another use model is thecharactertization for CDRdevices. Assuming the device isstimulated with a data signalincorporated with JitterModulation consisting of wideband noise (white noise), aCDR will filter this noiseaccording to the bandwidth ofits feedback loop design. Thefeedbacks have a certain band-with, so a jitter supression willoccur beyond this point. Figure24 gives such an example. Alsoone can see if there is somepeaking at the roll-off point.

• DEBUG:

100kHz 10MHz 100MHz

1MHz

Qualitative information on

frequency components within jitter

budget

Example: interference of 1 MHz signal

• Frequency Range of Jitter components not limited by bandwidth -> Inband and Outband frequency spectrum

• CDR can be characterized for all parameters:

InBand TransferJitter

PeakingOut BandTransfer

RollOff

1MHz

Tx PLL Bandwidth

InBand TransferJitter

PeakingOut BandTransfer

RollOff

1MHz

Tx PLL Bandwidth

CDR

Signal processing

Data with white noise

Outband Jitter is phase difference which CDR cannot compensate due to cut-off:

Amplitude

Frequency

Figure 23: What ParBERT’s Jitter Decomposition is good for (1)

Figure 24: What ParBERT’s Jitter Decomposition is good for (2)

19

The Jitter Modulation on adata signal (in this case asinusoidal modulation isassumed) causes the data sig-nal to toggle around the idealsampling point within the eye(on the right in Figure 25).For this measurement thecomparator strobe will be dis-placed by 0.5 UI from the nor-mal sampling point within thecentre of the eye. So the sam-pling occurs within the transi-tion (left in figure). Now whensampling and comparingagainst expected data, therewill be errors for those datacycles where the data is ‘late‘due to jitter. If the data is‘early‘, the sampling and com-paring deliver no errors. Nowthis stream of errors and noerrors is called the ‘ErrorDensity Variation or ErrorFunction‘. Within the ParBERTthis Error Function is gainedfor a configurable block lengthand stored in a memory.

Figure 26 explains the creationof the Error Function: At thetop is a sinusoidal jitter mod-ulation signal applied to aclock signal (middle). The edgeposition of the ideal positionsof this clock signal is dotted,and the position is straightdue to the modulating signal.Analyzing the modulated signalwith strobing at the ideal posi-tion and comparing against ‘1‘,create the errors as shown inthe bottom row of the table.As long as the modulating sig-nal delays the data cycles,there are errors; as long asthe modulation accelerates thedata signal, there are noerrors.

BER

BitTime

Strobe

ErrorDensityVariation

Eye Center

BER

BitTime

Strobe

ErrorDensityVariation

Eye Center

JitterModulation

Time

JitterModulation

Time

0.5UI

Sinusoidal Modulation Signal

Modulated data

Error Signal

So far it would make no dif-ference if the modulating sig-nal were sinusoidal, triangle orrectangle. Within this idealdescription the period/frequen-cy of the modulating signal isrecorded, but the shape wouldbe lost.

Figure 25: Basics of Method (1): Modulated Signal at Comparator

Figure 26: Basics of Method (2): Error Density Variation

Basics of the Jitter Decomposition Method

20

Figure 27 is a similar way oflooking at the method of sam-pling. This assumes that theincoming datastream runs frombottom to top. The sampling isset to strobe within the transi-tional area. The process is notideal because there is alwayssome noise within the sam-pling. Either this noise isincorporated with the incomingsignal or the there is noise(jitter) on the sampling edgeitself. In reality both willoccur. Normally a test systemis designed to reduce thisnoise to a minimum. Noise canactually very helpful for thistype of measurement. Whenlooking into the ErrorFunction, the noise will dis-place the positions of theerrors according to the shapeof the modulating signal. Soover the longer time, a sinu-soidal signal can be recognisedas sinusoidal, as long as theError Function is recordedlong enough. So the full spec-tral information is embeddedand the later DSP processingwill identify the whole spectralcontent. The digitizing does notchange the spectral content.

The ParBERT Waveform Viewerallows the Error Function tobe visualized. Errors appear inred in the GUI. They appearas a lighter grey in Figure 28.In this case a 1 MHz sinu-soidal modulation generates jit-ter on a data signal running at3.125 Gb/s. One can clearlysee that the error distributionoccurs with the period of themodulating signal. The randomnoise involved generates somedisplacement.

Jpk-pk

JitterModulation

CompareErrorSignal

OffsetStrobeposition

Jitter histogram

Dat

a-ey

e

Threshold

Optimalstrobeposition

Bit

Tim

e

Time(long term)

Same spectral content

3125 samples =1us (1MHz)

Figure 27: Basics of Method (3): The Noise is important

Figure 28: Error Density Modulation (1MHz Sinusoidal Jitter)

21

Already mentioned is that thenoise is important for thistype of measurement. As longas the noise is of similar mag-nitude to the DeterministicJitter, this will operate as alinear method So the spectrumof the Deterministic Jitter islinear in the error functionand the DSP algorithm oper-ates cleanly. If there is moreDeterministic Jitter than ran-dom jitter, the error functiongets clipped and operates inthe ideal way (as describedearlier). Therefore the shape ofthe modulation gets lost, whichcauses the DSP processing togenerate Harmonics, whichoccur if there is a modulationwith rectangular signals.Within the spectral view onewould see the Harmonics as arectangular waveform.

Some examples

This is the setup for someexamples: A ParBERT genera-tor (3.3 Gb/s, E4862B or 13.5Gb/s, N4872A) is modulatedvia the ‘Control Input’. We usethree different signals for jittermodulation: sine wave (1 MHz),Pulse with 10 MHz and 10%Duty Cycle (Width 1 us) andNoise with 80 MHz bandwidth.All these signals can beachieved with an Agilent33250A Arbitrary WaveformGenerator.

The generator output connectsby loop-back cable to an ana-lyzer. Any ParBERT analyzercan be used with the SpectralDecomposition Measurement aslong as the data rate is withinits operating limits.

Sinusoidal signal and noise floor are of similar magnitude

-> linear Spectrum

Sinusoidal signal is much larger than noise floor

-> non-linear Spectrum, Distortion, Harmonics

X(t)=Gauss(m=0, s ) + A*cos(2pft)

1 MHzSine

80 MHzNoise

Delay ControlInput

3.125

Gbps

Analyz

er

3.125

Gbps

Gener

ator

10 MHzPulse

10% Duty33250A

Figure 29: Sinusoidal Signal and Noise, Harmonic Distortion

Figure 30: Simple Loop-back Measurements with help of Generator’s Delay Control

22

Jitter Decomposition Examples

Sine Wave: The graph repre-sents a single line at a singlefrequency (top left on Figure31).

Pulse: This delivers a spectrumaccording the sin x/x shape(top right on Figure 31).

Noise: There is a spectrum ofconstant energy level up to thebandwidth of the noise source(80 MHz). Then the powerdecreases to the noise floor ofthe system (bottom left onFigure 31).

The Spectral Decompositionoffers a couple of parametersfor setup and configuring theresults. Figure 32 shows theViewing parameters. First ofall one specifies the PowerScaling. This allows a setup forcalibrating the jitter powerscale with a pilot tone. Themeasured jitter spectrum willbe referenced power wise tothis reference signal.

Then it allows the FrequencyRanges to be specified. Thesewill be highlighted as shown inthe figure before. Furtherchoices are on scaling of axis,markers and range of x-axis.

Sinusoidal (1MHz, 0.08UI pp)

Pulse with 10% Duty Cycle 0.15UI pulse jitter injection (Period 10us, Width 1us ->

sin(x)/x shape

Noise

(80MHz, 0.04UI rms)

Snapshot of the Parameters

affecting the measurement

Figure 31: Jitter Decomposition Examples

Figure 32: Calibration and Pilot Tone

23

Windowing reduces the effects of unwanted frequency components by the Fourrier Transformation due to finite length of acquired bits

Some more literature:

• The Fundamentals of Signal Analysis 5952-8898E

• On then Use of Windows for Harmonic Analysis with the Discrete Fourier Transform, IEEE, Vol. 66, No. 1

• A Refresher Course on Windowing and Measurements, Real-Time Update, Hewlett-Packard

• The Fundamentals of FFT-Based Signal Analysis and Measurement, AN041, National Instruments, is Source for:

Windowing

Windowing reduces the effectsof unwanted frequency compo-nents by the FurrierTransformation due to thefinite length of acquired bits.Some literature references aregiven in Figure 33 with theprimary recommendation for‘The Fundamentals of SignalAnalysis (AN243)’ available as:5952-8898E from Agilent Lit-station or from the web(www.agilent.com). [7]

There are three predefined fil-ters selectable from the config-uration: Hanning, Hammingand Blackman. Uniform is nota filter, but uses the data asmeasured. The filters reducethe amount of energy in theunwanted signal areas muchlarger than in the areas ofinterest.

There is a dependency betweenfrequencey resolution andacquisition depth. The longerthe segment of the Error func-tion, the lower the frequency.But this is also a matter ofthe data rate. This is of coursea function of measurementtime. Using a segment below 1MBit, let the measurement runwithin a few seconds. LargerAcquisition Depth will slowdown the measurement time.Frequency Resolution alsodefines also the minimum fre-quency. Therefore if the reso-lution is 1 kHz, then the firstenergy line is available at 1kHz, the next is at 2 kHz andso on.

Figure 33: FFT Windowing

Figure 34: Frequency Resolution vs. Data

24

References

[1]: NIST Technical Note 1337,“Characterization of Clocks andOscillators,” edited by D.B.Sullivan, D.W. Allan, D.A.Howe, F.L. Walls, 1990

[2]: National Committee forInformation TechnologyStandardization (NCITS)T11.2/Project 1230-DT “FibreChannel – Methodologies forJitter and Signal QualitySpecification” Rev. 5.0,February 21, 2002

[3]: Jan B. Wilstrup: A newmethod for jitter decompositionthrough its distribution tail fit-ting, ITC 1999

[4] Agilent Jitter InjectionModule (JIM), 5988-3583EN

[5] 10GbE Standard IEEE802.3ae

[6] Infiniium 54850 SeriesOscilloscopes, 5988-7976EN

[7]: The Fundamentals ofSignal Analysis, Agilent AN243,5952-8898E

MS Windows NT, Windows 2000 and Microsoftare U.S. trademarks of Microsoft Corporation.

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