timimg jitter in bandlimited systems - …midas.herts.ac.uk/helpsheets/tims/tims experiment...

timimg jitter in bandlimited systems copyright robert radzyner 2003 Vol D3 ch 05, rev 1.0 - 39

TIMIMG JITTER INTIMIMG JITTER INTIMIMG JITTER INTIMIMG JITTER INBANDLIMITED SYSTEMSBANDLIMITED SYSTEMSBANDLIMITED SYSTEMSBANDLIMITED SYSTEMS

PREPARATION................................................................................. 40

taming timing jitter.................................................................... 40

to do before the lab.................................................................... 41

what we will do ......................................................................... 41

EXPERIMENT................................................................................... 42

overview.................................................................................... 42

setting up with Bessel filter....................................................... 43

BER measurements ................................................................... 46

with Butterworth filter............................................................... 46

TUTORIAL QUESTIONS ................................................................. 48

40 – Vol D3 ch 05, rev 1.0 timimg jitter in bandlimited systems

TIMIMG JITTER INTIMIMG JITTER INTIMIMG JITTER INTIMIMG JITTER INBANDLIMITED SYSTEMSBANDLIMITED SYSTEMSBANDLIMITED SYSTEMSBANDLIMITED SYSTEMS

ACHIEVEMENTS: we observe how timing inaccuracy affects the performance ofdigital detection in systems operating over bandlimited channels. Thisexperiment demonstrates the relationship between bandwidthefficiency and BER when the decision process is subject to timingjitter.

PREREQUISITES: completion of the experiment entitled BER measurement inthe noisy channel (Volume D2, Chapter 1)

EXTRA BASIC MODULES: 2 * ADDER, SEQUENCE GENERATOR,

ADVANCED MODULES: BASEBAND CHANNEL FILTERS, DECISIONMAKER, DIGITAL UTILITIES, ERROR COUNTING UTILITIES,LINE-CODE DECODER, LINE-CODE ENCODER, NOISEGENERATOR, WIDEBAND TRUE RMS METER,

SCOPE: availability of a digital or PC-based oscilloscope would be an advantage foreye pattern displays.

PREPARATIONPREPARATIONPREPARATIONPREPARATION

taming timing jittertaming timing jittertaming timing jittertaming timing jitterAs described in other experiments, there are numerous hurdles to jump over to getdigital messages from one place to another without errors, for example, noise,intersymbol interference (ISI), base-line wander. In these experiments, ways to dealwith these difficulties are investigated, such as pulse shaping and line coding. Inexperiments about digital communication over bandwidth limited channels (see theexperiment entitled ISI: PAM and ASK over bandlimited channels in this Volume)we discover that ISI can be avoided by using Nyquist pulse shaping, provided thatdetection takes place at the “proper” instant in the symbol interval.

However, getting the timing right is a challenge in itself – in most of the TIMSexperiments we get around this by using “stolen” clocks. Extracting accurate symboltiming from the received signal, as has to happen in “real life” systems, is not trivial !(see Vol. D2, Chapter 3, entitled Bit clock regeneration). Even when a stable timingclock is generated from the received data waveform, the arrival time of an individual

timimg jitter in bandlimited systems Vol D3 ch 05, rev 1.0 - 41

symbol is unlikely to be in exact alignment with this clock – there will be a lot moremissed shots than “bulls eyes”! This variation about the desired decision instantis called “timing jitter”.

In this experiment we assess the performance of band-limited systems operating withNyquist formatted pulses in the presence of timing jitter induced ISI leakage. Thisissue is also considered in the experiment entitled ISI: pulse shaping for bandlimitedchannels (this Volume). In that experiment the focus is on the generation of wellbehaved Nyquist pulse shapes. In this lab we measure and compare performance inthe presence of timing jitter and noise when pulse shapes are excellent, and when notso good.

to do before the labto do before the labto do before the labto do before the labThis lab involves bit error rate (BER) measurements described in detail in theexperiment of Vol D2, Chapter 1, entitled BER measurement in the noisy channel.The procedure is similar to that used in the experiment entitled Base-line wanderand line coding (this Volume).

A brief review of this work will save time getting your system ready to use.

what we will dowhat we will dowhat we will dowhat we will doWe set up a basic bandwidth limited baseband test system for BER measurements inthe presence of additive noise. A selection of Nyquist or near Nyquist pulseformsare assessed for their sensitivity in the presence of timing jitter. Pulseforms thatgenerate eye patterns with “wide” horizontal opening of the inner envelope can beexpected to have less sensitivity to timing errors. Several of the TIMS filters aresuitable candidates for this purpose. The Bessel filter has the best performance.This will be compared with the Butterworth case. Other interesting cases are thelinear phase “Opfil”, and Butterworth combined with the RC LPF in the UTILITIESmodule. The elliptic filter in the TUNEABLE LPF provides excellent bandwidthefficiency at the price of high sensitivity to timing jitter.

The investigation consists of BER measurements with and without timing jitter. Thespread of test jitter is chosen to match the signals under test (40 –50 µs . Wemeasure the minimum SNR required to deliver a given BER – 40 per 100,000binary symbols is a convenient figure. Clearly, a low minimum SNR corresponds tohigh noise immunity.

Hence, the performance indicator is the additional SNR needed to meet the BERrequirement when jitter is introduced, i.e. the loss of noise margin, expressed in dB.The smaller this quantity, the better the performance.

It should be noted that the test set-up used here is not intended to model a real lifesystem. Its purpose is to provide a platform for generating timing errors andmeasuring the consequent degradation of SNR margin under various controlledconditions. For example we shall not be concerned with filtering of out-of-bandnoise. Moreover, the jitter effect is produced by varying the sampling instant in theDECISION MAKER, it is the variation in the arrival time of the pulse that is themore likely cause of timing error in practice. Naturally, multi-level examples are ofinterest, but outside the scope of this exercise.


EXPERIMENTEXPERIMENTEXPERIMENTEXPERIMENT

overviewoverviewoverviewoverviewThe set-up is essentially the same as described in other experiments. The procedureis similar to that used in the experiment entitled Base-line wander and line coding(this Volume). The only new feature is the jitter emulator (see Figure 1). Theexternal control input of the DECISION MAKER makes possible straightforwardphase modulation of the decision point by means of a time varying voltage. Asinusoidal variation is used for convenience1.

ERROR COUNT

TRANSMITTER RECEIVER CHANNEL

CLOCKED X-OR

LINE CODE

DECODER

INSTRUMENTATION

make and break for alignment

DETECTOR

NOISE

SEQUENCE GENERATOR

PRBS sync

reset bit clk

SEQUENCE GENERATOR

PRBS sync

reset bit clk

gate

MASTER CLOCK

8.333 kHz

2.083 kHz

stolen bit clock

bit clock retimed

Bandlimited Baseband Channel

LINE CODE

ENCODER

jitter implementation

Figure 1: Block diagram of the set-upWe use a symbol rate of 2083 per second as this is the best frequency for themonostable circuit in the DECISION MAKER. A spin-off is that the clock isobtained from MASTER SIGNALS.

Once the model has been set up and validated (using a Bessel waveform) timingjitter is introduced and the additional SNR needed to maintain the specified BER canbe determined. The experiment consists of repeating this with other filters, such asButterworth. It should be noted that while the elliptic filter yields interesting results,tuning for a suitable eye pattern is sensitive, and requires a little patience and care.

An additional exercise is to carry out the measurements with a fixed offset of thedecision point, and to compare the noise margin loss with the sinusoidal modulationcase.

Measurements of the gradients of the inner envelopes of the eye patterns will make itpossible to assess the ISI leakage generated by the jitter, hence provide a basis forpredicting the noise margin loss, and comparison with the direct measurements.

1 Although this may not reflect the characteristics of timing jitter in real life systems, there are severaladvantages in using a sinusoidal variation. The most important is ease of control and observation, sincethe maximum excursion is well defined. With a sinusoidal variation, the majority of the decision pointswill occur near the extremities of the range, representing a worst-case scenario.


setting up with Bessel filtersetting up with Bessel filtersetting up with Bessel filtersetting up with Bessel filterWe patch up the model for measuring BER over a noisy channel as depicted inFigure 2. It is similar to that examined in Experiment D2-01, entitled BERmeasurement in the noisy channel, to which you should refer for setting upprocedures. It includes BER measurement instrumentation.

Two additional modules have been added, namely an AUDIO OSCILLATOR and anADDER. They supply an AC signal to modulate the decision point of theDECISION MAKER.

data out Z-MOD

stolen bit clock

bit clock re-timed

?

DC supply

jitter source

data in

Figure 2: the model

T1 before inserting the SEQUENCE GENERATOR select a short sequence (on-board DIP switch with both toggles UP).

T2 patch up the model of Figure 1 up to the BASEBAND CHANNEL FILTERS(reminder: clock frequency division by four in the LINE-CODEENCODER).

T3 select the BESSEL FILTER from the BASEBAND CHANNEL FILTERS (frontpanel switch to channel 3), and DC on the other front panel switch.

T4 choose the BIP-RZ output on the LINE-CODE ENCODER.

T5 synchronize the scope to the SYNCH output from the SEQUENCEGENERATOR, and verify that a snapshot of the sequence at theBASEBAND CHANNEL FILTERS output is correct (Fig. 3a Xxx).


Figure 3: Bessel (a) snapshot and (b) eye patternT6 before inserting the DECISION MAKER set the on-board rotary switch SW1 to

NRZ-L (not BIP-RZ)2 , and the on-board switch SW2 to EXT.

T7 patch up the remainder of the model of Figure 2, i.e. the NOISEGENERATOR3, the DECISION MAKER and associated externaldecision point control set-up, the LINE-CODE DECODER and theBER instrumentation. Choose the NRZ-L line code on the LINE-CODE DECODER. Set both SEQUENCE GENERATOR modules to ashort sequence (both toggles of the on-board DIP switch UP).Synchronize the scope to the SYNCH output from the first SEQUENCEGENERATOR, for displaying sequence waveform snapshots.

T8 temporarily disconnect the noise input and the sinusoidal modulation at theexternal decision-point control ADDER. Set the signal level at theDECISION MAKER input to (approx) 1.6 V p-p. Using the externalvariable DC control voltage4, guided by the bright spot on the eyepattern5, carry out a preliminary adjustment of the position of thedecision instants to occur at the peaks of the message pulses. Finetuning will be done later when we have the eye pattern displayed.

T9 observe the outputs of the DECISION MAKER and LINE-CODE DECODER,and verify that the transmitted sequence has been correctlyregenerated. Note the time delay between the transmitted andregenerated sequences.

2 BIP-RZ is used in the transmitter to produce an eye pattern of better quality in terms of ISI thanpossible with NRZ-L excitation. The output of the filter is effectively NRZ-L, and is decoded as an NRZ-L formatted pulse stream.3 In a representative model the bandwidth of the noise would be limited to the bandwidth of the channel.To simplify the setting up we insert the wideband noise from the NOISE GENERATOR after the filtermodule. This does not affect the validity of our measurements since the error generation mechanismremains unaltered.4 Since the variable DC source is already taken up for DC offset adjustment of the message waveform, itis recommended that the 5V TTL source be used for the DECISION POINT control set-up.5 If you do not have access to a scope with compatible z-modulation, DOWN (falling) transitions of theB.CLK output can be used to indicate the position of the decision point.


T10 using the procedure described in the Experiment in Vol. D2, Chapter 1,entitled BER measurement in the noisy channel confirm that thesecond SEQUENCE GENERATOR is properly aligned6, and thatthe error count is zero7 at the X-OR output in the ERROR COUNTINGUTILITIES.

We return now to eye patterns for fine tuning, and set up for jitter modulation.

T11 re-set the SEQUENCE GENERATOR modules to a long sequence (bothtoggles of the on-board DIP switch DOWN). Synchronize theoscilloscope to the clock of the SEQUENCE GENERATOR, andobserve the eye pattern at the input of the DECISION MAKER(without noise at this stage). Check the DC offset. For this experimentthere is no need for adjustment if the offset is in the order of 30 mV orless.

T12 verify that the decision point can travel up to around 50 µs either side of thepoint of maximum eye opening. If you encounter the end of theadjustment range below this value, use the INVERTER in theDIGITAL UTILITIES module to produce a 180 degree shift (240 µs)in the input B.CLK, and check again. Align the decision point to fallon the position of maximum eye opening.

This is a good opportunity to adjust and verify the jitter control.

T13 re-connect the sinusoidal signal to the input of the external decision pointcontrol ADDER. Set the frequency of the sine wave to around 800 Hz.Gradually increase the corresponding gain of the ADDER andobserve the oscillations of the decision point on the eye pattern. Adjustthe gain to generate approximately 40 µs of travel either side of thecentre position. If needed, alter the frequency of the sinewave.Disconnect the sinewave until required for jitter measurements later.

T14 record the appearance of the eye pattern. Measure and record the p-pamplitude of the inner envelope of the eye pattern at its maximum.Repeat this 40 µs either side of the maximum.

T15 re-confirm that the second SEQUENCE GENERATOR is properly aligned,and that the error count is zero at the X-OR output in the ERRORCOUNTING UTILITIES.

6 The alignment procedure should be carried out with snapshot displays. If you experience problemsgetting the second SEQUENCE GENERATOR to lock, the problem may be an inversion of the sequenceahead of the DECISION MAKER.7 Reminder: the number of errors is the counter reading minus 1.


BER measurementsBER measurementsBER measurementsBER measurementsT16 re-connect the noise input. Gradually increase the noise level until you begin

to register errors (if needed, refer to the Experiment in Vol. D2,Chapter 1, entitled BER measurement in the noisy channel for thedetails of the procedure). Set the noise level to obtain a BER near 40in 100,000. Using the WIDEBAND TRUE RMS METER measure andrecord the RMS noise voltage at the input of the DECISION MAKER(temporarily disconnect the message to do this).

T17 again using the WIDEBAND TRUE RMS METER measure and record thesignal voltage at the input of the DECISION MAKER (with noisedisconnected). Calculate and record the SNR in dB.

T18 repeat T16 with the jitter modulation re-connected. Verify that the peak jitteris approx. 40 µs. Carefully adjust the noise level to obtain the sameBER as closely as manageable (repeat the BER count a few times ifneeded). Record the results as in T16, and note the difference in SNRfor the two cases (expressed in dB).

This SNR increase is needed to offset the degradation of the BER when timing jitteris introduced. It represents the noise margin loss due to the timing jitter.

T19 repeat T16 with a 40 µs fixed offset of the decision point instead of sinusoidaljitter. Again, carefully adjust the noise level to obtain the same BERas closely as manageable (repeat the BER count a few times ifneeded). Record the results as in T16, and note the difference in SNRfor the two cases (expressed in dB).

The outcome in T19 should be a greater loss of noise margin compared with T18.Moreover, you should also compare this with the measurements carried out in T14.To do this, simply reduce the effective SNR according to the amplitude ratio at 40 µsoffset relative to the peak.

with Butterworth filterwith Butterworth filterwith Butterworth filterwith Butterworth filterThe eye pattern obtained with a Butterworth filter is relatively narrow compared tothe Bessel case. Hence we can expect an increase in sensitivity to timing jitter. Thechanges required for the SNR measurements are set out below.

T20 first select the BUTTERWORTH FILTER from the BASEBAND CHANNELFILTERS (front panel switch to channel 2). Verify that the other frontpanel switch is set to DC.

T21 re-set the SEQUENCE GENERATOR modules to a short sequence (bothtoggles of the on-board DIP switch UP).


T22 synchronize the scope to the SYNCH output from the SEQUENCEGENERATOR, and verify that a snapshot of the sequence at theBASEBAND CHANNEL FILTERS output is correct (Fig. Xxx).

Figure 4: Butterworth (a) snapshot and (b) eye patternT23 repeat the adjustment and verification procedures as with the Bessel filter. If

needed, remove the clock inversion to obtain the desired range for themodulation of the decision point.

T24 measure the loss in noise margin due to jitter using the same value of peakjitter. Also repeat the measurement with fixed offset. Using themeasurements in T14, compare the gradients of the eye envelopes forthe two cases near the centre of the detection range, and determinewhether the difference in SNR margin loss is consistent with thesegradient estimates.

T25 (optional) repeat the exercise with an elliptic filter (TUNEABLE LPF). Inthis case you will need to tune the filter to generate a suitable eyepattern (obtainable at 3dB bandwidth setting near 2kHz).

The eye pattern of the elliptic filter is even more narrow than the Butterworth case.While bandwidth efficiency with the elliptic characteristic is significantly greaterthan with Butterworth (or Bessel), the penalty is a much higher sensitivity to timingjitter. The elliptic filter waveform also has a much higher ratio of peak amplitude toamplitude at the detection (Nyquist) point (for a given noise level, it is the amplitudeat the detection point that determines the BER). Since the permissible signal poweris usually determined by the peak amplitude, the effective SNR is significantlypenalized by the high peaking ratio. Thus, the high bandwidth efficiency of theelliptic channel is of dubious value when timing jitter and peak power limitations areconsidered. Even if you don’t have the time to carry out all the measurements, it’sworthwhile at least to examine the eye pattern and snapshot of the elliptic case.


TUTORIAL QUESTIONSTUTORIAL QUESTIONSTUTORIAL QUESTIONSTUTORIAL QUESTIONSQ1 Were you impressed by the clean lines of the Bessel eye pattern? Did you

notice how the inner envelope is neatly circumscribed by twosinewaves?(see Figure 3b).

a) In Task T14 you measured eye envelope amplitudes at the maximum and at40 µs offset. Bearing in mind that 40 µs represents π/6 rad, confirm thatthe ratio of the two amplitudes is 0.866, i.e. 1.25 dB. Does this agree withyour lab measurements?

b) Confirm that the jitter range used in this experiment (i.e. 80 µs), represents16.7% of the symbol interval. We made use of this relatively large rangefor effect and for ease of measurement. In practice, the range is likely tobe considerably smaller. Suppose in some application we are dealing witha range of 4%, i.e. ±2%. Again, noting the sinusoidal shape of the eyeenvelope, obtain the amplitude reduction factor at the extremities of thisrange (i.e. offset of 9.6µs).

c) It’s interesting to discover yet another advantage of the Bessel eye pattern.Let’s compare the result in (b) with the Butterworth case. The eye patternsare significantly different. The peak of the Butterworth envelope is at theintersection of two curves meeting quite sharply (as shown in Figure 4b).On the basis of your measurements in Task T24 (or by inspection of Fig.4b) estimate the reduction in eye opening for the same offset 9.6 µs as usedfor the Bessel eye in (b) above, and compute their ratio. Compare this ratiowith the ratio obtained when the offset is 40 µs, as used in the lab. Describewhy the Bessel eye performance advantage is much greater when jitterlevels are low.

d) Suppose the probability of error in the absence of timing jitter is 10 –4.Using the results in (b) and (c) above, and assuming the amplitudedistribution of the noise is normal (gaussian), calculate the probability oferror at a timing offset of 9.6 µs for the Bessel and for the Butterworthcases, respectively.

Q2 In this question we consider a method for estimating noise margin lossresulting from timing jitter when the jitter distribution is known.

We make up a hypothetical example in which the jitter distribution isdiscrete, with seven timing offsets, 0, ±10, ±20, ±30 µs,respectively. Unlike the situation in the lab, we suppose a binomialdistribution, i.e. with probability decreasing as timing errorincreases. Using the results obtained in the lab and the toolsdeveloped in Q1, estimate the average loss of noise margin foreach filter for this jitter distribution.


Q3 Obtain the probability distribution for the sinusoidally modulated jitteremulation used in the experiment. Discretize this as a 13-cellhistogram to compute an alternative to the result in Q2. Beforestarting, predict which of the jitter distributions will give the morepessimistic prediction, and which makes the difference betweenButterworth and Bessel greater.

Q4 Suppose we are operating in a low noise channel, with SNR better than40dB, say. This provides an opportunity to consider increasing the bittransfer rate through the application of multi-level formatting. Notethat the effective SNR is reduced by 6dB each time the inter-levelspacing is halved.

Could this possibility be successfully exploited in a scenario like the one wemodelled in this experiment, in the presence of frequent jitterexcursions exceeding 30 µs? Suggest an upper bound on effectivejitter range to provide a reasonable chance of success for a four-level scheme, assuming the Bessel channel model 8.

Compare this with the outcome for eye patterns generated by joiningNyquist nodes by straight line. Would this result be suitable as anestimate for the Butterworth case?

8 You could synthesize a four-level eye pattern based on sinusoidal transitions and estimate the shape ofthe eye envelopes near the detection points from the maximum amplitudes. Three-level Bessel eyepatterns are used in the experiment entitled Base-line wander & line coding (this Volume; seeFigure 5b).

timimg jitter in bandlimited systems - …midas.herts.ac.uk/helpsheets/tims/tims experiment...

Documents