Estève, R

Jiménez de Parga, A

Mota, B

Musa, L

CERN Document Server

Digital Implementation of a Tail Cancellation Filter for the Time Projection Chamber of the ALICEExperiment.Mota B., Musa L., Esteve R., Jimenez de Parga A.CERN, 1211 Geneva 23, SwitzerlandBernardo.Mota@cern.chAbstractIn the ALICE TPC (Time Projection Chamber), the readoutchambers are conventional proportional chambers with cathode padreadout. The pad signal has a rather complex shape, which dependson the details of the chamber and the pad geometry, characterised bya long tail due to the motion of the positive ions. Since the zero-suppression has to be done before the data transfer, the high channeloccupancy calls for a very precise tail cancellation. In order to becompatible with the required dE/dx resolution, a suppression to 0.1%or better of the maximum pulse height, is required. We present adigital implementation of a shortening digital filter based on theapproximation of the tail by the sum of exponential functions. Thehardware implementation of the filter is described and the resultsanalysed.I. INTRODUCTIONThe ALICE TPC [1], [5] is a gas detector, of cylindrical shape,with a sensitive gas volume of about 80 m3 subdivided into driftspaces by a central high voltage plane. A charged particle passingthrough the gas volume creates electrons by ionisation. The electronsdrifting in the electrical field towards the readout chamber, wherethey are amplified in the field of the sense wires. The signal iscoupled to the pads (570 000), which are at few mm distance behindthe sense wire-plane. The charge collected on each pad, integratedand subsequently shaped, is sampled at 5.66MHz over the 88ms driftime.A single readout channel is comprised of three basic units: acharge sensitive preamplifier/shaper (PASA); a 10-bit 5.66 MHzlow-power ADC; and an ASIC that contains a shortening digital forthe tail cancellation, the baseline subtraction and the zero-suppression circuits [2]. The large granularity of the TPC (2.85x108samples), leads to event sizes of 356Mbyte/event and a data volumein the front-end electronics which is far beyond of present data-handling techniques. To achieve the necessary rate capability –about 200 events/s written to permanent storage – data has to be pre-processed directly in the front-end before it is transferred to theDAQ system. One way to compress the data stream is to discard“zero” data. According to M ntecarlo simulations the zero-suppression in the front-end will reduce the data throughput by afactor of 4. However, owing to the high channel occupancy (up to40%), the traditional zero-suppression algorithms are very inefficientdue to pile-up effects. The minimisation of such effects requires avery precise tail cancellation, 1‰ or better of maximum pulseheight, which implies the design of a very accurate digital filter.A technique to cancel the tail was developed for a proportionalchamber and implemented in a analogue circuit based on discretecomponents proposed in [3]. The same technique underlies the tailcancellation scheme used in the preamplifier/shaper circuitdeveloped for the readout of the CERES TPC [4]. The accuracy of ashortening filter realised by discrete analogue network is limited bythe tolerance of the components. Owing to the poor precision in thematching of the passive elements, provided by the current integratedcircuit technologies, an analogue filter would not reach the1‰accuracy if it has to be built in an integrated circuit with no externaltuneable components. On the other hand, individual tuning wouldnot be feasible considering the number of circuits to beimplemented. A digital circuit allows better control of therequirements by choosing the word length and type of arithmetic.Flexibility is also given by the possibility of reconfiguring the digitalsignal processing operations by changing programmablecoefficients. With a digital circuit, we can cope with different signalshapes due to the chamber geometry and gas mixturesIn section II of this paper, the basic idea of approximating thetail by the sum of three exponential functions will be addressed.Section III describes the VLSI implementation of the circuitperforming the digital filtering operations and the comparison ofseveral structures according to area and error versus word length.The results of such implementation for measured signals using twodifferent amplifiers are given on section IV. Section V concludes thepaper.II. BASIC CONCEPTThe tail of the signal received from the TPC analogue readout,is(t), can be approached by the sum of n exp nential functions:Where r(t) is a residual function due to the error of theapproximation. The sum of the gains Ai should be one so that inputand output have the same height. The input signal can be expressedin the Z domain as:The signal is passed through a linear digital network that cancelsall but the fastest of the exponential terms. The n-1 pole-zeronetwork has a transfer function that expressed in the Z domain is:The numerator of F(z) will perfectly cancel all the poles of Is(z)except one. The constants L1, L2,..,Ln-1 are chosen such that thenumerator of the expanded form of Is(z) disappears. The response ofthis linear network to the incoming signal is the convolution in thetime of the impulse response function of the filter and the signalitself:One can easily observe from this expression that theperformance of the tail cancellation is strongly related to r(t). Theremaining fast exponential is a constraint of the system and can bechosen such that:)()(10 treAItis itnii +´´=×-=å taå =<<<<<<1...21inAttt).....1())./exp(1))..(./exp(1()(1122111112-------+++---=nnnzLzLzLzTzTzFatat)(*)()/exp()(*)( 00 tftrttItftis +-= a%1.0)/exp( 0 <- tt a st m1³)()./exp(1.)(110zRzTAIzIsni ii +-= å=-atThe Tail Cancellation scheme can be shown in a block diagram:Figure1: The Tail Cancellation schemeThe digital signal from the ADC is approached by n exponentialfunctions. From the coefficients (gains and exponents), one canderive the Z transform, H(z), impulse response function of the inputsignal. The coefficients of the filter F(z) are chosen so that theproduct of F(z) and H(z) is the Z transform of the fastest exponential.It should be noted that as the coefficients of the filter depend on theapproximating exponential functions (gain and exponent), some setsof parameters generate unstable filters. It is common on the casesanalysed that the filter poles tend to be quite close to the unit circleand stability problems occur if care is not taken when coding thecoefficients [7].III. HARDWARE IMPLEMENTATIONIn case of the ALICE TPC signal shape, approximations with 3and 4 exponential functions were considered, generating IIR filtersof order 2 and 3 respectively. There are numerous architectures forimplementing such filters [6], [8]. In this section three differentstructures were analysed and compared in terms of area for a givenword length, and error as function of the number of bits. Both casesuse fixed-point arithmetic. Figure 2 shows the three differentstructures analysed. Filter A is a Direct Form realisation, Filter B is aLattice-Ladder structure and Filter C two first order filters cascaded.These filters were synthesised using a 0.35-micron CMOS process.The comparison in terms of area is shown is table 1 for 18-bit filters.Figure 3 shows the Error as function of the number of bits for thethree structures.Table 1: Silicon area for Filter A, B and C for 18-bitFilter A Filter B Filter CArea (mm^2) 1.024 1.901 1.068From these values, one concludes that Filter C reaches thehighest accuracy for a given number of bits. Its area is notconsiderably higher than Filter A. When implementing Filter C, onehas access to the poles and zeros directly via the registersFigure 2: Filter A (top), B (middle) and C (bottom)Figure3: Sum of the squared errors expressed in LSB as function of thenumber of bits.IV. RESULTS WITH MEASURED SIGNALSMeasurements were performed using a TPC prototype with thesame cathode plane layout as the ALICE TPC, operated with ArCH495% - CO2 5%. Two different analogue amplifiers were used: theNA35/ALEPH and the NA49-FTPC Preamplifier/Shaping Amplifier[9]. The two amplifiers produce signals with different shapestherefor have to be treated using different approximations.v2b1b2a1a2z1z1z1z1z1z1Scope3Scope2Scope1[X,Y]Input2[X,Y]Input1[X,Y]InputK1K0K1L0K1K0K0K1v1 v014 15 16 17 18 19 20 21 22 230.8850.890.8950.90.9050.91Error versus #bits for all stable configurations#bitsError Power in LSBFilter AFilter BFilter CADC quantizedinput signaln exponentialaproximationPole - Zero Transferfunction in the Z-DomainOutput of theDigital FilterResultH(z) = C1 - gz-1B1 - bz-1A1 - az-1 +F(z) H(z) = 11 - az-1+A. NA35/ALEPH Preamplifier/Shaping AmplifierThe input of the Digital Filter is shown in figure 4. We can seethat this amplifier induces an initial undershoot before the beginningof the tail itself at 1 microsecond. Figure 5 and figure 6 showrespectively the approximation with 3 and 4 exponential functionsand the error committed by each one of these fittings. Clearly the 4exp. approximation fits best the tail. The coefficients (exponent andgain) for each of the exp. were computed in such a way that before 1microsecond the approximation is relatively rough, but quiteaccurate afterwards. Such weighted least-mean squareapproximation scheme allows the error to be within 1‰ after 1ms.The approximation can be decomposed in the elementaryexponential function. As an example, figure 7 shows the case for the4 exponential approximation.Figure 4: The filter input signal (from NA35/ALEPH preamp/shaper)Figure 5: The Exponential ApproximationsFigure 6: Error for 3 and 4 exponential functionsFigure 7: The 4 exponential functions and their sum.Two of the exponential functions have negative gain and one hasgain superior to one. This configuration is required in order to bestfit the initial undershoot. Performances for both filters, one ofsecond order and one of third order (3EXP and 4EXP) are shown intable2 and figure8.Table 2: Comparison between the input and the output of a 2nd order and3rd order filters.Input 3EXP 4EXPTime to 0.1% (us) 40 2 3Max. Undershoot (%) 0.5 9.5 4.50 1000 2000 3000 4000 5000 6000 7000 8000 9000 1000000.10.20.30.40.50.60.70.80.91TPC signal-10MHz:482 EventsnanosecondsNormalized Amplitude0 500 1000 1500 2000 2500 300000.10.20.30.40.5nanosecondsNormalized AmpExponentials Approximations3 EXP mathcad error4 EXP mathcad error0 200 400 600 800 1000 1200 140000.10.20.30.40.50.60.70.80.91nanosecondsAmpExponentials ApproximationsData         3 EXP mathcad4 EXP mathcad0 500 1000 1500 2000 2500-1.5-1-0.500.511.522.5nanosecondsNormalized AmplitudeThe 4 ExponentialsalfabetagamatetaSum Figure 8: Input, output of the 2nd and 3rd order filter.B. NA49/FTPC Preamplifier/Shaping AmplifierFigure 9 shows the input signal, figure 11 and figure 10 presentthe error of the approximation and the approximation itself. Figure12 and table 3 show the output of both filters. This amplifier isbipolar and a slight mismatch of poles and zeros on the analoguecircuit creates an undershoot. In this case the tail tends towards zerofrom the negative values. For this reason the gain of two of the 4exp. should be negative. The principle exposed in section II isgeneral enough and the tail cancellation is achieved after 1.2microseconds. We can observe that the 4 exp. approximation is moreaccurate before 1 microsecond and as good as the 3 Exp. afterwards.In order to test the proposed filter Filter under more realisticconditions, 20 different measured clusters were distributed in 50microseconds according to the occupancy given by Montecarlosimulations (table 4). The measured signals were taken at a rate of10MHz, and 505 samples were collected for each single event in adrift time of 50 microseconds. The Mont carlo statistics assumed a5.66MHz sampling rate and a 80 microseconds drift time. The inputsignal is shown in figure 13 and the results of a second order digitalfilter in figure 14.Figure 9: The filter input signal (from NA49-FTPC preamp/shaper)Figure 10: The Exponential ApproximationsThe input signal was constructed using single measured events(not the average). The input signal presents a downward baselineshift that is clearly visible in the case of multi-cluster events. We canobserve that the filter cancels the baseline shift caused by the addedtail of each one of the events. The linearity of the system allows thetail cancellation even in the very likely scenario of havingsuperimposed clusters, assuring, in such way, an efficient zero-suppression.Figure 11: Error for 3 and 4 exponential functionsTable 3: Comparison between the input and the output of a 2nd order and3rd order filters.1000 2000 3000 4000 5000 6000 7000 8000 9000 1000000.050.10.150.20.250.3TPC signal-10MHz:347 EventsnanosecondsNormalized Amplitude0 500 1000 1500 2000 2500 300000.050.10.150.20.250.30.35nanosecondsNormalized AmpExponentials Approximations3 EXP mathcad error4 EXP mathcad error0 500 1000 1500 2000 2500 300000.10.20.30.40.50.60.70.80.91nanosecondsAmpExponentials ApproximationsData         3 EXP mathcad4 EXP mathcad0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-0.1-0.0500.050.10.150.20.250.30.350.4Digital filter Results from measured signalsnanosecondsNormalized AmplitudeInput data3 Exp     4 Exp     Input 3EXP 4EXPTime to 0.1% (us) 35 1.5 1.2Max. Undershoot (%) 2.5 0 0Figure 12: Input, output of the 2nd and 3rd order filter.Table 4: Statistic data from M ntecarlo simulationsFigure 13: Input signal. 20 events in 50 microsecs randomly distributed.V. CONCLUSIONSFrom the results presented, the proposed scheme can achieve thedesired precision of 1‰ within 1-3 ms by a manageable size DigitalFilter. The performance increases with the number of approximatingexponential functions, in other words, to the expanse of extra silicon.If the input from the analogue electronics presents undershoots, theperformance decreases. This is due to the fact that it becomes moredifficult, with a limited number of exponential functions, to fitbipolar signals. The Digital Filter can also perform under realisticconditions with several events per pad, allowing a correct zero-suppression. Different architectures of Digital Filters were simulatedand compared in terms of silicon area and error vs. number of bits.All the circuits were synthesised using Synopsys and simulated withVerilog. Other problems of filtering and shaping on the time domaincan be addressed using the method proposed here. Nowadays theCMOS sub-micron processes allow arithmetic operations inrelatively small area and achieve an accuracy that could not be metusing analogue circuits. More measurements will be performedallowing a better understanding of the physics and the correct tuningof the coefficients of the Filter.REFERENCES[1] A Large Ion Collider Experiment, ALICE TPC -TechnicalDesign Report, Dec. 1999, ISBN 92-9083-155-3, Geneva,Switzerland.[2] L. Musa et al., Front_End Electronics for the ALICE-TPCDetector, Proc. of the 4th Workshop on Electronics forLHC Experiments, Rome, Sept. 21-25, 1998.[3] R. A. Boie, A. T. Hrisoho, P. Rehak, Signal Shaping andtail cancellation for gas proportional detectors at highcounting rates, Nucl.-Instrum.-and-Methods-in-Physics-Research, vol.192, no.2-3, p.365-74, 1,Feb. 1982..[4] R. Baur et al. , Nucl. Instrum. Methods A409 (1998) 278and in Proc. of the 3rd Workshop on Electronics for LHCExperiments, CERN-LHCC-97-60.[5] CERN/LHCC 95-71 LHCC/P3, A Large Ion ColliderExperiment, ALICE-Technical proposal, Dec. 1995, ISBN92-9083-077-8, Geneva, Switzerland.[6] Neil H. E. Weste, K. Eshraghian, Principles of CMOSDesign, A Systems Perspective, ISBN 0-201-53376-6,Addison-Wesley Publishing Company.[7] Blinchikoff, Zverev, Filtering in the Time and FrequencyDomains, ISBN 0-89874-952-2, Robert E. PublishingCompany, Malabar, Florida.[8] J.G. Proakis, D. G. Manolakis, Digital Signal Processing,Principles, Algorithms and Applications, 2nd ed., ISBN 0-02-946378-5, Macmillan Publishing Company, New York.[9] J.Bracinik et al., Status Report on the ALICE Prototype TPC withRing-Cathode Readout, ALICE/1999-48, Internal notes.Figure 14: Output of the Digital FilterMean time between clusters 3.3 microsecondsSamples/Pad 150Clusters/Pad 240 5 10 15 20 25 30 35 40 45 50-0.200.20.40.60.811.2microsecondsNormalized AmplitudeInput Signal0 5 10 15 20 25 30 35 40 45 50-0.200.20.40.60.811.2microsecondsNormalized AmplitudeOutput of the Digital Filter500 1000 1500 2000 2500 3000 3500 4000-0.0500.050.10.15Digital filter Results from measured signalsnanosecondsNormalized AmplitudeInput data3 Exp     4 Exp     

Digital implementation of a tail cancellation filter for the time projection chamber of the ALICE experiment

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