Dulny, B

Fent, J

Haberer, W

Kiesling, C

Osthoff, A

CERN Document Server

1Jet Determination in Lar- Calorimeters using a Heavily InterconnectedSystem of FPGA’sB. Dulny, J.Fent, W. Haberer,C. Kiesling A. Osthoff                               Max Planck Institut für Physik                                 Werner Heisenberg Institut                                      München, Germany  Abstract.New fast and highly complex ‘Field ProgrammableGate Arrays’ allow the design of sophisticateddecision logic within the trigger latency time ofdetectors.As an example we show the Jet Determination ofthe Hera-H1 detector at DESY Hamburg. It has tocalculate all existing localized energy depositions(jets) in the calorimeter and deliver the result,sorted according to energy.The system is implemented by a network of threetimes 440 high density FPGA's which have todeliver the results in less than 1 µs. The computingpower of the system is equivalent to 70 Billionoperations per second.1.   The calorimeter trigger.To understand the new system, it is necessary togive an survey of the environment in which  it willbe integrated.The basic elements of the calorimeter trigger arebuilt by about 700 projective, i.e. to the interactionregion pointing, triggertowers.These towers are the result of 40000electromagnetic and hadronic channels which arereadout and stored after the trigger decision.The triggertowers are further summed to 512 socalled Bigtowers (BT).The electromagnetic and hadronic components ofthe BT-signals are digitized by 10 MHz Flash-ADC's and are summed to different topological andglobal quantities.The electromagnetic and hadronic fractions areindividually weighted in lookup tables. Furtherlookup tables and summing stages calculatedifferent quantities as there are: total energy,transverse energy, missing energy etc.The energy sums are discriminated byprogrammable thresholds, and the outputs are fedto the central trigger logic, where the decision forstoring all the experiment data has to be made.All this complex signal processing has to beaccomplished in less than 1  µs.2. The FPGA - Jet-Trigger.In the new proposed system, the summing overlarge calorimeter areas will be replaced by anintelligent algorithm identifying regions withsignals well above the noise ( jets ).The complicated scheme based on many thresholdsat different levels can thus be replaced by anintuitive system where ideas popping up in aphysics analysis can be easily implemented in thehardware.All topological information will be available such,that physical correlations can be exploited to keepthe trigger rate under control.3.  Design Principles.The physical idea of the jet trigger is quite simpleto formulate: It should find localized regions ofenergy depositions corresponding to a typicalradius, together with the coordinates of the jetcenter.In a trigger application a sequential algorithm isprohibitive because of timing limitations. Aparallel hardwired solution is needed. The systemis logically  divided into four stages:3.1 Preprocessor       Here, the analog pulses from the individualtrigger towers, separated in electromagnetic (em)and hadronic (had) sections are sampled anddigitized. The em and had sections are passedthrough look-up tables for thresholding andweighting and are subsequently added. Theresulting 440 weighted towers are fed into the so-called bumpfinder. 23.2 Bumpfinder  The basic algorithm to find the jets is realizedhere. Each of the towers, formed in the previousstage, interrogates its nearest neighbors ( known a priori by the fixed geometry of thetowers ) to determine whether any      of them hasmore energy than the interrogating tower (calledIT). If this is not the case the IT is a local energymaximum or „bump“.  The jet energy is thenformed by adding all the energies of theneighboring towers to the energy of the bump.Since this algorithm only interrogates theimmediate neighborhood, it is suited for parallelexecution: All the trigger towers determine theirbump property independent of the others. Theresult of the bumpfinder is a list of jets, defined byenergy and coordinates. A finite number of jets(maximum of 24) is fed into the next stage , theenergy sorter.3.3 Energy Sorter  Here a fixed number of jets (24) are sortedaccording to energy. Again the algorithm is carriedout in a parallel manner, similar to the     bumpidentification algorithm: Each jet compares itselfwith all the others and  determines the number ofjets with smaller or equal energy. The jet with thenumber 23 is the largest, the one with number 22the next etc. In case of equality in the energies, aunique ordering  based on the topological locationof  the bumps is forced.  From the 24 possiblebumps only the first 12 (highest  energy)  bumpsare passed to the next stage.3.4 Trigger Quantity Determination  The trigger element generator ( TQD) housesthe necessary logic to construct the trigger decisionfrom the jets found. Typical actions of the TQD isto discriminate the individual jet energies, countjets  above certain thresholds and determinetopological correlations on the basis of positioninformation of the jets. The TQD is designed in avery flexible and expandable way, since theoptimal strategies of triggering will largely dependon the changing physics interests.4. Hardware Realization.4.1 Design overview      The triggertowers have to be re-assembled tooptimize their granularities   depending on theposition in the calorimeter. The re-assembly of thesignals is   done in the ACS system ( ADC,Calculation, Summing).      The  Bump Finder Unit (BFU) processes thesesignals to find „bumps“ and  their addresses.„Bumps“ are defined as the maxima of local energy  depositions, including their immediate nextneighbors. The BFU consists of eight boards,mapping eight octants of the calorimeter, arrangedin cylindrical form. Each board delivers the fifteenpossible „bumps“ to its Primary Sorting  Unit(PSU). This unit selects,  for each octant, the threebumps with the  highest energies and transfersthem to the central Secondary Sorting Unit      (SSU). Here the total of 3 * 8  bumps are sortedby energy in decreasing   order. The 12 largestbumps are sent to the Trigger QuantityDetermination  box (TQD), where the   triggerelements will be generated.       Fig. 1 shows the timing of the pipelinedsystem, in time units of  particle  crossings of theaccelerator. Note that one unit is 0.1  µs and thatonly a total  of 8 units are available for the digitalpart of the jet algorithm.   If one considers the sample N at unit 0, thedigital value is obtained at unit 1. The ACS unitcan complete its processing within one unit. Withcable delay  the BFU receives the data at unit 3. Atunit 4 the output of the BFU  is available and PSUand SSU finish their work until unit 6. In theremaining two units the final trigger elements aregenerated.4.2  ADC-Calculation-Storage Unit (ACS)       The ACS cards convert the signals from the568 EM-Trigger Towers and  the  624 Had-TriggerTowers in 1192   8 Bit words, weight them,N-1,N,  N+1,N+2,N+3SignalHeraClock      t-1  t 0   t1   t2    t3    t4    t5    t6    t7  t0  sampling of signal, start of conversion for sample t0  t1  digital output for sample t0 ( 5 internal clock cycles)  t2,t3 processing of sample t0, transfer to BFU  t4  output of Bump Finder Processor (BFU)  t5  output of Primary Sorting Unit ( 3 Maxima/sector)  t6  output of secondary Sorting Unit ( 12 Maxima in     decreasing order at Trigger Quantity Distributor TQDFig. 1   Timing of     the pipelined     System3calculate the EM- and Had-sum, send the resulting440 Bytes to the BFU ( Bump Finder Unit) andstore simultaneously the data in circular buffers.      Except the AD- conversion, the logic isimplemented in 440 FPGA’s. ( Altera 10K30).4.3  Bump Finder Unit (BFU)       The current energy content in each input toweris compared with the eight or  nine (depending onthe local granularity ) nearest neighbors ( see fig2).  This operation is done for all input towers inparallel. The towers which win, i.e. have thehighest energy value compared to the neighbors,are bump  centers. They sum the neighbor energiesto their own energy and put the result onto theThree - State output bus, together with the addressof the bump center.    The Input Towers are grouped to tower clusters.Only one member in a group can be a „bump“.Fig.3 shows one of the eight boards with InputTowers, Tower Clusters and the bus connections ofa single Input Tower. Note that there are eight 8Bit input busses from the neighbor towers,  outputaddress bus, 8 Bit output bus for the summedenergy  and  a fanout of eight  8 Bit busses to theneighbor towers.            The bump energy ( 8 Bits ) and the addresswithin a cluster ( 2 Bits ) are  transferred to thePSU ( Primary Sorting Unit). The evaluation ofbump  centers and the formation of the bumpenergies  is done in large FPGA’s   (one for each InputTower, 440 all together ), which are all networkedtogether. The total computing power of the BFUsums up to about 70 Billion calculations persecond.  Because of the high complexity ofnetworking, it is necessary to arrange the  systemin form of a cylinder, just like the calorimeteritself.   . 4.4  Primary Sorting Unit  (PSU)        One of the eight identical sections in thecylinder contains 55 FPGA’s with  the BFUfunction. The fifteen bump energies ( 8 bits wide )and two address  bits  for every group are preparedfor the Primary Sorting Unit (PSU).  In the PSUthe energies of each of the 15 bumps are comparedwith all   others. The result is a coded position inthe hierarchy of energies. After decoding, the threebiggest bumps and their addresses are stored.. Theyare  sent to the Secondary Sorting Unit (SSU) forthe next sorting step. The PSU needs one time unit( 0.1 µs) to process its function and isimplemented in one large FPGA for each section.4.5 Secondary Sorting Unit (SSU)         The 24 biggest bumps together with theiraddresses ( 3 maxima from each section), arecollected in the PSU’s for the whole calorimeterand are transferred to the SSU for the final sortingoperation.In the SSU the energies of each of the 24 bumpsare compared with all others. If two bumps areFig. 2Local granularityTT GranularityBT GranularitySUM outOut Data NIn Data NInput TowerTower ClusterPhi IndexTheta IndexFig. 3  Networkof  a single inputtower4equal, the global position in the calorimeter istaken into account to force a strict ordering.Therefore the result of each comparison is anunambiguously coded number which gives theposition in the hierarchy of energies. Afterdecoding, the 24 energy bumps and their addressesare stored in decreasing order. The 12 largestenergy bumps are distributed to a general bussystem ( „jet container“), where trigger quantitiescan be calculated in the remaining time units. TheSecondary Sorting Unit will be implemented in fewlarge FPGA’s  ( 250 k  gate equivalents )  .4.6  Trigger Quantity Determination (TQD). The output of the third stage of the jet trigger isthe list of 12 largest jets found, ordered by energy.In the forth and last stage of the trigger , this list isused  to generate the trigger elements leading to anactual trigger. Since the „jet container“ is a bussystem, an arbitrary number of modules may haveaccess to it and  trigger elements can be easilyadded if needed without disturbing thedetermination of the already implemented triggerelements in the jet trigger. The amount ofcomplexity of trigger elements is limited by thetwo time units ( .2µ ) which are left for the TQD.5. Status of the Project The project was started in the second half of 1997.The simulations for the different components(ADC Unit, Bump Finder and Primary andSecondary  Sorting units ) showed that theprocessing time can be kept in the  available timeunits. The logic synthesis of all FPGA’s was successful. A first demonstrator model of the Bumpfinder forone octant showed its functionality.6. ConclusionsThe proposed level 1 jet trigger is the last missingpiece of an ambitious upgrade program for theHERA H1 Liquid Argon Calorimeter. The physicsidea of the trigger is to find the localized energydepositions in the calorimeter, order them by theirenergies and provide decisions in a very flexibleway  based on the multiplicity, energy andtopological information  of the jets.      The trigger will overcome the limitations of thepresent global trigger  philosophy and will allow toselect specific physics reactions with higherefficiency and higher background rejection.      The realization of this ambitious project ispossible due to the fact that very complex and fastFPGA’s came to the market  and the secondimportant fact is the availability of reliable designsystems  . 5

Jet determination in Lar calorimeters using a heavily interconnected system of FPGAs

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