1

SCA Cell Utilizing SchemeSCA Cell Utilizing Scheme

• The output of each preamp-shaper channel is sampled continuously at 20 MHz and stored the SCA cells.

• There are 96 cells for each SCA channel. They are used as 12 blocks of 8 cells each.

• The blocks to be used in the sampling are kept in a (constantly updating) pool of free blocks.

• At any time, 2 blocks (16 cells) are taken from this pool to capture 8 useful voltage samples. They are put back into the pool when one of the following condition is satisfied. – No LCT trigger is found 800 ns later.– There is an LCT trigger, but there is no L1 accept s later. – L1-LCT match found and digitization completed 26 s later.

2

LHC Rate AssumptionsLHC Rate Assumptions

L1 accept: 100 kHzLCT rate: 69 kHz per CFEB (worst case – ME1/1) Estimated LCT rate for 10**34 lumi (D. Acosta et al, 2001) Chamber Type LCT rate per CFEB (kHz) ME1/1 69 ME1/2 4 ME1/3 2 ME2/1 21 ME2/2 3 ME3/1 11 ME3/2 2 ME4/1 8 ME4/2 9

L1-LCT coincidence rate per CFEB: 100 kHz x 70 kHz x 75 ns = 0.5 kH

Digitization time (with 6 ADCs on each CFEB) 16 channels x 16 samples/channel x 100 ns = 26 s

3

Effective Buffer Size of SCA at LHCEffective Buffer Size of SCA at LHC

• Average number of LCT’s during 2.2 s (=3s-0.8s) holding time for 2-blocks: =2.2x10-6x70x103=0.15

• Average number of L1-LCT matches during 26 s digitization time: =26x10-6x0.5x103=0.013

• Probability of overwriting SCA: 6.1x10-10

n Free Used P( ,n) Q( ,n)0 12 0 0.86 0.991 10 2 0.13 0.122 8 4 0.0097 0.000173 6 6 0.00048 2.20E-064 4 8 0.000018 2.80E-085 2 10 5.40E-07 3.70E-106 0 12 1.30E-08 4.70E-11

4

Effective Buffer Size of SCA at SLHCEffective Buffer Size of SCA at SLHC

• At SLHC: use same L1 accept rate, exclude ME1/1, assuming rates go up linearly. Maximum LCT rate is 200 kHz (excluding ME1/1), L1-LCT match rate is 1.5 kHz.

• Average number of LCTs during 2.2 s (=3s-0.8s) holding time for 2-blocks: =2.2x10-6x200x103=0.44

• Average number of L1-LCT matches during 26 s digitization time: =26x10-6x1.5x103=0.04

• Probability of overwriting SCA: 9.3x10-6

n Free Used P( ,n) Q( ,n)0 12 0 0.64 0.961 10 2 0.28 0.0382 8 4 0.062 0.00153 6 6 0.0091 6.10E-054 4 8 0.001 2.10E-065 2 10 8.80E-05 9.80E-086 0 12 6.40E-05 3.90E-09

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10-4

10-6

10-8

10-10

LHC

SLHC

Test Beam

LCT•L1A Rate (KHz)

LC

T R

ate

(KH

z)

SCA Overflow Probability

2 GigHzFiber Limit

6

SC

A O

verf

low

Pro

bab

ilit

y

L1A-LCT time (sec)

SLHC NominalLCT 200 KHzL1A•LCT 2 KHz

SCA Overflow versus L1A Latency

7

CSC FE Electronics Issues at SLHC

Radiation (Probably OK) - present electronics tested to 3x(safety factor) 10 LHC years - SEU resets at LHC ~20 minutes -> 2 minutes at SLHC

25 nsec -> 12 nsec Crossing Time (OK Firmware Change) - no problems anticipated

Data Flow (OK if LCT scales linearly) - we have seen no SCA overflows at 5X LHC rates - SCA rate calculations show CFEB can take even higher rates - SCA rates sensitive to LCT and L1A Latency - DAQMB has buffer overruns at ~15X LHC rates

CFEB/DAQMB - cathode dominates data volume

Viability of CFEB and DAQMB designs depend solely onLCT and L1A rates and latency.

8

Peripheral Crate2 DMB, 2 TMB1 CCB, 1 MPC

FED crate 1 DDU

PC

TTC crate

DAQ Data

Trigger primitives

S1 S2 S3

beam

Track finder Crate

TRIDAS

Rate Capabilites of Present System2003 Time Structured Beam Test

Nominal LHC Rate/Chamberexcluding ME1/1 and ME1/A200 kHz LCT 2 kHz L1A•LCTCPT Week: Nov. 6, 2003 J. Mumford

We ran 100 kHz pion LCTs into 1 CFEB (5x LHC)

1 kHz LCT•L1A (LHC) 16 time samples no problem 8 time samples no problem

10 kHz LCT•L1A (10xLHC)16 time samples buffer overrun 8 time samples no problem

Note: Buffer overwrites were on DAQMB. No overflow of SCAs was observed. SCA buffer calculations agree with results.

9

Paul, The usage of capacitors in the SCA has two bottlenecks.The first is a pipeline, while the second isa classic queuing problem. To solve probabilities correctlyone should run a MonteCarlo, but here is a simplified backof the envelope calculation. There are 12 blocks of 8 capacitors in the firmwarealgorithm. Four are in use at anytime, though theoreticallywe can use all of the blocks. After the beam crossing thefour blocks are shifted through until an LCT arrives (~800 nsec). Pipeline:When an LCT arrives two blocks are stored for a period of timeT=L1A(time)-LCT(time)=~2usec. Since multiple sets of two blocks canbe in the pipeline probabilities are given by a poissonian pdf with:  mu=Rate*T ps0=poissonian(mu,0) ps1=poissonian(mu,1) ... ps6=poissonian(mu,6) Queue:When the L1A arrives events with a correlated LCT will be digitized. In terms of queing theoryour rate of arrival is the LCT*L1A rate of 1kHz. It takes approximately 25 usecto process the two blocks.(for queuing theory equations see http://www.cs.panam.edu/~meng/Course/CS6354/Notes/meng/master/node4.html)   rho=Rate*T=1.e3*25e-6=0.025 P0=1/(1+rho+rho**2+...) P1=rho*P0 P2=rho**2*p0 ... P6=rho**6*p0  Since the pipeline and queue are uncorrelated one wouldexpect the probability of have more than 6 sets of 2 blocks occupiedis: Prob:=1-ps0*(p0+p1+p2+p3+p4+p5+p6)-ps1*(p0+p1+p2+p3+p4+p5)- ps2*(p0+p1+p2+p3+p4)- ...-ps6*p0   I will point you to slides monday.  Cheers, Stan