Position, Charge and Time measurements with AFTER+ Eric Delagnes

1. Position, Charge and Time measurements with AFTER+Eric Delagnes

2. Q AFTER +: The Analog Side Required for spark protection Q/Cf Pole-zero + Shaper 2nd stage + SCA Digitization + digital treatment Cc CSA 1 zéro (Z1=P1) CR-(RC)2 filter BandPass filter (1 zero @ origin + 3 programmable poles) Sampling @ programmable frequency (beware of the Nyquist criterium for signal & noise to avoid aliasing) Integrator + Low Pass pole P1 2ND STAGE & SCA noise 1/f 20dB/dec 40dB/dec Noise 10dB/dec white

3. Q Q AFTER +: The timing Side (1) Ext Trig (opt) Trig AFTER 0 Trigger Synchroniser + Processor + STOP timing AFTER STOP Time calibrator CK AFTER Trig AFTER i • Everything is synchronous with the same CK (TCK period) • (not exactly the case with T2K FEM 10ns incertitude) • Timing offsets between boards supposed to be stable and calibrated • => calibration system required to achieve fine timing. • STOP = Trigger + NPOST x TCK = signal synchronizing everything

4. AFTER +: The timing Side (2) • Each SCA sample Ni can be « absolutely » timed with the ck precision: • ti = tstop – (Nstop –Ni) mod 511 x TCK Precision can be far better than TCK limited by uncalibrated skew and jitters from trigger processor must be known • Nstop = N last written cell • In AFTER+ the readout can start NReadoff cells after the last written cell => If Nj is the index of the cell during the readout (1= first cell read) • (Nstop –Ni) mod 511 = 511 - (NReadoff +Nj) • If we implement time zero-suppress option in AFTER+: • different time readout window can be read for different AFTER chips. • The readout index Nj is not sufficient to calculate the time. • Each chip must provide an extra information Noffsetm. AFTER+# m Noffsetm AFTER+# n STOP Noffsetn NReadoff

5. fast e- signal ~10% of Q ion signal ~90% of Q. 25-100ns duration depending of amplification gap The signal for TPC with a Micromegas endplate • Elementary Current signal from a primary electron collected on a TPC pad. • Widened by: • longitudinal diffusion for large Z. • geometry for tracks with non 0 angles. • In all cases: sum of elementary signals with eventually different time offsets • Rectangular shape is a reasonable approximation for simulations.

6. XY position determination • @ first order: given by the position of the pad with maximum of charge. • => resolution s0~ pad size/√12 • Centroïd calculation may help. But the lateral diffusion is very small for small Z for standard Micromegas (diffusion is typ s~ 15µm) • Colas et al., simulations/exp. for ILC TPC. • limited resolution for small Z. For higher Z, diffusion helps. • Very large improvements for resistive anodes. • Weights for centroïd calculation = Q (see next slides) • Centroïd calculations are only effective is S/N is very good. • Crosstalks and transfer function spread deteriorates resolution.

7. Crosstalk et al • Crosstalk in the modern FE can be very small. Typically ~0.3% for AFTER. It is mainly derivative. • The main crosstalk comes from the FE to detector coupling Gain depend on CD and CAC (Xtalk effect neglect) Crosstalk (non derivative) CAC must be large compared to CD and CP

8. Charge measurement (cont) • Qtot = SUM( Qi) Ballistic deficit illustrated: (100ns CR-RC4 shaper) • For accurate charge measurement shaping time >> signal duration • If signal duration is constant => Ballistic deficit is constant => just a small decrease of S/N. • If not ( tracks with angle, large Z)=> dependancy of transfer function with signal duration => degradation of Q resolution.

9. Taking advantage of sampling for charge measurement. • Samples Si can be combined • FIR filter for example: • a0 =1, ai=0 => peak measure. • ai =1 (0<=i<=w) => gated integrator. • optimal filter (calculated from signal shape +noise spectrum). W. Cleland,  NIM A 338 (1994) • Other techniques may be used (fit, correlation…) allowing also to extract timing (P. Bertin et al. DVCS/E00-110 experiment : Final Readiness Report). • What can be done : • Reduce the effect of the asynchron beahvior of the pulse. • ENC improvement. • ballistic deficit removing. change the effective filter

10. Effect of asynchronism Pulse/sampling Ck.

11. Improving Equivalent noise charge by filtering ? • No magic improvement to expect: • CR-RC(n) filter noise performances are typ. 10% worst than optimal one. • What can only be done => change the effective filter peaking time. • The optimum will depend on the noise spectral density • limited by 1/f and 2nd stage noise. • Be careful to aliased second stage noise. We can numerically change the shaping time to have an optimal resolution 1/f floor +2nd stage

12. Toy montecarlo simulator • Time domain simulation. • Noise generator with spectral density = those at preamp output. • “Micromegas” Signal generator. • Model of filter. • Model of sampler. • Digital Filter (FIR) • Exemple: • slowing down of the 100ns shaping by convoluting with triangular shape • -> 400ns and 800ns effective peak time. • noise decrease. • Ballistic deficit reduction (not studied yet)

13. Effect of digital filtering on noise Black curve: simulated (with the toy MC) ENC for various peaking times, (Fs=50MHz) => reasonable agreement with measurements. Red curve: ENC simulated the 100 ns peak time sampled @Fs =50MHz with increasing duration triangular digital filters. => noise reduction equivalent to those obtain with analog filter. In real conditions, would not probablybe so good because of aliased noise (not simulated here).

14. Fine Timing measurements. • Several possible methods: efficiency depending on signal shape and its reproducibility. • optimal filtering (works well if the signal shape is constant). • deconvolution. • fit of known shape. • peak finding (with quadratic interpolation). • crossing of linear extrapolation of the rising edge start with baseline. • CFD => studied here (linear interpolation method). • Expected timing resolution ? • In the continuous analog world. • st = sn . dV/dT. • sn proportional to tpeak-1/2 (if dominated by serie noise) • dV/dT proportional to 1/tpeak • classic results • => A fast shaping is better for timing. • Better timing for high S/N

15. Simulations of timing capabilities. • CFD (fraction =0.4) is simulated using : • Micromegas signal (elementary signal). • No amplitude or shape variation (up to now). • Perfect clock: no clock jitter • Realistic Noise spectral density with white noise and 1/f (T2K) • for various tp • various noise levels (“nominal”, x2,x3,/2).=> various S/N values • various sampling Frequency S/N in « nominal » condition

16. Simulations of timing capabilities. Fsample=100MHz • Time resolution increase ~ linearly with tp (not expected) • Time resolution increase ~linearly with input “noise level”. • Problems occur when S/N < 6. • Very good time resolution can be achieved

17. Timing Simulations. « nominal » noise (S/N= 22 for tp=200ns) • Time resolutions are flat for sampling frequency down to Fs.tp =3-4 • (3 samples on the rising edge) • Resolution far better than TCK/ (12)1/2 are obtained for reasonable S/N

18. Conclusion and other things to try. • Charge measurement and timing capabilities of AFTER electronics well understood. • How can we deal with tracks with angles: • Pulse deconvolution? => simulation with noise. • What can we learn from shaped signal duration. • …