1. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 2006 1 Digital Signal Processing

2. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 20062 Selection of an appropriate sequence of transfer function for the processing Simulated ADC response ADC gain = 1000 Delta charge injection: Time Value 120 0,34 121 0,33 122 0,33 160 0,2 161 0,2 Processed: Original: F n ; n=z,N <= FADC n ; n=z,N transfer function? Example: FADC n n=50,250 Optimized to extract physical quantities (charge, etc.)

3. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 20063 Example:The moving window deconvolution transfer function F[n] = a i * FADC[n-i] i=0,N For an arbitrary window of L samples : a 0 = 1 a i = 1/TAU preamp i = 1, L-1 (TAU preamp in units of the sampling period) a L = -1 + 1/TAU preamp Properties Transforms an exponential into a rectangular function of L points. L

4. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 20064 Simplified implementation in favorable cases In the previous example, a i = 1/TAU preamp i = 1, L-1 (equal weight factors) The term with identical a i ’s,: G[n] = a i * FADC[n-i] i=1,L-1 Reduces to : G[n] = G[n-1] + a * (FADC[n-1] – FADC[n-L] ) Add the new element at the head Remove the out of range element at the tail Value for the previous point A - B Accumulator += Sampling Clock G[n] Hardware implementation: Counter Constant N-1 Sampling Clock A - B Dual Port Memory Write address Read Address a * FADC[n-1] Data In a * FADC[n-L] Data Out

5. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 20065 Deconvolution in the presence of noise Remark: For series noise, the RMS value of the noise in the resulting function is increased by a factor SQRT(2) Note: It can be demonstrated that the transfer function shown on the next slide will yield the best estimate of the trend of the “flat” portion of the deconvolution

6. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 20066 Floating average (boxcar) filter applied to the deconvolution result G[n] = a j * F[n-j]; a j = 1/K j = 0, K -1 Transfer function: Example with K = 16; Note parameter K => Peaking time G[n]

7. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 20067 Some interesting properties of the filter L K 1- For an input step function, the resulting shape is a symetrical trapeze with a peaking time of K and a flat-top equal to L - K 2- As long as the charge collection in the detector is shorter than L - K, the pulse shape will reach its full amplitude. => NO ballistic deficit 3- The S/N ratio is slighly better than that of an analog CR-(RC)n or pseudo gaussian filter of the same FWHM.

8. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 20068 Performance summary of the « trapezoidal » filter - The S/N of the trapezoidal signal is a few % better than that of a pseudo-gaussian analog filter - For signal rise-times shorter than the parameter K, the filtered signal has zero ballistic deficit. (Same filtered pulse height for all rise-times) - The trapezoidal signal has no « tail ». (Good behaviour for pile-up) Other considerations: As for its analog counterpart with pole-zero suppression, the transfer function is not zero for the DC or low frequency components. It requires the equivalent of a « baseline restorer », or double sampling.

9. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 20069 Time measurement Example: the Constant Fraction Discriminator (CFD) Principle: Compensates for the time walk associated with the pulse height. “Black” Threshold “Blue” Threshold ΔtΔtSame for all amplitudes if Tr is constant If Tr is not constant: Use a “delay line clip” ≤ than the shortest rise time “Black” Threshold “Blue” Threshold ΔtΔtSame again! (in the case of a linear rise time) Clipped Not Clipped Threshold set at MAX * Fraction: Tr Tr1 T clipped

10. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 200610 Time measurement, digital CFD implementation example Step 1: Clip the raw data samples: F[n] = a i * FADC[n-i] ; (a 0 =1, a MinTr =-1) = FADC[n] – FADC[n-MinTr] i=0,N Step 2: Arm the “find Max” process when F[n] goes above a pre defined threshold (leading edge) Step 3: Find the maximum value of F[n] Step 4: Calculate the constant fraction threshold ( F[Max] * Fraction) Step 5: Produce a delayed clipped pulse shape Step 6: Find the two points of F[n] delayed on either side of the threshold level Step 7: Interpolate the value between the two points result: 1) Value of the index “n” at the crossover point 2) Time interpolation value (“vernier”) ( precision << sampling period) => “High resolution Time Stamp”

11. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 200611 Timing resolution in the digital CFD ΔtΔt Tr Sources of error in the presence of noise: Amplitude Time fraction threshold Error on the evaluation of the maximum = Nrms Error on the evaluation of the fraction threshold = Nrms * Fraction Error on the evaluation of the signal amplitude = Nrms S

12. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 200612 Timing resolution in the digital CFD (zoom) ΔtΔt Tr fraction threshold S Extra source of errors for the discrete sampling: - linear intrapolation of the rise time function Notes: - Valid for analog or digital CFD - independant of digital sampling rate to first order - Error may be much smaller than the sampling rate for large signal to noise (S/Nrms) ratios Resulting error in the evaluation of time: TError_rms = Nrms * (1+Fraction) * Tr/S error Position of the sample with no noise Position of the sample with noise nominal

13. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 200613 The TIG-10 Module Characteristics: Form factor: VXI-C Interface :a) Stand-alone: VME-A24D16 :b) System: 200 MHz source synchronous LVDS Number of channels: 10 Digitizers : 100 MHz 14-bit Signal processing: Raw data - Trigger latency buffer - Data sample buffers Charge Channel: - Preamplifier decay pole deconvolution - Trapezoidal filter - Baseline restorer Timing channel - Hit detector - CFD - Trigger generate / accept logic Data flow/control: - Parameters read/write - Event builder - Communication links

14. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 200614 Example 4: the VF48 card, (Rev 0 shown) 48 Differencial Channels FADCs: - 10 bit, 20-65 MS/sec Interfaces - Serial LVDS - VME64 Signal processing: 7 Altera Cyclone FPGAs - Raw data segments - Hit detection - Charge calculation - Time stamp - Event formatting Applications: TPC readout - ILC prototypes - TACTIC detector - PET readout Silicon and scintillation detectors readout ASIC preamp multiplexer readout (ALPHA)

15. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 200615 Properties of the VF48 card Form Factor: VME 6U Number of channels: 48 Number of bits: 10 (12 bits under development) Max sampling frequency: 65 MS/sec. Max number of samples/event: 2048 (for each channel) Interface:: 1) VME64X 2) Source synchronous serial, 200 mbits/sec, copper (RJ45) Common system clock: From front panel connector or serial link Local trigger signalling output: Front panel conector or serial link Trigger accept input: « « «

16. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 200616 Example 3, TIGRESS DAQ architecture 720 Signals + Aux. 720+ Channels Local Collectors Communication links Detectors Communication links System concentrators Interface to computers Master Communication links Trigger requests, Data elements: -pulse shapes - charge - time - other “features” Event fragments, (one crystal) Sub Events,(one clover or more) Trigger decision Run control (parameters) System clock Optional logic signals TIG-10 TIG-C

17. J.P.Martin, Université de Montréal, ILC EndCap Meeting, Paris, Sept 12-14 200617 Example 2, TIG-C serial readout module, PCB, component layer 12 RJ45 links connector 1 RJ45 master link connector (820 Mbit/sec. Max) VME64 Altera Stratix FPGA