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

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

1

Digital Signal Processing


2

Selection of an appropriate sequence of transfer function for the processing

Simulated ADC responseADC gain = 1000

Delta charge injection: Time Value120 0,34121 0,33122 0,33

160 0,2161 0,2

Processed: Original:Fn ; n=z,N <= FADCn ; n=z,N

transfer function?

Example: FADC output

0

200

400

600

800

1000

1200

50 70 90 110 130 150 170 190 210 230 250

Sample

Am

plitu

de (

FA

DC

co

de)

FADCn n=50,250

Optimized to extractphysical quantities(charge, etc.)


3

Example:The moving window deconvolution transfer function

F[n] = ai * FADC[n-i] i=0,N

For an arbitrary window of L samples :

a0 = 1

ai = 1/TAUpreamp i = 1, L-1

(TAUpreamp in units of the sampling period)

aL = -1 + 1/TAUpreamp

With deconvolution, 24-point window

-200

0

200

400

600

800

1000

1200

50 100 150 200 250

Time (nsec. X 10)

Co

rre

cte

d a

mp

litu

de

Properties Transforms an exponential intoa rectangular function of L points.

L


4

Simplified implementation in favorable cases

In the previous example, ai = 1/TAUpreamp i = 1, L-1 (equal weight factors)The term with identical ai’s,: G[n] = ai * 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 ClockA -B

Dual PortMemory

Write address

Read Address

a * FADC[n-1]

Data Ina * FADC[n-L]

Data Out


5

Deconvolution in the presence of noise

With deconvolution, 24-point window

-200

0

200

400

600

800

1000

1200

50 100 150 200 250

Time (nsec. X 10)

Co

rre

cte

d a

mp

litu

de

Remark:

For series noise, theRMS value of the noisein the resulting function is increased by a factorSQRT(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

With 16-point boxcar filter

-200

0

200

400

600

800

1000

1200

50 70 90 110 130 150 170 190 210 230 250

Sample

Fil

tere

d a

mp

litu

de

Floating average (boxcar) filter applied to the deconvolution result

G[n] = aj * F[n-j]; aj = 1/K j = 0, K -1

Transfer function:

Example with K = 16; Note parameter K => Peaking time

G[n]


7

Some interesting properties of the filter

3 points in rise time

-200

0

200

400

600

800

1000

1200

110 120 130 140 150 160 170

Sample

Filt

ere

d a

mp

litu

de

8 points in rise time

-200

0

200

400

600

800

1000

1200

110 120 130 140 150 160 170

Sample

Filt

ere

d a

mp

litu

de

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

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

Time measurementExample: the Constant Fraction Discriminator (CFD)Principle: Compensates for the time walk associated with the pulse height.

“Black” Threshold

“Blue” Threshold

ΔtSame 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

ΔtSame again! (in the case of a linear rise time)

Clipped

Not Clipped

Threshold set at MAX * Fraction:Tr

Tr1

Tclipped


10

Time measurement, digital CFD implementation example

Step 1: Clip the raw data samples:F[n] = ai * FADC[n-i] ; (a0=1, aMinTr=-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

Timing resolution in the digital CFD

Δt

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

Timing resolution in the digital CFD (zoom)

Δt

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

The TIG-10 ModuleCharacteristics:

Form factor: VXI-CInterface :a) Stand-alone: VME-A24D16 :b) System: 200 MHz source synchronous LVDSNumber of channels: 10

Digitizers : 100 MHz 14-bit

Signal processing:Raw data - Trigger latency buffer - Data sample buffersCharge Channel: - Preamplifier decay pole deconvolution - Trapezoidal filter - Baseline restorerTiming channel - Hit detector - CFD - Trigger generate / accept logicData flow/control: - Parameters read/write - Event builder - Communication links


14

Example 4: the VF48 card, (Rev 0 shown)

48 Differencial ChannelsFADCs: - 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

Properties of the VF48 card

Form Factor : VME 6UNumber of channels : 48Number 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 linkLocal trigger signalling output : Front panel conector or serial

linkTrigger accept input : « « «


16

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,(oneclover or more)

Trigger decisionRun control (parameters)System clock

Optional logic signals

TIG-10

TIG-C


17

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

Documents

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