Signal Processing for
High Energy Physics Detectors
Luciano Musa - CERN / EP
Workshop on Advanced Instrumentation
for Future Accelerator Experiments
Bergen, 3-6 April 2005
06 April 2005
Luciano Musa
1
Signal Processing in High Energy Physics
Introduction
 Signal Processing is a way of converting an obscure signal into useful
information
 Signal processing includes signal formation due to a particle passage within a
detector, signal amplification, signal shaping (filtering) and readout
 The basic goal is to extract the desired and pertinent information from the
obscuring factors (e.g. noise, pile-up)
 The two quantities of greatest importance to be extracted from detector signals
are:
• amplitude:
energy, nature of the particle, localization
• time of occurrence:
localization
06 April 2005
Luciano Musa
2
Signal Processing in High Energy Physics
Means of Detection
 Each detection method has to extract some energy from the particle to be
detected
 Nearly all detection methods (Cerenkov and Transition Radiation Detector being
an exception) make use of ionization or excitation
 Charged particles: ionization and excitation is produced directly by the interaction
of the particle electromagnetic field with the electrons of the detection medium
 A typical particle energy (today’s experiments) is of the order of few GeV, while
the energy loss can be below the MeV level. This is an example of a nondestructive
method for detection of charged particles.
 All neutral particles must first undergo some process that transfers all or part of
their energy to charged particles. The detection method is destructive
06 April 2005
Luciano Musa
3
Signal Processing in High Energy Physics
Detection of Ionization (1/2)

In most ionization detectors the total ionization is collected using an
externally applied electrical field

Sometimes an amplification process by avalanche formation in a high
electrical field is used. Examples of detectors are:
a)
Proportional chamber;
b)
Liquid-argon chamber;
c)
Semiconductor detector.

All of them provide a certain amount of charge onto an output electrode

The electrode represents a certain capacitance

For signal-processing point of view these detectors are capacitive sources, i.e.
their output impedance is dominated by the capacitance
06 April 2005
Luciano Musa
4
Signal Processing in High Energy Physics
Detection of Ionization (2/2)
 This common feature of all detectors for particle physics allows a rather unified
approach to signal processing
 Despite of common features among various detectors used in high-energy physics,
great differences exist among them
• The typical charge at the detector output can differ by six orders of magnitude
• The output capacitances can differ by the same factor
• Signal dynamics
• Time available for the measurement
06 April 2005
Luciano Musa
5
Signal Induced by a Moving Charge
Example I
Parallel Plate Ion Chamber
QA,el = -q
Anode (A)
E
d
i
QA,ion = q
Vb
 
x
x
= -q
V’A
d
V’A(P)
x
V’A
=q
Applaying
Green’s
Theorem
d
A constant induced current flows in the external circuit
Cathode (C)
i=
06 April 2005
V’A(P)
Luciano Musa
dQA,el
dt
=-
q dx
d dt
6
Signal Induced by a Moving Charge
Cylindrical Proportional Chamber
Example II
Avalanche
region
(amplification)
Charged
particle
primary
ionization
cathode
gas
anode
electron – ion
pair
Electron
cloude
E≠0
Ion
cloude
i(t) = i0 / (1+t/t0)
06 April 2005
Luciano Musa
7
Detector Signal Processing Model
series
series
white noise
1/f noise
e2W=a
e2f=c/|f|
noiseless
preamplifier
signal
A
processor
Q · s(t)
Cd
i2W=b
i2f=d·f
parallel
parallel
white noise
f noise
Ci
If s(t) = d(t)
A(Q/(Cd+Ci))
noise power spectral density
Ax[a+b/w(Cd+Ci)2]
The detector is modeled as a current source, delivering in a current
pulse with time profile s(t) and charge Q, proportional to the energy
released, across the parallel combination of the detector capacitance Cd
and the preamplifier input capacitance Ci.
06 April 2005
Luciano Musa
8
Electronic Signal Processing
F(f)
U(f)
h(f)
F(f)
U(f)
f
Noise floor
f0
f0
f0
f
f
Improved
Signal/Noise Ratio
Example of signal filtering - the figure shows a “typical” case of noise filtering
In particle physics, the detector signals have very often a very large frequency
spectrum
The filter (shaper) provides a limitation in bandwidth, and the output signal shape
is different with respect to the input signal shape.
06 April 2005
Luciano Musa
9
Electronic Signal Processing
F(f)
U(f)
h(f)
F(f)
U(f)
f
Noise floor
f0
f0
f
f
Improved
Signal/Noise Ratio
The output signal shape is determined, for each application, by the following
parameters:
• Input signal shape (characteristic of detector)
• Filter (amplifier-shaper) characteristic
The output signal shape is chosen such to satisfy the application requirements:
• Time measurement
• Amplitude measurement
• Pile-up reduction
• Optimized Signal-to-noise ratio
06 April 2005
Luciano Musa
10
Electronic Signal Processing
f0
06 April 2005
f
Filter cuts noise. Signal BW
is preserved
Luciano Musa
11
Signal Processing
f0
06 April 2005
f
Filter cuts inside signal BW :
modified shape
Luciano Musa
12
Signal Processing for Charge Measurement
OPTIMUM PROCESSOR
signal
A
noiseless
f(t)
processor
T(s)
i(t)
Cd+Ci
n(w)
System Transfer function
AT(s) / (s  (Cd+Ci))
System Impulse response function vs(t) = ʆ-1AT(s) / (s  (Cd+Ci))
Output root mean square noise [vN2]1/2
Optimum Processor maximize
r = {Q  A/(Cd+Ci)  MAX ʆ-1(I(s)  T(s) / s) } / [vN2]1/2
06 April 2005
Luciano Musa
13
Real-time Digital Filters
Filters

A filtering device is a signal processor, capable of signal discrimination on
the basis of either frequency-domain or time-domain characteristics.

Continuous-time (analogue) filters predominant in the past


Passive:
R–L-C

Active:
Operational Amplifiers + R-L-C or R-C feedback
Nowadays discrete-time (sampled) filters, analogue (switched-capacitors)
and digital, have replaced the analogue filters in most applications:

communication, radar, seismic, biomedical, etc.

exceptions are the ultra-low power and high-speed applications

A sampled signal unitized in amplitude becomes a sequence of numbers
(digits): digital filter

As the IC scale integration progresses the employment of digital filters
increases
06 April 2005
Luciano Musa
14
Real-time Digital Filters
Analogue vs. Digital Filters
Advantages of Digital Filters

Finite-duration impulse responses are achievable

Time-varying filters (even self-adaptive) are realized without any special
component by simply programming a different set of numbers in the filter

Certain realization problems, such as negative element values, and
practical problems, such as inconveniently large components at low
frequencies, do not arise

Programmability

Greater accuracy is achieved

No sensitive to environmental conditions (e.g. temperature, supply
voltages, etc.)
Disadvantages of Digital Filters

Power

Limited by A/D speed and resolution
06 April 2005
Luciano Musa
15
Real-time Digital Filters
Why Analogue circuits?

“Real-World” signals are analogue

Analogue Signal Processing (ASP) has certain specific advantages, e.g.
low-power, no A/D conversion,speed

Mixed-mode Signal Processing (i.e. combining ASP with DSP on a VLSI
chip has become technologically possible, and is gaining in popularity)

Switched-Capacitor (SC) circuits (sampled-data, or discrete-time analogue
circuits) have largely proved themselves in VLSI technology
What about HEP?
 Filtering is almost exclusively based on continuous-time signals
 Analogue filters based on “classical” architectures
 Marginal use of discrete-time filters, both analogue and digital
06 April 2005
Luciano Musa
16
Analogue to Digital Converter
Example - 4 bits A/D Converter
D0
analog
input
Analog
ADC
4-bit
Input
D1
D2
0100 1 0111…
1
Digital
Output
D3
t
Output
Code
Full scale amplitude
1111
LSB=Full scale/2N
62.5 mV for 1V/4bits Sampling
Clock
reconstructed
signal
t
16 possible output codes
06 April 2005
1
1
Luciano Musa
0000
17
Analogue to Digital Converter
Time and Amplitude Resolution
Limiting Factors in the Time and Amplitude resolution
• Time: Aperture time and Clock Jitter
• Amplitude: Noise floor
signal
jitter
clock
06 April 2005
Luciano Musa
18
Analogue to Digital Converter
Accuracy – Speed
ENOB
22
20
18
16
14
12
10
8
6
4
2
0
10K
06 April 2005
Heisenberg
1Kohm thermal
1ps jitter
Sampling
Sample/s
100K
1M
10M
100M
Luciano Musa
1G
10G
100G
19
The Uniform Sampling Theorem
The Uniform Sampling Theorem

Introduced by Shannon in 1948 (original idea by Nyquist in 1928)

It establishes the theoretical maximum sampling interval for complete
signal reconstruction

The theorem holds (rigorously) only for physically unrealizable bandlimited signals

Band-limited signals are a good approximation of many signal
encountered in practice
06 April 2005
Luciano Musa
20
The Uniform Sampling Theorem
Fourier Spectrum of a band-limited function f(t)
F(ω) = f  t 
|F(w)|
p(w)
(low pass filter)
 wc
wc
0
F(ω) = 0
ω  ωc
ωc = 2 πf c
w
Theorem
f(t) is uniquely determined by its values at uniform time intervals that are 1/2fc
seconds apart
fn = f
06 April 2005







n
2f
c







=f







nπ
ω
c







Cardinal function




sin ωc t  nπ 

f (t ) =
fn
ωc t  nπ
n = 
n =
Luciano Musa
Nyquist frequency
2fc
21
Difference Equation
Key element of a sampled-data system
ANALOG
antialias
WORLD
filter
S&H
A&D
input samples f(nT)
DSP
reconstr.
D/A
Readout & Recording
filter
DIGITAL FILTER
ANALOG
WORLD
output samples u(nT)
Difference Equation
The operation of the filter is described by a difference equation that relates
u(nT) as a function of the present input sample f(nT) and any number of past
input and output samples
Recursion
formula
06 April 2005
u nT =
q
m
L f  nT iT    K u nT iT 
i=0 i
i =1 i

Luciano Musa
22
Difference Equation
Example of a Difference Equation Computation
First-order difference equation (m=1, q=3)
u(nT) = 3f(nT) – 2f(nT – T) + 6f(nT - 2T) + 2f(nT – 3T) – u(nT-T)
fs(t)
us(t)
5
50
4
40
Input function
3
30
2
20
1
10
Ouput function
…
1
0
1
2
3
4
t/T 
0
3
2
5
4
7
6
t/T 
-10
-20
06 April 2005
Luciano Musa
23
Difference Equation
The recursiveness of the Difference Equation suggest for its implementation:
a)
program a General Purpose Computer
b)
program a Digital Signal Processor
c)
Hardwired Digital Filter
Digital Filter Simulation of a First-Order Difference Equation
Recursion
formula
u nT = K u nT T   L f(nT)
1
0
u(nT)
f(nT)
L0
+
+
Adder
L0
Multiplier
T
Delay (Register)
T
K1
06 April 2005
Luciano Musa
24
The z-Transform
Continuous-Time
The Laplace transform reduces constant-coefficient linear
Domain
differential equations to linear algebraic equations
Discrete-Time
The z-transform reduces constant-coefficient linear
Domain
difference equations to linear algebraic equations
Four tools for the analysis, synthesis, and understanding of linear timeinvariant electronic systems, either continuous or discrete time:
• Fourier transform
• Laplace transform
• Hilbert transform
• z-transform
06 April 2005
Luciano Musa
25
The z-Transform
The ideal sampler circuit
f(t)
F(s)
fs(t)
Fs(s)
T
f(t) is a real-life causal signal

f(t) = 0 for t < 0
fs(t)
f(t)
We consider f(t) as modulating d(t)
d(t) is a train of periodic impulse
functions of area T
...
0
T
2T
3T
4T
5T
t
   
f s (t) = f(t) d(t) = T  f  nT δ t  nT
n=0
06 April 2005
Luciano Musa
26
The z-Transform
The sampling process regarded as a modulation process
   
f s (t) = f(t) d(t) = T  f  nT δ t  nT
n=0
LAPLACE TRANSFORM
    nTs
Fs (s) =  f  nT e
n=0
Unfortunately Fs(s) contains exponentials, hence is not algebraic in s.
Z-transform
z= esT
06 April 2005
or
s= 1 lnz
T

Zf s (t ) = F(z) =  f  nT  z n
n=0
Luciano Musa
27
Mapping the s-Plane into the z-Plane
z= esT
Im
s = σ jω
Im
z = e jωT
jw
s-plane
z-plane
s
0
0
Re
Sampled time functions that exponentially
1
Re
Oscillating sampled time functions
decrease with increasing time
Sampled time functions that exponentially
Z=1, constant or increasing functions
increase with increasing time
depending on the multiplicity of the pole
06 April 2005
Luciano Musa
28
Frequency-Domain Characteristics
1 
Fs (s) =   F(s jnωs )
T n=0
|F(jw)|
Function not band-limited
0
w
EFFECT OF SAMPLING
|Fs(jw)|
ws
06 April 2005
0
Luciano Musa
Aliasing or Foldover
ws
w
29
The z-Transform
|F(jw)|
Band-limited function
wc
ws  2wc
wc
w
wc
ws
|Fs(jw)|
2ws
ws
wc
0
2ws
w
|Fs(jw)|
ws< 2wc
3ws
06 April 2005
0
2ws
ws wc
0
wc
Luciano Musa
ws
2ws
3ws
w
30
Digital Networks
Digital filter network values are easily obtained, often by inspection
q
Lz i
U(z) i = 0 i
H(z)=
=
i
F(z) 1 m
 Kz
i
i= 1

q
m
u(nT) =  L f(nT iT)  Ku(nT iT)
i
i
i= 0
i= 1
Difference equation
Canonic Form
System Function
Feed-forward path
L0
L1
L2
Lq
fs(t)
+
Z-1
Z-1
Z-1
Z-1
+
us(t)
-K1
m delays
-K2
-Kq
-Km
Feed-back path
06 April 2005
Luciano Musa
31
Digital Networks
Digital filter network values are easily obtained, often by inspection
q
Lz i
U(z) i = 0 i
H(z)=
=
i
F(z) 1 m
 Kz
i
i= 1

q
m
u(nT) =  L f(nT iT)  Ku(nT iT)
i
i
i= 0
i= 1
Difference equation
System Function
If all Ki’s are 0
Non-recursive
L0
L1
L2
fs(t)
+
Z-1
Z-1
Z-1
Lq
+
us(t)
q delays
06 April 2005
Luciano Musa
32
An example of Ionization Detector - Time Projection Chamber
TPC Working Principle
GAS VOLUME
88 m3
E
E
DRIFT GAS
90% Ne - 10%CO2
400 V / cm
88ms
06 April 2005
Luciano Musa
33
An example of Ionization Detector - Time Projection Chamber
TPC WORKING PRINCIPLE
06 April 2005
Luciano Musa
34
How to Measure in a High Track Density?
Aliroot: Montecarlo with microscopic TPC simulation
1000
cluster peaks
montecarlo data
900
800
700
600
Pad Row:
9
Nr samples after zero suppression:
310
Nr clusters:
76
Mean time between clusters:
1.2 ms
500
400
Physics of the Aliroot Monte Carlo
300
 Ionization in gas
 Generation of secondary electrons
200
 Diffusion of electrons
 Electron attachment
100
 E x B effect near the anode wires
 Avalanche of the anode wire
0
0
100
200
300
400
 Charge induced
500
600
on700
pads and pad response function
 Shaping and sampling time signal
06 April 2005
Luciano Musa
35
The Ion–Tail Problem
Test of Inner Readout Chamber with final FEE in Field Cage prototype
Ionization from 83Kr Decay
Ion tail
06 April 2005
Luciano Musa
36
The Ion–Tail Problem
Aliroot:
Montecarlo
with
microscopic
TPC simulation
Aliroot
data
convoluted
measured
signal
Montecarlo
data through with
NA49-FTPC
amplifier
1000
1000
cluster peaks
cluster peaks
montecarlo
NA49-FTPC
amplifierdata
response
900
900
800
800
700
700
600
600
Pad Row:
9
Nr samples after zero suppression:
310
Nr clusters:
76
Mean time between clusters:
1.2 ms
500
500
400
400
300
300
200
200
100
100
00
00
06 April 2005
100
100
200
200
300
300
400
400
Luciano Musa
500
500
600
600
700
700
37
The Ion–Tail Problem
Aliroot data
convoluted
measured
signal
Montecarlo
data through with
NA49-FTPC
amplifier
200
cluster peaks
NA49-FTPC amplifier response
150
100
50
0
Signal corresponding to 1 MIP
-50
06 April 2005
0
100
200
300
400
Luciano Musa
500
600
700
38
TPC FEE OVERVIEW
Front End Card (128 CHANNELS)
DETECTOR
L2: < 100 ms
200 Hz
L1: 6.5ms
1 KHz
drift region
88ms
Capton
cable
power consumption
< 40 mW / channel
Custom
Backplane
8 CHIPS (16 CH / CHIP)
8 CHIPS (16 CH / CHIP)
gating grid
ALTRO
PASA
anode
wire
570132 PADS
pad
plane
1 MIP = 4.8 fC
S/N = 30 : 1
DYNAMIC = 30 MIP
06 April 2005
CUSTOM IC
(CMOS 0.35mm)
CSA
SEMI-GAUSS. SHAPER
GAIN = 12 mV / fC
FWHM = 190 ns
Digital
Circuit
ADC
CUSTOM IC (CMOS 0.25mm )
RAM
RCU
(3200 CH / RCU)
• LINEARIZATION
10 BIT
< 12 MHz
• BASELINE CORR.
• TAIL CANCELL.
MULTI-EVENT
MEMORY
• ZERO SUPPR.
Luciano Musa
39
Pre-Amplifier Shaping Amplifier (PASA)
Q
Q/Cf
Noise < 103 e
Cf
MIP =
< 1mV
T0
Tp
30mV
3x104 e
OPA
Cd
OPA
OPA
T0
integrator with
continuos reset
CSA
charge sensitive amplifier
PZ
differentiator
4 integrators
(RC)4
diff output
amplifier
OA
SA
4th order semi-gaussian shaper
REQUIREMENTS

Gain:
12mV / fC

INL:
< 0.3%

FWHM:
190ns

Crosstalk:
< 0.1%

Noise:
< 1000

Power:
< 20mW / ch
06 April 2005
Luciano Musa
40
Pre-Amplifier Shaping Amplifier (PASA)
PASA TRANSFER FUNCTION
n

1 sTp  A 
Q

Vout(s) =


(1 sT )C 1 sT 1 sT 
0 
0
f f
n

ʆ-1

 t 
n
n
Q

A

n
Vout(t) =
  e
C n!  T 
f
 s
n
Peaking time Ts = nT0
 nt
Ts
n
Vout(peak) = QA n /Cf n!e
n
1
0.8
0.6
0.4
0.2
2
4
5
6
7
Vout peak vs. n
Vout (normalized to 1 ) vs. n
06 April 2005
3
Luciano Musa
41
Pre-Amplifier Shaping Amplifier (PASA)
IMPULSE RESPONSE FUNCTION
Q = 149 fC
out-
FWHM = 190 ns out+
06 April 2005
Luciano Musa
A(t / t)4e-4(t/t)
42
ALTRO Block Diagram
Data Processor
TSA1001
10-bit
25 MSPS
40 MSPS
Correction of:
• Slow drifts and systematic effects
• Non-systematic effects
Tail filtering
Data compression
40-bit back
linked format
• Channel
address
• Time stamp
Memory
5 kbyte
4 or 8
buffers
Input Signal
0
L1: acquisition
L2: event freeze
Trigger signals
40-bit wide bus
Bandwidth: 300 Mbyte/s
Readout bus
06 April 2005
Luciano Musa
43
Baseline Correction 1
Systematic perturbation
Baseline drift
Fixed pedestal
Slow drifts
Systematic perturbation
Combination
H(z) = (1-z-1) / (1-0.5)z-1
fpd = 0
06 April 2005
Luciano Musa
44
Tail Cancellation Filter
 Functions
 signal (ion) tail suppression
 pulse narrowing  improves cluster separation
 gain equalization
Filtro
compensates undershoot
 Architecture
 3rd order IIR filter
 18-bit fixed point 2’sC arithmetic
 single channel configuration  6 coefficients / channel
11 bits
word
extension
2’sC
18 bits
3rd order
IIR filter
2’sC
18 bits
2’sC
Filtro
Narrows the pulse
word
rounding
11 bits
2’sC
input
output
11 bit
11 bit
-1
Z
K1
06 April 2005
L1
-1
Z
L2
K2
-1
Z
L3
K3
1 L1 z 1  1 L2 z 1  1 L3 z 1
H
(
z
)
=
18-bit fixed point arithmetic
1 K1 z 1 1 K 2 z 1 1 K 3 z 1
Luciano Musa
45
The Ion–Tail Problem
ADC counts
DIGITAL TAIL CANCELLATION PERFORMANCE
200
filter input
threshold
150
filter off
100
50
0
Signal corresponding to 1 MIP
-50
0
100
200
300
400
500
600
700
Time samples (170 ns)
ADC counts
Filtered data and fixed threshold
200
filter output
threshold
150
filter on
100
50
0
-50
06 April 2005
0
100
200
300
400
Luciano Musa
500
600
700
Time samples (170 ns)
46
Baseline Correction 2
After Tail Cancellation Filter
After Baseline Correction II
Characteristics:
Double threshold
• Corrects non-systematic perturbations during the
processing time
• Moving Average Filter (MAF)
• Double threshold scheme (acceptance window)
Operation
BC II
A fixed
threshold can
now be
applied safely
1. Slow variations of the signal  Baseline updated
2. Fast variations of the signal  Baseline value frozen
din - bsl + offset
, 0  dout  1023
0
, dout < 0
din - bsl + offset - 1024, dout > 1023
bslbsl
calculation
frozen
bsl =
1
 dinn
8 8


1 

1

2

8

1

H ( z) = z 1 1 z  z  z 
8


Unsigned 11-bit FIR system
06 April 2005
Luciano Musa
47
Experimental Results
Analysis of the ion signal tail
cosmic rays
Baseline
Moving average
06 April 2005
Luciano Musa
48
Experimental Results
ALTRO Signal Processing
Tail Cancellation
• raw signal
• moving average
• after signal processing
Baseline Restoration
06 April 2005
Luciano Musa
49
Experimental Results
ALTRO Signal Processing
HIGH MULTIPLICITY COSMIC RAYS
Occupancy ~ 50%
• raw samples
• after signal processing
06 April 2005
Luciano Musa
50
ALTRO layout and production data
Process
HCMOS-7 (0.25 µm)
Area
64 mm2
Dimensions
7.70 × 8.35 mm2
Transistors
6 milions
Embedded
800 kbit
The ALTRO Chip: a 16-channel A/D Converter and Digital Processor
for Gas Detectors
memory
R. Esteve et al.
- IEEE Transactions on Nuclear Science, Vol. 50,
No. 6 December 2003
Supply
voltage
06 April 2005
Luciano Musa
2.5 V
Power
16mW / channel
Package
TQFP-176
ER (12 wafers)
Apr ’02
Mass prod.
(125 wafers)
Dec ’02
Yield
84%
51
Digital Conditioning of the TPC Signal
ALIROOT CLUSTERS
+
BASELINE PERTURBATIONS
ADC counts
EVENT 2
Baseline perturbations:
• temp. variation (ramp-up)
• gating grid switching
• power supply instability
• pick-up noise
EVENT 1
EVENT 3
time samples
06 April 2005
Luciano Musa
52
Digital Conditioning of the TPC Signal
ADC
BC I
TCF
BC II
06 April 2005
Luciano Musa
53