1
ELEC

2005
Electronics in High Energy Physics
Winter Term: Introduction to electronics in HEP
ANALOG SIGNAL PROCESSING
OF PARTICLE DETECTOR SIGNALS
PART 1
Francis ANGHINOLFI
January 20, 2005
Francis.Anghinolfi@cern.ch
CERN Technical Training 2005
2
ANALOG SIGNAL PROCESSING
OF PARTICLE DETECTOR SIGNALS
•
Introduction
•
Detector Signal collection
•
Electronic Signal Processing
•
Front

End : Preamplifier & Shaper
•
Considerations on Detector Signal Processing
3
CREDITS :
Dr. Helmut SPIELER, LBL Laboratory
Dr. Veljko RADEKA, BNL Laboratory
Dr. Willy SANSEN, KU Leuven
REFERENCES
Low

Noise Wide

Band Amplifiers in Bipolar and CMOS Technologies,
Z.H. Chang, W. Sansen, Kluwer Academics Publishers
Low

Noise Techniques in Detectors, V. Radeka, Annual Review of
Nuclear Particle Science 1988
28: 217

277
Pierre JARRON, CERN
4
Introduction
In this one hour lecture we will give an insight into electronic signal processing,
having in mind the application for particle physics.
•
Specific issue about signal processing in particle physics
•
Time/frequency signal and circuit representation
•
(Short) description of a typical “front

end” channel for particle physics
detector
In the next one hour lecture, there will be an approach of the “noise” problem :
•
Noise sources in electronics circuit
•
Introduction to the formulation of Equivalent Noise Charge (ENC) in case of
circuits used for detector signals.
5
Introduction
We will look at both frequency and time domain representations
•
Time domain : what we see on a scope
•
Frequency domain : mathematics, representations are easier *
OF SIGNALS AND CIRCUITS
* Frequency representation is not applicable to all types of circuits
6
Introduction
What we will NOT cover in this lecture :
Detail representation of either detector system or amplifier circuit.
Active components models (as for MOS or Bipolar transistors).
The above items, or a part of them, will be covered in other lectures of the present
course ...
7
Detector Signal Collection
Amplifier
Particle detector collects charges :
ionization in gas detector, solid

state
detector
a particle crossing the medium generates
ionization + ions avalanche (gas detector)
or electron

hole pairs (solid

state).
Charges are collected on electrode plates
(as a capacitor), building up a voltage or a
current
Function is multiple :
signal amplification (signal multiplication
factor)
noise rejection
signal “shape”
Typical “front

end” elements
Final objective :
amplitude measurement and/or
time measurement
Z
+

Board, wires, ...
Particle Detector
Circuit
Rp
8
Detector Signal Collection
If Z is high, charge is kept on capacitor
nodes and a voltage builds up (until
capacitor is discharged)
If Z is low charge flows as a current
through the impedance in a short time.
In particle physics, low input impedance
circuits are used:
•
limited signal pile up
•
limited channel

to

channel crosstalk
•
low sensitivity to parasitic signals
Typical “front

end” elements
Z
+

Board, wires, ...
Particle Detector
Circuit
Rp
9
Detector Signal Collection
Particle Detector
Circuit
Tiny signals (Ex: 400uV collected
in Si detector on 10pF)
Noisy environment
Collection time fluctuation
Large signals, accurate in amplitude
and/or time
Affordable S/N ratio
Signal source and waveform
compatible with subsequent circuits
Zo
Z
+

Board, wires, ...
Particle Detector
Circuit
Rp
10
Detector Signal Collection
Circuit
Low Z output voltage source circuit can drive any load
Output signal shape adapted to subsequent stage (ADC)
Signal shaping is used to reduce noise (unwanted fluctuations) vs. signal
Zo
Z
+

High Z
Low Z
Low Z
T
Voltage source
•
Impedance adaptation
•
Amplitude resolution
•
Time resolution
•
Noise cut
Rp
11
Electronic Signal Processing
H
X(t)
Y(t)
Time domain :
Electronic signals, like voltage, or current, or charge can be described in time
domain.
H in the above figure represents an object (circuit) which modifies the (time)
properties of the incoming signal X(t), so that we obtain another signal Y(t). H
can be a filter, transmission line, amplifier, resonator etc ...
If the circuit H has linear properties
like :
if X1

> Y1 through H
if X2

> Y2 through H
then X1+X2

> Y1+Y2
The circuit H can be represented by a linear function of time H(t) , such that
the knowledge of X(t) and H(t) is enough to predict Y(t)
12
Electronic Signal Processing
H(t)
X(t)
Y(t)
Y(t) = H(t)*X(t)
In time domain, the relationship between X(t), H(t) and Y(t) is expressed
by the following formula :
This is the convolution function, that we can use to completely
describe Y(t)
from the knowledge of both X(t) and H(t)
u)du

H(u)X(t
X(t)
*
H(t)
Where
Time domain prediction by using convolution is complicated …
13
Electronic Signal Processing
H(t) = H(t)*
d
(t)
H(t)
d
(t)
H(t)
d
(t)
H
What is H(t) ?
(Dirac function)
If we inject a “Dirac” function to a linear system, the output signal is the
characteristic function H(t)
H(t) is the transfer function in time domain, of the linear circuit H.
14
Electronic Signal Processing
dt
.
ft)
j2
X(t).exp(
x(f)
Frequency domain :
The electronic signal X(t) can be represented in the frequency domain by
x(f), using the following transformation
(Fourier Transform)
This is *not* an easy transform, unless we assume that X(t) can be
described as a sum of “exponential” functions, of the form :
The conditions of validity of the above transformations are
precisely defined. We assume here that it applies to the signals
(either periodic or not) that we will consider later on
)
2
exp(
X(t)
t
f
j
c
k
k
15
6
4
2
2
4
6
1
0.5
0.5
1
Electronic Signal Processing
0
dt
.
ft)
(j2
exp
.
(at)
exp
x(f)
Example :
The “frequency” domain representation x(f) is using complex
numbers.
)
exp(
X(t)
at
For (t >0)
0
dt
.
f)t)
j2
exp((a
x(f)
x(f)
6
4
2
2
4
6
0.2
0.4
0.6
0.8
1
1
2
3
4
5
0.5
1
1.5
2
Arg(x(f))
f
j2
a
1
x(f)
X(t)
16
Electronic Signal Processing
Some usual Fourier Transforms :
–
d
(t)

> 1
–
(t)

> 1/j
w
–
e

at

> 1/(a+ j
w
)
–
t
n

1
e

at

> 1/(a+ j
w
)
n
–
d
(t)

a.e

at

> j
w
/(a+ j
w
)
The Fourier Transform applies equally well to the signal representation
X(t) x(f) and to the linear circuit transfer function H(t) h(f)
h(f)
x(f)
y(f)
17
Electronic Signal Processing
h(f)
x(f)
y(f)
y(f) = h(f).x(f)
With the frequency domain representation (signals and circuit transfer
function mapped into frequency domain by the Fourier transform), the
relationship between input, circuit transfer function and output is simple:
x(f)
y(f)
h2(f)
h3(f)
h1(f)
y(f) = h1(f). h2(f). h3(f). x(f)
Example : cascaded systems
18
Electronic Signal Processing
h(f)
y(f)
f
j2
1
1
h(f)
)
(
)
(
X
t
t
f
j2
1
)
f
(
x
f)
j2
f(1
j2
1
y(f)
RC low pass filter
1
t
1
2
3
4
5
0.2
0.4
0.6
0.8
1
)
exp(
1
)
(
Y
t
t
x(f)
R
C
19
Electronic Signal Processing
h(f)
x(f)
y(f)
Fourier Transform
dt
.
H(t).e
h(f)
f.t
.
j2

Frequency representation can be used to predict time response
X(t)

> x(f) (Fourier transform)
H(t)

> h(f) (Fourier transform)
h(f) can also be directly formulated from circuit analysis
Apply
y(f) = h(f).x(f)
Then y(f)

> Y(t) (inverse Fourier Transform)
Inverse Fourier Transform
df
.
h(f).e
H(t)
f.t
.
j2
20
Electronic Signal Processing
h(f)
x(f)
y(f)
•
THERE IS AN EQUIVALENCE BETWEEN TIME AND FREQUENCY
REPRESENTATIONS OF SIGNAL or CIRCUIT
•
THIS EQUIVALENCE APPLIES ONLY TO A PARTICULAR CLASS OF
CIRCUITS, NAMED “TIME

INVARIANT” CIRCUITS.
•
IN PARTICLE PHYSICS, CIRCUITS OUTSIDE OF THIS CLASS CAN
BE USED : ONLY TIME DOMAIN ANALYSIS IS APPLICABLE IN THIS
CASE
H(t)
X(t)
Y(t)
21
Electronic Signal Processing
y(f) = h(f).x(f)
d
(f)
h(f)
d
(f)
f
h(f)
f
h(f)
In frequency domain, a system (h) is a frequency domain “shaping”
element. In case of h being a filter, it selects a particular frequency domain
range. The input signal is rejected (if it is out of filter band) or amplified (if
in band) or “shaped” if signal frequency components are altered.
x(f)
y(f)
x(f)
f
y(f)
f
h(f)
Dirac function frequency representation
h(f)
f
22
Electronic Signal Processing
y(f) = h(f).x(f)
vni(f)
vno(f)
noise
f
h(f)
The “noise” is also filtered by the system h
Noise components (as we will see later on) are often “white noise”, i.e.: constant
distribution over all frequencies (as shown above)
So a filter h(f) can be chosen so that :
It filters out the noise “frequency” components which are outside of the frequency band
for the signal
Noise power limited by filter
f
“Unlimited” noise power
23
Electronic Signal Processing
x(f)
y(f)
x(f)
f
y(f)
f
h(f)
f
Noise floor
f0
f0
f0
Improved Signal/Noise
Ratio
Example of signal filtering : the above figure shows
a «
typical
» case
,
where only noise is filtered out.
In particle physics, the input signal, from detector, is often a very fast
pulse, similar to a “Dirac” pulse. Therefore, its frequency representation
is over a large frequency range.
The filter (shaper) provides a limitation in the signal bandwidth and
therefore the filter output signal shape is different from the input signal
shape.
24
Electronic Signal Processing
x(f)
y(f)
x(f)
f
f
h(f)
f
Noise floor
f0
f0
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, different form the input detector signal, is chosen
f
or
the application requirements:
•
Time measurement
•
Amplitude measurement
•
Pile

up reduction
•
Optimized Signal

to

noise ratio
y(f)
25
Electronic Signal Processing
f
f0
f
f0
Filter cuts noise. Signal BW is preserved
Filter cuts inside signal BW : modified shape
26
SOME EXAMPLES OF CIRCUITS USED AS SIGNAL SHAPERS ...
Electronic Signal Processing
(Time

invariant circuits like RC, CR networks)
27
1
2
3
4
5
0.5
1
1.5
2
Electronic Signal Processing
Integrator
s

transfer function
h(s) = 1/(1+RCs)
Example RC=0.5 s=j
w
R
C
Vout
Vin
Vin
R
Xc
Xc
Vout
C
j
fC
j
Xc
w
1
2
1
Vin
RCj
Vout
w
1
1
Integrator
time
function
RC
t
e
t
/
RC
1
)
(
H
Log

Log scale
t
f
0.01
0.05
0.1
0.5
1
5
10
0.05
0.1
0.2
0.5
1
Low

pass (RC) filter
1
2
3
4
5
0.2
0.4
0.6
0.8
1
Step function response
h(s)
28
1
2
3
4
5
2
1.5
1
0.5
0.5
1
Electronic Signal Processing
Differentiator
s

transfer function
h(s) = RCs/(1+RCs)
Vout
Vin
Vin
R
Xc
R
Vout
C
j
fC
j
Xc
w
1
2
1
Vin
RCj
RCj
Vout
w
w
1
Differentiator
time
function
RC
t
e
t
t
/
RC
1
)
(
)
(
H
d
R
C
Example RC=0.5 s=j
w
0.01
0.05
0.1
0.5
1
5
10
0.05
0.1
0.2
0.5
1
High

pass (CR) filter
1
2
3
4
5
0.2
0.4
0.6
0.8
1
Step response
Log

Log scale
f
h(s)
Impulse response
29
0.01
0.05
0.1
0.5
1
5
10
0.015
0.02
0.03
0.05
0.07
0.1
0.15
0.2
Electronic Signal Processing
CR

RC
s

transfer function
h(s) = RCs/(1+RCs)
2
Vout
Vin
RCj
ω
(
RCj
ω
Vout
2
)
1
CR

RC
time
function
RC
t
e
RC
t
t
/
)
/
1
(
)
(
H
Example RC=0.5 s=j
w
1
2
3
4
5
0.2
0.2
0.4
0.6
0.8
1
Vin
R
C
R
C
1
Combining one low

pass (RC) and one high

pass (CR) filter :
2
4
6
8
10
12
14
0.025
0.05
0.075
0.1
0.125
0.15
0.175
Step response
Log

Log scale
f
h(s)
HighZ
Low Z
Impulse response
30
Electronic Signal Processing
CR

RC
4
s

transfer function
h(s) = RCs/(1+RCs)
5
Vout
Vin
RCj
RCj
Vout
n
)
1
(
w
w
CR

RC
4
time
function
RC
t
e
t
RC
t
t
/
3
).
/
4
(
)
(
H
R
C
Example RC=0.5, n=5 s=j
w
Vin
R
C
1
Combining n low

pass (RC) and one high

pass (CR) filter :
0.001
0.005
0.01
0.05
0.1
0.5
1
0.0001
0.0002
0.0005
0.001
0.002
0.005
0.01
0.02
2
4
6
8
10
0.005
0.0025
0.0025
0.005
0.0075
0.01
2
4
6
8
10
0.002
0.004
0.006
0.008
0.01
0.012
Log

Log scale
f
h(s)
Step response
R
C
1
n times
Impulse response
31
Electronic Signal Processing
h(s) = RCs/(1+RCs)
5
Shaper circuit
frequency spectrum
Noise Floor
+20db/dec

80db/dec
The shaper limits the noise bandwidth. The choice
of the shaper function defines the noise power available at the ou
t
put.
Thus, it defines the signal

to

noise ratio
f
32
Preamplifier & Shaper
Preamplifier
Shaper
d
(t)
Q/C.
(t)
I
O
What are the functions of preamplifier and shaper (in ideal world) :
•
Preamplifier :
is an ideal integrator : it detects an input charge burst
Q
d
(t).
The output is a voltage step Q/C.
(t). Has large signal gain
such that noise of subsequent stage (shaper) is negl
i
gible.
•
Shaper :
a filter with : characteristics fixed to give a predefined
output signal shape, and rejection of noise frequency components
which are outside of the signal frequency range.
33
2
4
6
8
10
12
14
0.025
0.05
0.075
0.1
0.125
0.15
0.175
Preamplifier & Shaper
Preamplifier
Shaper
CR_RC2 shaper
Ideal Integrator
d
(t)
1/s
RCs /(1+RCs)
2
x
I
O
T.F.
from I to O
=
RC
t
e
t
t
/
1
)
(
RC
O
= RC/(1+RCs)
2
Output signal of preamplifier
+ shaper with one charge at
the input
t
1
2
3
4
5
0.2
0.2
0.4
0.6
0.8
1
1
2
3
4
5
0.2
0.4
0.6
0.8
1
0.01
0.05
0.1
0.5
1
5
10
0.015
0.02
0.03
0.05
0.07
0.1
0.15
0.2
0.2
0.5
1
2
5
10
0.1
0.2
0.5
1
2
5
t
f
t
f
Q/C.
(t)
34
5
10
15
20
25
30
35
0.02
0.04
0.06
0.08
0.1
Preamplifier & Shaper
2
4
6
8
10
0.005
0.0025
0.0025
0.005
0.0075
0.01
Preamplifier
Shaper
d
(t)
1/s
RCs /(1+RCs)
5
x
I
O
T.F.
from I to O
=
= RC/(1+RCs)
5
Output signal of
preamplifier + shaper with
“ideal” charge at the input
t
1
2
3
4
5
0.2
0.4
0.6
0.8
1
t
0.2
0.5
1
2
5
10
0.1
0.2
0.5
1
2
5
f
t
RC
t
e
t
t
O
/
4
4
RC
1
)
(
0.001
0.005
0.01
0.05
0.1
0.5
1
0.0001
0.0002
0.0005
0.001
0.002
0.005
0.01
0.02
f
CR_RC4 shaper
Ideal Integrator
Q/C.
(t)
35
Preamplifier & Shaper
Vout
Cf
Schema of a Preamplifier

Shaper circuit
N Integrators
Diff
Semi

Gaussian Shaper
Cd
T
0
T
0
T
0
Vout(s) = Q/sCf . [sT
0
/1+ sT
0
].[A/1+ sT
0
]
n
Vout(t) = [QA
n
n
n
/Cf n!].[t/Ts]
n
.e

nt/Ts
Peaking time Ts = nT0 !
Output voltage at peak is given by :
Vout shape vs. n order,
renormalized to 1
Vout peak vs. n
2
3
4
5
6
7
0.2
0.4
0.6
0.8
1
Voutp = QA
n
n
n
/Cf n!e
n
36
5
10
15
20
0.01
0.02
0.03
Preamplifier & Shaper
Preamplifier
Shaper
CR_RC shaper
Non

Ideal Integrator
d
(t)
1/(1+T1s)
RCs /(1+RCs)
2
I
O
T.F.
from I to O
x
Non ideal shape, long tail
Integrator
baseline
restoration
37
2
4
6
8
10
12
14
0.025
0.05
0.075
0.1
0.125
0.15
0.175
Preamplifier & Shaper
Preamplifier
Shaper
d
(t)
1/(1+T1s)
(1+T1s) /(1+RCs)
2
Pole

Zero Cancellation
I
O
T.F.
from I to O
x
CR_RC shaper
Non

Ideal Integrator
Ideal shape, no tail
Integrator
baseline
restoration
38
Preamplifier & Shaper
Vout
Schema of a Preamplifier

Shaper circuit
with pole

zero cancellation
Vout(s) = Q/(1+sTf)Cf . [(1+sTp)/1+ sT0].[A/1+ sT0]
n
By adjusting Tp=Rp.Cp and Tf=Rf.Cf such that Tp = Tf, we
obtain the same shape as with a perfect integrator at the input
Rf
Cf
N Integrators
Diff
Semi

Gaussian Shaper
Cd
Cp
T
0
T
0
Rp
39
Considerations on Detector Signal Processing
Pile

up :
A fast return to zero time is required to :
•
Avoid cumulated baseline shifts (average detector pulse rate should be known)
•
Optimize noise as long tails contribute to larger noise level
2
4
6
8
10
12
14
0.025
0.05
0.075
0.1
0.125
0.15
0.175
2
nd
hit
40
Considerations on Detector Signal Processing
Pile

up
•
The detector pulse is transformed by the front

end circuit to obtain a signal
with a
finite
return to zero time
2
4
6
8
10
12
14
0.025
0.05
0.075
0.1
0.125
0.15
0.175
5
10
15
20
25
30
35
0.02
0.04
0.06
0.08
0.1
CR

RC :
Return to baseline
> 7*Tp
CR

RC4 :
Return to
baseline < 3*Tp
41
Considerations on Detector Signal Processing
Pile

up :
A long return to zero time does contribute to excessive noise :
5
10
15
20
0.01
0.02
0.03
Uncompensated pole zero CR

RC filter
Long tail contributes to the increase of electronic noise (and
to baseline shift)
42
Considerations on Detector Signal Processing
Time

variant filters :
“TIME

VARIANT” filters have been developed which provide well

defined
“finite” time responses :
T
Ex : Gated Integrator
The time response is strictly limited in time because of the switching
The frequency representation does not apply : signal processing is analyzed
in time domain (an approach is given in this lecture, Part 2)
43
Considerations on Detector Signal Processing
Summary (1)
•
The detector pulse is transformed by the front

end circuit to obtain :
•
A linear Gain (Vout/Q
det
= Cte)
•
An impedance adaptation (Low input impedance, low output
impedance)
•
A signal shape with some level of integration
•
A reduction in the amount of electronic noise
•
A dynamic range (or Signal

to

Noise ratio)
44
Considerations on Detector Signal Processing
Summary (2)
•
Time

variant and time

invariant filters have been developed to cope
with the very specific demands of particle physics detector signal
processing
•
Very large dynamic range is attainable (16 bits, as for calorimeters)
•
Very low noise is achievable in some cases (a few electrons !)
•
Peaking time are varying from a few ns (tracking application) to ms
range (very low noise systems, amplitude resolution)
•
The choice of the suitable front

end circuit is usually a trade

off
between key parameters (peaking time, noise, power)
45
Considerations on Detector Signal Processing
Some parameters of front

end circuits used for LHC detectors
•
Pixel : 100ns shaping time, 180 el ENC, <1pF detector
•
Silicon strips : 25 ns shaping time, 1500 el ENC, 20pF detector
•
Calorimeter : 16 bits dynamic range, 20

40ns shaping time
•
Time

Of

Flight measurement : 1 ns peaking time, 3000 el ENC,
10pF detector
8 channel NINO front

end
For Alice TOF
46
ELEC

2005
Electronics in High Energy Physics
Winter Term: Introduction to electronics in HEP
ANALOG SIGNAL PROCESSING
OF PARTICLE DETECTOR SIGNALS
PART 1
Francis ANGHINOLFI
January 20, 2005
Francis.Anghinolfi@cern.ch
CERN Technical Training 2005
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