Transcript 1-Electronic signal Processing

CERN Technical Training 2005
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
[email protected]
1
ANALOG SIGNAL PROCESSING
OF PARTICLE DETECTOR SIGNALS
• Introduction
• Detector Signal collection
• Electronic Signal Processing
• Front-End : Preamplifier & Shaper
• Considerations on Detector Signal Processing
2
CREDITS :
Dr. Helmut SPIELER, LBL Laboratory
Dr. Veljko RADEKA, BNL Laboratory
Dr. Willy SANSEN, KU Leuven
Pierre JARRON, CERN
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
3
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.
4
Introduction
We will look at both frequency and time domain representations
OF SIGNALS AND CIRCUITS
• Time domain : what we see on a scope
• Frequency domain : mathematics, representations are easier *
* Frequency representation is not applicable to all types of circuits
5
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 ...
6
Detector Signal Collection
Typical “front-end” elements
Board, wires, ...
+
Rp
Z
-
Particle Detector
Circuit
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
Amplifierbuilding up a voltage or a
(as a capacitor),
current
Function is multiple :
Final objective :
signal amplification (signal multiplication
factor)
amplitude measurement and/or
noise rejection
time measurement
signal “shape”
7
Detector Signal Collection
Typical “front-end” elements
Board, wires, ...
+
Rp
Z
-
Particle Detector
Circuit
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
8
Detector Signal Collection
Board, wires, ...
+
Rp
Particle Detector
Tiny signals (Ex: 400uV collected
in Si detector on 10pF)
Z
Zo
-
Noisy environment
Collection time fluctuation
Circuit
Particle Detector
Circuit
Large signals, accurate in amplitude
and/or time
Affordable S/N ratio
Signal source and waveform
compatible with subsequent circuits
9
Detector Signal Collection
High Z
Low Z
+
Rp
-
• Impedance adaptation
• Amplitude resolution
• Time resolution
• Noise cut
Voltage source
Zo
Z
Circuit
Low Z
T
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
10
Electronic Signal Processing
Time domain :
X(t)
H
Y(t)
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)
11
Electronic Signal Processing
X(t)
Y(t)
H(t)
In time domain, the relationship between X(t), H(t) and Y(t) is expressed
by the following formula :
Y(t) = H(t)*X(t)
Where

H(t)* X(t)  H(u)X(t- u)du

This is the convolution function, that we can use to completely
describe Y(t) from the knowledge of both X(t) and H(t)
Time domain prediction by using convolution is complicated …
12
Electronic Signal Processing
What is H(t) ?
d(t)
d(t)
H(t)
H
H(t)
(Dirac function)
H(t) = H(t)* d (t)
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.
13
Electronic Signal Processing
Frequency domain :
The electronic signal X(t) can be represented in the frequency domain by
x(f), using the following transformation

x(f)   X(t).exp(-j2ft).dt
(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 :

X(t)   ck exp( j 2f k t )

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
14
Electronic Signal Processing
2
X(t)  exp( at )
X(t)
1.5
Example :
1
0.5
For (t >0)
1
2
3
4
5
1

x(f)   exp (-at ). exp (-j2ft ).dt
0.8
0.6
0
0.4
0.2

-6

-4
-2
x(f)  exp(-(a  j2f)t).dt
4
6
x(f)
0
1
x(f) 
a  j2f
2
1
0.5
-6
-4
-2
2
4
-0.5
-1
The “frequency” domain representation x(f) is using complex
numbers.
Arg(x(f))
15
6
Electronic Signal Processing
Some usual Fourier Transforms :
– d(t) --> 1
– (t) --> 1/jw
– e-at --> 1/(a+ jw)
– tn-1e-at --> 1/(a+ jw)n
– d(t)-a.e-at --> jw /(a+ jw)
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)
y(f)
x(f)
h(f)
16
Electronic Signal Processing
x(f)
y(f)
h(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:
y(f) = h(f).x(f)
Example : cascaded systems
x(f)
h1(f)
h2(f)
h3(f)
y(f)
y(f) = h1(f). h2(f). h3(f). x(f)
17
Electronic Signal Processing
y(f)
x(f)
1
x (f ) 
j2f
X(t )   (t )
h(f)
h(f) 
1
1  j2f
RC low pass filter
y(f) 
1
j2f(1  j2f)
Y(t )  1  exp( t )
1
R
1
0.8
0.6
t
C
0.4
0.2
1
2
3
4
5
18
Electronic Signal Processing
y(f)
x(f)
h(f)
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)
Fourier Transform
h(f) 

 H(t).e

- j2 .f.t
Inverse Fourier Transform
.dt
H(t) 

j2 .f.t
h(f).e
.df


19
Electronic Signal Processing
y(f)
x(f)
h(f)
X(t)
Y(t)
H(t)
• 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
20
Electronic Signal Processing
y(f) = h(f).x(f)
d(f)
h(f)
h(f)
d(f)
h(f)
f
f
Dirac function frequency representation
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)
h(f)
x(f)
y(f)
f
f
h(f)
f
21
Electronic Signal Processing
y(f) = h(f).x(f)
vni(f)
vno(f)
noise
h(f)
f
f
“Unlimited” noise power
Noise power limited by filter
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
22
Electronic Signal Processing
x(f)
y(f)
h(f)
x(f)
Noise floor
f0
y(f)
f
f0
f0
f
f
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.
23
Electronic Signal Processing
x(f)
y(f)
h(f)
x(f)
Noise floor
y(f)
f
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, different form the input detector signal, is chosen
for the application requirements:
• Time measurement
• Amplitude measurement
• Pile-up reduction
• Optimized Signal-to-noise ratio
24
Electronic Signal Processing
Filter cuts noise. Signal BW is preserved
f0
f
Filter cuts inside signal BW : modified shape
f0
f
25
Electronic Signal Processing
SOME EXAMPLES OF CIRCUITS USED AS SIGNAL SHAPERS ...
(Time-invariant circuits like RC, CR networks)
26
Electronic Signal Processing
R
C
Vin
Vout
Low-pass (RC) filter
Vout 
Xc
Vin
Xc  R
Xc 
1
1

j 2fC jwC
Vout 
1
Vin
1  RCjw
Example RC=0.5 s=jw
Integrator time function
H (t ) 
2
Integrator s-transfer function
1
e t / RC
RC
h(s) = 1/(1+RCs)
1.5
|h(s)|
1
1
0.5
0.5
1
2
3
4
5
0.2
Step function response
0.1
1
t
0.8
0.6
0.05
0.01
0.05
0.1
0.5
1
5
Log-Log scale
0.4
0.2
1
2
3
4
5
27
f
10
Electronic Signal Processing
C
Vin
Vout
R
High-pass (CR) filter
R
Vout 
Vin
Xc  R
Xc 
1
1

j 2fC jwC
Vout 
RCjw
Vin
1  RCjw
Example RC=0.5 s=jw
Differentiator time function
H(t )  d (t ) 
1
Differentiator s-transfer function
1 t / RC
e
RC
h(s) = RCs/(1+RCs)
Impulse response
0.5
1
2
3
4
5
|h(s)|
1
-0.5
-1
0.5
-1.5
0.2
-2
Step response
0.1
1
f
0.05
0.8
0.01
0.05
0.1
0.5
1
5
0.6
Log-Log scale
0.4
0.2
1
2
3
4
5
28
10
Electronic Signal Processing
HighZ
1
R
Vin
C
Low Z
Vout
C
R
Combining one low-pass (RC) and one high-pass (CR) filter :
Vout 
RCjω
( 1 RCjω) 2
Vin
Example RC=0.5 s=jw
CR-RC time function
CR-RC s-transfer function
H(t )  (1  t / RC)et / RC
h(s) = RCs/(1+RCs)2
1
0.8
|h(s)|
Impulse response
0.6
0.4
0.2
0.2
0.15
1
2
3
4
5
0.1
-0.2
0.07
0.05
0.03
0.175
Step response
0.15
0.02
0.125
0.015
0.01
0.1
0.05
0.1
0.5
1
5
0.075
0.05
Log-Log scale
0.025
2
4
6
8
10
12
14
10
f
29
Electronic Signal Processing
R
Vin
R
1
C
1
C
C
Vout
R
n times
Combining n low-pass (RC) and one high-pass (CR) filter :
RCjw
Vout 
Vin
n
(1  RCjw )
Example RC=0.5, n=5 s=jw
CR-RC4 time function
CR-RC4 s-transfer function
H(t )  (4  t / RC).t 3et / RC
0.01
h(s) = RCs/(1+RCs)5
Impulse response
0.0075
|h(s)|
0.005
0.0025
0.02
2
4
6
8
10
-0.0025
0.01
0.005
-0.005
0.002
Step response
0.001
0.0005
0.012
0.0002
0.01
0.0001
0.008
0.001
0.006
0.0050.01
0.05 0.1
0.5
1
Log-Log scale
0.004
0.002
2
4
6
8
10
30
f
Electronic Signal Processing
Shaper circuit frequency spectrum
+20db/dec
-80db/dec
Noise Floor
f
h(s) = RCs/(1+RCs)5
The shaper limits the noise bandwidth. The choice
of the shaper function defines the noise power available at the output.
Thus, it defines the signal-to-noise ratio
31
Preamplifier & Shaper
I
d(t)
Preamplifier
Shaper
O
Q/C.(t)
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 negligible.
• 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.
32
Preamplifier & Shaper
I
Preamplifier
Shaper
O
1
1
0.8
0.8
0.6
0.6
t
0.4
0.2
0.4
0.2
1
2
t
3
4
5
-0.2
1
2
3
4
5
5
2
d(t)
0.5
0.2
Q/C.(t)
f
1
0.15
0.05
0.2
0.03
0.1
0.02
0.2
0.5
1
2
5
f
0.1
0.07
10
0.015
0.01
=
0.1
0.5
1
5
10
CR_RC2 shaper
Ideal Integrator
T.F.
from I to O
0.05
RCs /(1+RCs)2 = RC/(1+RCs)2
x
1/s
0.175
Output signal of preamplifier
+ shaper with one charge at
the input
0.15
0.125
0.1
0.075
0.05
t
0.025
2
4
6
8
10
12
O(t )  t
14
1
RC
e t / RC
33
Preamplifier & Shaper
I
Preamplifier
Shaper
O
1
0.01
0.8
t
0.0075
0.6
0.005
t
0.4
0.2
0.0025
2
4
6
8
10
-0.0025
1
2
3
4
-0.005
5
0.02
5
2
d(t)
Q/C.(t)
f
1
0.5
0.01
0.005
0.002
f
0.001
0.0005
0.0002
0.2
0.0001
0.1
0.2
0.5
1
2
5
10
0.001
=
0.05 0.1
0.5
1
CR_RC4 shaper
Ideal Integrator
T.F.
from I to O
0.0050.01
x
1/s
RCs /(1+RCs)5 = RC/(1+RCs)5
0.1
Output signal of
preamplifier + shaper with
“ideal” charge at the input
0.08
0.06
0.04
0.02
t
5
10
15
20
25
30
O(t )  t 4
35
1 t / RC
e
4
RC
34
Preamplifier & Shaper
Schema of a Preamplifier-Shaper circuit
Cf
Diff
N Integrators
Vout
Cd
T0
Vout(s) = Q/sCf . [sT0/1+ sT0].[A/1+ sT0]n
Vout(t) = [QAn nn /Cf n!].[t/Ts]n.e-nt/Ts
Peaking time Ts = nT0 !
T0
T0
Semi-Gaussian Shaper
Output voltage at peak is given by :
Voutp = QAn nn /Cf n!en
1
0.8
0.6
0.4
0.2
2
Vout shape vs. n order,
renormalized to 1
3
4
5
6
7
Vout peak vs. n
35
Preamplifier & Shaper
I
d(t)
T.F.
from I to O
Shaper
Preamplifier
Non-Ideal Integrator
CR_RC shaper
Integrator
baseline
restoration
x
1/(1+T1s)
O
RCs /(1+RCs)2
0.03
Non ideal shape, long tail
0.02
0.01
5
10
15
20
36
Preamplifier & Shaper
I
d(t)
T.F.
from I to O
Preamplifier
Shaper
Non-Ideal Integrator
CR_RC shaper
Integrator
baseline
restoration
x
1/(1+T1s)
O
(1+T1s) /(1+RCs)2
Pole-Zero Cancellation
0.175
Ideal shape, no tail
0.15
0.125
0.1
0.075
0.05
0.025
2
4
6
8
10
12
14
37
Preamplifier & Shaper
Schema of a Preamplifier-Shaper circuit
with pole-zero cancellation
Rf
Cf
Diff
Rp
N Integrators
Vout
Cp
Cd
T0
T0
Semi-Gaussian Shaper
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
Vout(s) = Q/(1+sTf)Cf . [(1+sTp)/1+ sT0].[A/1+ sT0]n
38
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
0.175
0.15
0.125
0.1
0.075
0.05
0.025
2
4
6
8
10
12
14
2nd hit
39
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
0.175
0.15
0.125
CR-RC :
Return to baseline
> 7*Tp
0.1
0.075
0.05
0.025
2
4
6
8
10
12
14
0.1
0.08
CR-RC4 :
Return to
baseline < 3*Tp
0.06
0.04
0.02
5
10
15
20
25
30
35
40
Considerations on Detector Signal Processing
Pile-up :
A long return to zero time does contribute to excessive noise :
Uncompensated pole zero CR-RC filter
0.03
0.02
0.01
5
10
15
20
Long tail contributes to the increase of electronic noise (and
to baseline shift)
41
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)
42
Considerations on Detector Signal Processing
Summary (1)
• The detector pulse is transformed by the front-end circuit to obtain :
• A linear Gain (Vout/Qdet = 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)
43
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)
44
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
45
CERN Technical Training 2005
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
[email protected]
46