1-Electronic signal Processing

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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