1 pulse processing and noise filtering in radiation detectors chiara guazzoni politecnico di milano...
TRANSCRIPT
1
Pulse Processing and Noise Pulse Processing and Noise Filtering Filtering
in Radiation Detectorsin Radiation Detectors
Chiara GuazzoniChiara GuazzoniPolitecnico di Milano and INFN Sezione di Milano
e-mail: [email protected]: www.elet.polimi.it/upload/guazzoni
March 4th, 2004 - PhD Lessons
2
Table of ContentsTable of Contents
Introduction and summary
Time measurements
Optimum filters in particular cases
Lossy capacitor
Signal formation and Ramo’s theorem
Capacitive matching and power dissipation
Time-variant filters
Multiple read-out techniques
3
Introduction and Summary - IIntroduction and Summary - I
sculpturing
filtering
0.0 0.2 0.4 0.6 0.8 1.0tim e [a.u .]
0.0
0.1
0.2
0.3
0.4
0.0 0.2 0.4 0.6 0.8 1.0tim e [a.u .]
0.0
0.4
0.8
1.2
4
Introduction and Summary - IIIntroduction and Summary - II
The amount of charge delivered by the detector for a given energy E of the incident radiation fluctuates according to Fano previsions. We will neglect such statistical fluctuations in the following. Other unavoidable noise sources arising in the detector itself and in the electronic circuits affects the amplitude and time measurements precision.
The precision of the measurement is usually defined in terms of the Signal-to-Noise ratio (S/N). In the case of capacitive detectors, an alternative concept is the Equivalent Noise Charge (ENC), that is the charge that delivered by the detector would make the S/N equal to one.
5
Signal Formation and Ramo’s Signal Formation and Ramo’s Theorem - ITheorem - I
Reciprocity of induced charge
02
1
01
22112
4,3,14,3,2
VV V
Q
V
QCCPartial capacitance
2211 VQVQ
in general:
11VQVQ nn
3
1
(0 V)
4
2
(0 V)
V1 C14
C12
C13 n Q2
6
Signal Formation and Ramo’s Signal Formation and Ramo’s Theorem - IITheorem - II
Current induced by the motion of charge
By reciprocity:
q V Q V Q q Vm mV V
m m 1 1
11
1 ld
ld
dt
dVq
dt
Vqd
dt
dQti m
mmm
1
1
Induced current - RAMO Induced current - RAMO TheoremTheorem
Weighting Weighting fieldfield
Ew
(obtained by applying 1V on electrode 1 and grounding all the others)dV
dlEmwcos
vEqti wm1
(S.RAMO, Proc. IRE, 27 (1939) 584)
In general:
•find weighting field •find charge velocity•find x(t), y(t), z(t)
zyxEw ,,
zyxv ,,
ti
zyxi ,,
applied voltage
induced current
V1=1V
1 20V
0V
0V3
4
Ew
dlv
qm
7
Signal Formation and Ramo’s Signal Formation and Ramo’s Theorem - IIITheorem - III
Induced current (charge) in planar electrode geometrySingle carrier Continuous
ionization
0
dVb
i
Ne
E
Vd
zb
0
dVb
i
z
E
dz
E
w 1
true field
dd
ww ttt
e
d
vevEevEqti 0
induced current
collected charge
i(t)
ttd-z tdq(t)
ttd-z td
e(d-z)d
e
dt
t
d
vNeti 1
2
0 2
1
dd
ts t
t
t
tNeditQ
i(t)
ttdq(t)
ttd
Ne/2
8
Signal Formation and Ramo’s Signal Formation and Ramo’s Theorem - IVTheorem - IV
Induced current in strip electrodes
sensing electrode
Vb
M W
W M
i(t)
Ew
v
qm
dt
xdEqvEqti wmwm
xwm
t xdEqditQ 00
Induced current:
Induced charge:
weighting field streamlines
0.1
0.90.5
0.2
weighting potential contour lines
a b c
a)
b)
c)
td
i(t)m
xw qQxdE 10
dm
dm
dw
ttQ
ttQ
xdE
0
0
00
tm i(t)
i(t)
0.05
9
Signal Formation and Ramo’s Signal Formation and Ramo’s Theorem - VTheorem - V
electro ns focusingin the p otential minimu m
holes collection
t [ns]P2 sig
nal [el/ns]
600800
10001200
10001500200025000
50
100
150
200
250
300
electro ns focusingin the p otential minimu m
holes collection
600800
10001200
10001500200025000
50
100
150
200
250
300
electro ns focusingin the p otential minimu m
holes collection
600800
10001200
10001500200025000
50
100
150
200
250
300
electro ns focusingin the p otential minimu m
holes collection
600800
10001200
10001500200025000
50
100
150
200
250
300
electro ns focusingin the p otential minimu m
holes collection
600800
10001200
10001500200025000
50
100
150
200
250
300
drift coordinate [ m]
dept
h [
m]
P2P1
electrons and holes indu ction
t [ns]
anode sig
nal [el/ns]
electrons colle ction
t=0 ns
1ns
2ns
3ns
1ns
2ns 160ns
20ns
50ns
100ns
(multilinear drift detectors)
PHOTON INTERACTION
10
Signal Formation and Ramo’s Signal Formation and Ramo’s Theorem - VITheorem - VI
IONIZING PARTICLE INTERACTION
P2P1
drift coo rdinate [ m]
de
pth
[m
]
600800
10001200
10001500200025000
50
100
150
200
250
300
IONIZING PARTICLE INTERACTION
P2P1
drift coo rdinate [ m]
de
pth
[m
]
600800
10001200
10001500200025000
50
100
150
200
250
300
IONIZING PARTICLE INTERACTION
P2P1
drift coo rdinate [ m]
de
pth
[m
]
600800
10001200
10001500200025000
50
100
150
200
250
300
IONIZING PARTICLE INTERACTION
P2P1
drift coo rdinate [ m]
de
pth
[m
]
600800
10001200
10001500200025000
50
100
150
200
250
300
IONIZING PARTICLE INTERACTION
P2P1
drift coo rdinate [ m]
de
pth
[m
]
600800
10001200
10001500200025000
50
100
150
200
250
300
0 20 40 60 80 100t [ns]
0.0
0.4
P2 signal [e
l/ns]
0 50 100 150 200 250t [ns]
0.0
0.4anod
e signal [e
l/ns]
0 20 40 60 80 100t [ns]-0.04
0.00
0.04
P1 signal [e
l/ns]
i (t)outi (t)out
i (t)out
electrons focusingin the potential minimum
holes collection electrons and holes induction
electrons collection
T=0ns
2ns
6ns
2ns
20ns
50ns
100ns
160ns
(multilinear drift detectors)
11
Signal Formation and Ramo’s Signal Formation and Ramo’s Theorem - VIITheorem - VII
(multilinear drift detectors)
PHOTON INTERACTIONPoint generation at the center of P2
0 100 200 300z, depth of interaction [µm]-2
0
2
4
CrossT
ime[ns
]
gaussian bipolar shaping20 ns sh. time50 ns sh. time
t [ns]
output voltag
e [a.u.]
Output signal on P2 electrode
(bipolar gaussian sh aping)
sh= 20nssh=50ns
t [ns]
output voltag
e [a.u.]
Output signal on P1 electrode
(bipo lar gaus sian shaping)
sh=20ns
sh= 50ns
ind. current [e
l/ns]
t [ns]
Current induced on P2 electrode(Q=1el.)
holes contribution
elec trons contribution
ind. current [
el/ns]
Current induced on P1 electrode(Q= 1el.)
holes contribution
elec trons contribution
t[ns]
z=30 m
z=270 m
t [ns]
output voltag
e [a.u.]
Outpu t signal on P1 electrode
(bipolar gaussian shaping)
sh =20nssh=50ns
t [ns]
ind. current [
el/ns]
Current induced on P2 electrode(Q=1el.)
holes contribution
electrons contribution
t [ns]
output voltag
e [a.u.]
Output signal on P2 electrode
(bipolar gaussian shaping)
sh=20nssh=50ns
t [ns]
ind. current [
el/ns]
Current induced on P1 electrode(Q=1el.)
holes contribution
electrons contr ibution
z=270 m
z=30 m
The shape of the signal induced on the electrode collecting holes is unipolar and after a fast bipolar shaping the zero crossing gives the interaction time. The output signal from the adjacent electrodes has tripolar shape and can be discriminated.
affects both the zero-crossing time of the output waveform and its slope thus degrading the achievable time resolution.
The amplitude of the fast signal induced on P2 corresponds to a fraction the injected charge due to electrons’ storage in the potential minimum.
The pulse duration depends on the interaction coordinate and
Systematic variation of the zero-crossing time as a function of the
interaction coordinate z for the case of point ionization. No
appreciable difference between the 20ns and 50ns shaping time is
visible.
0 100 200 300 400 500 600 700 800 900 1000050
100150200250300
drift coordinate [µm]
depth
[µm]
P1 P2
12
1/f noise in a lossy capacitor1/f noise in a lossy capacitor(Van der Ziel - 1975)
Re
Im
Z RR
ZCC 1
tan
i
r
CA
do r
tan
1
CA
dR
oi
tan22
kTCR
kTSi
As far as the loss angle () is independent of frequency, the output voltage noise shows a 1/f
spectrum.
C (lossy)
ir j
in R
Power spectral density of the thermal noise current generator
C (loss-less)
d
AjjY oir
1R Cj
S SR
R C
kTCv i
2
2 2 21
2sin cos
At low frequency the loss resistance is merely a measure of the
conductivity () of the dielectric Sv() shows a frequency
dependence of the form
12221
CRo
vn
13
Equivalent Noise Charge - IEquivalent Noise Charge - IIdentification of the detector and preamplifier noise sources
• noise source with bilateral power spectrum superposition (in the time domain) of randomly distributed events with Fourier transform occurring at an average rate
shaping amplifie
r
preamp.
CdCi
(leakage currentfeedback resistor)
(capacitor dielectric losses)
(1/f voltage noise)(white voltage noise)
(gate current shot noise)
qIG
2kTgm
AfqI
kTRLf
2
tQ
Carson’s theorem 2 N
• the r.m.s. value of a noise process resulting from the superposition of pulses of a fixed shape randomly occurring in time with an average rate is:
Campbell’s theorem 2/1
2
2/1
2
dttvn
tan2kTC
14
Equivalent Noise Charge - IIEquivalent Noise Charge - IIEquivalent circuit for ENC calculation
shaping amplifie
r
noiselesspream
p.Cd+Cpar
Ci
(leakage currentfeedback resistorgate current)
(capacitor dielectric losses)
(1/f voltage noise)(white voltage noise)
2 2 2kTg Cm
T A Cf T
2qIkTR
qILf
G 2
tQ
Charge
Current
step
pulse
random walk
pulses
signal
white parallel
pulses
‘ pulses
doublets
white series
tan2kTC
15
Equivalent Noise Charge - IIEquivalent Noise Charge - II
Equivalent Noise Charge is the value of charge that injected across the detector capacitance by a -like pulse produces at the output of the shaping amplifier a signal whose amplitude equals the output r.m.s. noise, i.e. is the amount of charge that makes the S/N ratio equal to 1.
Equivalent circuit for ENC calculation
shaping amplifie
r
noiselesspream
p.Cd+Cpar
Ci
(capacitor dielectric losses)
(white voltage noise)
2 2 2kTg Cm
T (1/f voltage noise) A Cf T
2
(leakage currentfeedback resistorgate current)
qIkTR
qILf
G 2
tQ
tan2kTC
16
Equivalent Noise Charge - IIIEquivalent Noise Charge - IIIENC calculation in presence of 1/f noise and/or dielectric losses
shaping amplifie
r
noiseless
transamp
shaping amplifie
r
noiseless
transamp
tQ tan2kTCd
22TfT CACc c Af
tan2kTCd
CT
dfjHkTCCAdfjHNENC Tff
2222/1 tan2
88.02ln
42
dfjH
triangular shaping
222
/1 AdCcENC Tf ENC f1
2/ independent of shaping
time
T 2T0
h(t)1
ENC Cf T12 2/
RC-CR shaping
18.12
dfjH
CT
0
h(t)1
17
Equivalent Noise Charge - IVEquivalent Noise Charge - IVENC calculation in presence of white and 1/f + dielectric
noises
dielectricf
T dfHdCc
/1
22
parallel
dtthb
2
series
T dtthCa
22 'ENC2
dtthdfHA 222
1 '
dfHA 2
2
dtthdfHA 22
3
Introducing where is a typical width of h(t) as the peaking time or the FWHM
x t
dielectricf
T dfHdCc
/1
22
parallel
dxxhb
2
series
T dxxhCa
22
'
ENC2
dielectricf
T dCcA
/1
22
A b
parallel
3
series
TCaA
2
1
are shape factors depending only on the shape of the filter:
A A A1 2 3, ,
18
Equivalent Noise Charge - VEquivalent Noise Charge - VENC vs. shaping time ()
0 1 10 100, shaping tim e [s]
1
10
100
EN
C [
ele
ctro
ns]
.10 1 10 100, shaping tim e [s]
1
10
100
EN
C [
ele
ctro
ns]
.1
5mm2 SDD (on-chip JFET)C pF
C pF
d
G
0 15
0 15
.
.
g mSm 0 3.
I pAL 1 6.A Vf 1 1 10 11 2.
5mm2 pn-diode (NJ14 JFET)C pF
C pF
C pF
d
par
G
1 7
2
2
.
g mSm 6
I pAL 1 6.A Vf 1 10 15 2
19
Shape of the optimum filterShape of the optimum filterShape of the optimum filter
0
c
t
exp
Si() parallel
noise
ba CT2 2
input referred series noise
c c1
c TCab
noise corner time constant(reciprocal of the angular frequency at which the
contributions from white series and parallel noise at the
preamplifier input become equal)
dtthCadtthb
Q
ENC
thQ
N
S
T '
max22
2
2
222 signal-to-noise ratio
(in presence of only white noises and with infinite time)
the sought impulse response has the
indefinite cusp shape t
1
Search for h(t) which minimizes the denominator of S/N (variational method)
ENC abCopt T 44 2
20
• finite width (2T)
Tt
Tt
c
c
T
t
th
2
20
0
sinh
sinh
0 T 2T
1
Practically a triangle when T<c (only white series noise is “active”)
copt
c
coptT
TENC
T
T
ENCENC
coth
2exp1
2exp1
2
truncated cusp
t
Shape of the optimum filter in Shape of the optimum filter in presence of additional presence of additional
constraints - Iconstraints - I
T 2T t
Practically a -pulse when T>c (only white parallel noise is “active”)
0
1
T 2T t0
1
21
• ballistic deficit
“flat-top” regions contributes only to parallel (and1/f noise)
flat-top is needed
The shaper “sees” the finite-width input pulse as a
function
ENC ENC bTft ft2 2
(in presence of only white
noises)
0
Tft
1
t
Shape of the optimum filter in Shape of the optimum filter in presence of additional presence of additional
constraints - IIconstraints - II
In practical cases due to broadening (thermal diffusion + electrostatic repulsion) the signal pulse is not a -like pulses…
With a cuspid-like filter we loose signal, thus degrading the S/N.
22
• constant offset
• baseline drift
t tinput signal
response The value of the offset is filtered prior to the signal pulse and this value is “subtracted”
from the signal measurement.
t
input signal
t
response
v1
vp
vp
v1
v2vbp
t1 tp t2
v vt t
t tv
t t
t tbpp p
1
2
2 12
1
2 1
If t1, t2 and tp are equidistant
vv v
bp 1 22
Shape of the optimum filter in Shape of the optimum filter in presence of additional presence of additional
constraints - IIIconstraints - III
23
Capacitive Matching - ICapacitive Matching - I Fixed current density
FET cut-off frequency independent of sizeMOSFET frontend
The same result is valid also in presence of 1/f noise and applies to JFET frontend
g kI CWLJ Wm D ox D 2 2 MOSFET transconductance - strong inversion
ENC e Cs n tot2 2 2
112
white series noise
ekTgnm
2 4 23
Input voltage spectral noise
dtth2'
1 Series noise integral with h(t) impulse response
Optimum size of the input MOSFET (length L and impulse response h(t) constant)
W
LCWLCC
W
WLCC
LJ
C
kT
dW
ENCd oxoxox
Dox
s det2
2det1
242
20
C WL C WC
Lox opt detdet
oxC
24
Capacitive Matching - IICapacitive Matching - II Fixed current density
FET cut-off frequency independent of size
C g /C d
10
100
1000E
NC
[e
lect
ron
s]
10 -110 -210 -3 100 101 102 103
A C
L
D
t
f GJ
I pA
C fF
GHz
1 5 10
1
150
2
24.
L
G
D
D
GDGf
G
D
D
GD
tqIA
C
C
C
CCCAA
C
C
C
CC
kTAENC 3
2
2
22 12
1
25
Capacitive Matching - IIICapacitive Matching - IIIFixed power dissipation fixed drain current, white series
noiseMOSFET frontend
g kI CWLIm D ox D 2 2 MOSFET transconductance - strong inversion
1
122 ACaENC tots white series noise
3
22
mg
kTa Input voltage spectral noise
dtthA2'
11
Series noise integral with h(t) impulse response
Optimum size of the input MOSFET (length L, current ID and impulse response h(t) constant)
21det
23
2det1
22
2
1
2
20
W
LCWLCC
W
WLCC
LI
C
AkT
dW
ENCd oxoxox
Dox
s
WLCWLCC oxoxdet 4
gqInkTm
D MOSFET transconductance - weak inversion
26
Capacitive Matching - IIICapacitive Matching - IIIFixed power dissipation fixed drain current, white series
noiseOptimum size of the input MOSFET (length L, current ID and impulse response h(t) constant)
C WL C WC
Lox opt 13 det
det
ox3C
WLCWLCC oxoxdet 4
BUT….Large values of W/Id ratio eventually leads to weak inversion operation.
In this case gm is independent of W so any increase of W degrades the ENC.
Therefore
where defines the boundary of weak inversion.
wiopt W
LC
W ,3C
minox
det
ox
dwi
CqkT
LIW
2
3
2
27
Capacitive Matching - IVCapacitive Matching - IVFixed power dissipation fixed drain currentMOSFET frontend
I pA
C fF
GHz
J
L
D
t
A Cf G
1
150
2
1 5 10 24
.
13
C g /C d
1
10
100
1000
10000
100000
EN
C [
ele
ctro
ns]
10 -110 -210 -3 100 101 102 103
white series
1/f series
28
Capacitive Matching - VCapacitive Matching - VFixed power dissipation: graphical methodWhen the dependence of gm vs ID is not the nominal one, different matching conditions arise:
•direct measurement of the FET parameters
•graphical method
Low-power HEMT-based charge amplifier
I A mmns RC CR
C pF mm
A V mm
G
sh
G
fw
0 5202 5
8 10 12 2
. /
. /
gm has been directly measured
29
Time Measurements - ITime Measurements - IWe want to measure the arrival time of the signal pulse
as time information we choose the 0-crossing time of the output signal
A
tamplitude r.m.s.
time r.m.s.
•for simplicity we fix the 0-crossing time in t=0
•due to geometrical considerations:
noisy output signal
so, non-noisy output signal
time walk
0
t
o
t
A
dt
ds
2
0
22
t
o
At
dtds
time resolution improves as the slope at the 0-crossing increases
30
Time Measurements - IITime Measurements - II
dhtfQts0output signal
input current pulse shaper response
h w w ,0
w t h t ,
•t=0 nominal crossing time for the noiseless signal
•weighting function
2
22
0
0
0
0
'
'
dwtfQdt
ds
dwtfQtdt
ds
dwtfQts
t
22
222
2
0
22
'
'
dwfQ
dwbdwaC
dtds
T
t
o
At
by a variational method, minimising t
tf
tKtw
c
coopt 'exp
2
dxxwxfaC
QK
To
t '2
22min,
The optimum weighting function for time measurements is obtained as convolution of the cusp filter with the derivative of the input current pulse.
31
Time Measurements - IIITime Measurements - III
dttft
tfQ
Cab
c
Tt
'exp'
142
2min,
Optimum time resolution
•only white parallel noise ( )
c 0
tftw
tt
opt
cc
'
exp2
1
•only white series noise ( )
c
dttfQ
bt
22
2min,
'
1
2
1topt dftw
dttfQ
aCTt
22
22min,
1
wopt(t)
wopt(t)
input current
pulse f(t)
32
Time-variant Filters - ITime-variant Filters - IR
tQ CT
time-invariant
pre-shaper p(t)b
aA gated
integratorp(t)
p
•The switch conduction is synchronised with the detector-signal arrival and the switch remains conductive for Rp.
•The contribution of the pulses describing series and parallel noises generator to the r.m.s. noise at the measuring instant depends on their relationship with the signal.
The knowledge of the processor response to the -pulse-like detector current is not sufficient to evaluate the noise.
The noise evaluation of this time-variant filter is based upon a time domain approach which requires the knowledge of the so-called
“noise weighting function”A detector signal of charge Q occurring at t=t1 will produce at the pre-shaper output the signal
11 ttttpC
QA
T 1 that is integrated over the time interval [t1, t1 + R]
33
Time-variant Filters - IITime-variant Filters - II
Noise weigthing function [WFN(to)]: contribution to the noise at the measuring time instant given by a -pulse delivered by the parallel noise generator at a time to. (to[t1-p,t1+R])
As signals arriving to the gate have a finite width p, all the -pulses delivered by the parallel and series noise generator in the time interval [t1-p, t1+R] contribute to the noise at the measuring instant t1+R
•WFN (to) is given by the area of the shaded region of the signal induced at the pre-shaper output by a -pulse of the parallel noise generator •In fact the portion of this signal entering the gate is integrated and stored in the integrator therefore contributing to the noise at tm=t1+R
R
p t1t1+ Rt1- p
to=t1 -p
to
to
to
to
to
to
to
to
to = t1 +R
to
p
p WFN
RopRtt
ToN
pRopT
oN
optt
pT
oN
RopooN
tttdxxpC
AtWF
tttdxxpC
AtWF
tttdxxpC
AtWF
ttandtttWF
oR
p
po
110
110
110
11
1
1
0
34
Time-variant Filters - IIITime-variant Filters - III•The noise contribution from the parallel source can be evaluated by adding quadratically all the elementary contributions appearing at the integrator output and caused by -pulses occurring in time intervals [to, to+dto] as to varies.
•By sliding the derivative of (A/CT)p(t) through the integrator time window, the noise weighting function for doublet of current injected across the CT capacitor can be determined. •The resulting function, which is the derivative of WFN, allows the calculation of the output noise arising from the white series generator.
R
p
tt N
Tparalleln dxxWFb
C
Av
1
1
22
22
R
p
tt Nseriesn dxxWFaAv
1
1
222 '
20
222
21
1
1
1'
R
R
p
R
p
dxxp
dxxWFbdxxWFCaENC
tt
tt NNT
The knowledge of two different functions, p(x) for the signal and WFN(x) for the noise, is required in the analysis of a
time-variant shaper.
35
Non-destructive Multiple Readout - INon-destructive Multiple Readout - I conventional read-out: charge collected at the output electrode non destructive multiple read-out: signal charge only capacitively coupled to the output node signal charge can be read out multiple times.
sense
fclock
MOS gate used as sensing electrode in CCD for visible light applications
Reverse biased p+ electrode used as sensing electrode in DEPFET structures
fclock
sense
36
Non-destructive Multiple Readout - Non-destructive Multiple Readout - IIII
Shape of the induced signal depends on the device geometry and on the biasing conditions.
signal electrons travelling towards and backwards the sensing electrode
signal electrons stored underneath the sensing electrode
t
TTQti
oscoscref
2sin
oscosc
q
iref T
itT
itQti
4
14
4
34
1
tim e
ind
uce
d c
ha
rge
tim e
ind
uce
d c
ha
rge
tim e
ind
uce
d c
urr
en
t
t im e
ind
uce
d c
urr
en
t
37
Non-destructive Multiple Readout - Non-destructive Multiple Readout - IIIIII
Shape of the optimum filter
white voltage noise aw =1.510-18 V2/Hz white current noise bw =1.610-31 A2/Hz 1/f voltage noise af =1.510-12 V2
0 2 4 6 8 10tim e [s]
-0 .1
0.0
0.1
WF
[a
.u.]
white noises
+
1/f voltage noise
white noises
sinusoidal current signal
0 2 4 6 8 10tim e [s]
-0 .1
0.0
0.1
WF
[a
.u.]
series of pulses
0 2 4 6 8 10tim e [s]
-0 .1
0.0
0.1
WF
[a
.u.]
0 2 4 6 8 10tim e [s]
-0 .1
0.0
0.1
WF
[a
.u.]
38
Non-destructive Multiple Readout - Non-destructive Multiple Readout - IVIV
Number of waiting and lagging period
white voltage noise aw =1.510-18 V2/Hz white current noise bw =1.610-31 A2/Hz
sTosc 5
0 1 2 3 4 5 6m
1, num ber of v irtua l periods
0
2
4
6
8
EN
C2 [
ele
ctro
ns2
]
se ries
para lle l
sc 53.1
sTosc 1
0 1 2 3 4 5 6m
1, num ber o f v irtua l periods
0
5
10
15
20
25
EN
C2 [
ele
ctro
ns2
]
se ries
para lle l
sc 53.1
4q
-0 .5
0 .0
0 .5
0 5 1 0T [ s ]
39
Non-destructive Multiple Readout - Non-destructive Multiple Readout - VV
Number of waiting and lagging period
white voltage noise aw =1.510-18 V2/Hz white current noise bw =1.610-31 A2/Hz
0 1 2 3 4 5 6 7 8 9m
1=m
2, num ber o f w aiting and lagging periods
0.0
0.5
1.0
1.5
EN
C2/E
NC
2 -
pu
lse
2468101214161820q, num ber o f s ignal oscilla tions
Tosc=1s
Tosc=2s
Tosc=5s
Tosc=1s
Tosc=2s
Tosc=5s
tota lcurrent
vo ltage
-0.2
0.0
0.2
WF
[a
.u.]
0 10 20T[s]
sc 53.1
0 1 2 3m
1=m
2, num ber of w aiting and lagging periods
0.2
0.3
EN
C2/E
NC
2 -
pu
lse
14161820q, num ber o f s ignal oscilla tions
Tosc=1s
Tosc=2s
tota l
vo ltage
40
Non-destructive Multiple Readout - Non-destructive Multiple Readout - VIVI
Effect on the different noise components - I(for sake of simplicity we assume a sinusoidal current shape)white series noise + white parallel noise• oscillation time imposed • measurement time imposed
white voltage noise aw =1.510-18 V2/Hz white current noise bw =1.610-31 A2/Hz c =1.53 s
1 10q, num ber of s ignal oscilla tions
1
10
100
EN
C2[e
lect
ron
s2]
0.1
ENC 2=q
29.77
EN C 2series=
23.46q
EN C 2para lle l=
6.33q
25.0 12.5 5.0 2.5T
osc[s]
1 10q, num ber of s ignal oscilla tions
0
1
10
100
EN
C2[e
lect
ron
s2]
ENC 2
EN C 2para lle l=
31.68
q2
0.01
ENC 2series
1.25
.1
Tmeas=25s
Tosc=5s
41
Non-destructive Multiple Readout - Non-destructive Multiple Readout - VIIVII
Effect on the different noise components - II(for sake of simplicity we assume a sinusoidal current shape)
1/f series noise (Af=1.5 x 10-12 V2)
when the total measuring time is imposed, the same decrease law with the number of signal oscillation is obtained.
the non-destructive multiple readout is able to reduce the 1/f noise contribution.
1 10q, num ber of s ignal oscilla tions
1
10
100
1000
EN
C2[e
lect
ron
s2]
Tosc=1s
107.04EN C 2=
q0.97
42
Non-destructive Multiple Readout - Non-destructive Multiple Readout - VIIIVIII
Effect on the different noise components - III(for sake of simplicity we assume a sinusoidal current shape)
White noises + 1/f series noise
• oscillation time imposed • measurement time imposed
1 10q, num ber of s ignal oscilla tions
1
10
100
1000
10000
EN
C 2
[ele
ctro
ns2
] a f=1x10 -12V 2
a f=1x10 -13V 2
a f=5x10 -11V 2
a f=5x10 -13V 2
a f=1x10 -11V 2
a f=5x10 -12V 2
25 5T
osc[s]
Tm eas=25 s
m1 =0
1
white voltage noise aw =1.510-18 V2/Hz white current noise bw =1.610-31 A2/Hz c =1.53 s
1 10q, num ber of s ignal oscilla tions
1
10
100
1000
10000
EN
C 2
[ele
ctro
ns2
]
a f=1x10 -12V 2
a f=1x10 -13V 2
a f=5x10 -11V 2
a f=5x10 -13V 2
a f=1x10 -11V 2
a f=5x10 -12V 2
Tosc=5 s
m1 =0
43
Non-destructive Multiple Readout - Non-destructive Multiple Readout - IXIX
Effect on the different noise components - summarizing...
A) by imposing total measuring time (Tmeas)
1. ENC2 due to the white voltage noise is independent of the number of signal oscillations.
2. ENC2 due to the 1/f voltage noise decreases as
3. ENC2 due to the white current noise decreases as
B) by imposing time duration of the signal oscillation (Tosc)
ENC2 due to all the different noise contributions decreases as
1q
12q
1q
44
Non-destructive Multiple Readout - Non-destructive Multiple Readout - XX
Comparison with delta-pulse processingwhite series noise + white parallel noise + 1/f voltage noise
0
1
10
100
1000
EN
C2 [
ele
ctro
ns2
]
1 10q, num ber of s ignal oscilla tions
.1
0.01
white voltage noise aw =1.510-18 V2/Hz white current noise bw =1.610-31 A2/Hz 1/f voltage noise af =1.510-12 V2
Multiple readout: the ENC2 due to all the noise contributions decreases linearly with the number of signal oscillations (and therefore with the measurement time). Delta pulse: well-known behavior.
Voltage 1/f noise contribution is independent of the measurement time.
White voltage noise decreases as the measurement time is increased.
White current noise increases as the measurement time is increased.
45
Non-destructive Multiple Readout - Non-destructive Multiple Readout - XIXI
Effect of the shape of the induced signal
0
10
20
30
EN
C
[ele
ctro
ns
]2
2
0
10
20
EN
C
0 2 4 6m 1
2
series
para lle l
0 1 2 3 4 5 6m 1, num ber o f w aiting periods
white voltage noise aw =1.510-18 V2/Hz white current noise bw =1.610-31 A2/Hz c =1.53 s
Number of waiting periods
sTosc 1
1 10q, num ber o f s igna l oscilla tions
1
10
100
1000
EN
C2
[e
lect
ron
s2]
s inuso ida l current s igna l
current s igna l as a series o f pulses
Achievable resolution
sTosc 1
46
AcknowledgmentAcknowledgment
E. Gatti - Politecnico di MilanoE. Gatti - Politecnico di Milano
P.F. Manfredi - LBLP.F. Manfredi - LBL
V. Radeka - BNLV. Radeka - BNL
A. Castoldi, C. Fiorini, A. Geraci, A. Longoni, G. Ripamonti, M. Sampietro, S. Buzzetti, A. Galimberti - Politecnico di Milano
A.Pullia - Universita’ degli Studi, Milano
G. De Geronimo, P. O’Connor, P. Rehak - BNL
47