1 Pulse Processing and Noise Filtering in Radiation Detectors Chiara Guazzoni Politecnico di Milano and INFN Sezione di Milano e-mail: [email protected]

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


holes collection

600800

10001200

10001500200025000

50

100

150

200

250

300


holes collection

600800

10001200

10001500200025000

50

100

150

200

250

300


holes collection

600800

10001200

10001500200025000

50

100

150

200

250

300


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


P2P1


de

pth

[m

]

600800

10001200

10001500200025000

50

100

150

200

250

300


P2P1


de

pth

[m

]

600800

10001200

10001500200025000

50

100

150

200

250

300


P2P1


de

pth

[m

]

600800

10001200

10001500200025000

50

100

150

200

250

300


P2P1


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


11

Signal Formation and Ramo’s Signal Formation and Ramo’s Theorem - VIITheorem - VII


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.]


(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]


holes contribution

electrons contribution

t [ns]

output voltag

e [a.u.]


(bipolar gaussian shaping)

sh=20nssh=50ns

t [ns]

ind. current [

el/ns]


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)


(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


(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


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


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]


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

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

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



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

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


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

Documents

1 Pulse Processing and Noise Filtering in Radiation Detectors Chiara Guazzoni Politecnico di Milano and INFN Sezione di Milano e-mail: [email protected]