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3B2v7:51cGML4:3:1 NIMA : 42392 Prod:Type:COM

pp:1213ðcol:fig::4;9;10ÞED:VijayaT

PAGN: gopal SCAN: venki

Nuclear Instruments and Methods in Physics Research A ] (]]]]) ]]]–]]]

*Corresp

4572121.

E-mail a

0168-9002/$

doi:10.1016

RECTED PROOF

Time measurements by means of digital sampling techniques: astudy case of 100 ps FWHM time resolution with a

100 MSample=s; 12 bit digitizer

L. Bardelli, G. Poggi*, M. Bini, G. Pasquali, N. Taccetti

INFN and Department of Physics, University of Florence, Via G.Sansone 1, Sesto Fiorentino, 50019 Italy

Received 19 May 2003; received in revised form 13 October 2003; accepted 29 October 2003

Abstract

An application of digital sampling techniques is presented which can simplify experiments involving sub-nanosecond

time-mark determinations and energy measurements with nuclear detectors, used for Pulse Shape Analysis and Time of

Flight measurements in heavy ion experiments. The basic principles of the method are discussed as well as the main

parameters that influence the accuracy of the measurements. The method allows to obtain both time and amplitude

information with an electronic chain simply consisting of a charge preamplifier and a fast high resolution ADC (in the

present application: 100 MSample=s; 12 bit) coupled to an efficient on-line software. In particular an accurate Time of

Flight information can be obtained by mixing a beam related time signal with the output of the preamplifier. Examples

of this technique applied to Silicon detectors in heavy-ions experiments involving particle identification via Pulse Shape

analysis and Time of Flight measurements are presented. The system is suited for applications to large detector arrays

and to different kinds of detectors.

r 2003 Elsevier B.V. All rights reserved.

PACS: 29.40.M; 84.30.S; 25.70.Pq; 82.80.R

Keywords: Digital sampling; Time-of-flight measurements; Silicon detectors

R 49

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UNCO1. Introduction

In a recent paper [1] the applicability of digitalsampling techniques to particle identification withscintillator detectors has been demonstrated. Inthe present paper it is shown that the same basicapparatus previously described (a digitizer with100 MSample=s; 12 bit resolution) makes it possi-

57onding author. Tel.: +39-55-4572249; fax: +39-55-

ddress: poggi@fi.infn.it (G. Poggi).

- see front matter r 2003 Elsevier B.V. All rights reserve

/j.nima.2003.10.106

ble time-mark determinations with sub-nanose-cond resolution. In this way, the sampling methodcan be applied to Silicon detectors for bothparticle identification via DE � E and/or PulseShape Analysis (PSA) and Time of Flight (ToF)measurements. Extension of the proposed methodto coincidence measurements, where accuratesynchronization between different detectors isnecessary, is also possible.

While the feasibility of high-quality energymeasurements, given the 12 bit resolution of the

59

d.

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converter, represents a somewhat obvious applica-tion of the digitizer, the time-mark determinationcapability of the device deserves a more detailedillustration because this novel application mayconstitute a breakthrough for experimental setupsinvolving a large number of detectors, possibly ofdifferent types. In fact, the implementation of PSAand sub-nanosecond timing can be obtainedmerely using a charge preamplifier directly fol-lowed by a digitizer, thus greatly simplifying theelectronic chain: it is possible to get rid of the slowshaping of the signal and its analog conversion(either peak or charge) and—even more impor-tant—the timing electronics, like sub-nanosecondconstant fraction and/or leading edge discrimina-tors and TDC conversion. In summary, thetechnique can be applied to particle identification(charge and mass) with DE � E Silicon—CsI(Tl)telescopes (mainly exploiting the energy resolutionperformance), to ToF measurements in pulsedbeam experiments for mass and energy measure-ments and to PSA in reverse mounted SiliconDetectors. The last two applications mainly relyon both energy and timing performances of thesystem.

The paper is organized as follows: a simplifiedoverview of the time-mark determination proper-ties of a digital sampling system is presented in thenext section, where a definition of the requiredalgorithms is also given. That section also illus-trates the modification of the basic algorithmsnecessary to fully exploit the resolution capabilityof the system. The expected attainable timeresolutions, as estimated by means of detailedsimulations, are presented. Section 3 briefly recallsthe characteristics of the digitizer used for thetime-mark resolution tests. Section 4 showsexperimental data presenting the sub-nanosecondtiming achieved with the sampling system appliedto a Silicon detector for Light Charged Particles(LCP) and Intermediate Mass Fragments (IMF)detection. Sub–nanosecond timing with respect toan external time-reference—like the time markassociated to a pulsed beam—is described inSection 5; results of this approach are shown.

Previous work on extracting time informationfrom digitized sequences, although applied to

different experimental situations, can be found inRefs. [2–4].

TED PROOF

2. Determination of time marks by means of a

sampling system

In order to pin down the main issues involved inthe present approach, which consists in extractingone or more time-marks from a digitized signal, weexplicitly consider the system that we have alsoexperimentally tested, namely the output of acharge preamplifier connected to a Silicon detec-tor. This approach, while somewhat restricting thegenerality of the conclusions which can be drawn,permits—on the other side—to realistically con-sider the noise contribution on the signal (mainlyseries noise of the input FET).

Given a sequence of digitized samples of a signal(in most cases obtained by a fixed frequencyclocked digitizer), the problem of obtaining a time-mark from the signal basically consists of deter-mining the time at which a defined signalamplitude is reached (normally this time does notcoincide with any of the sampled points). The time‘‘slicing’’ provided by the digitizer introduces anatural time scale, which all the time determina-tions are naturally referred to. Furthermore, sincefor all practical purposes only time differences areof interest, the best approach to digital timemeasurements is to deduce all relevant time-differences associated with the signal from thesame sequence of digitized samples, which extendssufficiently to cover the whole region containingthe needed time marks. In this way the uncertaintyassociated with the asynchronous sampling of thesequence is removed. This issue will be furtheraddressed in Sections 4 and 5, while in this sectionthe uncertainty of a single time determinationattainable with the application of the samplingmethod is discussed, assuming fixed shape signalsand disregarding, for the moment, effects con-nected to very low-level signals; such effects will bebriefly addressed at the end of this section.

In Fig. 1 an idealized output of a charge-preamplifier is shown (thin line; markers indicatethe sampling points). Usually, with analog signals,the time mark determination requires an ad hoc

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Time (ns)

-50 0 50 100 150 200

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mpl

itude

A

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1Asymptotic amplitude: A

CFD levelα1 point

α2 point

Fig. 1. Solid thin line: schematic representation of the output of

a charge preamplifier. Markers: samplings of the signal. Full

line: output signal of the used charge preamplifier. Dashed line:

preamplifier output distorted by the presence of a long

transmission line (see Section 4).

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Constant Fraction Discriminator module (see forinstance Ref. [5]).

In the following we present an algorithm appliedto digital samples which permits to define theinstant of time at which the signal reaches apredetermined fraction f of the full amplitude; wecall it digital Constant Fraction Discriminator(dCFD). A simple estimate of the time-markresolution achievable with that approach is given,mainly to introduce the basic issues associatedwith digital sampling timing. The estimate will beperformed in the basic hypothesis that the timeneeded for the signal to pass from its zero value tofull amplitude (in practice the 10–90% risetime ofthe signal, briefly risetime tr in the following)contains a few sampling periods tclk: Moreover,the ‘‘first order’’ assumption of a linear shape ofthe signal around the chosen threshold region ismade (in the following we will extend the results tonon-linear behavior). The following notation willbe used (see also Fig. 1):

85

A

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1The Ef

measured a

specificatio

NCOasymptotic amplitude of the signal SðtÞ;with 0oAo1: The value 1 corresponds tothe full range of the converter in thechosen configuration.

89

tclk Usampling period (in our systemtclk ¼ 10 ns)

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ENOB Effective Number Of Bits of the converter(in our system ENOB ¼ 10:8)1

fective Number Of Bits of the converter has been

nd it is in good agreement with the manufacturer’s

ns.

f

dCFD fraction ð0ofo1Þ tdCFD time at which the amplitude of the signal

is fA

tr 10–90% risetime of the signal

A simple way to obtain tdCFD from sampled datais as follows:

(1)

Determine the asymptotic amplitude A of thesignal, for example with a simple average ofthe samples at time Tbtr; after havingsubtracted the baseline determined from thesample points preceding the signal;

(2)

FFind the two consecutive samples with ampli-tudes a1 and a2 such that a1ofAoa2 (see Fig.1).

(3)

OOObtain tdCFD with a linear interpolationbetween ðt1; a1Þ and ðt2; a2Þ (note:t2 � t1 ¼ tclk).

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TED PRFollowing this procedure, the contribution to the

time resolution due to this approach (i.e. the errorsdCFD on tdCFD) can be estimated as:

sdCFDpseþqdS

dt

��������tdCFD

" #�1

s2eþq ¼ s2e þ1

12� 4ENOBð1Þ

where s2e is the variance associated with theelectronic noise of the preamplifier (assumingwhite noise for the sake of simplicity). Thequantization error has been considered using theADC number ENOB of effective bits, accordingwith its definition. The error on A has beenneglected, because it can be sufficiently reduced byusing a proper algorithm (for example averagingover a large number of samples), as well as theerror on tclk (this error amounts to less then few pswith a proper electronic design).

The equality sign in Eq. (1) holds in the limitingcase of a value fA coinciding with one of the twosamples or when the two amplitude determinationsa1 and a2 are fully correlated; in the opposite caseof total independence of errors, the minimumvalue of the left member is obtained when fA ¼ða1 þ a2Þ=2:

The nominal resolution attainable with ananalog CFD treatment of the signal (assumingthe same noise bandwidth) is given by an expres-

F

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dCFD level

Fig. 2. Two different ideal (noiseless) samplings of the same signal with a non-linear time dependence. Sequences A and B have a

different phase with respect to the signal. The linear interpolation procedure for determining tdCFD produces significantly different

values for the two cases. The example refers to a 100 MSample=s digitizer.

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sion identical to Eq. (1), except for an equal sign,for the absence of the quantization error and foran additional factor

ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ f 2

pcoming from the

signal treatment performed in the CFD electronicmodule.

It is worth stressing that, if the quantizationerror is significantly lower that the electronic noise,i.e. if the number of effective bits is sufficientlyhigh to keep the electronic noise of the signal asthe dominant effect in the amplitude determina-tion, signals evolving linearly as a function of time

show a dCFD time resolution better or equal tothat attainable with analog CFD module. Thisresult actually means that the key issue for dCFDresolution is the number of effective bits necessaryto confine the quantization error below theelectronic noise of the signal, while the samplingperiod tclk must be sufficiently short to allow forthe presence of some samples during the risetimeof the signal. As it will be quantitatively shown inthe following, the FWHM resolution can be as lowas B100 ps for a proper choice of the usedconverter.

In the previous discussion the time markresolution of a digital sampling system has beenestimated, assuming a linear shape of the signalnear tdCFD: However, the non-linear shape of thesignal and the use of an asynchronous (withrespect to the signal) clock of period tclk producesa random error in the interpolating procedure,which translates in a degradation of the overalltime-resolution. In fact, while for a signal having alinear time dependence around the threshold the

TED PROOlinear interpolation procedure is free of systematic

errors related to the phase of the sampling, thisfeature is lost once the signal has a non-linear timedependence. Fig. 2 shows the different tdCFDvalues which are observed for a signal with anon-linear time-dependence near tdCFD; once twosampling sequences are considered, differing for atime shift. The linearly interpolated tdCFD differsby about 500 ps between the two cases. Due to therandom distribution of the sampling phase withrespect to the signal, this effect significantlydeteriorates the overall time resolution. Althoughmuch smaller than the sampling period tclk; thiserror can easily overcome the limiting resolution ofthe sampling system calculated before. Moreover,it depends strongly on the shape of the signal inthe proximity of tdCFD and in general does notcancel out when the difference between two distantpoints of the same signal is performed (e.g. twodigital constant fraction timings with different f

values).In order to quantitatively show the worsening of

the resolution associated with this effect a simula-tion has been implemented. The results of thesimulation are presented as a function of therisetime of the preamplifier; while in the PSAapplication presented in the following a fewfraction values have been used to estimate therisetime of the signal, the simulations have beenrun with a representative value f ¼ 0:2: A truepreamplifier output has been considered and itsshape is reported as a full solid line in Fig. 1: itmainly differs from the idealized curve by the non-

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FW

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dCFD timing (f = 0.2)Estimate of eq.1Total error of Linear int.Total error of Cubic int.

Resolution of Linear int.Resolution of Cubic int.

Fig. 3. Total error on digital Constant Fraction timing ðf ¼0:2Þ as a function of the preamplifier risetime, obtained with a

12 bit resolution, 100 MSample=s digitizer, using linear inter-

polation (thick dashed line) and cubic interpolation (thick full

line). The thin dashed and full lines report, for linear and cubic

interpolations respectively, the only time resolution (fluctua-

tions with respect to the average value, for each value of

preamplifier risetime). The shaded area represents the range for

the resolution expected on the basis of Eq. (1). The simulation

has been performed using realistic signals of amplitude equal to

half of the range of the converter.

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NIMA : 42392

UNCORREClinear onset of the signal. The reported behaviorrepresents the d-response of the preamplifier out-put ðtrE30 nsÞ used in the experimental testspresented in the next sections.2 The electronicnoise at the preamplifier output was assumed tohave the same amplitude and spectral density thatwe measured in our experimental set-up. Thedifferent risetimes tr are obtained by a simplescaling on the horizontal axis, keeping the overallshape; the electronic noise has been correspond-ingly changed, namely the associated full varianceincreases with the transmitted bandwidth ass2ep1=tr: The digitizer was assumed to have12 bit resolution and sampling rate of100 MSample=s; with a sharp antialiasing filtercutting at the Nyquist frequency of 50 MHz:

The shaded region in Fig. 3 represents the limitsdetermined by Eq. (1) for f ¼ 0:2 and a signalamplitude of half range ðA ¼ 0:5Þ: The thickdashed line represents the absolute error (systema-

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2The effect of a long transmission line that during the

experimental tests we were forced to insert between the

preamplifier output and the input of the digitizer will be

addressed in the following sections.

TED PROOF

tic and statistical) with respect to the true valueonce tdCFD is determined with a linear interpola-tion. Apart from the expected rapid increase of theerror at shorter risetimes, due to the insufficientnumber of interpolating points, a significantincrease of the error with respect to the estimateof Eq. (1) is apparent, even in regions wherelacking of interpolating samples can be excluded.

A solution to the problem can be found by usingeither a fit or a higher order interpolation. Theinterpolation procedure is preferred over the fittingbecause it does not rely on any assumption on theshape of the signal and it can usually becomputationally faster.

We have successfully tested a cubic polynomialinterpolation based on the Lagrange formula.Parabolic interpolation has also been tested, withpoorer results with respect to the cubic one. Themain reason is that in most cases, especially forfast evolving signals, they present a flex over thefew examined samples, which cannot be repro-duced by a second order polynomial. The methodextends the previously discussed results andproceeds as follows (using the adimensional timevariable x ¼ time=tclk):

* A time mark xdCFD;linear is obtained with theprocedure previously outlined.

* Four adjacent samples x1; x2; x3 and x4 arechosen, with x2oxdCFD;linearox3 and the uniquethird-order polynomial yðx� x2Þ through themis computed.

* The time xdCFD can be obtained solving theequation yðx� x2Þ ¼ fA: Numerically this canbe done using a successive approximationmethod (for example the Newton’s one) withxdCFD;linear as initial guess. It was verified that,with realistic signals, the iterative solution ofthis equation converges very fast and thus inmany cases the iterative loop can be replacedwith a single correction, thus coinciding with afirst-order approximation of yðx� x2Þ aroundthe point xdCFD;linear (the next approximationstep typically introduces a correction smallerthan 10–20 ps).

The presented method is well suited for onlineprocessing of data with DSP, because the compu-tation of the correction involves about 15 multiply

PROOF

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Tot

al e

rror

(F

WH

M, n

s)

00.10.20.30.40.50.60.70.80.9

1dCFD timing (f = 0.2)

(a) 12 eff. bit, 100 MS/s(b) 8 eff. bit, 1000 MS/s(c) 8 eff. bit, 2000 MS/s(d) 12 eff. bit, 400 MS/s(e) Analog CFD(f ) 12 eff. bit, 100 MS/s (digitizer only)(g) 10.8 eff. bit, 100 MS/s

(a)

(b),(c)

(d)

(e)

(g)

(f)

Fig. 4. Total error on digital Constant Fraction timing ðf ¼0:2Þ performed by various digital sampling systems (continuous

lines labeled from a through d). Data corresponding to a

standard analog CFD signal treatment are also shown

(continuous line e). For one of the digitizers (100 MSample=s-12 bit) the contribution due to digitization only is separately

presented (dashed line f ). The dotted curve g refers to the

digitizer used in our tests. The simulation has been performed

using realistic signals of half full range amplitude ðA ¼ 0:5Þ:

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accumulate (MAC) operations to obtain thecoefficients of the polynomial, and 10–20 addi-tional operations to obtain the desired correction.

The thick full line in Fig. 3 represents the resultsobtained by performing the described cubic inter-polation The improvement with respect to thefirst-order linear interpolation is apparent and thedata fall in the shaded region, as expected. Thethree quantities reported in Fig. 3 and discussedsince now refer to the total absolute error withrespect to the true value. When the timinginformation is used for discrimination purposes(like for PSA, see Section 4) only the fluctuationswith respect to the mean observed value are ofinterest. The thin full and dashed curves in Fig. 3represent indeed these resolutions (for f ¼ 0:2) forcubic and linear interpolations, respectively. Wehave verified that, while the details of the basicsignal shape may influence the behavior of thecurves in the region of the steep increase of thetotal absolute error towards short risetimes, theconclusions which can be drawn from Fig. 3 aboutthe quality of dCFD timing with a100 MSample=s-12 bit digitizer are quite general.

To better pin down the digitizer characteristicswhich indeed determine the timing quality attain-able with digital Constant Fraction Discrimina-tion, further simulations similar to those presentedin Fig. 3 have been run for digitizers with differentcharacteristics. The total absolute time markerrors are shown in Fig. 4, together with theresults simulated for an ideal analog CFD timing.The considered digitizers, apart from the one thatwe have developed (100 MSample=s-10.8 effectivebit), are a 100 MSample=s-12 eff. bit,1 GSample=s-8 eff. bit, 2 GSample=s-8 eff. bitand a 400 MSample=s-12 eff. bit. In the simulationthe signals are processed by the digitizers, eachhaving an antialiasing filter cutting at the corre-sponding Nyquist frequency. The risetime of thepreamplifier, as well as the corresponding noise,have been varied as already discussed. Fig. 4confirms that, apart from the very fast risetimeregion, the key feature for determining the timingquality is the digitizer bit resolution. It is worthnoting that both the 12 bit digitizers give timingperformances equivalent to the standard analogCFD timing, while for the faster ADCs the

TED increased sampling rate cannot compensate forthe poorer bit resolution. Finally, for the100 MSample=s-12 bit digitizer the dotted linereports the contribution to the absolute error dueto the quantization effects (including effective bits)and actually this represents the ultimate resolutionattainable with this converter in the non-realistichypothesis of a noiseless preamplifier output.

In the special case of very fast AD converters thestandard oversampling technique [6] may beapplied to increase the overall bit resolution: thesignal is sampled by the ADC at a much higherrate fs than the required Nyquist frequency fNy:Averaging over the collected data allows for anincrease of the resolution of the system by a factorffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

fs=ð2fNyÞp

: For example, the oversampling of asignal with an 8 effective bit, 2000 MSample=sdigitizer down to 100 MSample=s gives an im-provement by a factor B4:5; i.e. of about 2 bits:the final effective resolution of about 10 bits is stillworse than a ‘‘true’’ 100 MSample=s; 12 (and also10.8) effective bit converter. Moreover it has alsoto be noted that oversampling requires a white

input noise for proper effective operation.The presented simulated results of the dCFD

algorithm has been limited to a fixed value of

OOF

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dZC-dCFD timing

Fig. 6. Resolution (fluctuation with respect to average value)

obtained for a Pulse Shape related timing (dZC-dCFD time, see

text) from the simulation for linear (thin line) and cubic

interpolation (thick line).

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C

signal amplitude A ¼ 0:5: While the time resolu-tion obviously scales as sdCFDp1=A (see Eq. (1)),the behaviour of the centroid of the estimated timedistribution as a function of A; i.e. the time walk,has been studied by means of the same simulationspreviously discussed. For the case of our converter(100 MSample=s; 10:8 eff : bits) the results arereported in Fig. 5. The total time walk of thesystem comes out to be less than 120 ps for adynamic range of 250: this value compares wellwith the performances of standard analog CFDsystems. Very similar results have been obtainedusing linear interpolation.

The overall time resolution of a single dCFD, asdetermined by simulations, cannot be easily testedexperimentally and the difference of two timedeterminations is rather needed: as a matter offact, in Section 4 the Pulse Shape capability of thesystem is checked by studying the differencebetween two time marks—the dCFD with f ¼0:2 fraction and the Zero Cross of the digitallydifferentiated (delay-line–like) signal, indicatedhenceforth with ‘‘dZC-dCFD’’. In order to realis-tically compare simulations with data, Fig. 6presents the simulated FWHM for the dZC-dCFDtime information (for the experimental data seeFig. 8), as a function of preamplifier risetime. Thethick line represents the fluctuation with respect toaverage value, obtained with cubic interpolation,

UNCORRE 79

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k (n

s)

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Amplitude

1/1024 1/256 1/64 1/16 1/4

Converter: 10.8 eff. bits, 100 MS/s

Signal risetime: 30 ns

Signal risetime: 40 ns

Signal risetime: 50 ns

1

Fig. 5. dCFD walk for a 100 MSample=s; 10:8 eff : bits

converter and fraction f ¼ 0:2 as a function of signal amplitude

A: Note the logarithmic horizontal axis. The three curves

correspond to different risetimes (10–90%) of the input signal.

For this converter the signal risetime value tr ¼ 50 ns corre-

sponds roughly to the minimum of curve g in Fig. 3.

TED PRwhereas the thin one refers to linear interpolation.

As compared with the behavior of the thin dashedline of Fig. 3 which represents the resolution of asingle time determination, the FWHM of the dZC-dCFD difference obtained with linear interpola-tion presents some compensation effects for shortrisetimes: in these cases the two time determina-tions, being based on almost the same samples, arestrongly correlated in a way dependent on signaldetails. Anyway, the resolution for linear inter-polation is always worse than the one correspond-ing to cubic interpolation which, on the contrary,is almost free of any odd behavior because of thebetter reproduction of the signal shape. Besides,when comparing the performances with experi-mental data, it will be shown that the resolutionworsening due to the linear interpolation proce-dure also corresponds to a non-Gaussian shape ofthe timing peak.

According to the results presented in thissection, the timing information from our experi-mental data shown in the next sections has beenalways extracted by means of the cubic interpola-tion procedure.

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3. The digitizer

In this work the digitizer already described inRef. [1] has been used: the system is provided with

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four independent input channels, each sampled bya fast Analog to Digital Converter (ADC, AD9432from Analog Devices) with a resolution of 12 bitand 100 MSample=s: Specific measurements havedetermined the effective number of bits asENOB ¼ 10:8: The analog input stage of eachchannel is a 3-poles active Bessel filter, thatoperates as antialiasing filter while minimizingsignal distortion. The sampled data is stored on atemporary memory (FIFO) and the full sample isthen transferred to the acquisition system throughthe VME bus: an analysis of the acquired wave-form can then be performed off-line. As discussedin Ref. [1] and in the following, all the proposedalgorithms are simple and fast enough to be usedfor on-line analysis with Digital Signal Processors(DSPs). Tests performed with a calibrated pulseinjected into a Silicon detector preamplifier haveshown that the digitizer does not introduce anydeterioration of the energy resolution with respectto the value obtained with standard (spectroscopygrade) analog electronic chain, once the properalgorithms are applied, like semigaussian digitalfilters.

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UNCORREC4. Timing tests with a digital system

In order to verify the timing resolution of thedigital sampling system, a test has been performedat the Laboratori Nazionali di Legnaro of INFN(Padova, ITALY) using the 16Oþ 116Sn reactionat a beam energy of 250 MeV: A 300 mm NeutronTransmutation Doped (NTD) Silicon detector hasbeen placed inside a scattering chamber (about1 m from target, yC11�) in the reverse fieldconfiguration. The total active area isE700 mm2; the presented results were obtainedwith a centered circular collimator, which reducedthe exposed area down to E500 mm2: Thedetector (nominal depletion voltage of 120 V) hasbeen operated at 140 V: The preamplifier used inall the reported measurements was the onedescribed in Ref. [7], but for an input FETfollower stage. The preamplifier, due to its lowpower consumption, operates in vacuum. Therisetime of the preamplifier output for a d-likeexcitation is E30 ns: A 50 m long cable (RG58)

TED PROOF

connecting the output of the detector preamplifierto the digitizer deteriorates the intrinsic risetime.The resulting shape of the signal at the input of thedigitizer is shown in Fig. 1 as a dashed line. Thevery slow component appearing in the second partof the signal ðt\80 nsÞ; associated to the responsefunction of the cable, very marginally influencesthe time information for fractions of the signalsmaller than about 0.5 as those which are involvedin the present tests (see the following). Practicallythat means that the effective (with reference to thediscussed results) risetime of the preamplifier isabout 60 ns; i.e. twice the 10–50% time. Anyway,the final implementation will be provided withshorter cable connections to better exploit thepreamplifier characteristics, mounting the digiti-zers next to the scattering chamber.

It is well known (see for instance Ref. [8]) thatthe shape of the signal from a Silicon detectorcontains information about the type of thedetected particle; moreover the rear side injectiontechnique [9,10] increases the dependence of theshape of the signal on the charge (and even themass) of the impinging particle, because the effectson the pulse shape due to the high ionizationdensity are enhanced in the lower field regionsprobed by stopped particles. Therefore, the use ofPSA techniques in the DE detector of a standardDE � E Silicon telescope permits the identificationof particles that are fully stopped in the DEdetector, thus considerably lowering the thresholdsof the system. Good resolution in both energy andtime is required for this kind of application, as wellas a good doping uniformity of the chosen detector[11].

To perform the test, the simple electronic chainshown in Fig. 7 has been employed: for each eventthe signal from the detector has been sampled(total sampling time: 10 ms) and transferred to theacquisition system.

The offline analysis performed on the collectedwaveforms will be discussed in detail in a futurepaper [12]. Briefly, for each event:

* The asymptotic amplitude A (see Section 2) ofthe signal has been determined using a movingaverage filter [13].

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Charge Preamplifier

NTD

silicon detector

H.V.

Digitizer

(100 MS/s, 12 bit)

to acquisition

system

50m cable

Fig. 7. Electronic chain used for the timing test with pulse-

shape analysis. The Silicon detector is mounted in the reverse

field configuration. The electronics needed to trigger the

acquisition has not been shown.

dZC - dCFD (ns)114.6 114.8 115 115.2 115.4

Cou

nts

02000400060008000

1000012000140001600018000200002200024000

FWHM: 125 ps

Timing resolution for elastic peak

Fig. 8. Full line: dZC-dCFD time spectrum (see text) for the

elastic peak as obtained with the digital sampling system as in

Fig. 7 and cubic interpolation. Dashed line: the same quantity

obtained using linear interpolation: note the strongly non-

Gaussian shape of the peak and the worse resolution.

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UNCORREC* A digital constant fraction (dCFD, with f ¼ 0:2

and cubic interpolation) time mark has beenobtained.

* A digital zero crossing (dZC) time mark hasbeen obtained applying a digital Delay-Line-like shaping ðtDDL ¼ 100 nsÞ to the signal, andcomputing the zero-crossing time with a simplegeneralization of the dCFD algorithm.

* A quantity proportional to the energy releasedin the detector has been computed using adigital shaping of the signal (semigaussianCR� ðRCÞ4 digital filter [13,14] with t ¼ 2 ms).

All the proposed algorithms are well suited for faston-line processing of data. Given the used timeconstants for amplitude and time mark determina-tions and the intensity of particles impinging onour detector during test runs (about 104=s), nooptimization of the algorithms has been done withrespect to counting rate effects. The use of thezero-crossing algorithm to obtain the second timemark for the PSA is just one possible choice and itcan be easily replaced by the determination of the

TED PROOF

time associated to another dCFD having a largerfraction (typically 0.5–0.6). This point will bediscussed in Ref. [12].

The obtained results are shown in Fig. 8: thedifference dZC-dCFD (f ¼ 0:2) for elastic eventsis shown. At the used bombarding energy of250 MeV the elastically scattered 16O particles arenot stopped in the Silicon detector. The FWHM ofthe elastic peak is 125 ps: In Fig. 8 the timingspectrum obtained for the same events with alinear interpolation is also shown: as anticipated inSection 2 this low-order interpolation not onlyaffects the overall timing resolution, but producesa strongly non-Gaussian shape. These data are inagreement with the results of the realistic simula-tion presented in Fig. 6, for trE60 ns:

In Fig. 9 the overall pulse-shape correlation isshown: the amplitude of the digitally shaped signalis reported against the difference between thedigital zero crossing time dZC and the digitalconstant fraction (dCFD) time mark. One clearlysees that the system is able to discriminate betweendifferent particles with full charge resolution. Theexpanded view makes it possible to also appreciatethe existence of a somewhat marginal massresolution. The energy resolution (electronic con-tribution plus counting rate effects) on the verticalaxis was measured to be about 100 keV; estimated

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dZC-dCFD (ns)

114 116 118 120 122 124 126 128 130

Am

plitu

de (

a.u.

)

0

100

200

300

400

500

600

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10

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103

14C13C12C

14N15N

Digital Pulse Shape

Fig. 9. Digitally determined Amplitude vs. dZC-dCFD time

correlation: charge identification is apparent. In the inset: detail

of the isotope separation of carbon and nitrogen. Data have

been obtained with the electronic chain of Fig. 7.

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NIMA : 42392

by means of a calibrated charge injected into thepreamplifier during the measurements. The count-ing rate was about 10 kHz: Independent testsperformed on the same detector with low energy aparticles and proton bursts [7] have shown that thediscrimination obtained, mainly for short rangehighly ionizing particles as those in the right sideof the figure which explore only low electric fieldregions, is limited by the non-homogeneities of thesilicon doping [12].

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UNCORREC5. A novel approach to Time of Flight

measurements

The previous discussion on the timing perfor-mances of the digitizer suggests the possibility forsuch a system to be used for Time of Flightmeasurements in those cases where a timingresolution of B100 ps FWHM can be tolerated(i.e. a major part of heavy ions and nuclear physicsexperiments). As a matter of fact, we have deviseda new approach to ToF measurements, based onthe mixing of a beam related time signal with theto-be-sampled preamplifier output.3 On the leftside of Fig. 10 the electronic chain used in our testsis shown. It could be easily implemented withoutintroducing any change neither in the preamplifiernor in the digitizer: a beam related time signal (for

953This application has been briefly described in Ref. [15].

TED PROOF

example the Radio Frequency RF signal forpulsed beams) is gated with a delayed ðB7 msÞcopy of the general trigger of the experiment andinjected in the test input of the preamplifier. Onthe right side of Fig. 10 some examples of signalsacquired with this electronic chain are shown: themixed RF signal ð5 MHzÞ appears on the tail ofthe signals coming from the preamplifier. To getdigitized sequences like the ones shown in the rightside of Fig. 10, an alternative and more versatilesolution exists, consisting in the addition of asumming node at the digitizer input for mergingtogether the untouched preamplifier output andthe gated time reference signal. Anyway, regardlessto the solution adopted for the mixing, the RFtime reference does not affect the first part of thesignal: the analysis of the preamplifier output canstill be performed, as long as the whole interestingphysical information (signal amplitude, rise time,shape details) is confined in the first few micro-seconds. Moreover the ToF of the detectedparticle can be obtained, apart from an overalloffset as usual, as the difference between the mixedRF signal time and the starting time of thepreamplifier output (e.g. obtained with a digitalConstant Fraction algorithm, as already de-scribed). Because of the use of a simple AND gate,the first pulse of the mixed RF signal must bediscarded: both its starting time and width dependon the relative overlap between the trigger pulseand the RF signal. Any of the following RFperiods can be used for the determination of abeam related time mark: a better time determina-tion is obtained by using an average over allperiods (taking into account the associated time-shifts corresponding to integer multiples of the RFperiod).

Measurements have been performed to test thefeasibility of this technique, using the electronicchain of Fig. 10.

Unfortunately the intrinsic time resolution ofthe 16O beam as measured with a small fast plasticdetector and standard fast electronics was aboutB1:3 ns FWHM. The same resolution value isobtained with our technique; however, this value ismuch larger than the expected contribution arisingfrom the digital timing technique, thus preventinga direct comparison with the estimate of Section 2.

NCORREC

PROOF

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Delay

Charge Preamplifier

NTD

Digitizer(100 MS/s, 12 bit)

50m cable

Acquisitionsystem

RF or beam-related signal

H.V.

silicon detector

AND

Test input

Time (ns)

0 2000 4000 6000 8000 10000

0

500

1000

1500

2000

2500

Digitized signal

Mixed RF signal

Trigger

Fig. 10. Left panel: electronic chain employed for mixing a beam related signal with the signal coming from the detector. Right panel:

some signals collected using this electronic chain. The system performs energy, pulse-shape and ToF measurements at the same time.

Digital RF1- RF2 (ns)-0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3

Cou

nts

0

5000

10000

15000

20000

25000 FWHM: 106 ps FWHM (RF) ≈ 50 ps⇒

Digital RF determination

Fig. 11. Distribution of the difference between the two digital

RF time mark determinations RF1 and RF2 (a common offset

has been subtracted). Using the full RF train a resolution of

50 ps FWHM is deduced (see text).

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UTo perform this comparison the time mark relatedto the RF signal has been extracted in twoindependent ways for each event, using twodifferent sets of oscillations: with reference toFig. 11 (right panel), the first five periods (the last5) of the RF train have been used to evaluate thetime mark RF1 ðRF2Þ: The distribution of the

TEDdifference between these two determinations isshown in Fig. 11. The FWHM of the difference is106 ps: Under the realistic assumption that thefluctuations of the 10 considered determinationsare independent, the difference between RF1 andRF2 has a standard deviation differing by a factorffiffiffiffiffiffiffiffi

2=5p

from that of a single determination and twotimes larger than the one obtained from the totalaverage over 10 values. Therefore one extrapolatesa FWHM(RF) of the total average of E50 ps: Ofcourse this figure can be further reduced byincreasing the number of oscillations containedin the mixed RF train. In practice this means that,besides the resolution of the pulsed beam, thelimiting value to the ToF resolution is of the orderof 100 ps; given by the time mark extracted fromthe detector signal, namely the one associated withthe dCFD.

The poor time quality of the beam pulse did notpermit to check other important features con-nected with the determination of the time-mark ofthe signal, too. In fact, the residual dependence ofthe obtained time-mark on the signal shape is notonly expected to be present, but also enhanced bythe rear-side injection of the particles requested by

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RREC

PSA. Such effects—common to any signal time-analysis, analog or digital—would hinder a properdetermination of the ion velocity. To that purposea Silicon Detector mounted with the high field sidefaced to the impinging particles would be definitelypreferable and would guarantee a better shapeindependence. All these items, together with theoptimization of the time resolution of dCFD as afunction of the fraction f ; are beyond the scope ofthe present paper and will be deferred to the nextplanned step of studying the dCFD timingperformances in coincidence and lifetime measure-ments with independent detectors [12].

With reference to that application, it is worthstressing that the presented solution involving RFmixing in the digitized samples, implemented tointroduce an external time-reference mark for ToFapplications, can be easily extended to permitcoincidence measurements between different de-tectors: in fact, once in all digitized sequencesassociated to various detectors a common timereference mark is introduced at the analog level(either in the preamplifier input through capacitiveinjection or at the ADC input by means of asumming node) the time difference of all signalswith respect to this common reference is obtained,at the expenses of a small deterioration of the timeresolution—see discussion before. From that itimmediately follows that also the time differencesamongst all fired detectors are available andmultiple coincidence measurements can be per-formed. Systematic effects on timing, like walk andcounting rate sensitivity, common to all standardcoincidence measurements, deserve—as antici-pated—a careful and quantitative study.

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UNC6. Conclusions

In this paper the use of fast digital samplingtechniques for nuclear physics timing measure-ments has been discussed. Some simple calcula-tions and realistic simulations described in Section2 show that a sampling system, if provided with anadequate bit resolution and proper interpolatingsoftware (cubic dCFD), is able to reach a timingresolution much smaller (about two orders ofmagnitude) than the sampling period. Specifically,

TED PROOF

as long as the signal develops on a time intervallonger than the sampling period, the samplingperiod itself plays a minor role in the overalldigital time resolution, which—at the contrary—ismainly determined by the number of effective bitsof the converter. The results obtained using a100 MSample=s; 12 bit converter have been pre-sented: the performed tests (using a 300 mm Silicondetector with a 16Oþ 116Sn reaction at a beamenergy of 250 MeV) have shown that the timingresolution of this digital sampling system can be aslow as B100 ps FWHM, for both pulse-shape andTime of Flight applications. This sampling systemis well suited for application to a large number ofdetectors: the used ADC chip provides relativelylow cost, low power and higher resolutioncharacteristics, as compared, for example, withhigh sample rate commercial systems (as digitaloscilloscopes).

In our laboratory the prototype a new modulardigital sampling system is under test. It consists ofa single unit VME module, provided with eight125 MSample=s; 12 bit sampling channels: eachchannel is self-triggerable (using a programmableleading-edge discriminator) and it is provided witha fixed-point DSP processor (ADSP2189N) for on-line treatment of data. The system will also beprovided with the possibility of mixing in alldigitizers a common external time reference signal(e.g. a train of pulses), aimed at synchronizing allthe sampled sequences on the same event toperform sub-nanosecond timing between all de-tectors fired in an event. This avoids the somewhatcumbersome mixing at the test input of thepreamplifiers. The mixing of preamplifier outputand time reference signals at the ADC input will beprovided with a linear gate option meant toexclude the preamplifier output before introducingthe common time reference to all digitizers. Thisfeature guarantees a stable level to the referencesignal, regardless of the detectors’ counting rate.The synchronization can be also obtained bydriving all the ADCs with a unique samplingclock, although this implementation can be tech-nically more complicated.

More tests are actually under way with differentdetectors, as the Single Chip Telescope [16], with

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encouraging results: these new data will bereported in a future work [12].

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Acknowledgements

Thanks are due to the GARFIELD collabora-tion for the assistance provided during datataking. Helpful discussions with A. Olmi arekindly acknowledged.

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[4] M.A. Nelson, et al., Nucl. Instr. and Meth. A 505 (2003)

324.

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[5] G.F. Knoll, Radiation Detection and Measurement, 3rd

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[6] Improving ADC Resolution By Oversampling and Aver-

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[12] L. Bardelli, et al., to be published.

[13] S.W. Smith, The Scientist and Engineer’s Guide to Digital

Signal Processing, available on www.dspguide.com.

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Prentice-Hall, Englewood Cliffs, NJ, 1975.

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Laboratori Nazionali di Legnaro Annual Report, 2002.

[16] G. Pasquali, et al., Nucl. Instr. and Meth. A 301 (1991)

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TED