Fast Timing Techniques

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Fast timing techniques

A. Rivetti

INFN -Sezione di Torino [email protected]

June 2, 2016

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 1 / 32 Outline

1 Introduction

2 Time digitizers

3 Jitter and time walk

4 CFD and ARC timing

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 2 / 32 Other well known applications of high resolution timing: Mass analysis with ToF mass spectrometry Positrom Emission Tomography: ToF reduces image noise

With a peak luminosity of ≈ 1035, the HL-LHC will produce 140 to 200 collisions per bunch crossing

I Disentangling interesting events from background only with tracking and vertexing becomes challenging I The average collision distance in time is 100 ÷ 170 ps

The case for fast timing

Traditionally, high resolution timing detectors are used in HEP to indentify particles

I Measure the time to ﬂy between two points to obtain the velocity I Combine with momentum information to derive the mass 2 I Large systems: ALICE ToF: 160 m . Similar area for the CBM ToF wall at FAIR

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 3 / 32 With a peak luminosity of ≈ 1035, the HL-LHC will produce 140 to 200 collisions per bunch crossing

I Disentangling interesting events from background only with tracking and vertexing becomes challenging I The average collision distance in time is 100 ÷ 170 ps

The case for fast timing

Traditionally, high resolution timing detectors are used in HEP to indentify particles

Other well known applications of high resolution timing: Mass analysis with ToF mass spectrometry Positrom Emission Tomography: ToF reduces image noise

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 3 / 32 The case for fast timing

Traditionally, high resolution timing detectors are used in HEP to indentify particles

Other well known applications of high resolution timing: Mass analysis with ToF mass spectrometry Positrom Emission Tomography: ToF reduces image noise

With a peak luminosity of ≈ 1035, the HL-LHC will produce 140 to 200 collisions per bunch crossing

I Disentangling interesting events from background only with tracking and vertexing becomes challenging I The average collision distance in time is 100 ÷ 170 ps

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 3 / 32 Forward physics at HL-LHC

I Collision survivors can be used to probe new physics

pp → pγγp sensitive to extra-dimensions Intact protons detected 250 m far from the collision point Need of 10 ps timing to suppress pile-up

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 4 / 32 A typical timing system

The sensor signal is usually ampliﬁed and shaped A comparator generates a digital pulse The threshold crossing time is captured and digitized by a TDC TDC can be embedded on the front-end chip or external

I Timing is derived from a single sample

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 5 / 32 Outline

1 Introduction

2 Time digitizers

3 Jitter and time walk

4 CFD and ARC timing

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 6 / 32 High resolution TDCs: ASICs (1)

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 7 / 32 High resolution TDCs: ASICs (2)

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 8 / 32 High resolution TDCs: ASICs (3)

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 9 / 32 Non-HEP use of TDCs

TDC used to measure phase diﬀerence in ADPLL With scaling technologies speed of gates increases Work in the time domain also to measure voltages

K. Otsuga et al, IEEE International SoC Conference, 2012

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 10 / 32 High resolution TDCs: FPGA (1)

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 11 / 32 High resolution TDCs: FPGA (2)

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 12 / 32 Waveform sampling TDCs

The sensor signal is usually ampliﬁed and shaped The full waveform is sampled and digitized at high speed In many systems, sampling and digitization are decoupled Timing is extracted with DSP algorithms from the digitized waveform samples

I Timing is derived from multiple samples

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 13 / 32 Waveform samplers: some example

ASIC Year Node Time res. Max sample/ch. Channels

LABRADOR3 2005 250 nm 16 ps 260 8

BLAB 2009 250 nm < 5 ps 65536 1

DRS4 2014 250 nm ≈ 1 ps 1024 8

PSEC4 2014 130 nm ≈ 1 ps 256 6

SamPic 2014 180 nm ≈ 3ps 64 16

Typical small channel count per ASIC Resolution: same pulse split and sent to diﬀernt channels and time diﬀerence measured

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 14 / 32 Timing: yesterday and today

D. Breton et al., NIM A 629 (2011) 123-132

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 15 / 32 Trends in timing systems

Time digitizers with ps resolution are a commodity Detectors with time resolution of 100 ps or better already achieved in the sixties of last century Typical ToF systems have low channel density Electronics either discrete or based on front-end ASICs with few channels

Improve time resolution well below 100 ps (target 10 ps) Extend timing to densely packed detector systems. Need of highly integrated ASICs for timing

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 16 / 32 Timing: the issues

Several factors challenge the timing accuracy of a system: Random noise internal to the front-end electronics (can be traded with power) Random noise from external sources (e.g. clock distribution system) Signal integrity (substrate noise, PSSR, etc..) Pulse amplitude variations Pulse shape variations

I Timing below 100 ps rms is not trivial

I Research is now geared towards sub 10 ps system resolution

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 17 / 32 Outline

1 Introduction

2 Time digitizers

3 Jitter and time walk

4 CFD and ARC timing

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 18 / 32 Timing jitter: single sample

σ = σv dV ≈ V → σ = tr t dV dt tr t SNR dt Checks:

tr = 1 ns, SNR = 10 → σt = 100 ps

tr = 40 ns, SNR = 500 → σt = 80 ps

t ∝ 1 SNR ∝ √ 1 → σ ∝ √ 1 r BW BW t BW

I Match the front-end rise time with the sensor rise/collection time

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 19 / 32 Timing jitter: multiple sampling

Sample the input signal beyond Nyquist Assume ﬁrst-order system relationship

tr 1 tr σt = √ N = SNR N ts q 1 0.35 1 √ 1 σt = SNR BW ·f = SNR s 3f−3dB fs

SNR fs f−3db σt 10 1 Gs/s 150 MHz 150 ps 10 10 Gs/s 1.5 GHz 15 ps 100 1 Gs/s 150 MHz 15 ps 1000 10 Gs/s 1.5 GHz 0.15 ps

Redundacy is advantageous only if noise in uncorrelated

I Unfortunately, jitter is not the full story...

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 20 / 32 Common solutions Correct using the pulse amplitude Correction usually done oﬀ-line Time-over-threshold often used Track in real-time the pulse with the threshold

I Constant Fraction Timing

Time walk

Pulses of same shape and diﬀerent amplitude crosses the threshold at diﬀerent times Even worse if also the shape changes This is a problem for accurate timing

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 21 / 32 I Constant Fraction Timing

Time walk

Pulses of same shape and diﬀerent amplitude crosses the threshold at diﬀerent times Even worse if also the shape changes This is a problem for accurate timing

Common solutions Correct using the pulse amplitude Correction usually done oﬀ-line Time-over-threshold often used Track in real-time the pulse with the threshold

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 21 / 32 Time walk

Pulses of same shape and diﬀerent amplitude crosses the threshold at diﬀerent times Even worse if also the shape changes This is a problem for accurate timing

Common solutions Correct using the pulse amplitude Correction usually done oﬀ-line Time-over-threshold often used Track in real-time the pulse with the threshold

I Constant Fraction Timing

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 21 / 32 Outline

1 Introduction

2 Time digitizers

3 Jitter and time walk

4 CFD and ARC timing

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 22 / 32 The input signal is both delayed and attenuated The delayed and attenuated signals are combined to yield a bipolar waveform The zero crossing of the bipolar waveform is used for timing

CFD: the principle

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 23 / 32 The delayed and attenuated signals are combined to yield a bipolar waveform The zero crossing of the bipolar waveform is used for timing

CFD: the principle

The input signal is both delayed and attenuated

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 23 / 32 The zero crossing of the bipolar waveform is used for timing

CFD: the principle

The input signal is both delayed and attenuated The delayed and attenuated signals are combined to yield a bipolar waveform

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 23 / 32 CFD: the principle

The input signal is both delayed and attenuated The delayed and attenuated signals are combined to yield a bipolar waveform The zero crossing of the bipolar waveform is used for timing

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 23 / 32 CFD: the algorithm

Assume a step input signal:  0 for t < 0    V (t) = t V for 0 < t < t tr 0 r    V0 for t > tr

td > tr , amplitude compensation fV = t−td V t = ft + t 0 tr 0 zc r d

td < tr , ARC compensation f t V = t−td V t = td tr 0 tr 0 zc 1−f

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 24 / 32 CFD: in practice

Take now simple CR − RC shaping and an ideal delay line:

td t−t t t − td − d t − td e τ e τ − f e τd = 0 → t = zc td τ td e τ − f

Jitter optimization: τ = tcoll → sensitivity to pulse shape ﬂuctuations!

Can be reduced by reducing td , f , or both... CFDs rely of fully linear signal processing Not trivial to implement in modern CMOS technologies due to the reduced voltage headroom, but it can be done.

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 25 / 32 CFD underdrive

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 26 / 32 Digital timing extraction

Diﬀerent algorithms are used to compute the timing from the digitized samples There is nothing such an optimal method Some techiques can be more suited that others for real time execution on FPGA

Some examples of digital algorithm: Digital leading edge Digital constant fraction Interpolation Initial slope approximation Reference pulse ...

To learn more: E. Delagnes, Precise Pulse Timing based on Ultra-Fast Waveform Digitizers, Lecture given at the IEEE NSS Symposium, Valencia, 2011 A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 27 / 32 Some comparison

J. F. Genat et al. Signal processing for picosecond resolution timing measurements, NIM A 607 (2009) 387-393

Simulations based on MCP signal No sampling jitter added The barrier of 10 ps broken around 20 pe Practical equivalency between WS and CFD

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 28 / 32 This can be yourCharge signal collection – 100um thickness

Courtesy L. Pancheri, Trento Vbias = -30V

Width 50um Width 25um Current [A] Current

> 10ns for complete < 10ns for complete collection: Diffusion collection tail

Time [s] Time [s]

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 29 / 32 Simulation methodology

Generate a set of charges from the Landau distribution covering the dynamic range Send the charges in diﬀerent part of the sensing element Collect the resulting current waveforms in the form of time-amplitude lis Input them in SPICE with the timing chain (transistor level) Important to consider also the discriminators Analyze the SPICE outputs and extract the timing A lot of scripting...

A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 30 / 32 Can we have better timing algorithms?

Nuclear Instruments and Methods in Physics Research A 457 (2001) 347}355

Timing of pulses of any shape with arbitrary constraints and noises: optimum "lters synthesis method E. Gatti*, A. Geraci, G. Ripamonti

Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano 20133, Italy Received 9 June 2000; accepted 15 June 2000

Abstract

In this paper the optimum "ltering for the precise measurement of the occurrence time of any kind of time-limited signal is dealt with. We "nd the time-limited optimum weighting function (WF) in the presence of any kind of uncorrelated, stationary, additional noises and we allow the introduction of arbitrary assigned time domain constraints in the WF. The method can be easily translated into computer programs and it can be used as a tool for optimising a digital signal processing spectroscopy set-up in its digital "lter section. An application of the method to signals at the output of large volume HPGe !-ray detectors is "nally presented. ! 2001 Elsevier Science B.V. All rights reserved.

Keywords: Pulse timing; Optimum "lter; Digital signal processing; HPGe detectors

1. Introduction which could be well approximated both with a "-like pulse [1] and with waveforms of arbitrary Many measurement applications need a precise shape [2]. knowledge of the time of occurrence of the event In this paper, we consider the extension of the A. Rivetti (INFN-Torino)(e.g. coincidence}anticoincidence, positionFast detec- timingreferred techniques method to the case of synthesis of the WF June 2, 2016 31 / 32 tion, etc.). As in the case of the `optimuma measure- for optimum events timing. The proposed algo- ment of the pulse energy (i.e. pulse area), also in this rithm is easily retro"tted in a DSP spectrometer case a suitable "ltering has to be provided in order program, and can, therefore, be used in an auto- to obtain the best possible estimate of the pulse matic optimum WF synthesis algorithm. The re- occurrence time. sulting feature introduced in the present work to We have introduced a method for synthesising the established theory of optimum "lters allows the the optimum time-limited Weighting Function optimum timing of input signals of known wave- (WF) in the presence of noise of arbitrary power form and in many experimental conditions. Its density for the measurement of pulses energy. The validity is obviously not limited to the measure- method was suited for those cases of input signals, ment of nuclear pulses, although it is particularly "t to this case. As an example, we carry out the application of * Corresponding author. Tel.: #39-022-3996102; fax: #39- the method to the determination of the interaction 022-367604. positions for !-ray spectroscopy in a large-volume E-mail address: [email protected] (E. Gatti). segmented HPGe detector.

E. Gatti et al. / Nuclear Instruments and Methods in Physics Research A 457 (2001) 347}355 349

In order to check the method, we compared the result with a test case that has analytical solution. We consider a current noise spectrum

N(")"1#10\"

and a delta signal at the center of the measurement time interval ¹"24 !s. The analytical solution (see Appendix B) refers to an in"nite measurement time. Nevertheless, the results are comparable as the analytical solution derivative is practically zero for t'¹. In fact, for t'¹ the value of this derivative is lower than 10\ which has to be referred to the maximum slope value of the WF which is one. Fig. 1. Comparison between the approximated optimum syn- Fig. 1 shows the comparison between the approxi- thesised WF w(t) (a) and the analytical one (b)in the test case (see mated optimum synthesized WF w(t) and the exact text): the two curves almost coincide and the maximum diver- solution. gence is in correspondence with the cusp peak. This is to be expected, since our representation of w(t) involves an analytical function expressed with a "nite number of harmonics. The number of harmonics is 200. The di!erence in time resolution is 3. Example of application just 2%. Consider a coaxial HPGe "-ray detector cooled to cryogenic temperatures. An impinging "-ray re- When dealing with input signals i(t) having leases packets of energy due to the various scatter- A. Rivetti (INFN-Torino) Fast timing techniques June 2, 2016 32 / 32 zero area, the introduction of a Q"# [2] is neces- ing mechanisms (e.g. Compton e!ect). Depending sary. The factor Q"# represents an integral of i(t) on the position of such interactions, the slope de"ned between arbitrary limits t and t of the current signal on the collecting electrode(s) (0(t(t(¹), suitably chosen in order to make exhibit(s) characteristic steps, from which the Q"# di!erent from zero for every choice of i(t). In 3-D coordinates of each energy release event this most general case, the squared N/S ratio in can be reconstructed in principle [4}6]. Eq. (2) is written as Let us focus on the case of a segmented detector, in which the segmentation of the sensing electrodes > has been proposed to help the localization of the N \N(")"=(")" d" " > . (6) event in the volume of the detector (Fig. 2). !S " Q"# [ (i(%)/Q"#) ) w(%)d%] \ The shape of the signal generated at the detector Now, we can impose the denominator term in electrodes depends on the drift path of the charge brackets to be equal to one, obtaining an equation cloud generated in the interaction between the that can be used as a Lagrange constraint " photon and the detector [7]. The problem is extremely complex. The pulse shapes induced on the electrodes strongly depend on the three spatial >i(%) ) w(%)d%!1"0. (7) coordinates of the hit. This is true for the pulses at \ Q"# the electrodes collecting charge as well as for the zero-area pulses induced on the neighbor elec- By adding this condition, the squared N/S (Eq. (6)) trodes (Fig. 3a). In Ref. [8] pulse shapes in a truly becomes coaxial HPGe detector have been calculated in closed form and the following signatures dependent N >N(")"=(")" d" on a single interaction coordinate have been found. " \ . (8) !S " Q"# Beyond the initial rise, the current signal induced at