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1 Pulse Processing and Noise Filtering in Radiation Detectors Chiara Guazzoni Politecnico di Milano and INFN Sezione di Milano www: March 4th, PhD Lessons

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2 Table 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

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3 Introduction and Summary - I sculpturing filtering

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4 Introduction 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.

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5 Signal Formation and Ramo’s Theorem - I Reciprocity of induced charge Partial capacitance in general: 3 1 (0 V) 4 2 V1 C 14 C 12 C 13 n Q2

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6 Signal Formation and Ramo’s Theorem - II Current induced by the motion of charge By reciprocity: Induced current - RAMO Theorem Weighting field (obtained by applying 1V on electrode 1 and grounding all the others) (S.RAMO, Proc. IRE, 27 (1939) 584) In general: find weighting field find charge velocity find x(t), y(t), z(t) applied voltage induced current V1=1V 1 2 0V 3 4

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7 Signal Formation and Ramo’s Theorem - III Induced current (charge) in planar electrode geometry Single carrier Continuous ionization Ne true field induced current collected charge

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8 Signal Formation and Ramo’s Theorem - IV Induced current in strip electrodes Induced current: Induced charge: weighting field streamlines weighting potential contour lines a b c a) b) c) tdtd i(t) tmtm 0.05

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9 Signal Formation and Ramo’s Theorem - V (multilinear drift detectors) PHOTON INTERACTION

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10 Signal Formation and Ramo’s Theorem - VI (multilinear drift detectors)

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11 Signal Formation and Ramo’s Theorem - VII (multilinear drift detectors) PHOTON INTERACTION

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12 1/f noise in a lossy capacitor (Van der Ziel ) Re Im As far as the loss angle ( ) is independent of frequency, the output voltage noise shows a 1/f spectrum. C (lossy) inin R Power spectral density of the thermal noise current generator C (loss-less) At low frequency the loss resistance is merely a measure of the conductivity ( ) of the dielectric S v ( ) shows a frequency dependence of the form vnvn

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13 Equivalent Noise Charge - I Identification 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 amplifier preamp. CdCd CiCi (leakage current feedback resistor) (capacitor dielectric losses) (1/f voltage noise) (white voltage noise) (gate current shot noise) Carson’s theorem 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

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14 Equivalent Noise Charge - II Equivalent circuit for ENC calculation shaping amplifier noiseless preamp. C d +C par CiCi (leakage current feedback resistor gate current) (capacitor dielectric losses) (1/f voltage noise) (white voltage noise) Charge Current step pulse random walk pulses signal white parallel pulses ‘ pulses doublets white series

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15 Equivalent 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 amplifier noiseless preamp. C d +C par CiCi (capacitor dielectric losses) (white voltage noise) (1/f voltage noise) (leakage current feedback resistor gate current)

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16 Equivalent Noise Charge - III ENC calculation in presence of 1/f noise and/or dielectric losses shaping amplifier noiseless transamp shaping amplifier noiseless transamp CTCT triangular shaping independent of shaping time T 2T 0 h(t) 1 RC-CR shaping CTCT 0 h(t) 1

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17 Equivalent Noise Charge - IV ENC calculation in presence of white and 1/f + dielectric noises Introducing where is a typical width of h(t) as the peaking time or the FWHM are shape factors depending only on the shape of the filter:

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18 Equivalent Noise Charge - V ENC vs. shaping time ( ) 5mm 2 SDD (on-chip JFET) 5mm 2 pn-diode (NJ14 JFET)

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19 Shape of the optimum filter 0 Si()Si() parallel noise b input referred series noise 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) 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)

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20 finite width (2T) 0 T 2T 1 Practically a triangle when T< c (only white series noise is “active”) truncated cusp t Shape of the optimum filter in presence of additional constraints - I T 2T t Practically a -pulse when T> c (only white parallel noise is “active”) 0 1 T 2T t 0 1

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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 (in presence of only white noises) 0 T ft 1 t Shape of the optimum filter in presence of additional constraints - 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.

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22 constant offset baseline drift t t input 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 v1 v2 vbp t1 tp t2 If t1, t2 and tp are equidistant Shape of the optimum filter in presence of additional constraints - III

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23 Capacitive Matching - I Fixed current density FET cut-off frequency independent of size MOSFET frontend The same result is valid also in presence of 1/f noise and applies to JFET frontend MOSFET transconductance - strong inversion white series noise Input voltage spectral noise Series noise integral with h(t) impulse response Optimum size of the input MOSFET (length L and impulse response h(t) constant)

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24 Capacitive Matching - II Fixed current density FET cut-off frequency independent of size

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25 Capacitive Matching - III Fixed power dissipation fixed drain current, white series noise MOSFET frontend MOSFET transconductance - strong inversion white series noise Input voltage spectral noise Series noise integral with h(t) impulse response Optimum size of the input MOSFET (length L, current I D and impulse response h(t) constant) MOSFET transconductance - weak inversion

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26 Capacitive Matching - III Fixed power dissipation fixed drain current, white series noise Optimum size of the input MOSFET (length L, current I D and impulse response h(t) constant) BUT…. Large values of W/I d ratio eventually leads to weak inversion operation. In this case g m is independent of W so any increase of W degrades the ENC. Therefore where defines the boundary of weak inversion.

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27 Capacitive Matching - IV Fixed power dissipation fixed drain current MOSFET frontend white series 1/f series

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28 Capacitive Matching - V Fixed power dissipation: graphical method When the dependence of g m vs I D is not the nominal one, different matching conditions arise: direct measurement of the FET parameters graphical method Low-power HEMT-based charge amplifier g m has been directly measured

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29 Time Measurements - I We want to measure the arrival time of the signal pulse as time information we choose the 0-crossing time of the output signal AA tt amplitude 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 s o, non-noisy output signal time walk time resolution improves as the slope at the 0-crossing increases

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30 Time Measurements - II output signal input current pulse shaper response t=0 nominal crossing time for the noiseless signal weighting function by a variational method, minimising t The optimum weighting function for time measurements is obtained as convolution of the cusp filter with the derivative of the input current pulse.

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31 Time Measurements - III Optimum time resolution only white parallel noise ( ) only white series noise ( ) w opt (t) input current pulse f(t)

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32 Time-variant Filters - I RR CTCT time-invariant pre-shaper p(t) b a A gated integrator p(t ) pp The switch conduction is synchronised with the detector-signal arrival and the switch remains conductive for R p. 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=t 1 will produce at the pre-shaper output the signal that is integrated over the time interval [t 1, t 1 + R ]

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33 Time-variant Filters - II Noise weigthing function [WF N (t o )]: contribution to the noise at the measuring time instant given by a -pulse delivered by the parallel noise generator at a time t o. (t o [t 1 - p,t 1 + 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 [t 1 - p, t 1 + R ] contribute to the noise at the measuring instant t 1 + R WF N (t o ) 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 t m =t 1 + R RR pp t1t1 t1+ Rt1+ R t1- pt1- p t o= t 1 - p toto toto toto toto toto toto toto toto t o = t 1 + R toto pp pp WF N

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34 Time-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 [t o, t o +dt o ] as t o varies. By sliding the derivative of (A/C T )p(t) through the integrator time window, the noise weighting function for doublet of current injected across the C T capacitor can be determined. The resulting function, which is the derivative of WF N, allows the calculation of the output noise arising from the white series generator. The knowledge of two different functions, p(x) for the signal and WF N (x) for the noise, is required in the analysis of a time-variant shaper.

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35 Non-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. f clock MOS gate used as sensing electrode in CCD for visible light applications Reverse biased p+ electrode used as sensing electrode in DEPFET structures f clock

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36 Non-destructive Multiple Readout - II 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

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37 Non-destructive Multiple Readout - III Shape of the optimum filter white voltage noise a w = V 2 /Hz white current noise b w = A 2 /Hz1/f voltage noise a f = V 2 white noises + 1/f voltage noise white noises sinusoidal current signal series of pulses

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38 Non-destructive Multiple Readout - IV Number of waiting and lagging period white voltage noise a w = V 2 /Hz white current noise b w = A 2 /Hz T[ s]

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39 Non-destructive Multiple Readout - V Number of waiting and lagging period white voltage noise a w = V 2 /Hz white current noise b w = A 2 /Hz

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40 Non-destructive Multiple Readout - VI 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 a w = V 2 /Hz white current noise b w = A 2 /Hz c =1.53 s T meas =25 s T osc =5 s

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41 Non-destructive Multiple Readout - VII Effect on the different noise components - II (for sake of simplicity we assume a sinusoidal current shape) 1/f series noise (A f =1.5 x V 2 ) 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.

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42 Non-destructive Multiple Readout - VIII 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 white voltage noise a w = V 2 /Hz white current noise b w = A 2 /Hz c =1.53 s

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43 Non-destructive Multiple Readout - IX Effect on the different noise components - summarizing... A) by imposing total measuring time (T meas ) 1.ENC 2 due to the white voltage noise is independent of the number of signal oscillations. 2.ENC 2 due to the 1/f voltage noise decreases as 3.ENC 2 due to the white current noise decreases as B) by imposing time duration of the signal oscillation (T osc ) ENC 2 due to all the different noise contributions decreases as

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44 Non-destructive Multiple Readout - X Comparison with delta-pulse processing white series noise + white parallel noise + 1/f voltage noise white voltage noise a w = V 2 /Hz white current noise b w = A 2 /Hz 1/f voltage noise a f = V 2 Multiple readout: the ENC 2 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.

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45 Non-destructive Multiple Readout - XI Effect of the shape of the induced signal white voltage noise a w = V 2 /Hz white current noise b w = A 2 /Hz c =1.53 s Number of waiting periods Achievable resolution

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46 Acknowledgment E. Gatti - Politecnico di Milano P.F. Manfredi - LBL V. 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

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