Moderne Teilchendetektoren - Theorie und Praxis 2. Dr. Bernhard Ketzer Technische Universität München SS 2013
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1 Moderne Teilchendetektoren - Theorie und Praxis 2 Dr. Bernhard Ketzer Technische Universität München SS 2013
2 7 Signal Processing and Acquisition 7.1 Signals 7.2 Amplifier 7.3 Electronic Noise 7.4 Analog-to-Digital Conversion 7.5 Time-to-Digital Conversion 7.6 Trigger 7.7 Data Readout and Acquisition
3 Overview General scheme of a measurement system: 1. Radiation deposits energy in a detecting medium 2. Energy is converted into an electric signal direct conversion: ionization ionization chamber: e -ion pairs semiconductor detector: e -hole pairs indirect conversion: excitation emission of light conversion into charge scintillation detectors primary signal charge absorbed energy Energy required per e ~ 30 ev ~ 3 ev ~ 300 ev
4 Overview 3. Signal amplitude small amplification necessary secondary amplification proportional counter photomultiplier tube avalanche photodiode electronic circuit introduction of random fluctuations (noise) 4. Pulse shaping, e.g. [H. Spieler, Semiconductor Detector Systems, Oxford 2005]
5 Overview 5. Digitization extraction of information detector channel position signal amplitude energy time 6. Based on this information decision to keep or discard the event store data read other detectors reset / clear information Trigger
6 Overview Example: [H. Spieler, Semiconductor Detector Systems, Oxford 2005]
7 7.1 Signals
8 7.1.1 Fluctuations in Signal Charge Consider Si detector: average number of e -hole pairs average energy loss average energy required per e -hole pair Two limiting cases: Only a very small fraction E 0 of the total energy E of the incident particle is converted into e -hole pairs statistically independent processes Poisson statistics (i.e. energy loss can vary within Poisson statistics)
9 Fluctuations in Signal Charge Total energy of incident particle is converted into e -hole pairs (no other process of energy dissipation!) no fluctuations (i.e. each particle of the same total energy will create the same number of e -hole pairs) Real detector: Fano factor, Si: processes for creation of single charge carriers statistically not independent (fixed value of energy deposition) in solids: electronic excitation in connection with lattice excitation (phonons)
10 Fluctuations in Signal Charge Fano factor determined by all fundamental processes for energy dissipation in the detector, including non-ionizing ones depends on material difficult to calculate from first principles mostly: empirical values Further source of fluctuations: electronic noise
11 Fluctuations in Signal Charge Example: 2 types of interactions in solid lattice excitation (phonon production): N x excitations produce N p phonons ionization: N i ionizations produce N Q charge pairs sum of energies going in excitation and ionization is equal to energy E 0 deposited by incident radiation: E x = energy required for single excitation = average phonon energy in semicond. E i = energy required for single ionization = bandgap in semiconductor
12 Fluctuations in Signal Charge For a single event: E 0 fixed (but can vary from event to event) For there is always some combination of excitation and ionization to dissipate exactly the deposited energy fluctuation in excitation is balanced by fluctuation in ionization Averaging over many events With
13 Fluctuations in Signal Charge With follows In Silicon: Experiment:
14 Fluctuations in Signal Charge Energy resolution: Peaks can be resolved if separation of peaks larger than their FWHM [W.R. Leo, Techniques for Nuclear and Particle Physics Experiments, Springer 1994]
15 Energy Resolution [H. Spieler, Semiconductor Detector Systems, Oxford University Press 2005]
16 7.1.2 Signal Formation Charge moving in sensitive volume of detector signal current Ramo s Theorem: [H. Spieler, Semiconductor Detector Systems, Oxford University Press 2005]
17 7.1.3 Terminology baseline pulse height, amplitude pulse width FWHM rising edge falling edge rise time fall time unipolar - bipolar [W.R. Leo, Techniques for Nuclear and Particle Physics Experiments, Springer, 1994]
18 Terminology Analog signal: continuously varying characteristics (amplitude, time, shape) e.g. proportional counter Digital signal: discretely varying, quantized property e.g. Geiger-Müller counter: yes/no normally two states: 0, 1 technically more reliable (resistant to external perturbations), but carries less information per pulse
19 Logic Elements Common logic functions: Logic symbols: [H. Spieler, Semiconductor Detector Systems, Oxford University Press 2005]
20 7.1.4 Frequency Domain, Bandwidth
21 Bandwidth Example: rectangle pulse F( ω)= ωt sin AT 2 2π ωt 2 continuous frequency spectrum!
22 Bandwidth Perfect electronic device for processing of f(t) uniform response to infinite range of frequencies Real device transmission limited to finite range in ω (R, C, L) Typ. frequency response of an electr. circuit [W.R. Leo, Techniques for Nuclear and Particle Physics Experiments, Springer, 1994]
23 Pulse Signals and Bandwidth Important: transmission of information carrying parts of signal, e.g. amplitude, rising edge Effect of limited bandwith on rectangular pulse [W.R. Leo, Techniques for Nuclear and Particle Physics Experiments, Springer, 1994] minimum bandwidth: typical bandwidths: 100 khz 1 GHz
24 7.1.5 Signal Transmission
25 Signal Transmission I(z,t) I(z+ z,t) U(z,t) U(z+ z,t)
26 Signal Transmission
27 Signal Transmission
28 Signal Transmission
29 Signal Transmission
30 Signal Transmission
31 Signal Transmission [W.R. Leo, Techniques for Nuclear and Particle Physics Experiments, Springer, 1994]
32 Signal Transmission
33 Pulse Transmission by Cable [W.R. Leo, Techniques for Nuclear and Particle Physics Experiments, Springer, 1994]
34 7.2 Amplifier Amplifies weak signals from detector Drives signal through cable Low noise close to detector
35 7.2.1 Bipolar Transistor Structure: 3 subsequent regions of different doping (npn, pnp) Example: npn transistor U C > U E > U B : both diodes BC and EB reverse biased only reverse current I C = I C (U CE ) through BC, depending on n p (minority carrier concentration) U C > U B > U E (U BE > 0): diode BE forward biased, BC reverse e - get from n+ into p-zone increase of n p = n p (U BE ) [Ibach, Lüth, Festkörperphysik, Springer, 2002]
36 Bipolar Transistor [Ibach, Lüth, Festkörperphysik, Springer, 2002]
37 Bipolar Transistor If p-zone very thin (~µm) d < λ (mean free path for recombination) e - may reach pn junction of diode BC transported into n-zone by U CE current I C = I C (U BE ) strongly non-linear most important property of transistor
38 Bipolar Transistor Behavior of transistor described by characteristic curves, i.e. relation between currents and voltages (static situation) Common emitter circuit: Forward (active) region: application as amplifier I C I B > 0, U BE > 0, U CE U CE,sat ~ U BE BE forward, BC reverse Saturation region U BE I B I E U CE I B > 0, U BE > 0, U CE U BE BE forward, BC forward Cut-off region I B 0, U BE 0, U CE > 0 BE reverse, BC reverse application as switch Here: U BE > 0 BE forward
39 Transistor Characteristics Transmission characteristics: I C (U BE ) exponential dependence (diode) [Tietze, Schenk, Halbleiter-Schaltungstechnik, Springer, 1999]
40 Transistor Characteristics Output characteristics: I C (U CE ) Saturation region: U CE < U CE,sat BC forward I C increases strongly with U CE transistor saturates Active region: U CE > U CE,sat weak dependence of I C on U CE (finite slope: Early effect) Definition: differential output resistance (at working point A) [Tietze, Schenk, Halbleiter- Schaltungstechnik, Springer, 1999]
41 Transistor Characteristics Input characteristics: I B (U BE ) exponential dependence (diode BE) Definition: differential input resistance (at working point A) at 300 K: thermal voltage typ.: [Tietze, Schenk, Halbleiter-Schaltungstechnik, Springer, 1999]
42 Transistor Characteristics Similar dependence of I B (U BE ) and I C (U BE ) in active region Definition: small signal current gain (at working point A) In active region of transistor: [Tietze, Schenk, Halbleiter-Schaltungstechnik, Springer, 1999] i.e. small signal current gain agrees with DC current gain
43 Transistor Characteristics [
44 Transistor Circuits Rohe, Elektronik für Physiker, Teubner, 1978]
45 7.2.2 Grounded Emitter Amplifier bias voltage
46 Grounded Emitter Amplifier [A. Schlachetzki, Halbleiter-Elektronik, Teubner, 1990]
47 Grounded Emitter Amplifier
48 Grounded Emitter Amplifier
49 Grounded Emitter Amplifier
50 Grounded Emitter Amplifier Voltage amplification (w/o load): A 0 R r C = BE β 200 typ. only valid for U BE <<U T (linear relation R BE = U BE / I B ) strong distortions for U BE U T A 0 depends directly on β, r BE (vary with T and between devices) T dependence of I C at fixed U BE (diode)
51 Grounded Emitter Amplifier
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