1 / 35

New England Particle Physics Student Retreat (NEPPSR)

New England Particle Physics Student Retreat (NEPPSR). Front End Electronics for Particle Detection Case study : ATLAS Muon Spectrometer August 20, 2003 John Oliver. Signal formation in gas detectors Basic electronic components & noise sources Noise calculations

aman
Download Presentation

New England Particle Physics Student Retreat (NEPPSR)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. New England Particle Physics Student Retreat (NEPPSR) Front End Electronics for Particle Detection Case study : ATLAS Muon Spectrometer August 20, 2003 John Oliver • Signal formation in gas detectors • Basic electronic components & noise sources • Noise calculations • Amplifier/Shaper/Discriminators (ASDs) for ATLAS Muon Spectrometer Disclaimer This will be a fairly analytical approach. The idea is to develop a tool-box of methods you will need to analyze similar applications. If you find the need, you can explore any of these subjects in more detail later. You don’t need to memorize this stuff!! Homework There will be numerous examples given as homework. Go as far with them as you can. We’ll go over the solutions Wednesday/Thursday evening.

  2. D (10 mm) x Anode Cathode Vhv (1 kV) Q Signal formation in gas detectors Simple example : Uniform electric field in drift gas (eg Ar/CO2) A • Electric field  E = 1e 5 Volts/meter • Particle track ionizes N electron/ion(Ar) pairs with total charge N*e = Q • Electrons/ions drift toward Anode/Cathode with velocity given by their mobilities • Question : What signal current i(t) is seen by ideal ammeter in series with battery ?

  3. Electrons drift to Anode, ions to Cathode • First the electrons… In time Dt, electrons move distance through potential Work done by field is Work done by battery is In general  -------------------- (1) In this example  -------------------- (1b) Total signal charge collected in arbitrary time t, -------------------- (2)

  4. i(t) 4 nA 50 ns t 10 mm Vhv (5 kV) • Example : • Q = 1fc , x = 2 mm • electron signal current i(t) = 4 nA • velocity = mE =4*10^4 met/sec • time to hit anode = 50 ns • total electron signal charge collected in 50 ns • q = 4 nA * 50 ns = 0.2 fc ( from eq #2,  Q*200V/1kV) • What happened to the rest of the ionization charge? • Homework : Liquid argon ionization chamber (or calorimeter) • Liquid argon filled gap, horizontal track • me = 0.01 met^2/(V-s) (neglect ion drift) • Ionization density = 7000 electron-ion pairs per mm of track (MIP) • Vhv = 5kV •  Find signal current i(t) •  Total signal charge

  5. -------------------- (3) • Wire radius : r0=25 microns • Tube radius : R= 15 mm • Gas : Ar/C02 (93%/7%) • Vhv = 3080 Volts • Gas gain: G = 2e4 • mion = 6e-5 m^2/V-s • me = 0.4 m^2/V-s Signals in circular drift tube (ATLAS Muon Spectrometer) • Electric field  • Primary electrons drift to Anode wire • High field at wire surface (~ 2e7 V/m) causes avalanche “centered” very close to wire, typically ~ 10V from wire surface[1] • Each primary electron liberates Qtot ~ 2e4 secondary electrons • Must analyze both electron and ion signal response to single primary electron • Electron signal • Charge centroid very close to wire  short collection time , < 1 ns • i(t)=qelectron * d(t) • qelectron= Qtot* DV/Vhv =Qtot * (~10V/3080V) ~ (1/3 % ) Qto t~ 130 e

  6. -------------------- (4) • Simple diff-e in can be integrated to give r(t) -------------------- (5) -------------------- (6) • From (1)  -------------------- (7a) • Ion signal • Ion velocity where t0 is a constant of integration given by, and integrated signal charge : -------------------- (7b)

  7. -------------------- (8) -------------------- (9) -------------------- (10) • Pulse properties • Initial current • Extremely long pulse. (See eq #5) Pulse terminates when ions arrive at cathode at time • Question: What proportion of charge is collected in time t0 (11ns) ? • Conclusions: • Ion charge is not much but its a lot more then the electron signal charge. For ATLAS MDT its about 1000 electrons for each primary electron. • Electron charge can generally be neglected in simulations & calculations HW: Go through this analysis to make sure you understand it. It will come in handy some day!

  8. Basic electronic components & noise sources Part – I : Mathematical note • Circuit analysis is almost always done by means of Laplace (not Fourier) transforms • More convenient than Fourier when • circuit is considered quiescent before t = 0 • stimulus occurs after t = 0 • Steady state (fixed frequency) response is obtained by sjw=j2pf • Universal method of inverting Laplace transforms • Look them up in a table or use Maple or Mathematica

  9. Basic electronic components and noise sources Part -II • Inductor • Stores energy in magnetic field • E = ½ L i2 • Impedance Z(s)= sL • Lossless, noiseless • Capacitor • Stores energy in electric field • E = ½ C v2 • Impedance Z(s) = 1/(sC) • Lossless, noiseless • Ideal transmission line • Considered infinite sequence of series inductors & parallel capacitors • Results in wave equation with phase velocity : • and a constraint between voltage and current : • noiseless • Note that an infinitely long transmission line is indistinguishable from a resistor of value Z0 • As corollary, a finite line with a resistor of value Z0 at its end, is also indistinguishable from a resistor of value Z0. • In other words, if you launch a pulse into a terminated line, it never comes back (no reflection).

  10. Length L, total time L/v, Impedance Z0 ½ in ½ in Z0 Z0 • Resistor • Electric field pushes conduction electrons through a lattice • Dissipates power = I*V • Conduction electrons (generally) in thermal equilibrium with environment • Noisy  Noise characterized by “noise power density” p(f) [watts/hz] • p(f) is frequently expressed as a voltage (in series) or current density (in parallel) • en(f) & in(f) given in volts/sqrt(hz) & amps/sqrt(hz) • To get values of en(f) & in(f) ; [Nyquist, Phys Rev, Vol 32, 1928, p. 110] Total noise current in cable

  11. Disconnect resistors trapping noise power in cable • Total energy in cable, in frequency band Df is • Open circuit cable requires current at ends to be zero, and voltage at ends to be nodes • Standing waves (integer number of half-waves) • In frequency band Df , number of modes is • Energy equipartition requires that each mode (one for voltage, one for current) corresponds to energy kT/2  from which we get } ---------------------------- (11) Independent of frequency  “white” noise

  12. H(s) G(s) G(s)H(s) C V1 V2 R Basic electronic components and noise sources Part III : General circuit analysis primer • Objective • To find response of arbitrary circuits to arbitrary stimulus in both time and frequency domains. • Use this to get expected response from MDT Amp/Shaper to • calibration pulses injected into drift tubes • real ion-tail pulses in chambers • Method - A • Define ratio of “output” variable to “input” variable : Transfer function: H(s) • Write node and loop equations and solve for transfer function • Delta function response of circuit is just h(t), the inverse transform of H(s) • To get response to other inputs g(t) • Get transform of g(t)  G(s) • Transform of response is  F(s)=G(s)H(s) • Invert to get f(t) • Simple example • Find step response of simple low-pass filter

  13. Basic electronic components and noise sources Part III : General circuit analysis primer • Objective • To find response of arbitrary circuits to arbitrary stimulus in both time and frequency domains. • Use this to get expected response from MDT Amp/Shaper to • calibration pulses injected into drift tubes • real ion-tail pulses in chambers • Method – B • What if method A fails?  ie the transforms or inverse transforms cannot be found in closed form • Resort to the time domain solution  Convolution integral and use numerical solution if necessary • Simulation (SPICE)

  14. General circuit analysis - Homework An ideal integrator is followed by a 2-pole “RC-CR shaper” as follows Unity gain buffers C R 1x 1x R C • Show that transfer function of system is : • a) With delta function input, what do the signals look like throughout the circuit? • b) Is this circuit suitable for use in “high rate” (eg LHC/ATLAS) environment? • Extra credit part • c) Replace ideal integrator (1/s) with “leaky” integrator, 1/(sT+1) with T=15ns • Same questions as (a) and (b)

  15. vrms R in C = 1 pf • In general, such integrals can either be looked up or done by contour integration. Part-IV : Noise calculations • Example # 1 • What is the rms terminal voltage of the following simple circuit? 10k • Solution • Add noise current source, • Solve for circuit “transfer function” This gives you output voltage density • set s = jw=2pjf • Integrate over frequencies (quadrature)

  16. At room temperature kT ~ 4e-21  ADC Vin • In this case, ---------------------------- (12) • Called “kT over C” noise, or kTC noise (when dealing with charge instead of voltage). • Example (Homework) : • Suppose we want to use an array of 100 femtofarad capacitors to build an integrated “voltagewaveform recorder” in a 3.3Volt CMOS process. • Note that the “switches” are CMOS devices and are actually voltage controlled resistors which switch between some finite resistance in the “On” state to “near infinite” resistance in the “Off” state • Assume maximum signal swing inside the circuit is limited to about half the supply voltage, or 1.6 volts • What is the maximum possible dynamic range (in bits) of this device? (Dynamic range is max signal divided by rms noise). • If we plan to digitize this signal, should we pay more money for a 16 bit ADC, or will a 14-bit ADC do the job?

  17. gate n+ n+ source drain CMOS components : Field effect transistors (nfets) • In undoped (intrinsic) silicon, electron and hole densities are the same • n-doped (arsenic, phosphorous, antimony,..) : electron density increases, hole density decreases • p-doped (boron, aluminum, gallium, ..) : vice-versa • Strength of doping denoted by + sign  n, n+, p, p+ • + sign indicates higher doping, lower resistivity Conductive gate electrode Dielectric “gate oxide”: Si02 n+ source and drain implants p substrate (~ 10kW/sq) • With Vgate = 0, structure is non-conductive (back to back diodes) • Increasing Vgate in positive direction, attracts electrons from substrate • When Vgate > Vthreshold, “channel” becomes conductive. Conductance increases as Vgate increases. • As Vdrain is made more positive than Vsource, current starts to flow • Voltage gradient appears from drain to source. • Electric field is strongest near source, weakest near drain..

  18. n+ n+ CMOS components : Field effect transistors (nfets) • In undoped (intrinsic) silicon, electron and hole densities are the same • n-doped (arsenic, phosphorous, antimony,..) : electron density increases, hole density decreases • p-doped (boron, aluminum, gallium, ..) : vice-versa • Strength of doping denoted by + sign  n, n+, p, p+ • + sign indicates higher doping, lower resistivity Conductive (polysilicon) gate electrode Dielectric “gate oxide”: Si02 n+ source and drain implants gate source drain p substrate (~ 10kW/sq) • With Vgate = 0, structure is non-conductive (back to back diodes) • Increasing Vgate in positive direction, attracts electrons from substrate • When Vgate > Vthreshold, “channel” becomes conductive. Conductance increases as Vgate increases. • As Vdrain is made more positive than Vsource, current starts to flow • Voltage gradient appears from drain to source. • Electric field is strongest near source, weakest near drain. • Channel charge density “tilts” toward source. • Drain current increases with Vdrain • When Vdrain comes within a “threshold voltage” of Vgate, (Vdrain = Vgate – Vthreshold) current “saturates” • Saturation region also called “pinch-off

  19. gate n+ p+ n+ p+ source drain CMOS components : Field effect transistors pfets nfet gate source drain p substrate (~ 10kW/sq) n well • Generally, pfet drain current constant, Kp, is about 1/3 that of nfets due to lower hole mobility • For same size transistor at same current, pfet transconductance is smaller by ~sqrt(3)

  20. ---------------------------- (13) FET properties (simplified model) Linear, resistor, or triode region “Saturation” region • Drain current properties in saturation region • Id increases quadradically with Vgs • Increases linearly with transistor channel width, W • Decreases linearly with transistor gate length, L • Increases linearly with transistor channel width, W • Decreases linearly with transistor gate length, L • Definition: “Transconductance” = ratio of change in drain current per unit change in gate voltage. ---------------------------- (14)

  21. FET properties (con’t) • Terminal “impedances” • Gate: No dc current flow, just gate capacitance Cgate (of order ~tens of femtofarads to pf) • Drain: • “Wiggle” the drain voltage a little, what’s the change in drain current? • Ans: no (or very little) change so  • Source • “Wiggle” the source voltage a little bit. • This changes Vgs and thus drain current (and source current) by (Vgs) x (gm). • Typical numbers depending on application; • Example; • Idrain = 1 ma, L=0.5u, W=100u

  22. C) Current mirror A) Source follower Iin Iout d d d d d d g g g g g g Vin s s s s s s Vout Used as (almost) unity gain buffer. Hi-Z in, Lo-Z out. B) Common source amplifier D) Differential amplifier R Vout Vin Some common FET circuits

  23. F) Common gate or “cascode” d d d g g g Iout s s s Iin Z1 Z2 Used as current buffer. Lo-Z in, Hi-Z out. Some common FET circuits – con’t E) Fancier differential amplifier • “Boxes” Z1 & Z2 can be whatever you need • example: • Z1 is parallel RC • Z2 is series RC • Transfer function is  Implements a “Bipolar” shaping function (See table of Laplace transforms)

  24. d g s in R Vout Vin Noise in Fets • Fet channel is resistive and will thus have a thermal noise current component, in • Channel is not a single resistor, but rather a series of increasing resistances (from source to drain) • A fudge factor will be needed! (ff = 2/3) en • Noise current in drain is equivalent to noise voltage in gate with ---------------------------- (15)

  25. Noise in Fets • HW • What is the noise voltage density (nV/sqrt(Hz)) of a 100W resistor? • How much transconductance is required of a fet to have this same noise voltage density ? • Assuming we have a power budget of 1 ma (drain current) for this transistor and that the transistor has minimum allowed gate length of L = 0.5 microns, how wide (W) does the transistor have to be? • How much improvement in en do we get by doubling the drain current? …or the transistor width?

  26. d g s 1x Cstray Vin Front end amplifiers (eg ATLAS MDT) • “Open loop” gain • Example • Cstray = 500ff • Gm = 0.006 • What is “unity gain frequency”? |G(f)| f • What’s the gain at 1 Hz?

  27. d g s 1x Cstray • Example • Cstray = 500ff • Gm = 0.006 • What is “unity gain frequency”? Vin |G(f)| <100 f Front end amplifiers (eg ATLAS MDT) • “Open loop” gain R0 • What’s the gain at 1 Hz? • Answer: 2x10^9 !!!! • This can’t be right! Actually, gain rarely exceeds 100.Why is this? • Ans: Output (drain) impedance of fet is not actually infinite… same thing for current source

  28. Rf=15k Cf=1pf G(s) Front end amplifiers (eg ATLAS MDT) To make this a practical amplifier  use feedback “Transimpedance” amplifier • For high rate environment we want RC to be small ~ 15 ns is optimal for MDTs (electronics + chamber simulations) • Important question is input impedance. In general, it is given by • We’d like it to be • real or resistive (alternatives are capacitive or inductive) • low ( a hundred W or so) • as constant over frequency as possible • HWQuestions: • Why the above criteria? • How might you go about assuring this? • Second important concept is “Sensitivity” or Peak voltage output per unit charge input (typically in mv/fc) • HW Question: What is the Sensitivity (in mv/fc) of the above circuit?

  29. Rterm=390W Front end amplifiers (con’t) Now attach this to an ATLAS Muon tube and add a shaper Question : Why do we need the terminating resistor? • For extra credit (LOTs of extra credit!) • What’s the delta function response at preamp output, shaper output? • Characterize system gain in peak shaper signal output per unit charge input. (volts/coul or mv/fc) • How might you get the response to the actual ion signal from the gas tube? (Don’t actually do it!) • What is the rms noise voltage at the shaper output produced by the terminating resistor? • How much charge is this equivalent to (equivalent noise charge, or enc)? • Ans: Hint: For the purposes of this exercise, you can assume input impedance of amplifier is zero.

  30. Serial string register MDT-ASD topology 1 of 8 channels Transimpedance preamps Signal Discriminator (delta response) Bipolar shaper LVDS Control logic Dummy Wilkinson ADC DACs Calibration Mode Deadtime

  31. Transimpedance Preamplifier Vdd Vb4 M4 M3 Vb3 OUT R1 Vb2 M2 Cf R2 IN M1 Vb1 MDT-ASD topology Two transistor current source (Better than single fet current version) Vb[1:4] are bias voltages supplied from elsewhere Source follower Common gate “cascode” Current sink (half of a current mirror) Common source amplifier Feedback R & C • Detailed circuit descriptions can be found in the following documents • ATLAS-MUON-2002-003 • http://doc.cern.ch//archive/electronic/cern/others/atlnot/Note/muon/muon-2002-003.pdf • ATLAS-MUON-080 • http://doc.cern.ch/tmp/convert_muon-95-080.pdf • muon-96-127 • http://doc.cern.ch/cgi-bin/extractFigs.check.sh?check=/archive/electronic/cern/others/atlnot/Note/muon/muon-96-127.ps.gz Extra conductance on Hi-Z node to tailor gain vs frequency, & Zin

  32. MDT-ASD preamp layout 180u 300u

  33. MDT-ASD topology Shaper differential amplifiers Vdd Vref M5b M5 M5a Vb2 M4a M4b M4 OUTb R OUTa Z1(s) M3b INa M3 M3a INb Z2(s) M2c M2b Vb1 M2a M2 “Fancy” differential amplifier (pg 23) M1c M1b M1 M1a GND Bias network

  34. MDT-ASD topology Shaper differential amplifiers

  35. Summary & conclusions • Analysis/design methodology • Understand requirements • Noise, dynamic range,.. • Impedances • Signal shapes • etc • Hand calculations will get you close and/or guide design • Noise contributions of worst offenders • Transfer functions, response shapes, etc • Transistor sizing for CMOS circuits • SPICE modelling • Vendor SPICE models can be very accurate but very complicated • Produce best analysis at expense of intuitive understanding • To learn more • Attend IEEE Nuclear Science Symposia and take “Short course” programs in Front End Electronics (IEEE NSS 2003 Portland, Oregon, Oct 19-25) • Bibliography & lending library • “Particle Detection with Drift Chambers” W.Blum, L. Rolandi Springer Verlag, pg 134, 155-158 • “Tables of Laplace Transforms” Oberhettinger & Badii, Springer Verlag • “Complex Variables and Laplace Transform for Engineers” LePage, Dover • “Electronics for the Physicist” Delaney, Halsted Press • “Noise in Electronic Devices and Systems” Buckingham, Halsted Press • “Low-Noise Electronic Design” Motchenbacher & Fitchen, Wiley Interscience • “Processing the signals from solid state detectors” Gatti & Manfredi, Nuovo Cimento • “Analog MOS Integrated Circuits for Signal Processing” Gregorian & Temes, Wiley Interscience • “Detector Physics of the ATLAS Precision Muon Chambers” Viehhauser, PhD thesis, Technical University Vienna. • “MDT Performance in a High Rate Background Environment” Aleksa, Deile, Hessey, Riegler – ATLAS internal note, 1998

More Related