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Introduction to Electronics in HEP Experiments Philippe Farthouat CERN Introduction to Electronics Summer 2009 [email protected] Credits and sources of information I have “stolen” a lot from the previous summer student lectures from Christophe de la Taille and Jorgen Christiansen and from colleagues from the PH electronics group (PH-ESE) Useful and more complete information can be found in the following sites: CERN technical training ELEC 2005: http://indico.cern.ch/conferenceDisplay.py?confId=62928 LEB/LECC/TWEPP workshops from last 12 years: http://lhc-electronics-workshop.web.cern.ch/lhc%2Delectronics%2Dworkshop/ PH-ESE seminars: http://indico.cern.ch/categoryDisplay.py?categId=1591 Introduction to Electronics Summer 2009 [email protected] 2 Outline Detector Analog Processing Analog To Digital Conversion On-detector On-detector Or Off-detector Data Acquisition & Processing Off-detector Analog processing Analog to digital conversion Technology evolution Off-detector digital electronics Introduction to Electronics Summer 2009 [email protected] 3 Outline Detector Analog Processing Analog To Digital Conversion On-detector On-detector Or Off-detector Data Acquisition & Processing Off-detector Analog processing Analog to digital conversion Technology evolution Off-detector digital electronics Introduction to Electronics Summer 2009 [email protected] 4 Analog Processing A few basic reminders Modelisation of the detector Charge and current amplifiers Noise Example of a preamplifier design Introduction to Electronics Summer 2009 [email protected] 5 The foundations of electronics Voltage generators or source Ideal source : constant voltage, independent of current (or load) In reality : non-zero source impedance RS Current generators Ideal source : constant current, independent of voltage (or load) In reality : finite output source impedance RS Ohms’ law Z = R, 1/jωC, jωL Note the sign convention Introduction to Electronics Summer 2009 [email protected] V RS → 0 RS → ∞ i i V Z 6 Frequency domain & time domain Frequency domain : V(ω,t) = A sin (ωt + φ) Described by amplitude and phase (A, φ) Transfer function : H(ω) [or H(s)] The ratio of output signal to input signal in the frequency domain assuming linear electronics Vout(ω) = H(ω) Vin(ω) vin(ω) H(ω) vout(ω) h(t) vout(t) F -1 Time domain Impulse response : h(t) The output signal for an impulse (delta) input in the time domain The output signal for any input signal vin(t) is obtained by convolution * : Vout(t) = vin(t) * h(t) = ∫ vin(u) * h(t-u) du vin(t) Correspondance through Fourier transforms X() Fx(t) jt x(t) e dt A few useful Fourier transforms in appendix below Introduction to Electronics Summer 2009 [email protected] 7 Appendix: Fourrier Transform F() jt x(t) e dt Usualfunctions (t) 1 1 (t) j 1 eat j a 1 1 eat j ( j a) 1 t n1eat ( j a) n IMPEDANCES Capacitor Q CV I(t) CV '(t) I( ) CjV ( ) V ( ) 1 Z( ) I( ) jC Linearity ah1 (t) bh2 (t) aF1 ( ) bF2 ( ) Inductor V (t) LI'(t) V ( ) LjI( ) V ( ) Z( ) jL I( ) Integration,derivation h(t) F( ); h'(t) jF( ) F( ) h(t) F( ); h(t)dt j Introduction to Electronics Summer 2009 [email protected] 8 Using Ohm’s law Example of photodiode readout Used in high speed optical links Signal : ~ 10 µA when illuminated Modelisation : volts Ideal current source Iin pure capacitance Cd Simple I to V converter : R light R = 100 kΩ gives 1V output for 10 µA 10 Gb/s optical receiver Speed ? Transfer function H(ω) = vout/iin H has the dimension of Ω and is often called « transimpedance » and even more often (improperly) « gain » H( ) 1 jCd 1 R V I in Cd 100K 1 C d ( j 1 ) RC d 1/RCd is called a « pole » in the transfer function Introduction to Electronics Summer 2009 [email protected] 9 Frequency response Bode plot Magnitude (dB) 20log H( ) 20log 1 1 Cd ( j ) RC d -3dB bandwidth : f-3dB = 1/2πRCd Magnitude 100 dBΩ 80 dBΩ R=105Ω, Cd=10pF => f-3dB=160 kHz At f-3dB the signal is attenuated by 3dB = √2, the phase is -45° Above f-3dB , gain rolls-off at -20dB/decade (or -6dB/octave) Phase Introduction to Electronics Summer 2009 [email protected] 10 Time response Impulse response h(t) F 1 ( R 1 1 Cd ( j ) RC d ) 10Gb/s eye diagramresponse (10 ps/div) Impulse t exp( ) τ (tau) = RCd = 1 µs : time constant Step response : rising exponential h(t) F 1 ( 1 1 ) j C ( j 1 ) d RC d pulse response t R(1 exp( )) Rise time : t10-90% = 2.2 τ « eye diagram » tr 10-90% Speed : ~ 10 µs = 100 kb/s ! 5 orders ofmagnitude away from a 10 Gb/s link ! Introduction to Electronics Summer 2009 [email protected] 11 Feedback Y is a source linked to X y=μx Open loop x=δe y=µx s=σy=σμδe Closed loop x e y y x e y e y 1 e s y 1 s e 1 Introduction to Electronics Summer 2009 e x µ y σ δ s ß μ is the open loop gain βμ is the loop gain [email protected] 12 Interest of feedback e x µ y σ δ s ß In electronics μ is an amplifier gain β is the feedback loop If μ is large enough the gain of the system is independent of the amplifier gain s e 1 Introduction to Electronics Summer 2009 [email protected] 13 Operational Amplifier - 120 -A e 80 A (dB) e 100 60 40 20 0 + 1.0E+00 -20 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 -40 Frequency (Hz) Gain A very large Input impedance very high i.e input current = 0 A(ω) as shown Introduction to Electronics Summer 2009 [email protected] 14 How does it work? Direct gain calculation Vin e I R1 Vout Ae ; Vout ( R1 R 2) I Vout A Vin 1 A R1 R1 R 2 R2 - -A e e Feedback equation s e 1 R1 ; 1 R1 R 2 Vout A Vin 1 A R1 R1 R 2 I R1 + Vout A; Vin Ideal Opamp A ; Vout R1 R 2 Vin R1 Introduction to Electronics Summer 2009 [email protected] 15 Overview of readout electronics Most front-ends follow a similar architecture fC Detector V Preamp V Shaper bits ADC DAQ & Processing Very small signals (fC) -> need amplification Measurement of amplitude and/or time (ADCs, discris, TDCs) Several thousands to millions of channels Introduction to Electronics Summer 2009 [email protected] 16 Readout electronics : requirements Low noise High speed Low power Large dynamic range High reliability Radiation hardness Low cost ! Low material (and even less) Introduction to Electronics Summer 2009 [email protected] 17 Detector(s) A large variety A similar modelization PMT for Antares 6x6 pixels,4x4 mm2 CMS Pixel module ATLAS Liquid Argon Electromagnetic calorimeter Introduction to Electronics Summer 2009 [email protected] 18 Detector modelization Detector = capacitance Cd Silicon : 0.1-10 pF PMs : 3-30pF Ionization chambers 10-1000 pF Signal : current source Silicon : ~1fC/100µm PMs : 1 photoelectron -> 105-107 e Wire chambers : a few 103 e Modelized as an impulse (Dirac) : i(t)=Q0δ(t) I in Cd Detector modelisation Typical PM signal Missing : High Voltage bias Connections, grounding Neighbours Calibration… Introduction to Electronics Summer 2009 [email protected] 19 Reading the signal Signal Signal = current source Detector = capacitance Cd Quantity to measure + I in Cd Charge => integrator needed + ADC Time => discriminator + TDC Integrating on Cd Simple : V = Q/Cd « Gain » : 1/Cd : 1 pF -> 1 mV/fC Need a follower to buffer the voltage… Input follower capacitance : Ca // Cd Gain loss, possible non-linearities Crosstalk Need to empty Cd… Introduction to Electronics Summer 2009 [email protected] Q/Cd Impulse response 20 Ideal charge preamplifier Ideal opamp in transimpedance Shunt-shunt feedback Transimpedance : vout/iin Cf - Vin-=0 =>Vout(ω)/iin(ω) = - Zf = - 1/jω Cf Integrator : vout(t) = -1/Cf ∫ iin(t)dt + I in Cd vout(t) = - Q/Cf « Gain » : 1/Cf : 0.1 pF -> 10 mV/fC Cf determined by maximum signal Integration on Cf Simple : V = - Q/Cf Unsensitive to preamp capacitance CPA Turns a short signal into a long one The front-end of 90% of particle physics detectors… But always built with custom circuits… Introduction to Electronics Summer 2009 [email protected] Charge sensitive preamp - Q/Cf Impulse response with ideal preamp 21 Non-ideal charge preamplifier Finite opamp gain Z f Vout ( ) Iin ( ) 1 Cd G 0C f Small signal loss in Cd / G0 Cf << 1 (ballistic deficit) Finite opamp bandwidth First order open-loop gain G(ω) = G0/(1 + j ω/ω0) G0 : low frequency gain G0ω0 : ωc gain bandwidth product Preamp risetime Due to gain variation with ω Time constant : τ (tau) = Cd / G0ω0 Cf Rise-time : t 10-90% = 2.2 τ Rise-time optimised with G0ω0 (ωc) or Cf Introduction to Electronics Summer 2009 [email protected] Impulse response with non-ideal preamp 22 Input Impedance Cf Vin e I 1 Ie Vout Ge ; Vout C f j 1 1 Vin Zin C f j (1 G) C f jG I G Zin 0 G0 G j 1 I Vin e + 0 1 Zin -G e Vout j 1 1 0 C f jG0 jC f G0 C f G0 0 Introduction to Electronics Summer 2009 [email protected] 23 Charge preamp seen from the input Input impedance with ideal opamp Zin = Zf / G+1 Zin->0 for ideal opmap « Virtual ground » : Vin = 0 Minimizes sensitivity to detector impedance Minimizes crostalk Input impedance of charge preamp Input impedance with real opamp Z in 1 1 jG0C f G0 0C f Resistive term : Rin 1 G0 0C f 1 cC f Example : ωC = 109 rad/s Cf= 2 pF => Rin = 500Ω Determines the input time constant : t = ReqCd Good stability Introduction to Electronics Summer 2009 [email protected] 24 Pile up Rf It is necessary to discharge the feedback capacitor Successive input pulses would add up until saturation Several ways to do it, the simpler being to put a resistor in parallel Cf - -A e + Time 0 2 4 6 1.5 8 10 12 1 Input current 0.5 0 RC network -0.5 -1 1 Input & Output Input and Output 1.5 Capacitor only Input current 0.5 0 -0.5 0 4 6 8 10 12 14 16 -1 Output -1.5 -2 Time -1.5 Introduction to Electronics Summer 2009 2 [email protected] 25 Crosstalk Capacitive coupling between neighbours Crosstalk signal is differentiated and with same polarity Small contribution at signal peak Proportionnal to Cx/Cd and preamp input impedance Slowed derivative if RinCd ~ tp => non-zero at peak Inductive coupling Inductive common ground return “Ground apertures” = inductance Connectors : mutual inductance Introduction to Electronics Summer 2009 [email protected] 26 Current preamplifiers Transimpedance configuration Vout()/iin() = - Rf / (1+Zf/GZd) Gain = Rf High counting rate Typically optical link receivers Rf Current sensitive preamp Easily oscillatory Unstable with capacitive detector Inductive input impedance 1 Resonance at : Fres 2 Leq Cd R Quality factor : Q L eq Cd Q > 1/2 -> ringing Damping with capacitance Cf in parallel to Rf Easier with fast amplifiers Step response of current sensitive preamp Introduction to Electronics Summer 2009 [email protected] 27 Charge vs Current preamps Charge preamps Best noise performance Best with short signals Best with small capacitance Current preamps Best for long signals Best for high counting rate Significant parallel noise Current Charge Charge preamps are not slow, they are long Current preamps are not faster, they are shorter (but easily unstable) Introduction to Electronics Summer 2009 [email protected] 28 Electronics noise Definition of Noise Random fluctuation superimposed to interesting signal Statistical treatment Three types of noise Fundamental noise (Thermal noise, shot noise) Excess noise (1/f …) Parasitics -> EMC/EMI (pickup noise, ground loops…) Introduction to Electronics Summer 2009 [email protected] 29 Electronics noise Modelization Noise generators : en, in Noise spectral density of en & in : Sv(f) & Si(f) Sv(f) Si(f) Noise spectral density = | F (en)|2 (V2/Hz) = | F (in) |2 (A2/Hz) Rms noise Vn Vn2 = ∫ en2(t) dt = ∫ Sv(f) df When going through a device H(2πf) Svout(f) = |H(2πf)|2 Svin(f) rms Rms noise vn Introduction to Electronics Summer 2009 [email protected] 30 Calculating electronics noise Fundamental noise Thermal noise (resistors) : Sv(f) = 4kTR Shot noise (junctions) : Si(f) = 2qI 1/f noise in CMOS devices Noise referred to the input All noise generators can be referred to the input as 2 noise generators : A voltage one en in series : series noise A current one in in parallel : parallel noise Two generators : no more, no less… why ? Thermal noise generator To take into account the source impedance en Noiseless Golden rule Always calculate the signal before the noise what counts is the signal to noise ratio Don’t forget noise generators are V2/Hz => calculations in module square Practical exercice next slide Introduction to Electronics Summer 2009 Noisy [email protected] Noise generators referred to the input 31 Noise in charge pre-amplifiers 2 noise generators at the input Parallel noise : ( in2) (leakage currents) Series noise : (en2) (preamp) Output noise spectral density : 2 e in n 2 2 2 2 in en C d | Zd | Sv ( ) 2 2 2 2C f 2 Cf Cf 2 Noise spectral density at Preamp output Parallel noise in 1/ω2 Series noise is flat, with a « noise gain » of Cd/Cf rms noise Vn Parallel noise Vn2 = ∫ Sv(ω) dω/2π -> ∞ (!) Benefit of shaping… Introduction to Electronics Summer 2009 [email protected] Series noise 32 Equivalent Noise Charge (ENC) after CRRCn Noise reduction by optimising useful bandwidth Step response of CR RCn shapers Low-pass filters (RCn) to cut-off high frequency noise High-pass filter (CR) to cut-off parallel noise -> pass-band filter CRRCn Equivalent Noise Charge : ENC Noise referred to the input in electrons ENC = Ia(n) enCt/√τ Ib(n) in* √τ Series noise in 1/√τ Paralle noise in √τ 1/f noise independant of τ Optimum shaping time τopt= τc/√2n-1 ENC vs tau for CR RCn shapers Peaking time tp (5-100%) ENC(tp) independent of n Complex shapers are obsolete : Power of digital filtering Analog filter = CRRC ou CRRC2 Introduction to Electronics Summer 2009 [email protected] 33 Equivalent Noise Charge (ENC) after CRRCn A useful formula : ENC (e- rms) after a CRRC2 shaper : ENC 174 en Ctot 166in t p tp en in nV/ √Hz, in in pA/ √Hz are the preamp noise spectral densities Ctot (in pF) is dominated by the detector (Cd) + input preamp capacitance (CPA) tp (in ns) is the shaper peaking time (5-100%) Noise minimization Minimize source capacitance Operate at optimum shaping time Preamp series noise (en) best with high trans-conductance (gm) in input transistor => large current, optimal size Introduction to Electronics Summer 2009 [email protected] 34 ENC for various technologies ENC for Cd=1, 10 and 100 pF at ID = 500 uA MOS transistors best between 20 ns – 2 µs Parameters Bipolar : Introduction to Electronics Summer 2009 [email protected] gm = 20 mA/V RBB’=25 Ω en= 1 nV/√Hz IB=5uA in = 1 pA/√Hz CPA=100fF PMOS 2000/0.35 gm = 10 mA/V en = 1.4 nV/√Hz CPA = 5 pF 1/f : 35 MOS input transistor sizing Capacitive matching : strong inversion gm proportionnal to W/L √ID CGS proportionnal to W*L ENC propotionnal to (Cdet+CGS)/ √gm Optimum W/L : CGS = 1/3 Cdet Large transistors are easily in moderate or weak inversion at small current © P O’Connor BNL Optimum size in weak inversion gm proportionnal to ID (indep of W,L) ENC minimal for CGS minimal, provided the transistor remains in weak inversion Introduction to Electronics Summer 2009 [email protected] 36 Design in micro-electronics Performant design is at transistor level Simples models Hybrid π model Similar for bipolar and MOS Essential for desgin Three basic bricks Common emitter (CE) = V to I (transconductance) Common collector (CC) = V to V (voltage buffer) Common base (BC) = I to I (current conveyor) Numerous « composites » Darlington, Paraphase, Cascode, Mirrors… Introduction to Electronics Summer 2009 [email protected] Low frequency hybrid model of bipolar BC CE CC 37 Example : designing a charge preamp (1) From the schematic of principle Using of a fast opamp (OP620) Removing unnecessary components… Similar to the traditionnal schematic «Radeka 68 » Optimising transistors and currents Schematic of a OP620 opamp ©BurrBrown Introduction to Electronics Summer 2009 [email protected] Cf + Charge preamp ©Radeka 68 38 Example : designing a charge preamp (2) Simplified schematic Optimising components What transistors (PMOS, NPN ?) What bias current ? What transistor size ? What is the noise contributions of each component, how to minimize it ? What parameters determine the stability ? Waht is the saturation behaviour ? How vary signal and noise with input capacitance ? How to maximise the output voltage swing ? What the sensitivity to power supplies, temperature… Introduction to Electronics Summer 2009 Q1 : CE IC1=500µA Q2 : CB IC2=100µA Q3 : CC IC3=100µA Simplified schematic of charge preamp [email protected] 39 Example : designing a charge preamp (3) Small signal equivalent model Transistors are reaplaced by hybrid π model Allows to calculate open loop gain Small signal equivalent model of charge preamp vin gm1 vout R0 C0 R0 = Rout2//Rin3//r04 Gain (open loop) : vout/vin = - gm1 R0 /(1 + jω R0 C0) Ex : gm1=20mA/V , R0=500kΩ, C0=1pF => G0=104 ω0=2106 G0ω0=2 1010 = 3 GHz ! Introduction to Electronics Summer 2009 [email protected] 40 Example : designing a charge preamp (4) Complete schematic Adding bias elements Input Cf Introduction to Electronics Summer 2009 [email protected] Output 41 Example : designing a charge preamp (5) Complete simulation Checking hand calculations against 2nd order effects Testing extreme process parameters (« corner simulations ») Testing robustness (to power supplies, temperature…) Saturation behaviour Simulated open loop gain 10 ns 20 ns Qinj=4.25 pC Qinj=1.75 pC Qinj=3.75 pC Qinj=3.25 pC Qinj=2.75 pC Qinj=1.25 pC Qinj=0.75 pC Qinj=0.25 pC mV Qinj=2.25 pC 3.30 3.10 2.90 2.70 2.50 (V) 2.30 2.10 1.90 1.70 1.50 1.30 0.0 10 20 30 40 50 Time (ns) 1 MHz Introduction to Electronics Summer 2009 [email protected] 42 Example : designing a charge preamp (6) Layout Each component is drawn They are interconnected by metal layers Checks DRC : checking drawing rules (isolation, minimal dimensions…) ERC : extracting the corresponding electrical schematic LVS (layout vs schematic) : comparing extracted schematic and original design Simulating extracted schematic with parasitic elements 100 µm Generating GDS2 file Fabrication masks : « reticule » Introduction to Electronics Summer 2009 [email protected] 43 Device available Acces to microelectronics preamp driver Q1 FET Cf Q2 6 cm Charge preamp in SMC hybrid techno Q3 100 µm Z0 Charge preamp in 0.8µm BiCMOS Cf Zf Introduction to Electronics Summer 2009 [email protected] 44 Summary Charge sensitive preamplifiers Output proportionnal to the incoming charge vout(t) = - Q/Cf « Gain » : 1/Cf : Cf = 1 pF -> 1 mV/fC Transforms a short pulse into a long one Low input impedance -> current sensitive Virtual resistance Rin-> stable with capacitive detector The front-end of 90% of particle physics detectors… But always built with custom circuits… Charge preamplifier architecture Noise minimization Minimize source capacitance Operate at optimum shaping time Preamp series noise (en) better with high trans-conductance (gm) in input transistor Introduction to Electronics Summer 2009 [email protected] 45