1. 1 ELEC-2005 Electronics in High Energy Physics Winter Term: Introduction to electronics in HEP ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS PART 1 Francis ANGHINOLFI January 20, 2005 Francis.Anghinolfi@cern.ch CERN Technical Training 2005

2. 2 ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS Introduction Detector Signal collection Electronic Signal Processing Front-End : Preamplifier & Shaper Considerations on Detector Signal Processing

3. 3 CREDITS : Dr. Helmut SPIELER, LBL Laboratory Dr. Veljko RADEKA, BNL Laboratory Dr. Willy SANSEN, KU Leuven REFERENCES Low-Noise Wide-Band Amplifiers in Bipolar and CMOS Technologies, Z.H. Chang, W. Sansen, Kluwer Academics Publishers Low-Noise Techniques in Detectors, V. Radeka, Annual Review of Nuclear Particle Science 1988 28: 217-277 Pierre JARRON, CERN

4. 4 Introduction In this one hour lecture we will give an insight into electronic signal processing, having in mind the application for particle physics. Specific issue about signal processing in particle physics Time/frequency signal and circuit representation (Short) description of a typical “front-end” channel for particle physics detector In the next one hour lecture, there will be an approach of the “noise” problem : Noise sources in electronics circuit Introduction to the formulation of Equivalent Noise Charge (ENC) in case of circuits used for detector signals.

5. 5 Introduction We will look at both frequency and time domain representations Time domain : what we see on a scope Frequency domain : mathematics, representations are easier * OF SIGNALS AND CIRCUITS * Frequency representation is not applicable to all types of circuits

6. 6 Introduction What we will NOT cover in this lecture : Detail representation of either detector system or amplifier circuit. Active components models (as for MOS or Bipolar transistors). The above items, or a part of them, will be covered in other lectures of the present course...

7. 7 Detector Signal Collection Amplifier Particle detector collects charges : ionization in gas detector, solid-state detector a particle crossing the medium generates ionization + ions avalanche (gas detector) or electron-hole pairs (solid-state). Charges are collected on electrode plates (as a capacitor), building up a voltage or a current Function is multiple : signal amplification (signal multiplication factor) noise rejection signal “shape” Typical “front-end” elements Final objective : amplitude measurement and/or time measurement Z + - Board, wires,... Particle Detector Circuit Rp

8. 8 Detector Signal Collection If Z is high, charge is kept on capacitor nodes and a voltage builds up (until capacitor is discharged) If Z is low charge flows as a current through the impedance in a short time. In particle physics, low input impedance circuits are used: limited signal pile up limited channel-to-channel crosstalk low sensitivity to parasitic signals Typical “front-end” elements Z + - Board, wires,... Particle Detector Circuit Rp

9. 9 Detector Signal Collection Particle Detector Circuit Tiny signals (Ex: 400uV collected in Si detector on 10pF) Noisy environment Collection time fluctuation Large signals, accurate in amplitude and/or time Affordable S/N ratio Signal source and waveform compatible with subsequent circuits Zo Z + - Board, wires,... Particle Detector Circuit Rp

10. 10 Detector Signal Collection Circuit Low Z output voltage source circuit can drive any load Output signal shape adapted to subsequent stage (ADC) Signal shaping is used to reduce noise (unwanted fluctuations) vs. signal Zo Z + - High Z Low Z T Voltage source Impedance adaptation Amplitude resolution Time resolution Noise cut Rp

11. 11 Electronic Signal Processing H X(t) Y(t) Time domain : Electronic signals, like voltage, or current, or charge can be described in time domain. H in the above figure represents an object (circuit) which modifies the (time) properties of the incoming signal X(t), so that we obtain another signal Y(t). H can be a filter, transmission line, amplifier, resonator etc... If the circuit H has linear properties like :if X1 ---> Y1 through H if X2 ---> Y2 through H then X1+X2 ---> Y1+Y2 The circuit H can be represented by a linear function of time H(t), such that the knowledge of X(t) and H(t) is enough to predict Y(t)

12. 12 Electronic Signal Processing H(t) X(t) Y(t) Y(t) = H(t)*X(t) In time domain, the relationship between X(t), H(t) and Y(t) is expressed by the following formula : This is the convolution function, that we can use to completely describe Y(t) from the knowledge of both X(t) and H(t) Where Time domain prediction by using convolution is complicated …

13. 13 Electronic Signal Processing H(t) = H(t)*  (t) H(t)  (t) H(t)  (t) H What is H(t) ? (Dirac function) If we inject a “Dirac” function to a linear system, the output signal is the characteristic function H(t) H(t) is the transfer function in time domain, of the linear circuit H.

14. 14 Electronic Signal Processing Frequency domain : The electronic signal X(t) can be represented in the frequency domain by x(f), using the following transformation (Fourier Transform) This is *not* an easy transform, unless we assume that X(t) can be described as a sum of “exponential” functions, of the form : The conditions of validity of the above transformations are precisely defined. We assume here that it applies to the signals (either periodic or not) that we will consider later on

15. 15 Electronic Signal Processing Example : The “frequency” domain representation x(f) is using complex numbers. For (t >0) X(t)

16. 16 Electronic Signal Processing Some usual Fourier Transforms : –  (t) --> 1 – (t) --> 1/j  –e -at --> 1/(a+ j  ) –t n-1 e -at --> 1/(a+ j  ) n –  (t)-a.e -at --> j  /(a+ j  ) The Fourier Transform applies equally well to the signal representation X(t) x(f) and to the linear circuit transfer function H(t) h(f) h(f) x(f) y(f)

17. 17 Electronic Signal Processing h(f) x(f) y(f) y(f) = h(f).x(f) With the frequency domain representation (signals and circuit transfer function mapped into frequency domain by the Fourier transform), the relationship between input, circuit transfer function and output is simple: x(f) y(f) h2(f)h3(f) h1(f) y(f) = h1(f). h2(f). h3(f). x(f) Example : cascaded systems

18. 18 Electronic Signal Processing h(f) y(f) RC low pass filter 1 t x(f) R C

19. 19 Electronic Signal Processing h(f) x(f) y(f) Fourier Transform Frequency representation can be used to predict time response X(t) ----> x(f) (Fourier transform) H(t) ----> h(f) (Fourier transform) h(f) can also be directly formulated from circuit analysis Apply y(f) = h(f).x(f) Then y(f) ----> Y(t) (inverse Fourier Transform) Inverse Fourier Transform

20. 20 Electronic Signal Processing h(f) x(f) y(f) THERE IS AN EQUIVALENCE BETWEEN TIME AND FREQUENCY REPRESENTATIONS OF SIGNAL or CIRCUIT THIS EQUIVALENCE APPLIES ONLY TO A PARTICULAR CLASS OF CIRCUITS, NAMED “TIME-INVARIANT” CIRCUITS. IN PARTICLE PHYSICS, CIRCUITS OUTSIDE OF THIS CLASS CAN BE USED : ONLY TIME DOMAIN ANALYSIS IS APPLICABLE IN THIS CASE H(t) X(t) Y(t)

21. 21 Electronic Signal Processing y(f) = h(f).x(f)  (f) h(f)  (f) f h(f) f In frequency domain, a system (h) is a frequency domain “shaping” element. In case of h being a filter, it selects a particular frequency domain range. The input signal is rejected (if it is out of filter band) or amplified (if in band) or “shaped” if signal frequency components are altered. x(f) y(f) x(f) f y(f) f h(f) Dirac function frequency representation h(f) f

22. 22 Electronic Signal Processing y(f) = h(f).x(f) vni(f) vno(f) noise f h(f) The “noise” is also filtered by the system h Noise components (as we will see later on) are often “white noise”, i.e.: constant distribution over all frequencies (as shown above) So a filter h(f) can be chosen so that : It filters out the noise “frequency” components which are outside of the frequency band for the signal Noise power limited by filter f “Unlimited” noise power

23. 23 Electronic Signal Processing x(f) y(f) x(f) f y(f) f h(f) f Noise floor f0 Improved Signal/Noise Ratio Example of signal filtering : the above figure shows a « typical » case, where only noise is filtered out. In particle physics, the input signal, from detector, is often a very fast pulse, similar to a “Dirac” pulse. Therefore, its frequency representation is over a large frequency range. The filter (shaper) provides a limitation in the signal bandwidth and therefore the filter output signal shape is different from the input signal shape.

24. 24 Electronic Signal Processing x(f) y(f) x(f) f f h(f) f Noise floor f0 Improved Signal/Noise Ratio The output signal shape is determined, for each application, by the following parameters: Input signal shape (characteristic of detector) Filter (amplifier-shaper) characteristic The output signal shape, different form the input detector signal, is chosen for the application requirements: Time measurement Amplitude measurement Pile-up reduction Optimized Signal-to-noise ratio y(f)

25. 25 Electronic Signal Processing f f0 f Filter cuts noise. Signal BW is preserved Filter cuts inside signal BW : modified shape

26. 26 SOME EXAMPLES OF CIRCUITS USED AS SIGNAL SHAPERS... Electronic Signal Processing (Time-invariant circuits like RC, CR networks)

27. 27 Electronic Signal Processing Integrator s-transfer function h(s) = 1/(1+RCs) Example RC=0.5 s=j  R C Vout Vin Integrator time function Log-Log scale t f Low-pass (RC) filter Step function response |h(s)|

28. 28 Electronic Signal Processing Differentiator s-transfer function h(s) = RCs/(1+RCs) Vout Vin Differentiator time function R C Example RC=0.5 s=j  High-pass (CR) filter Step response Log-Log scale f |h(s)| Impulse response

29. 29 Electronic Signal Processing CR-RC s-transfer function h(s) = RCs/(1+RCs) 2 Vout CR-RC time function Example RC=0.5 s=j  Vin R C R C 1 Combining one low-pass (RC) and one high-pass (CR) filter : Step response Log-Log scale f |h(s)| HighZLow Z Impulse response

30. 30 Electronic Signal Processing CR-RC 4 s-transfer function h(s) = RCs/(1+RCs) 5 Vout CR-RC 4 time function R C Example RC=0.5, n=5 s=j  Vin R C 1 Combining n low-pass (RC) and one high-pass (CR) filter : Log-Log scale f |h(s)| Step response R C 1 n times Impulse response

31. 31 Electronic Signal Processing h(s) = RCs/(1+RCs) 5 Shaper circuit frequency spectrum Noise Floor +20db/dec -80db/dec The shaper limits the noise bandwidth. The choice of the shaper function defines the noise power available at the output. Thus, it defines the signal-to-noise ratio f

32. 32 Preamplifier & Shaper Preamplifier Shaper  (t) Q/C. (t) IO What are the functions of preamplifier and shaper (in ideal world) : Preamplifier : is an ideal integrator : it detects an input charge burst Q  (t). The output is a voltage step Q/C. (t). Has large signal gain such that noise of subsequent stage (shaper) is negligible. Shaper : a filter with : characteristics fixed to give a predefined output signal shape, and rejection of noise frequency components which are outside of the signal frequency range.

33. 33 Preamplifier & Shaper Preamplifier Shaper CR_RC2 shaper Ideal Integrator  (t) 1/s RCs /(1+RCs) 2 x I O T.F. from I to O = = RC/(1+RCs) 2 Output signal of preamplifier + shaper with one charge at the input t t f t f Q/C. (t)

34. 34 Preamplifier & Shaper Preamplifier Shaper  (t) 1/s RCs /(1+RCs) 5 x I O T.F. from I to O = = RC/(1+RCs) 5 Output signal of preamplifier + shaper with “ideal” charge at the input t t f t f CR_RC4 shaper Ideal Integrator Q/C. (t)

35. 35 Preamplifier & Shaper Vout Cf Schema of a Preamplifier-Shaper circuit N Integrators Diff Semi-Gaussian Shaper Cd T0T0 T0T0 T0T0 Vout(s) = Q/sCf. [sT 0 /1+ sT 0 ].[A/1+ sT 0 ] n Vout(t) = [QA n n n /Cf n!].[t/Ts] n.e -nt/Ts Peaking time Ts = nT0 ! Output voltage at peak is given by : Vout shape vs. n order, renormalized to 1 Vout peak vs. n Voutp = QA n n n /Cf n!e n

36. 36 Preamplifier & Shaper Preamplifier Shaper CR_RC shaperNon-Ideal Integrator  (t) 1/(1+T1s)RCs /(1+RCs) 2 IO T.F. from I to O x Non ideal shape, long tail Integrator baseline restoration

37. 37 Preamplifier & Shaper Preamplifier Shaper  (t) 1/(1+T1s) (1+T1s) /(1+RCs) 2 Pole-Zero Cancellation IO T.F. from I to O x CR_RC shaperNon-Ideal Integrator Ideal shape, no tail Integrator baseline restoration

38. 38 Preamplifier & Shaper Vout Schema of a Preamplifier-Shaper circuit with pole-zero cancellation Vout(s) = Q/(1+sTf)Cf. [(1+sTp)/1+ sT0].[A/1+ sT0] n By adjusting Tp=Rp.Cp and Tf=Rf.Cf such that Tp = Tf, we obtain the same shape as with a perfect integrator at the input Rf Cf N Integrators Diff Semi-Gaussian Shaper Cd Cp T0T0 T0T0 Rp

39. 39 Considerations on Detector Signal Processing Pile-up : A fast return to zero time is required to : Avoid cumulated baseline shifts (average detector pulse rate should be known) Optimize noise as long tails contribute to larger noise level 2 nd hit

40. 40 Considerations on Detector Signal Processing Pile-up The detector pulse is transformed by the front-end circuit to obtain a signal with a finite return to zero time CR-RC : Return to baseline > 7*Tp CR-RC4 : Return to baseline < 3*Tp

41. 41 Considerations on Detector Signal Processing Pile-up : A long return to zero time does contribute to excessive noise : Uncompensated pole zero CR-RC filter Long tail contributes to the increase of electronic noise (and to baseline shift)

42. 42 Considerations on Detector Signal Processing Time-variant filters : “TIME-VARIANT” filters have been developed which provide well-defined “finite” time responses : T Ex : Gated Integrator The time response is strictly limited in time because of the switching The frequency representation does not apply : signal processing is analyzed in time domain (an approach is given in this lecture, Part 2)

43. 43 Considerations on Detector Signal Processing Summary (1) The detector pulse is transformed by the front-end circuit to obtain : A linear Gain (Vout/Q det = Cte) An impedance adaptation (Low input impedance, low output impedance) A signal shape with some level of integration A reduction in the amount of electronic noise A dynamic range (or Signal-to-Noise ratio)

44. 44 Considerations on Detector Signal Processing Summary (2) Time-variant and time-invariant filters have been developed to cope with the very specific demands of particle physics detector signal processing Very large dynamic range is attainable (16 bits, as for calorimeters) Very low noise is achievable in some cases (a few electrons !) Peaking time are varying from a few ns (tracking application) to ms range (very low noise systems, amplitude resolution) The choice of the suitable front-end circuit is usually a trade-off between key parameters (peaking time, noise, power)

45. 45 Considerations on Detector Signal Processing Some parameters of front-end circuits used for LHC detectors Pixel : 100ns shaping time, 180 el ENC, <1pF detector Silicon strips : 25 ns shaping time, 1500 el ENC, 20pF detector Calorimeter : 16 bits dynamic range, 20-40ns shaping time Time-Of-Flight measurement : 1 ns peaking time, 3000 el ENC, 10pF detector 8 channel NINO front-end For Alice TOF

46. 46 ELEC-2005 Electronics in High Energy Physics Winter Term: Introduction to electronics in HEP ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS PART 1 Francis ANGHINOLFI January 20, 2005 Francis.Anghinolfi@cern.ch CERN Technical Training 2005