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  1. Laboratorio di Elettronica Modulo preamplificatori: misure di guadagno, linearità, rumore

  2. Preamplificatori • Preamplificatore (PA) = primo elemento della catena di amplificazione • In genere il PA è seguito dallo “shaper” (formatore) detto anche “shaping amplifier” (SA) • Il segnale prodotto in un rivelatore di radiazione è quasi sempre un segnale in corrente i(t) • Molto spesso l’informazione è data dalla carica Q = ∫i(t)dt • I preamplificatori più usati in questo campo sono di corrente (CA) o di carica (CSA = Charge Sensitive Amplifier) • Le caratteristiche più rilevanti dei PA sono la sensibilità o “guadagno”, la linearità e il rumore

  3. VTH S&H Architetture di lettura (1) ANALOGICA - vantaggi • informazione completa • facile da verificare - svantaggi • grande volume didati • trattamento analogico PA DIGITALE (BINARIA) - vantaggi • semplice, veloce • piccolo volume di dati - svantaggi • difficile da verificare • informazione ridotta PA DISCRIM.

  4. ADC Architetture di lettura (2) ANALOGICO/DIGITALE - vantaggi • informazione completa • robusto - svantaggi • grande volume didati • sistema misto A/D • La scelta del tipo di architettura e della tecnologia (circuito ibrido, VLSI, …) dipende tra l’altro da: • Numero di canali da trattare (da 1 a 10 milioni) • Limiti sulla potenza dissipata • Limiti sulla velocità di acquisizione dati e quindi sul volume dati • Richiesta di risoluzione energetica (MIP, raggi X, raggi γ…)

  5. 2 cm 1 cm PA a componenti discreti (ibrido) AmpTek A225 1channel minimum power:10mW power supply:4V to 25V current:2.3mA shaping time:2.4ms noise <280 e- rms size:2cm x 1cm energy timing

  6. 1cm PA su circuito integrato (chip VLSI) PASCAL (Front – end ALICE SDD) CMOS 0.25mm technology 64 channels 32 10-bits ADC Power: 8mW/ch Shaping time: 40ns Noise < 280 e- rms Size:1cm x 0.9cm

  7. Catena di amplificazione CSA + SA da F. Anghinolfi (2005) - parte 1, slides 7-41 • in particolare: • slides 11-25 => principi generali del trattamento del segnale • funzione di trasferimento H(t) • rappr. nel dominio del tempo e della frequenza • slides 27-31 => esempi di formatori (shaper): RC, CR, (RC)n-CR • slides 32-38 => ruolo di PA e SA • slide 35 => shaper CR-(RC)n

  8. Board, wires, ... + Rp Z - Circuit Particle Detector Detector Signal Collection Typical “front-end” elements 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 Amplifier Function is multiple : signal amplification (signal multiplication factor) noise rejection signal “shape” Final objective : amplitude measurement and/or time measurement

  9. Board, wires, ... Rp + Z - Circuit Particle Detector Detector Signal Collection Typical “front-end” elements 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

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

  11. Detector Signal Collection Circuit High Z • Impedance adaptation • Amplitude resolution • Time resolution • Noise cut Low Z Voltage source + Zo Z Rp - Low Z T 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

  12. Electronic Signal Processing Time domain : Y(t) X(t) H 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)

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

  14. Electronic Signal Processing What is H(t) ? H(t) d(t) H H(t) d(t) (Dirac function) H(t) = H(t)* d (t) 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.

  15. 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

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

  17. 1 t Electronic Signal Processing Some usual Fourier Transforms : • (t)  1 • (t)  1/jw • e-at  1/(a+ jw) • tn-1e-at  1/[(n-1)!(a+ jw)n] • (t)-a.e-at  jw /(a+ jw) 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) y(f) x(f) h(f)

  18. x(f) y(f) h(f) Electronic Signal Processing 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: y(f) = h(f).x(f) Example : cascaded systems x(f) y(f) h2(f) h3(f) h1(f) y(f) = h1(f). h2(f). h3(f). x(f)

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

  20. Electronic Signal Processing y(f) x(f) h(f) 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) Fourier Transform Inverse Fourier Transform

  21. Electronic Signal Processing y(f) x(f) h(f) X(t) Y(t) H(t) • 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

  22. Electronic Signal Processing y(f) = h(f).x(f) h(f) d(f) h(f) h(f) d(f) f f Dirac function frequency representation 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) h(f) x(f) y(f) f f h(f) f

  23. Electronic Signal Processing y(f) = h(f).x(f) vni(f) vno(f) noise h(f) f f “Unlimited” noise power Noise power limited by filter 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

  24. Electronic Signal Processing x(f) y(f) h(f) x(f) y(f) f f f0 Noise floor f0 Improved Signal/Noise Ratio f f0 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.

  25. Electronic Signal Processing x(f) y(f) h(f) x(f) y(f) f f Noise floor f0 Improved Signal/Noise Ratio f f0 • 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

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

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

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

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

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

  31. R C 1 C R Electronic Signal Processing R 1 Vin C Vout n-1 times Combining (n-1) low-pass (RC) and one high-pass (CR) filter : Example RC=0.5, n=5 s=jw CR-RC4 time function CR-RC4s-transfer function h(s) = RCs/(1+RCs)5 Impulse response |h(s)| t Step response f Log-Log scale t

  32. Electronic Signal Processing Shaper circuit frequency spectrum -80db/dec +20db/dec Noise Floor f h(s) = RCs/(1+RCs)5 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

  33. Preamplifier & Shaper Preamplifier Shaper I O d(t) Q/C.n(t) • What are the functions of preamplifier and shaper (in ideal world) : • Preamplifier : is an ideal integrator : it detects an input charge burst Q d(t).The output is a voltage step Q/C.n(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.

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

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

  36. N Integrators Diff Cd T0 T0 T0 Semi-Gaussian Shaper Preamplifier & Shaper Schema of a Preamplifier-Shaper circuit Cf Vout Vout(s) = Q/sCf . [sT0/(1+ sT0)].[A/(1+ sT0)]n Output voltage at peak is given by : Vout(t) = [QAn nn /Cf n!].[t/Ts]n.e-nt/Ts Voutp = QAn nn /Cf n!en Peaking time Ts = nT0 ! Vout shape vs. n order, renormalized to 1 Vout peak vs. n

  37. Preamplifier & Shaper Shaper Preamplifier I O Non-Ideal Integrator CR_RC shaper d(t) Integrator baselinerestoration T.F. from I to O x 1/(1+T1s) RCs /(1+RCs)2 Non ideal shape, long tail

  38. Preamplifier & Shaper Preamplifier Shaper I O Non-Ideal Integrator CR_RC shaper d(t) Integrator baselinerestoration T.F. from I to O 1/(1+T1s) x (1+T1s) /(1+RCs)2 Pole-Zero Cancellation Ideal shape, no tail

  39. Preamplifier & Shaper Schema of a Preamplifier-Shaper circuit with pole-zero cancellation Rf Cf Diff N Integrators Rp Vout Cp Cd T0 T0 Semi-Gaussian Shaper 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 Vout(s) = Q/(1+sTf)Cf . [(1+sTp)/(1+ sT0)].[A/(1+ sT0)]n

  40. 2nd hit 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

  41. 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

  42. 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)

  43. Segnali e guadagni tipici • Segnali tipici: Q [e] = E/W ≈ 1000 E[keV] / 3.7 (W = 3.7 eV per Si) 1 elettrone = 1.6 10-4 fC 3.7 keV = 1000 el. = 0.16 fC 92 keV = 25000 el. = 4 fC (1 MIP in 300 µm di Si ≈ 92 keV) • Guadagno di un CSA + shaper CR-RC: G = Avs/(e Cf) [V/C] con Avs = guadagno in tensione dello shaper, e = 2.71828…, Cf = condensatore di retroazione del CSA esempio di guadagno alto [RX64]: G ≈ 20 mV/keV ≈ 500 mV/fC esempio di guadagno tipico [A250CF]: G ≈ 0.18 mV/keV ≈ 4 mV/fC

  44. Segnale in rivelatori a semiconduttore Radiation ionization energy(W): determines the number of primary ionization events Band gap energy (Eg): lower value  easier thermal generation of e-h pairs (kT = 26 meV for T = 300 K)

  45. Risoluzione energetica intrinseca DE (FWHM) = 2.35FEW il fattore di Fano “F” quantifica la riduzione nelle fluttuazioni rispetto alla statistica di Poisson Per Si e Ge: F = 0.10 ― 0.20 (Fano factor) W (Si) = 3.6 eV W (Ge) = 2.9 eV

  46. Rivelatori a microstrip SEGNALE = numero di coppie elettrone-lacuna: ne-h = DE/W, con W=3.62 eV per il silicio • DIODO in polarizzazione inversa: • Regione svuotata => ovvero, libera da portatori di carica: le coppie e-h possono essere rivelate (e non riassorbite) • Tensione di polarizz. (VB)=> controlla lo spessore di svuotamento, cioe’ il volume attivo • Capacità della giunzione p-n per unità di area C:1/C2 cresce linearmente con VB => una misura C-V determina la tensione di completo svuotamento VFD Substrato di tipo n Capacità per unità di area:

  47. Rivelatore + Elettronica collegamento tipico (accoppiamento AC), elementi circuitali rilevanti Tensione di polarizzazione Resistenza in serie Capacita’ di disaccoppiamento

  48. Principali sorgenti di rumore, ENC

  49. Rumore elettronico e sorgenti di rumore nei circuiti da F. Anghinolfi (2005) – parte 2, slides 3-37 + 44 • in particolare: • slides 3-7 => introduzione al rumore • slides 8-15 => rumore termico (resistori, transistor MOS) • slides 16-17 => rumore granulare (diodi, transistor bipolari) • slides 18-19 => rumore 1/f (transistor MOS) • slides 20-37 => rumore nei circuiti (circuiti equiv. per calcolo rumore) • slides 44 => conclusione (Equivalent Noise Charge)

  50. Noise in Electronic Systems Signal frequency spectrum Circuit frequency response Noise Floor f Amplitude, charge or time resolution What we want : Signal dynamic Low noise