Laboratorio di Elettronica

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

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

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

Architetture di lettura (2)
ANALOGICO/DIGITALE - vantaggi informazione completa robusto - svantaggi grande volume di dati sistema misto A/D ADC 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…)

PA a componenti discreti (ibrido)
AmpTek A225 2 cm 1 cm 1 channel 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

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 1 cm

Catena di amplificazione CSA + SA
da F. Anghinolfi (2005) - parte 1, slides 7-41 in particolare: slides => principi generali del trattamento del segnale funzione di trasferimento H(t) rappr. nel dominio del tempo e della frequenza slides => esempi di formatori (shaper): RC, CR, (RC)n-CR slides => ruolo di PA e SA slide 35 => shaper CR-(RC)n NOTA: ho controllato e corretto ove necessario le formule dello shaper CR-(RC)^n secondo Nygard et al., CMOS low noise amplifier for microstrip readout – design and results, NIM A 301 (1991) 506

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

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

Zo Z + - Board, wires, ... Particle Detector Circuit Rp 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

Circuit High Z Impedance adaptation Amplitude resolution Time resolution Noise cut Low Z Voltage source + Zo Rp Z - 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

Electronic Signal Processing
Time domain : X(t) Y(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)

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 …

What is H(t) ? d(t) H(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.

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

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

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) 1 t 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) x(f) y(f) h(f)

h(f) x(f) y(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: y(f) = h(f).x(f) Example : cascaded systems x(f) y(f) h1(f) h2(f) h3(f) y(f) = h1(f). h2(f). h3(f). x(f)

y(f) x(f) h(f) RC low pass filter 1 t R C

x(f) y(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

x(f) y(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

y(f) = h(f).x(f) d(f) h(f) h(f) d(f) h(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 h(f) f f

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

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.

x(f) y(f) h(f) x(f) y(f) f Noise floor f f0 Improved Signal/Noise Ratio f0 f 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

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

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

Vout Vin Low-pass (RC) filter Example RC= s=jw Integrator time function Integrator s-transfer function h(s) = 1/(1+RCs) |h(s)| t Step function response f Log-Log scale t

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

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

1 R R C 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-RC4 s-transfer function h(s) = RCs/(1+RCs)5 Impulse response Formule verificate con l’appendice A.1 dell’articolo Nygard et al., NIM A 301 (1991) 506 |h(s)| t Step response f Log-Log scale t

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

Preamplifier & Shaper Preamplifier Shaper d(t)
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.

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

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

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

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

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

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

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 2nd hit

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

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)

Segnali e guadagni tipici
Segnali tipici: Q [e] = E/W ≈ 1000 E[keV] / (W = 3.7 eV per Si) 1 elettrone = fC 3.7 keV = el. = 0.16 fC 92 keV = 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 = …, 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 NOTA: il preamplificatore+shaper (tipo AMPLEX) di Nygard et al. (1991) ha un guadagno di 15 mV/fC.

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)

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

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:

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

Principali sorgenti di rumore, ENC

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

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

Power EM emission Crosstalk System noise EM emission Crosstalk Ground/power noise Signals In & Out All can be (virtually) avoided by proper design and shielding Shielding

Fundamental noise Physics of electrical devices Detector Unavoidable but the prediction of noise power at the output of an electronic channel is possible What is expressed is the ratio of the signal power to the noise power (SNR) Front End Board In detector circuits, noise is expressed in (rms) numbers of electrons at the input (ENC)

Current conducting devices Only fundamental noise is discussed in this lecture

Current conducting devices (resistors, transistors) Three main types of noise mechanisms in electronic conducting devices: THERMAL NOISE SHOT NOISE 1/f NOISE Always Semiconductor devices Specific

THERMAL NOISE Definition from C.D. Motchenbacher book (“Low Noise Electronic System Design, Wiley Interscience”) : “Thermal noise is caused by random thermally excited vibrations of charge carriers in a conductor” R The noise power is proportional to T(oK) The noise power is proportional to Df K = Boltzmann constant ( V.C/K) T = Temperature @ ambient 4kT = V/C

THERMAL NOISE Thermal noise is a totally random signal. It has a normal distribution of amplitude with time.

THERMAL NOISE R The noise power is proportional to the noise bandwidth: The power in the band 1-2 Hz is equal to that in the band Hz Thus the thermal noise power spectrum is flat over all frequency range (“white noise”) P f

THERMAL NOISE Bandwidth limiter R G=1 Only the electronic circuit frequency spectrum (filter) limits the thermal noise power available on circuit output Circuit Bandwidth P f

THERMAL NOISE R The conductor noise power is the same as the power available from the following circuit : R * Et is an ideal voltage source R is a noiseless resistance <v> gnd

THERMAL NOISE R * RL=hi gnd The thermal noise is always present. It can be expressed as a voltage fluctuation or a current fluctuation, depending on the load impedance. R * RL=0 gnd

Some examples : Thermal noise in resistor in “series” with the signal path : For R=100 ohms For 10KHz-100MHz bandwidth : Rem : 0-100MHz bandwidth gives : For R=1 Mohms For 10KHz-100MHz bandwidth : As a reference of signal amplitude, consider the mean peak charge deposited on 300um Silicon detector : electrons, ie ~4fC. If this charge was deposited instantaneously on the detector capacitance (10pF), the signal voltage is Q/C= 400mV

Thermal Noise in a MOS Transistor Ids Vgs The MOS transistor behaves like a current generator, controlled by the gate voltage. The ratio is called the transconductance. The MOS transistor is a conductor and exhibits thermal noise expressed as : G : excess noise factor (between 1 and 2) or

Shot Noise I q is the charge of the electron (1.602·10-19 C) Shot noise is present when carrier transportation occurs across two media, as a semiconductor junction. As for thermal noise, the shot noise power <i2> is proportional to the noise bandwidth. The shot noise power spectrum is flat over all frequency range (“white noise”) P f

Shot Noise in a Bipolar (Junction) Transistor Ic Vbe The current carriers in bipolar transistor are crossing a semiconductor barrier  therefore the device exhibits shot noise as : The junction transistor behaves like a current generator, controlled by the base voltage. The ratio (transconductance) is : or

1/f Noise Formulation 1/f noise is present in all conduction phenomena. Physical origins are multiple. It is negligible for conductors, resistors. It is weak in bipolar junction transistors and strong for MOS transistors. 1/f noise power is increasing as frequency decreases. 1/f noise power is constant in each frequency decade (i.e. from 0 to 1 Hz, 10 to 100 Hz, 100 MHz to 1Ghz)

1/f noise and thermal noise (MOS Transistor) 1/f noise Circuit bandwidth Thermal noise Depending on circuit bandwidth, 1/f noise may or may not be contributing

Noise in Detector Front-Ends
Circuit Note that (pure) capacitors or inductors do not produce noise Detector How much noise is here ? (detector bias) As we just seen before : Each component is a (multiple) noise source

Circuit Rp Circuit equivalent voltage noise source Ideal charge generator Detector gnd Passive & active components, all noise sources en A capacitor (not a noise source) noiseless in Rp gnd Circuit equivalent current noise source

gnd Noiseless circuit en in Av Rp From practical point of view, en is a voltage source such that: when input is grounded in is a current source such that: when the input is on a large resistance Rp

In case of an (ideal) detector, the input is loaded by the detector capacitance C Detector gnd Noiseless circuit en iTOT Av Cd Detector signal node (input) i2TOT is the combination of the circuit current noise and Rp bias resistance noise : The equivalent voltage noise at the input is: (per Hertz)

gnd Noiseless circuit en iTOT Av Cd input The detector signal is a charge Q. The voltage noise <e2input> converts to charge noise by using the relationship (per Hertz) The equivalent noise charge at the input, which has to be compared to the signal charge, is function of the amplifier equivalent input voltage noise <en>2 and of the total “parallel” input current noise <iTOT>2 There are dependencies on C and on

gnd en iTOT Av Cd Noiseless circuit (per Hertz) For a fixed charge Q, the voltage built up at the amplifier input is decreased while C is increased. Therefore the signal power is decreasing while the amplifier voltage noise power remains constant. The equivalent noise charge (ENC) is increasing with C.

Now we have to consider the TOTAL noise power integrated over the circuit bandwidth Detector en Noiseless circuit, transfer function Av Cd iTOT gnd Equiv. Noise Charge at input node (per hertz) Gp is a normalization factor (peak voltage at the output for 1 electron charge at input)

gnd Noiseless circuit en iTOT Av Cd In some case (and for our simplification) en and iTOT can be readily estimated under the following assumptions: The <en> contribution is coming from the circuit input transistor Input node Active input device The <iTOT> contribution is only due to the detector bias resistor Rp Rp (detector bias)

gm Rp Input signal node Cd gnd Av (voltage gain) of charge integrator followed by a CR-RCn-1 shaper : t~(n-1)RC Step response

For a CR-RCn-1 transfer function, the ENC expression is : Rp : Resistance in parallel at the input gm : Input transistor transconductance t : CR-RCn-1 shaping time C : Capacitance at the input Series (voltage) Parallel (current) Series (voltage) thermal noise contribution ENCs is inversely proportional to the square root of CR-RC peaking time and proportional to the input capacitance. Parallel (current) thermal noise contribution ENCp is proportional to the square root of CR-RCn-1 peaking time

Fp, Fs factors depend on the CR-RCn-1 shaper order (n-1): 1.27 1.16 1.11 0.99 0.95 0.84 0.92 Fs 7 6 5 4 3 2 1 n-1 0.34 0.36 0.40 0.45 0.51 0.63 0.92 Fp 7 6 5 4 3 2 1 n-1 CR-RC2 CR-RC CR-RC3 CR-RC6

“Series” noise slope “Parallel” noise (no C dependence) ENC dependence to the detector capacitance

The “optimum” shaping time is depending on parameters like : C (detector) Gm (input transistor) R (bias resistor) optimum Shaping time (ns) ENC dependence to the shaping time (C=10 pF, gm=10 mS, R=100 kΩ)

Example: Dependence of optimum shaping time to the detector capacitance C=15pF C=10pF C=5pF Shaping time (ns) ENC dependence to the shaping time

ENC dependence to the parallel resistance at the input

The 1/f noise contribution to ENC is only proportional to input capacitance. It does not depend on shaping time, transconductance or parallel resistance. It is usually quite low (a few 10th of electrons) and has to be considered only when looking to very low noise detectors and electronics (hence a very long shaping time to reduce series noise effect)

Analyze the different sources of noise Evaluate Equivalent Noise Charge at the input of front-end circuit Obtained a “generic” ENC formulation of the form : Series noise Parallel noise

The complete front-end design is usually a trade off between “key” parameters like: Noise Power Dynamic range Signal shape Detector capacitance

Conclusion Noise power in electronic circuits is unavoidable (mainly thermal excitation, diode shot noise, 1/f noise) By the proper choice of components and adapted filtering, the front-end Equivalent Noise Charge (ENC) can be predicted and optimized, considering : Equivalent noise power of components in the electronic circuit (gm, Rp …) Input network (detector capacitance C in case of particle detectors) Electronic circuit time constants (t, shaper time constant) A front-end circuit is finalized only after considering the other key parameters Power consumption Output waveform (shaping time, gain, linearity, dynamic range) Impedance adaptation (at input and output)

ENC: dipendenza da Cd, t ENC2 = in2Fit + Cd2vn2Fv/t + Cd2FvfAf
in2 = current noise spectral density (A2/Hz) vn2 = voltage noise spectral density (V2/Hz) t = shaping time; Fi , Fv , Fvf = shaper form factors NOTA: confrontare con pag. 44 della pres. N. 2 di F. Anghinolfi

ENC per un sistema CSA + shaper
K1+K2 (dovuti a resistenza del canale e del bulk) ↔ vn2Fv K3 (dovuto a difetti nel canale) ↔ FvfAf K4, K5 ↔ in2Fi da notare rispetto allo schema della pagina precedente: Cstray, Ci, Cf compaiono in aggiunta alla capacità del rivelatore Cd Rf compare in aggiunta (in parallelo) alla resistenza di “bias” Rb

Modello di rumore per l’A250 (1)

Modello di rumore per l’A250 (2)

A250CF: configurazione di fabbrica

A250CF: caratteristiche (1)

A250CF: caratteristiche (2)

A225 + A206: caratteristiche (1)

A225 + A206: caratteristiche (2)

Esempio di misura del guadagno
mV mV/elettrone Ne = Q/e = Ct Vt / e RX64: Ct = 75 fF (integrata sul chip)

Esempio di misura del rumore
caso dell’architettura digitale (binaria) 1 Obtain Counts vs. Discriminator Threshold (threshold scan) 3 Differential Spectrum  Gaussian Fit extract mean and s 2 Smoothing of Counting Curve  Error function Fit, or …

Risultati con il chip RX64
6xRX64 + fanout + detector GAIN ENC30 ENC50 241Am source 62.8 V/el. 154 el. 179 el. X-ray tube 63.7 V/el. 151 el. 182 el. internal calib. 64.6 V/el. 141 el. 164 el.

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