laboratorio di elettronica modulo preamplificatori: misure di guadagno, linearità, rumore
TRANSCRIPT
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Laboratorio di Elettronica
Modulo preamplificatori:
misure di guadagno, linearità, rumore
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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
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Architetture di lettura (1)
S&H
- vantaggi informazione completa facile da verificare - svantaggi grande volume di dati trattamento analogico
- vantaggi semplice, veloce piccolo volume di dati - svantaggi difficile da verificare informazione ridotta
VTH
ANALOGICA
DIGITALE (BINARIA)
PA
PA
DISCRIM.
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Architetture di lettura (2)
ADC
- vantaggi informazione completa robusto - svantaggi grande volume di dati 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…)
ANALOGICO/DIGITALE
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PA a componenti discreti (ibrido)
2 cm
1 cm
1 channelminimum power: 10mWpower supply: 4V to 25Vcurrent: 2.3mAshaping time: 2.4snoise < 280 e- rmssize: 2cm x 1cm
AmpTek A225
energy
timing
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PA su circuito integrato (chip VLSI)
1 cm
PASCAL (Front – end ALICE SDD) CMOS 0.25m technology64 channels32 10-bits ADCPower: 8mW/chShaping time: 40nsNoise < 280 e- rmsSize: 1cm x 0.9cm
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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
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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
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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
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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
ZoZ+
-
Board, wires, ...
Particle Detector Circuit
Rp
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Detector Signal CollectionCircuit
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
ZoZ+
-
High Z
Low Z
Low Z
T
Voltage source
• Impedance adaptation• Amplitude resolution• Time resolution• Noise cut
Rp
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Electronic Signal Processing
HX(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+Y2The 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)
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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)
u)du-H(u)X(tX(t)*H(t)
Where
Time domain prediction by using convolution is complicated …
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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.
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Electronic Signal Processing
dt.ft)j2X(t).exp(-x(f)
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
)2exp(X(t) tfjc kk
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-6 -4 -2 2 4 6
-1
-0.5
0.5
1
Electronic Signal Processing
0
dt.ft)(-j2 exp . (-at) expx(f)
Example :
The “frequency” domain representation x(f) is using complex numbers.
)exp(X(t) at For (t >0)
0
dt.f)t)j2exp(-(ax(f) x(f)-6 -4 -2 2 4 6
0.2
0.4
0.6
0.8
1
1 2 3 4 5
0.5
1
1.5
2
Arg(x(f))
fj2a
1x(f)
X(t)
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Electronic Signal Processing
Some usual Fourier Transforms :
(t) 1 (t) 1/j– e-at 1/(a+ j)– tn-1e-at 1/[(n-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)
1 t
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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
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Electronic Signal Processing
h(f)
y(f)
fj21
1h(f)
)()(X tt
fj2
1 )f(x
f)j2f(1j2
1y(f)
RC low pass filter
1t
1 2 3 4 5
0.2
0.4
0.6
0.8
1
)exp(1)(Y tt
x(f)
R
C
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Electronic Signal Processing
h(f)x(f) y(f)
Fourier Transform
dt.H(t).eh(f) f.t.j2-
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
df.h(f).eH(t) f.t.j2
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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)
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Electronic Signal Processingy(f) = h(f).x(f)
(f) h(f)
(f)
f
h(f)
f
h(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)
fy(f)
f
h(f)
Dirac function frequency representation
h(f)
f
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Electronic Signal Processingy(f) = h(f).x(f)
vni(f) vno(f)noise
fh(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 filterf
“Unlimited” noise power
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Electronic Signal Processing
x(f) y(f)
x(f)f
y(f)f
h(f)
f
Noise floorf0
f0
f0Improved 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.
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Electronic Signal Processingx(f) y(f)
x(f)
f f
h(f)
f
Noise floor
f0
f0Improved 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)
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Electronic Signal Processing
ff0
ff0
Filter cuts noise. Signal BW is preserved
Filter cuts inside signal BW : modified shape
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SOME EXAMPLES OF CIRCUITS USED AS SIGNAL SHAPERS ...
Electronic Signal Processing
(Time-invariant circuits like RC, CR networks)
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1 2 3 4 5
0.5
1
1.5
2
Electronic Signal Processing
Integrator s-transfer function
h(s) = 1/(1+RCs)
Example RC=0.5 s=j
RC Vout
Vin
VinRXc
XcVout
CjfCjXc
1
2
1
Vin
RCjVout
1
1
Integrator time functionRCtet /
RC
1)(H
Log-Log scalet
f0.01 0.05 0.1 0.5 1 5 10
0.05
0.1
0.2
0.5
1
Low-pass (RC) filter
1 2 3 4 5
0.2
0.4
0.6
0.8
1
Step function response
|h(s)|
t
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1 2 3 4 5
-2
-1.5
-1
-0.5
0.5
1
Electronic Signal Processing
Differentiator s-transfer function
h(s) = RCs/(1+RCs)
VoutVin
VinRXc
RVout
CjfCjXc
1
2
1
Vin
RCj
RCjVout
1
Differentiator time functionRCtett /
RC
1)()(H
R
C
Example RC=0.5 s=j
0.01 0.05 0.1 0.5 1 5 10
0.05
0.1
0.2
0.5
1
High-pass (CR) filter
1 2 3 4 5
0.2
0.4
0.6
0.8
1
Step response
Log-Log scale
f
|h(s)|Impulse response
t
t
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0.01 0.05 0.1 0.5 1 5 100.015
0.02
0.03
0.05
0.07
0.1
0.15
0.2
Electronic Signal Processing
CR-RC s-transfer function
h(s) = RCs/(1+RCs)2
Vout
VinRCjω(
RCjωVout
2)1
CR-RC time functionRCteRCtt /)/1()(H
Example RC=0.5 s=j
1 2 3 4 5
-0.2
0.2
0.4
0.6
0.8
1
Vin
R
CR
C
1
Combining one low-pass (RC) and one high-pass (CR) filter :
2 4 6 8 10 12 14
0.025
0.05
0.075
0.1
0.125
0.15
0.175
Step response
Log-Log scale f
|h(s)|
HighZ Low Z
Impulse response
t
t
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Electronic Signal Processing
CR-RC4 s-transfer function
h(s) = RCs/(1+RCs)5
Vout
VinRCj
RCjVout
n)1(
CR-RC4 time functionRCtetRCtt /3)./4()(H
R
C
Example RC=0.5, n=5 s=j
Vin
R
C
1
Combining (n-1) low-pass (RC) and one high-pass (CR) filter :
0.001 0.0050.01 0.05 0.1 0.5 1
0.0001
0.0002
0.0005
0.001
0.002
0.005
0.01
0.022 4 6 8 10
-0.005
-0.0025
0.0025
0.005
0.0075
0.01
2 4 6 8 10
0.002
0.004
0.006
0.008
0.01
0.012
Log-Log scalef
|h(s)|
Step response
R
C
1
n-1 times
Impulse response
t
t
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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 choiceof the shaper function defines the noise power available at the output.
Thus, it defines the signal-to-noise ratio
f
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Preamplifier & Shaper
Preamplifier Shaper
(t) Q/C.(t)
I O
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.
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2 4 6 8 10 12 14
0.025
0.05
0.075
0.1
0.125
0.15
0.175
Preamplifier & Shaper
Preamplifier Shaper
CR_RC shaperIdeal Integrator
(t)
1/s RCs /(1+RCs)2x
I O
T.F. from I to O
=
RCtett /1)(
RCO
= RC/(1+RCs)2
Output signal of preamplifier + shaper with one charge at the input
t
1 2 3 4 5
-0.2
0.2
0.4
0.6
0.8
1
1 2 3 4 5
0.2
0.4
0.6
0.8
1
0.01 0.05 0.1 0.5 1 5 100.015
0.02
0.03
0.05
0.07
0.1
0.15
0.2
0.2 0.5 1 2 5 100.1
0.2
0.5
1
2
5
t
f
t
fQ/C.(t)
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5 10 15 20 25 30 35
0.02
0.04
0.06
0.08
0.1
Preamplifier & Shaper
2 4 6 8 10
-0.005
-0.0025
0.0025
0.005
0.0075
0.01
Preamplifier Shaper
(t)
1/s RCs /(1+RCs)5x
I O
T.F. from I to O
= = RC/(1+RCs)5
Output signal of preamplifier + shaper with “ideal” charge at the input
t
1 2 3 4 5
0.2
0.4
0.6
0.8
1
t
0.2 0.5 1 2 5 100.1
0.2
0.5
1
2
5
f
t
RCtettO /
4
4
RC
1)(
0.001 0.0050.01 0.05 0.1 0.5 1
0.0001
0.0002
0.0005
0.001
0.002
0.005
0.01
0.02
f
CR_RC4 shaperIdeal Integrator
Q/C.(t)
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Preamplifier & Shaper
Vout
Cf
Schema of a Preamplifier-Shaper circuit
N IntegratorsDiff
Semi-Gaussian Shaper
Cd T0 T0 T0
Vout(s) = Q/sCf . [sT0/(1+ sT0)].[A/(1+ sT0)]n
Vout(t) = [QAn nn /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. n2 3 4 5 6 7
0.2
0.4
0.6
0.8
1
Voutp = QAn nn /Cf n!en
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5 10 15 20
0.01
0.02
0.03
Preamplifier & Shaper
Preamplifier Shaper
CR_RC shaperNon-Ideal Integrator(t)
1/(1+T1s) RCs /(1+RCs)2
I O
T.F. from I to O
x
Non ideal shape, long tail
Integrator baseline
restoration
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2 4 6 8 10 12 14
0.025
0.05
0.075
0.1
0.125
0.15
0.175
Preamplifier & Shaper
Preamplifier Shaper
(t)
1/(1+T1s) (1+T1s) /(1+RCs)2
Pole-Zero Cancellation
I O
T.F. from I to O x
CR_RC shaperNon-Ideal Integrator
Ideal shape, no tail
Integrator baseline
restoration
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Preamplifier & Shaper
Vout
Schema of a Preamplifier-Shaper circuitwith 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
CfN IntegratorsDiff
Semi-Gaussian Shaper
CdCp
T0 T0
Rp
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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 4 6 8 10 12 14
0.025
0.05
0.075
0.1
0.125
0.15
0.175
2nd hit
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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
2 4 6 8 10 12 14
0.025
0.05
0.075
0.1
0.125
0.15
0.175
5 10 15 20 25 30 35
0.02
0.04
0.06
0.08
0.1
CR-RC :Return to baseline > 7*Tp
CR-RC4 :Return to baseline < 3*Tp
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Considerations on Detector Signal Processing
Pile-up :
A long return to zero time does contribute to excessive noise :
5 10 15 20
0.01
0.02
0.03 Uncompensated pole zero CR-RC filter
Long tail contributes to the increase of electronic noise (and to baseline shift)
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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/fCesempio di guadagno tipico [A250CF]: G ≈ 0.18 mV/keV ≈ 4 mV/fC
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Segnale in rivelatori a semiconduttore
Radiation ionization energy (W):determines the number of primaryionization events
Band gap energy (Eg):lower value easier thermal generation of e-h pairs(kT = 26 meV for T = 300 K)
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Risoluzione energetica intrinseca
E (FWHM) = 2.35FEW il fattore di Fano “F”quantifica la riduzionenelle fluttuazionirispetto alla statisticadi Poisson
Per Si e Ge:F = 0.10 ― 0.20(Fano factor)
W (Si) = 3.6 eVW (Ge) = 2.9 eV
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Rivelatori a microstrip
SEGNALE = numero di coppie elettrone-lacuna:
ne-h = E/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
2/1
2
B
D
V
eNC
d
C
Substrato di tipo n
Capacità per unità di area:
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Rivelatore + Elettronica
Tensione di polarizzazione
Resistenza in serie
Capacita’ di disaccoppiamento
collegamento tipico (accoppiamento AC), elementi circuitali rilevanti
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Principali sorgenti di rumore, ENC
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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)
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Noise in Electronic Systems
Signal frequency spectrum
Circuit frequency response
Noise Floor
What we want :
Amplitude, charge or time resolution
Signal dynamic
Low noise
f
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Noise in Electronic Systems
EM emission
Shielding
Power
Crosstalk
Signals In & Out
System noise
EM emissionCrosstalkGround/power noise
All can be (virtually) avoided by proper design and shielding
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Noise in Electronic Systems
Front End Board
Detector
Fundamental noise
Physics of electrical devices
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)
In detector circuits, noise is expressed in (rms) numbers of electrons at the input (ENC)
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Noise in Electronic Systems
Only fundamental noise is discussed in this lecture
Current conducting devices
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Noise in Electronic Systems
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
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Noise in Electronic Systems
THERMAL NOISE
fkTRv .42
R
K = Boltzmann constant (1.383 10-23 V.C/K)T = Temperature@ ambient 4kT = 1.66 10 -20 V/C
“Thermal noise is caused by random thermally excited vibrations of charge carriers in a conductor”
Definition from C.D. Motchenbacher book (“Low Noise Electronic System Design, Wiley Interscience”) :
The noise power is proportional to T(oK)The noise power is proportional to f
fR
kTi .1
42
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Noise in Electronic Systems
THERMAL NOISE
Thermal noise is a totally random signal. It has a normal distribution of amplitude with time.
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Noise in Electronic Systems
THERMAL NOISE
fkTRv .42
R
P
The noise power is proportional to the noise bandwidth:The power in the band 1-2 Hz is equal to that in the band 100000-100001Hz
Thus the thermal noise power spectrum is flat over all frequency range(“white noise”)
0 f
fR
kTi .1
42
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Noise in Electronic Systems
THERMAL NOISE
noisetot
BWkTRv .42
R
f
P
0
Only the electronic circuit frequency spectrum (filter) limits the thermal noise power available on circuit output
Circuit Bandwidth
G=1
Bandwidth limiter
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Noise in Electronic Systems
THERMAL NOISE
fkTRv .42
R
R
fkTREt .4*
The conductor noise power is the same as the power available from the following circuit :
Et is an ideal voltage sourceR is a noiseless resistance
gnd
<v>
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Noise in Electronic Systems
THERMAL NOISE
R
fkTREt .4*
R
fkTREt .4*
gnd
gnd
RL=hi
RL=0
fkTRv .42
fR
kTi .
42
The thermal noise is always present. It can be expressed as a voltage fluctuation or a current fluctuation, depending on the load impedance.
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Noise in Electronic Systems
fkTRv .42
Some examples :
Thermal noise in resistor in “series” with the signal path :
For R=100 ohms
HznVv /28.12
For 10KHz-100MHz bandwidth : rmsVv 88.122
Rem : 0-100MHz bandwidth gives : rmsVv 80.122
For R=1 Mohms
For 10KHz-100MHz bandwidth : rmsmVv 28.12
As a reference of signal amplitude, consider the mean peak charge deposited on 300um Silicon detector : 22000 electrons, ie ~4fC. If this charge was deposited instantaneously on the detector capacitance (10pF), the signal voltage is Q/C= 400V
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Noise in Electronic Systems
Thermal Noise in a MOS Transistor
fgmkTvG ...3
24 12fgmkTid ...
3
242
GS
DS
V
Igm
IdsVgs
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 :
or
: excess noise factor(between 1 and 2)
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Noise in Electronic Systems
Shot Noise
Shot noise is present when carrier transportation occurs across two media,as a semiconductor junction.
I
fqIishot 22 q is the charge of the electron (1.602·10-19 C)
P
0 f
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”)
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Noise in Electronic Systems
Shot Noise in a Bipolar (Junction) Transistor
fqIcicol 22
IcVbe
kTqIcgm /The junction transistor behaves like a current generator, controlled by the base voltage. The ratio (transconductance) is :
The current carriers in bipolar transistor are crossing a semiconductor barrier therefore the device exhibits shot noise as :
orfgmkTicol .2
142 fgmkTvB .
2
14 12
Vbe
Igm C
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Noise in Electronic Systems
1/f Noise
ff
Av f .2
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)
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Noise in Electronic Systems
1/f noise and thermal noise (MOS Transistor)
Depending on circuit bandwidth, 1/f noise may or may not be contributing
1/f noise
Thermal noise
Circuit bandwidth
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Noise in Detector Front-Ends
DetectorCircuit
Each component is a (multiple) noise source
How much noise is here ?
Note that (pure) capacitors orinductors do not produce noise
As we just seen before :
(detector bias)
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Noise in Detector Front-Ends
Circuit
gnd
A capacitor (not a noise source)
Passive & active components, all noise sources
Ideal charge generator
Detector
Detector
gnd
noiseless
en
in
Circuit equivalent current noise source
Circuit equivalent voltage noise source
Rp
Rp
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Noise in Detector Front-Ends
From practical point of view, en is a voltage source such that:
fA
Vnoe
v
measn .
2
22
when input is grounded
in is a current source such that:
fRA
Vnoi
pv
measn
22
22 1
.
when the input is on a large resistance Rp
Detector
gnd
Noiseless circuiten
in
Av
Rp
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Noise in Detector Front-Ends
22
2
22
jC
iee
d
TOT
ninput
In case of an (ideal) detector, the input is loaded by the detector capacitance C
Detector
gnd
Noiseless circuiten
iTOT
AvCd
The equivalent voltage noise at the input is:
(per Hertz)
i2TOT is the combination of the
circuit current noise and Rp bias resistance noise :
pp
RkTi
1.42
222pnTOT iii
Detector signal node (input)
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Noise in Detector Front-Ends
2
2222
)(.
j
iCeq
TOT
dninput
Detector
gnd
Noiseless circuiten
iTOT
AvCd
The detector signal is a charge Q. The voltage noise <e2
input> converts to charge noise by using the relationship
vCq d .
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
(per Hertz)
f 2
input
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Noise in Detector Front-Ends
2
2222 .
j
iCeq
TOT
dninput
Noiseless circuit
Detector
gnd
en
iTOT
AvCd
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.
(per Hertz)
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Noise in Detector Front-Ends
dAv
j
iCe
GENC
TOT
dnp
tot .)(..1 2
02
222
22
Detector
gnd
Noiseless circuit, transfer function
en
iTOT
AvCd
Now we have to consider the TOTAL noise power integrated over the circuit bandwidth
Equiv. Noise Charge at input node (per hertz)
)(Av
Gp is a normalization factor (peak voltage at the output for 1 electron charge at input)
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Noise in Detector Front-Ends
Detector
gnd
Noiseless circuiten
iTOT
AvCd
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
Active input device
Rp (detector bias)
Input node
dAv
j
iCe
GENC
TOT
dnp
tot .)(..1 2
02
222
22
The <iTOT> contribution is only due to the detector bias resistor Rp
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Noise in Detector Front-Ends
Detector
gnd
Cd
gm
Rp
Input signal node
gmkTen 3
242
RpkTin
142
dAv
Rp
kT
jCgmkT
GENC d
ptot .)(.
4.
1..
3
24
1 2
02
212
2
Av (voltage gain) of charge integrator followed by a CR-RCn-1 shaper :
njRC
jRCAv
).1(
.)(
2 4 6 8 10 12 14
0.025
0.05
0.075
0.1
0.125
0.15~(n-1)RC
Step response
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Noise in Detector Front-Ends
For a CR-RCn-1 transfer function, the ENC expression is :
Rp : Resistance in parallel at the input
gm : Input transistor transconductance
: CR-RCn-1 shaping time
C : Capacitance at the input
p
d
Rq
kTFp
Cgm
q
kTFsENC
2
21
22 4
.3
24.
Parallel (current) thermal noise contribution ENCp is proportional to the
square root of CR-RCn-1 peaking time
Series (voltage) thermal noise contribution ENCs is inversely proportional to the square root of CR-RC peaking time and proportional to the input capacitance.
Series (voltage) Parallel (current)
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Noise in Detector Front-Ends
1 2 3 4 5
0.05
0.1
0.15
0.2
0.25
0.3
0.35
1 2 3 4 5 6 7
0.05
0.1
0.15
0.2
0.25
2 4 6 8 10
0.05
0.1
0.15
0.2
2 4 6 8 10 12 14
0.025
0.05
0.075
0.1
0.125
0.15
CR-RC CR-RC2
CR-RC3 CR-RC6
0.340.360.400.450.510.630.92Fp
7654321n-1
1.271.161.110.990.950.840.92Fs
7654321n-1
Fp, Fs factors depend on the CR-RCn-1 shaper order (n-1):
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Noise in Detector Front-Ends
ENC dependence to the detector capacitance
“Parallel” noise
“Series” noise slope
(no C dependence)
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Noise in Detector Front-Ends
ENC dependence to the shaping time (C=10 pF, gm=10 mS, R=100 kΩ)
optimumThe “optimum” shaping time is depending on parameters like :
C (detector)Gm (input transistor)R (bias resistor)
Shaping time (ns)
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Noise in Detector Front-Ends
ENC dependence to the shaping time
Example:Dependence of optimum shaping time to the detector capacitance
C=5pF
C=10pF
C=15pF
Shaping time (ns)
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Noise in Detector Front-Ends
ENC dependence to the parallel resistance at the input
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Noise in Detector Front-Ends
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)
22 . Df CKENC
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Noise in Detector Front-Ends
• 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 :
p
ds
Rq
kTFp
CR
q
kTFsENC
2
2
22 4
.4
.
Parallel noiseSeries noise
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Noise in Detector Front-Ends
• The complete front-end design is usually a trade off between “key” parameters like:
Noise PowerDynamic rangeSignal shapeDetector capacitance
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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 (, 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)
p
ds
Rq
kTFp
CR
q
kTFsENC
2
2
22 4
.4
.
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ENC: dipendenza da Cd, ENC2 = in2Fi + Cd
2vn2Fv/ + Cd
2FvfAf
in2 = current noise spectral density (A2/Hz)
vn2 = voltage noise spectral density (V2/Hz)
= shaping time; Fi , Fv , Fvf = shaper form factors
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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
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Modello di rumore per l’A250 (1)
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Modello di rumore per l’A250 (2)
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A250CF: configurazione di fabbrica
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A250CF: caratteristiche (1)
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A250CF: caratteristiche (2)
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A225 + A206: caratteristiche (1)
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A225 + A206: caratteristiche (2)
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Esempio di misura del guadagno
600
500
400
300
200
(m
V)
90008000700060005000400030002000Elettroni in ingresso
a = 5.1 ± 1.8b = 0.064966 ± 0.000486
Ne = Q/e = Ct Vt / e RX64: Ct = 75 fF (integrata sul chip)
mVmV/elettrone
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Esempio di misura del rumore
200
150
100
50
0
Co
nte
gg
i
340320300280260240Soglia (mV)
200
150
100
50
0
Conte
ggi
340320300280260240Soglia (mV)
1Obtain Counts vs.
Discriminator Threshold(threshold scan)
2Smoothing of Counting
Curve
Error function Fit, or …
3Differential Spectrum
Gaussian Fit
extract mean and
15
10
5
0
340320300280260240Soglia (mV)
x0 = 291.4 ± 0.446sigma = 11.34 ± 0.51
caso dell’architettura digitale (binaria)
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Risultati con il chip RX64450
400
350
300
250
200
150
(m
V)
24222018161412108Energia (keV)
CuGe
Mo
Ag
Sn
Rb
Mo
Ag
Retta calibrazione con la sorgente Retta calibrazione con il tubo
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.