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

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)

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.

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

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

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

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

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


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, ...


Rp


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, ...


Rp

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

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)


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 …


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.


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

-6 -4 -2 2 4 6

-1

-0.5

0.5

1


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)


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


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


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


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


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)

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

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


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.

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)


ff0

ff0

Filter cuts noise. Signal BW is preserved

Filter cuts inside signal BW : modified shape

SOME EXAMPLES OF CIRCUITS USED AS SIGNAL SHAPERS ...


(Time-invariant circuits like RC, CR networks)

1 2 3 4 5

0.5

1

1.5

2


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

1 2 3 4 5

-2

-1.5

-1

-0.5

0.5

1


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

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


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


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


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

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.

2 4 6 8 10 12 14

0.025

0.05

0.075

0.1

0.125

0.15

0.175


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)

5 10 15 20 25 30 35

0.02

0.04

0.06

0.08

0.1


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)


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

5 10 15 20

0.01

0.02

0.03


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

2 4 6 8 10 12 14

0.025

0.05

0.075

0.1

0.125

0.15

0.175


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


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

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


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


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)

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

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)

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

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:

Rivelatore + Elettronica

Tensione di polarizzazione

Resistenza in serie

Capacita’ di disaccoppiamento

collegamento tipico (accoppiamento AC), elementi circuitali rilevanti

Principali sorgenti di rumore, ENC

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)

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


EM emission

Shielding

Power

Crosstalk

Signals In & Out

System noise

EM emissionCrosstalkGround/power noise

All can be (virtually) avoided by proper design and shielding


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)


Only fundamental noise is discussed in this lecture

Current conducting devices


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

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


THERMAL NOISE

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


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


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


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>


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.


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


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)


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”)


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


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)


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

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)


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


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


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)


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


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)


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)


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


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


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)


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):


ENC dependence to the detector capacitance

“Parallel” noise

“Series” noise slope

(no C dependence)


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)


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)


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)

22 . Df CKENC


• 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


• The complete front-end design is usually a trade off between “key” parameters like:

Noise PowerDynamic rangeSignal shapeDetector 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 (, 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

.

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

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

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

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)

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.

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

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