1 ELEC-2005 Electronics in High Energy Physics Winter Term: Introduction to electronics in HEP...

1

ELEC-2005Electronics in High Energy Physics

Winter Term: Introduction to electronics in HEP

ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS

PART 2

Francis ANGHINOLFIJanuary 20, 2005

[email protected]

CERN Technical Training 2005

2

ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS – Part 2

• Noise in Electronic Systems

• Noise in Detector Front-Ends

• Noise Analysis in Time Domain

• Conclusion

3

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

4


EM emission

Shielding

Power

Crosstalk

Signals In & Out

System noise

EM emissionCrosstalkGround/power noise

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

5


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)

6


Only fundamental noise is discussed in this lecture

Current conducting devices

7


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

8


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

9


THERMAL NOISE

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

10


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 h

fR

kTi .1

42

11


THERMAL NOISE

noisetot

BWkTRv .42

R

h

P

0

Only the electronic circuit frequency spectrum (filter) limits the thermal noise power available on circuit output

Circuit Bandwidth

G=1

Bandwidth limiter

12


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>

13


THERMAL NOISE

R

fkTREt .4*

R

fkTREt .4*

gnd

gnd

RL=h

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.

14


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

15


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

(*) : physics of MOS current conduction is discussed in another session

: excess noise factor(between 1 and 2)

16


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 one electron (1.602 E-19 C)

P

0 h

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”)

17


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

18


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 100Hz, 100MHz to 1Ghz)

19


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

20

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)

21


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

22


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

23


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)

ITOT is the combination of the circuit current noise and Rp bias resistance noise :

pp

RkTi

1.42

222pnTOT iii

Detector signal node (input)

24


2

2222

)(.

j

iCeq

TOT

dninput

Detector

gnd

Noiseless circuiten

iTOT

AvCd

The detector signal is a charge Qs. The voltage noise <einput> converts to charge noise by using the relationship

vCq d .

The equivalent charge noise at the input, which has to be ratioed 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

25


22

222 .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)

26


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 over circuit bandwidth

Eq. Charge noise at input node per hertz

)(Av

Gp is a normalization factor (peak voltage at the output for 1 electron charge)

27


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

28


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 shaper :

njRC

jRCAv

).1(

.)(

2 4 6 8 10 12 14

0.025

0.05

0.075

0.1

0.125

0.15~n.RC

Step response

29


For CR-RCn transfer function, ENC expression is :

Rp : Resistance in parallel at the input

gm : Input transistor

: CR-RCn 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 is proportional to the square root of CR-RC peaking time

Series (voltage) thermal noise contribution is inversely proportional to the square root of CR-RC peaking time and proportional to the input capacitance.

.4

..3

24.

21

2p

d

Rq

kTFp

Cgm

q

kTFsENC

30


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

1.271.161.110.990.950.840.92Fs

7654321n

Fp, Fs factors depend on the CR-RC shaper order n

31


ENC dependence to the detector capacitance

“Parallel” noise

“Series” noise slope

(no C dependence)

32


ENC dependence to the shaping time (C=10pF, gm=10mS, R=100Kohms)

optimumThe “optimum” shaping time is depending on parameters like :

C detectorGm (input transistor)R (bias resistor)

Shaping time (ns)

33


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)

34


ENC dependence to the parallel resistance at the input

35


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

36


• 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

37


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

Noise PowerDynamic rangeSignal shapeDetector capacitance

38

Noise Analysis in Time Domain

• A class of circuits (time-variant filters) are used because of their finite time response

• These circuits cannot be represented by frequency transfer function

• The ENC estimation is possible by introducing the “weighting function” for a time-variant filter

39


dttWiENC TOTp222 )(

2

1

Detector

gnd

en

iTOT

W(t)Cd

Example : leakp

TOT IqR

kTi ..21

.42

Rp Ileak

40


dttWCeENC dn2222

s )('..2

1

Detector

gnd

en

iTOT

W(t)Cd

Example : 12 .3

2.4.4 gmkTRskTeTOT

RS

input device

gm

41


For time invariant filter (like CR-RC filters), W(t) is represented by the mirror function in time of the impulse response h(t) :

h(Tm-t) (Tm is signal measurement time)

Example : RC circuit

RCtet /1)( RC

h

1 2 3 4 5

0.5

1

1.5

2

If noise hit occurs at measurement time t=Tm, contribution is h(0) (maximum)If noise hit occurs at t=RC before Tm, contribution is 1/e the maximumIf noise hit occurs at t>Tm, contribution is zero

42


For time variant filter, W(t) represents the “weight” of a noise impulse occurring at time t, whereas measurement is done at time Tm

Example : Gated integrator

GTtfort 01)(W

If noise hit occurs at time between t=Tm-TG and Tm, contribution is maximumIf noise hit occurs before Tm-TG or after Tm, contribution is zero

elsewheret 0)( W0 TG

Remark : a perfect gated integrator would give ENCs negligible

Practically, rise and fall time are limited. They are in fact limited on purpose to predict and optimize the total ENC

C

switch

0)(' tW

TMTM-TG

43

Noise in Analysis Time Domain

Example : Trapezoidal Weighting Function

0

T1

The formulation can be compared to

T1

T2

21.3

2)( 2

2 TTIdttW 1

2)(' 1

2

TIdttW

)22

11

3

1.(

1

1.. 2222 TTiT

CeENC TOTdnTOT

2222 ).33.0(1

.).12.1( ndn iCeENC

Obtained in case of a continuous time CR-RC quasi-Gaussian filter with peaking time

44

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

.

45

ELEC-2005Electronics in High Energy Physics

Winter Term: Introduction to electronics in HEP

ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS

PART 2

Francis ANGHINOLFIJanuary 20, 2005

[email protected]

CERN Technical Training 2005

1 ELEC-2005 Electronics in High Energy Physics Winter Term: Introduction to electronics in HEP...

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Transcript of 1 ELEC-2005 Electronics in High Energy Physics Winter Term: Introduction to electronics in HEP...