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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
Francis.Anghinolfi@cern.ch
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
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
5
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)
6
Noise in Electronic Systems
Only fundamental noise is discussed in this lecture
Current conducting devices
7
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
8
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
9
Noise in Electronic Systems
THERMAL NOISE
Thermal noise is a totally random signal. It has a normal distribution of amplitude with time.
10
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 h
fR
kTi .1
42
11
Noise in Electronic Systems
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
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>
13
Noise in Electronic Systems
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
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
15
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
(*) : physics of MOS current conduction is discussed in another session
: excess noise factor(between 1 and 2)
16
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 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
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
18
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 100Hz, 100MHz to 1Ghz)
19
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
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
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
22
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
23
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)
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
Noise in Detector Front-Ends
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
Noise in Detector Front-Ends
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
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 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
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
28
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 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
Noise in Detector Front-Ends
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
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
1.271.161.110.990.950.840.92Fs
7654321n
Fp, Fs factors depend on the CR-RC shaper order n
31
Noise in Detector Front-Ends
ENC dependence to the detector capacitance
“Parallel” noise
“Series” noise slope
(no C dependence)
32
Noise in Detector Front-Ends
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
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)
34
Noise in Detector Front-Ends
ENC dependence to the parallel resistance at the input
35
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
36
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
37
Noise in Detector Front-Ends
• 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
Noise Analysis in Time Domain
dttWiENC TOTp222 )(
2
1
Detector
gnd
en
iTOT
W(t)Cd
Example : leakp
TOT IqR
kTi ..21
.42
Rp Ileak
40
Noise Analysis in Time Domain
dttWCeENC dn2222
s )('..2
1
Detector
gnd
en
iTOT
W(t)Cd
Example : 12 .3
2.4.4 gmkTRskTeTOT
RS
input device
gm
41
Noise Analysis in Time Domain
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
Noise Analysis in Time Domain
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
Francis.Anghinolfi@cern.ch
CERN Technical Training 2005
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