Download 1-Electronic signal Processing

Electronics in High Energy Physics
Introduction to electronics in HEP
ANALOG SIGNAL PROCESSING
OF PARTICLE DETECTOR SIGNALS
PART 2
based on Francis ANGHINOLFI lecture at Cern (2005)
1
ANALOG SIGNAL PROCESSING
OF PARTICLE DETECTOR SIGNALS – Part 2
• Noise in Electronic Systems
• Noise in Detector Front-Ends
• Noise Analysis in Time Domain
• Conclusion
2
Noise in Electronic Systems
Signal frequency spectrum
Circuit frequency response
Noise Floor
f
Amplitude, charge or time resolution
What we want :
Signal dynamic
Low noise
3
Noise in Electronic Systems
EM emission
Power
Crosstalk
System noise
EM emission
Crosstalk
Ground/power noise
Signals
In & Out
All can be (virtually)
avoided by proper design
and shielding
Shielding
4
Noise in Electronic Systems
Fundamental noise
Physics of electrical
devices
Detector
Front End Board
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)
5
Noise in Electronic Systems
Current
conducting
devices
Only fundamental noise is discussed in this lecture
6
Noise in Electronic Systems
Current conducting devices
(resistors, transistors)
Three main types of noise mechanisms in electronic conducting
devices:
• THERMAL NOISE
Always
• SHOT NOISE
Semiconductor devices
• 1/f NOISE
Specific
7
Noise in Electronic Systems
THERMAL NOISE
Definition from C.D. Motchenbacher book (“Low Noise Electronic System Design, Wiley Interscience”) :
“Thermal noise is caused by random thermally
excited vibrations of charge carriers in a
conductor”
R
v 2  4kTR.f
i 2  4kT
1
.f
R
The noise power is proportional to T(oK)
The noise power is proportional to f
K = Boltzmann constant (1.383 10-23 V.C/K)
T = Temperature
@ ambient 4kT = 1.66 10 -20 V/C
8
Noise in Electronic Systems
THERMAL NOISE
Thermal noise is a totally random signal. It has a normal distribution of
amplitude with time.
9
Noise in Electronic Systems
THERMAL NOISE
R
v 2  4kTR.f
i 2  4kT
1
.f
R
The noise power is proportional to the noise bandwidth:
The power in the band 1-2 Hz is equal to that in the band
100000-100001Hz
Thus the thermal noise power spectrum is flat over all frequency range
(“white noise”)
P
0
h
10
Noise in Electronic Systems
THERMAL NOISE
R
Bandwidth limiter
G=1
v2
tot
 4kTR.BWnoise
Only the electronic circuit frequency spectrum (filter) limits the
thermal noise power available on circuit output
Circuit Bandwidth
P
0
h
11
Noise in Electronic Systems
THERMAL NOISE
R
v 2  4kTR.f
The conductor noise power is the same as the power available from the
following circuit :
R
*
Et  4kTR.f
gnd
<v>
Et is an ideal voltage source
R is a noiseless resistance
12
Noise in Electronic Systems
THERMAL NOISE
R
*
Et  4kTR.f
RL=h
v 2  4kTR.f
gnd
R
*
Et  4kTR.f
gnd
i2 
RL=0
4kT
.f
R
The thermal noise is always
present. It can be expressed as a
voltage fluctuation or a current
fluctuation, depending on the load
impedance.
13
Noise in Electronic Systems
Some examples :
Thermal noise in resistor in “series” with the signal path :
v 2  4kTR.f
For R=100 ohms
v 2  1.28nV / Hz
For 10KHz-100MHz bandwidth :
v 2  12.88Vrms
2
Rem : 0-100MHz bandwidth gives : v  12.80Vrms
For R=1 Mohms
2
For 10KHz-100MHz bandwidth : v  1.28mVrms
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= 400V
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Noise in Electronic Systems
Thermal Noise in a MOS Transistor
Ids
Vgs
The MOS transistor behaves like a current generator(*), controlled by
the gate voltage. The ratio is called the transconductance.
gm 
I DS
VGS
The MOS transistor is a conductor and exhibits thermal noise
expressed as :
id2  4kT
2
..gm.f
3
or
2
vG2  4kT ..gm 1.f
3
(*) : physics of MOS current conduction is discussed in another session
 : excess noise
factor
(between 1 and 2)
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Noise in Electronic Systems
Shot Noise
I
2
ishot
 2qIf
q is the charge of one electron (1.602 E-19 C)
Shot noise is present when carrier transportation occurs across two media,
as a semiconductor junction.
As for thermal noise, the shot noise power <i2> is proportional to the
noise bandwidth.
The shot noise power spectrum is flat over all frequency range
(“white noise”)
P
16
0
h
Noise in Electronic Systems
Shot Noise in a Bipolar (Junction) Transistor
Ic
gm 
Vbe
I C
Vbe
The current carriers in bipolar transistor are crossing a semiconductor
barrier  therefore the device exhibits shot noise as :
2
icol
 2qIcf
The junction transistor behaves like a current generator, controlled by
the base voltage. The ratio (transconductance) is : gm  qIc / kT
2
icol
 4kT
1
gm.f
2
or
v B2  4kT
1
gm 1.f
2
17
Noise in Electronic Systems
1/f Noise
Formulation
v
2
f
A
  .f
f
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)
18
Noise in Electronic Systems
1/f noise and thermal noise (MOS Transistor)
1/f noise
Circuit bandwidth
Thermal noise
Depending on circuit bandwidth, 1/f noise may or may not be contributing
19
Noise in Detector Front-Ends
Circuit
Detector
How much noise is here ?
Note that (pure) capacitors or
inductors do not produce noise
(detector bias)
As we just seen before :
Each component is a
(multiple) noise
source
20
Noise in Detector Front-Ends
Detector
Circuit
Rp
Ideal
gnd
charge
generator A capacitor
(not a noise
source)
Circuit equivalent
voltage noise
source
Detector
en
Passive & active
components, all
noise sources
noiseless
Rp
in
gnd
Circuit equivalent
current noise
source
21
Noise in Detector Front-Ends
Detector
en
Noiseless circuit
Av
Rp
in
From practical point of view, en is a
voltage source such that:
en2

2
Vnomeas
Av2
.f
when input is grounded
gnd
in is a current source such that:
in2

2
Vnomeas
Av2
.
1
R 2p
f
when the input is on a large
resistance Rp
22
Noise in Detector Front-Ends
In case of an (ideal) detector, the input is loaded by the detector capacitance C
Detector
Detector signal node (input)
en
Noiseless circuit
ITOT is the combination of the
circuit current noise and Rp bias
resistance noise :
Av
Cd
i 2p  4kT.
iTOT
1
Rp
2
iTOT
 in2  i 2p
gnd
The equivalent voltage noise at the input is:
2
einput
 en2 
2
iTOT
Cd
2
 j 
2
(per Hertz)
23
Noise in Detector Front-Ends
Detector
input
en
Noiseless circuit
Av
Cd
iTOT
The detector signal is a charge Qs.
The voltage noise <einput> converts
to charge noise by using the
relationship
q  Cd .v
gnd
2
qinput
 en2 .C d 2 
2
iTOT
( j )
2
(per Hertz)
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   2f
24
Noise in Detector Front-Ends
Detector
en
Noiseless circuit
Av
Cd
iTOT
2
qinput
 en2 .C d 2 
2
iTOT
 j 
2
(per Hertz)
gnd
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.
25
Noise in Detector Front-Ends
Now we have to consider the TOTAL noise power over circuit bandwidth
Detector
en
Noiseless circuit, transfer
function Av ( )
Av
Cd
iTOT
gnd
2
ENCtot
Eq. Charge noise at input node per hertz
2

i
TOT
2
2
.Av ( )2 .d
 2  en .C d 
Gp 0 

j 2 


1


Gp is a normalization factor (peak voltage at the output for 1 electron charge)
26
Noise in Detector Front-Ends
Detector
2
ENCtot

1

 
G p2 0

en2
.C d
2
2

iTOT
.Av ( )2 .d

 j 2 
en
Noiseless circuit
Av
Cd
iTOT
gnd
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
The <iTOT> contribution is only due to
the detector bias resistor Rp
Input node
Active input device
Rp (detector bias)
27
Noise in Detector Front-Ends
Detector
en2  4kT
2
gm
3
Input signal node
Cd
gm
in2  4kT
Rp
1
Rp
gnd
2
ENCtot



2
1
4kT 
2
2
1


4
kT
.
gm
.
C

.
.
Av
(

)
.d


d
2
2
3
G p 0 
 j  Rp 
1

Av (voltage gain) of charge integrator followed by a CR-RCn shaper :
Av( ) 
RC. j
(1  RC. j )
t~n.RC
0.15
0.125
0.1
n
0.075
0.05
0.025
2
4
6
8
Step response
10
12
14
28
Noise in Detector Front-Ends
For CR-RCn transfer function, ENC expression is :
2
4kT 2
4kT
1 C d
ENC  Fs. 2
gm
 Fp. 2 t
t
q 3
q Rp
2
Rp : Resistance in parallel at the input
gm : Input transistor
t : CR-RCn Shaping time
ENC  Fs.
4kT 2
4kT
1 Cd
gm
.

Fp
.
. t
2
2
q 3
q Rp
t
C : Capacitance at the input
Series (voltage) thermal noise contribution is inversely proportional to the square root of
CR-RC peaking time and proportional to the input capacitance.
Parallel (current) thermal noise contribution is proportional to the square root of CRRC peaking time
29
Noise in Detector Front-Ends
Fp, Fs factors depend on the CR-RC shaper order n
n
Fs
1
0.92
2
0.84
3
0.95
4
0.99
5
1.11
6
1.16
7
1.27
n
Fp
1
0.92
2
0.63
3
0.51
4
0.45
5
0.40
6
0.36
7
0.34
0.25
0.35
0.3
0.2
CR-RC2
0.25
CR-RC
0.2
0.15
0.15
0.1
0.1
0.05
0.05
1
2
3
4
5
1
2
3
4
5
6
7
0.15
0.2
0.125
0.15
0.1
CR-RC3
0.1
CR-RC6
0.075
0.05
0.05
0.025
2
4
6
8
10
2
4
6
8
10
12
14
30
Noise in Detector Front-Ends
“Series” noise slope
“Parallel” noise
(no C dependence)
ENC dependence to the detector capacitance
31
Noise in Detector Front-Ends
The “optimum” shaping
time is depending on
parameters like :
optimum
C detector
Gm (input transistor)
R (bias resistor)
Shaping time (ns)
ENC dependence to the shaping time
(C=10pF, gm=10mS, R=100Kohms)
32
Noise in Detector Front-Ends
C=15pF
C=10pF
Example:
Dependence of
optimum shaping
time to the detector
capacitance
C=5pF
Shaping time (ns)
ENC dependence to the shaping time
33
Noise in Detector Front-Ends
ENC dependence to the parallel resistance at the input
34
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)
ENC2f  K.CD 2
35
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 :
ENC  Fs.
2
4kT
q
2
Rs
C d2
t
Series noise
 Fp.
4kT
2
q Rp
t
Parallel noise
36
Noise in Detector Front-Ends
• The complete front-end design is usually a trade off between “key”
parameters like:
Noise
Power
Dynamic range
Signal shape
Detector capacitance
37
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
38
Noise Analysis in Time Domain
Detector
en
W(t)
Cd
iTOT
gnd
ENC p2
Example :
1
2
2
  iTOT  W (t ) dt
2
2
iTOT
 4kT.

1
Rp
 2.q.I leak
Rp
Ileak
39
Noise Analysis in Time Domain
Detector
en
W(t)
Cd
iTOT
gnd
ENCs2
Example :
2
eTOT
1
  en  2 .Cd 2 . W ' (t )2 dt
2

2
 4kT.Rs  4kT. .gm 1
3
input device
RS
gm
40
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
2
h(t ) 
1 t / RC
e
RC
1.5
1
0.5
1
2
3
4
5
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 maximum
If noise hit occurs at t>Tm, contribution is zero
41
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
switch
Example : Gated integrator
W(t )  1 for 0  t  TG
W(t )  0 elsewhere
C
0G
TM-T
TTGM
If noise hit occurs at time between t=Tm-TG and Tm, contribution is maximum
If noise hit occurs before Tm-TG or after Tm, contribution is zero
Remark : a perfect gated integrator would give ENCs negligible
W ' (t )  0
Practically, rise and fall time are limited. They are in fact limited on purpose to
predict and optimize the total ENC
42
Noise in Analysis Time Domain
Example : Trapezoidal Weighting Function
T2
T1
T1
0
2
2


W
(
t
)
dt

I

.T1  T 2
2

2


W
'
(
t
)
dt  I1 

3
2
ENCTOT
2
T1
1
1
2 1
 en  .Cd .   iTOT  .( T1  T 2)
T1
3
2
2
2
The formulation can be compared to
ENC 2  (1.12 ).  en  2 .C d2
1
t
 (0.33).  in  2 t
Obtained in case of a
continuous time CR-RC quasiGaussian filter with t peaking
43
time
Conclusion
ENC  Fs.
2
4kT
q
2
Rs
C d2
t
 Fp.
4kT
2
q Rp
t
• Noise power in electronic circuits is unavoidable (mainly thermal excitation, diode
shot noise, 1/f noise)
• By the proper choice of components and adapted filtering, the front-end
Equivalent Noise Charge (ENC) can be predicted and optimized, considering :
– Equivalent noise power of components in the electronic circuit (gm, Rp …)
– Input network (detector capacitance C in case of particle detectors)
– Electronic circuit time constants (t, shaper time constant)
• A front-end circuit is finalized only after considering the other key parameters
– Power consumption
– Output waveform (shaping time, gain, linearity, dynamic range)
– Impedance adaptation (at input and output)
44