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

1
ELEC-2005Electronics in High Energy
PhysicsWinter Term Introduction to electronics
in HEP
CERN Technical Training 2005

• ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR
  SIGNALS
• PART 2
• Francis ANGHINOLFI
• January 20, 2005
• Francis.Anghinolfi_at_cern.ch

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

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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
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Noise in Electronic Systems
Power
EM emission
Crosstalk
System noise
EM emission Crosstalk Ground/power noise
Signals In Out
All can be (virtually) avoided by proper design
and shielding
Shielding
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Noise in Electronic Systems
Fundamental noise
Physics of electrical devices
Detector
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)
Front End Board
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
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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
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
The noise power is proportional to T(oK) The
noise power is proportional to Df
K Boltzmann constant (1.383 10-23 V.C/K) T
Temperature _at_ ambient 4kT 1.66 10 -20 V/C
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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
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
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Noise in Electronic Systems
THERMAL NOISE
Bandwidth limiter
G1
Only the electronic circuit frequency spectrum
(filter) limits the thermal noise power available
on circuit output
Circuit Bandwidth
P
0
h
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Noise in Electronic Systems
THERMAL NOISE
The conductor noise power is the same as the
power available from the following circuit
Et is an ideal voltage source R is a noiseless
resistance
ltvgt
gnd
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Noise in Electronic Systems
THERMAL NOISE
RLh
gnd
The thermal noise is always present. It can be
expressed as a voltage fluctuation or a current
fluctuation, depending on the load impedance.
RL0
gnd
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Noise in Electronic Systems
Some examples
Thermal noise in resistor in series with the
signal path
For R100 ohms
For 10KHz-100MHz bandwidth
Rem 0-100MHz bandwidth gives
For R1 Mohms
For 10KHz-100MHz bandwidth
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 400mV
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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.
The MOS transistor is a conductor and exhibits
thermal noise expressed as
G excess noise factor (between 1 and 2)
or
() physics of MOS current conduction is
discussed in another session
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Noise in Electronic Systems
Shot Noise
I
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 lti2gt
is proportional to the noise bandwidth.
The shot noise power spectrum is flat over all
frequency range (white noise)
P
0
h
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Noise in Electronic Systems
The current carriers in bipolar transistor are
crossing a semiconductor barrier ? therefore the
device exhibits shot noise as
or
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Noise in Electronic Systems
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)
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Noise in Electronic Systems
1/f noise and thermal noise (MOS Transistor)
1/f noise
Thermal noise
Depending on circuit bandwidth, 1/f noise may or
may not be contributing
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Noise in Detector Front-Ends
Circuit
Note that (pure) capacitors or inductors do not
produce noise
Detector
How much noise is here ?
(detector bias)
As we just seen before
Each component is a (multiple) noise source
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Noise in Detector Front-Ends
Circuit
Rp
Circuit equivalent voltage noise source
Detector
Ideal charge generator
en
Passive active components, all noise sources
A capacitor (not a noise source)
noiseless
in
Rp
Circuit equivalent current noise source
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Noise in Detector Front-Ends
From practical point of view, en is a voltage
source such that
when input is grounded
in is a current source such that
when the input is on a large resistance Rp
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Noise in Detector Front-Ends
In case of an (ideal) detector, the input is
loaded by the detector capacitance C
Detector signal node (input)
ITOT is the combination of the circuit current
noise and Rp bias resistance noise
The equivalent voltage noise at the input is
(per Hertz)
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Noise in Detector Front-Ends
input
The detector signal is a charge Qs. The voltage
noise lteinputgt converts to charge noise by using
the relationship
(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 ltengt2 and of the total parallel
input current noise ltiTOTgt2 There are
dependencies on C and on
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Noise in Detector Front-Ends
Noiseless circuit
(per Hertz)
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.

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Noise in Detector Front-Ends
Now we have to consider the TOTAL noise power
over circuit bandwidth
Detector
en
Noiseless circuit, transfer function
Av
Cd
iTOT
Eq. Charge noise at input node per hertz

Gp is a normalization factor (peak voltage at
the output for 1 electron charge)
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Noise in Detector Front-Ends
In some case (and for our simplification) en and
iTOT can be readily estimated under the following
assumptions
The ltengt contribution is coming from the circuit
input transistor
Input node
Active input device

The ltiTOTgt contribution is only due to the
detector bias resistor Rp
Rp (detector bias)
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Noise in Detector Front-Ends
Detector
Cd
Av (voltage gain) of charge integrator followed
by a CR-RCn shaper

tn.RC
Step response
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Noise in Detector Front-Ends
For CR-RCn transfer function, ENC expression is
Rp Resistance in parallel at the input gm
Input transistor t CR-RCn Shaping time 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 CR-RC peaking
time
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Noise in Detector Front-Ends
Fp, Fs factors depend on the CR-RC shaper order n
CR-RC2
CR-RC
CR-RC3
CR-RC6
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Noise in Detector Front-Ends
Series noise slope
Parallel noise
(no C dependence)
ENC dependence to the detector capacitance
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Noise in Detector Front-Ends
The optimum shaping time is depending on
parameters like C detector Gm (input
transistor) R (bias resistor)
optimum
Shaping time (ns)
ENC dependence to the shaping time (C10pF,
gm10mS, R100Kohms)
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Noise in Detector Front-Ends
Example Dependence of optimum shaping time to
the detector capacitance
C15pF
C10pF
C5pF
Shaping time (ns)
ENC dependence to the shaping time
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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)
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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
  

Parallel noise
Series 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
• Power
• Dynamic range
• Signal shape
• Detector capacitance

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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

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Noise Analysis in Time Domain
Example
Ileak
Rp
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Noise Analysis in Time Domain
input device gm
Example
RS
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
If noise hit occurs at measurement time tTm,
contribution is h(0) (maximum) If noise hit
occurs at tRC before Tm, contribution is 1/e the
maximum If noise hit occurs at tgtTm, contribution
is zero
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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
C
0
TG
TM
TM-TG
If noise hit occurs at time between tTm-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 Practically, rise and fall time
are limited. They are in fact limited on purpose
to predict and optimize the total ENC
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Noise in Analysis Time Domain
Example Trapezoidal Weighting Function
T2
T1
T1
0
The formulation can be compared to
Obtained in case of a continuous time CR-RC
quasi-Gaussian filter with t peaking time
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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 (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)

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ELEC-2005Electronics in High Energy
PhysicsWinter Term Introduction to electronics
in HEP
CERN Technical Training 2005

• ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR
  SIGNALS
• PART 2
• Francis ANGHINOLFI
• January 20, 2005
• Francis.Anghinolfi_at_cern.ch