1. CERN Technical Training 2005
ELEC-2005 Electronics in High Energy Physics Winter Term: Introduction to electronics in HEP
ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS
PART 2
Francis ANGHINOLFI
January 20, 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 f
Amplitude, charge or time resolution
What we want :
Signal dynamic
Low noise

4. 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

5. 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)

6. Noise in Electronic Systems
Current conducting devices
Only fundamental noise is discussed in this lecture

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
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
The noise power is proportional to T(oK)
The noise power is proportional to Df
K = Boltzmann constant ( V.C/K)
T = Temperature
@ ambient 4kT = V/C

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 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 Hz
Thus the thermal noise power spectrum is flat over all frequency range
(“white noise”) P h

11. Noise in Electronic Systems
THERMAL NOISE
Bandwidth limiter R
G=1
Only the electronic circuit frequency spectrum (filter) limits the thermal noise power available on circuit output
Circuit Bandwidth P h

12. Noise in Electronic Systems
THERMAL NOISE R
The conductor noise power is the same as the power available from the following circuit : R *
Et is an ideal voltage source
R is a noiseless resistance
<v>
gnd

13. Noise in Electronic Systems
THERMAL NOISE R *
RL=h
gnd
The thermal noise is always present. It can be expressed as a voltage fluctuation or a current fluctuation, depending on the load impedance. R *
RL=0
gnd

14. Noise in Electronic Systems
Some examples :
Thermal noise in resistor in “series” with the signal path :
For R=100 ohms
For 10KHz-100MHz bandwidth :
Rem : 0-100MHz bandwidth gives :
For R=1 Mohms
For 10KHz-100MHz bandwidth :
As a reference of signal amplitude, consider the mean peak charge deposited on 300um Silicon detector : electrons, ie ~4fC. If this charge was deposited instantaneously on the detector capacitance (10pF), the signal voltage is Q/C= 400mV

15. 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

16. 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 <i2> is proportional to the noise bandwidth.
The shot noise power spectrum is flat over all frequency range
(“white noise”) P h

17. Noise in Electronic Systems
Shot Noise in a Bipolar (Junction) Transistor Ic
Vbe
The current carriers in bipolar transistor are crossing a semiconductor barrier  therefore the device exhibits shot noise as :
The junction transistor behaves like a current generator, controlled by the base voltage. The ratio (transconductance) is : or

18. Noise in Electronic Systems
1/f Noise
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)
1/f noise
Circuit bandwidth
Thermal noise
Depending on circuit bandwidth, 1/f noise may or may not be contributing

20. 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

21. Noise in Detector Front-Ends
Circuit Rp
Circuit equivalent voltage noise source
Ideal charge generator
Detector
gnd
Passive & active components, all noise sources en
A capacitor (not a noise source)
noiseless in Rp
gnd
Circuit equivalent current noise source

22. Noise in Detector Front-Ends
gnd
Noiseless circuit en in Av Rp
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

23. Noise in Detector Front-Ends
In case of an (ideal) detector, the input is loaded by the detector capacitance C
Detector
gnd
Noiseless circuit en
iTOT Av Cd
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)

24. Noise in Detector Front-Ends
gnd
Noiseless circuit en
iTOT Av Cd
input
The detector signal is a charge Qs. The voltage noise <einput> 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 <en>2 and of the total “parallel” input current noise <iTOT>2
There are dependencies on C and on

25. Noise in Detector Front-Ends
gnd en
iTOT Av Cd
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.

26. 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
gnd
Eq. Charge noise at input node per hertz
Gp is a normalization factor (peak voltage at the output for 1 electron charge)

27. Noise in Detector Front-Ends
gnd
Noiseless circuit en
iTOT Av Cd
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
Input node
Active input device
The <iTOT> contribution is only due to the detector bias resistor Rp
Rp (detector bias)

28. Noise in Detector Front-Endsgm Rp
Input signal node Cd
gnd
Av (voltage gain) of charge integrator followed by a CR-RCn shaper :
t~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
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

30. Noise in Detector Front-Ends
Fp, Fs factors depend on the CR-RC shaper order n
1.27
1.16
1.11
0.99
0.95
0.84
0.92 Fs 7 6 5 4 3 2 1 n
0.34
0.36
0.40
0.45
0.51
0.63
0.92 Fp 7 6 5 4 3 2 1 n
CR-RC2
CR-RC
CR-RC3
CR-RC6

31. Noise in Detector Front-Ends
“Series” noise slope
“Parallel” noise
(no C dependence)
ENC dependence to the detector capacitance

32. 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
(C=10pF, gm=10mS, R=100Kohms)

33. Noise in Detector Front-Ends
Example:
Dependence of optimum shaping time to the detector capacitance
C=15pF
C=10pF
C=5pF
Shaping time (ns)
ENC dependence to the shaping time

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)

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 :
Series noise
Parallel noise

37. 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

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
Detector
gnd en
iTOT
W(t) Cd
Example :
Ileak Rp

40. Noise Analysis in Time Domain
Detector
gnd en
iTOT
W(t) Cd
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 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

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
switch
Example : Gated integrator C
TM-TG TG TM
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
Practically, rise and fall time are limited. They are in fact limited on purpose to predict and optimize the total ENC

43. Noise in Analysis Time Domain
Example : Trapezoidal Weighting Function T2 T1 T1
The formulation can be compared to
Obtained in case of a continuous time CR-RC quasi-Gaussian filter with t 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 (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)

45. CERN Technical Training 2005
ELEC-2005 Electronics in High Energy Physics Winter Term: Introduction to electronics in HEP
ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS
PART 2
Francis ANGHINOLFI
January 20, 2005