New England Particle Physics Student Retreat (NEPPSR)

1
New England Particle Physics Student Retreat
(NEPPSR)
Front End Electronics for Particle Detection Case
study ATLAS Muon Spectrometer August 20,
2003 John Oliver

• Signal formation in gas detectors
• Basic electronic components noise sources
• Noise calculations
• Amplifier/Shaper/Discriminators (ASDs) for ATLAS
  Muon Spectrometer

Disclaimer This will be a fairly analytical
approach. The idea is to develop a tool-box of
methods you will need to analyze similar
applications. If you find the need, you can
explore any of these subjects in more detail
later. You dont need to memorize this stuff!!
Homework There will be numerous examples given as
homework. Go as far with them as you can. Well
go over the solutions Wednesday/Thursday evening.
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Signal formation in gas detectors
Simple example Uniform electric field in drift
gas (eg Ar/CO2)
A

• Electric field ? E 1e 5 Volts/meter
• Particle track ionizes N electron/ion(Ar) pairs
  with total charge Ne Q
• Electrons/ions drift toward Anode/Cathode with
  velocity given by their mobilities

• Question What signal current i(t) is seen by
  ideal ammeter in series with battery ?

3

• Electrons drift to Anode, ions to Cathode
• First the electrons
• In time Dt, electrons move distance

through potential
Work done by field is
Work done by battery is
In general ?
-------------------- (1)
In this example ?
-------------------- (1b)
Total signal charge collected in arbitrary time t,
-------------------- (2)
4

• Example
• Q 1fc , x 2 mm
• electron signal current i(t) 4 nA
• velocity mE 4104 met/sec
• time to hit anode 50 ns
• total electron signal charge collected in 50 ns
• q 4 nA 50 ns 0.2 fc ( from eq 2, ?
  Q200V/1kV)

• What happened to the rest of the ionization
  charge?

• Homework Liquid argon ionization chamber (or
  calorimeter)
• Liquid argon filled gap, horizontal track
• me 0.01 met2/(V-s) (neglect ion drift)
• Ionization density 7000 electron-ion pairs per
  mm of track (MIP)
• Vhv 5kV
• ? Find signal current i(t)
• ? Total signal charge

5
Signals in circular drift tube (ATLAS Muon
Spectrometer)

• Electric field ?
• Primary electrons drift to Anode wire
• High field at wire surface ( 2e7 V/m) causes
  avalanche centered very close to wire,
  typically 10V from wire surface1
• Each primary electron liberates Qtot 2e4
  secondary electrons
• Must analyze both electron and ion signal
  response to single primary electron

• Electron signal
• Charge centroid very close to wire ? short
  collection time , lt 1 ns
• i(t)qelectron d(t)
• qelectron Qtot DV/Vhv Qtot (10V/3080V)
  (1/3 ) Qto t 130 e

6

• Ion signal
• Ion velocity

where t0 is a constant of integration given by,
and integrated signal charge
-------------------- (7b)
7

• Pulse properties
• Initial current

• Extremely long pulse. (See eq 5) Pulse
  terminates when ions arrive at cathode at time

• Question What proportion of charge is collected
  in time t0 (11ns) ?

• Conclusions
• Ion charge is not much but its a lot more then
  the electron signal charge. For ATLAS MDT its
  about 1000 electrons for each primary electron.
• Electron charge can generally be neglected in
  simulations calculations

HW Go through this analysis to make sure you
understand it. It will come in handy some day!
8
Basic electronic components noise sources Part
I Mathematical note

• Circuit analysis is almost always done by means
  of Laplace (not Fourier) transforms
• More convenient than Fourier when
• circuit is considered quiescent before t 0
• stimulus occurs after t 0
• Steady state (fixed frequency) response is
  obtained by s?jwj2pf

• Universal method of inverting Laplace transforms
• Look them up in a table or use Maple or
  Mathematica

9
Basic electronic components and noise
sources Part -II

• Inductor
• Stores energy in magnetic field
• E ½ L i2
• Impedance Z(s) sL
• Lossless, noiseless
• Capacitor
• Stores energy in electric field
• E ½ C v2
• Impedance Z(s) 1/(sC)
• Lossless, noiseless
• Ideal transmission line
• Considered infinite sequence of series inductors
  parallel capacitors

• Results in wave equation with phase velocity

• and a constraint between voltage and current

• noiseless
• Note that an infinitely long transmission line
  is indistinguishable from a resistor of value Z0
• As corollary, a finite line with a resistor of
  value Z0 at its end, is also indistinguishable
  from a resistor of value Z0.
• In other words, if you launch a pulse into a
  terminated line, it never comes back (no
  reflection).

10

• Resistor
• Electric field pushes conduction electrons
  through a lattice
• Dissipates power IV
• Conduction electrons (generally) in thermal
  equilibrium with environment
• Noisy ? Noise characterized by noise power
  density p(f) watts/hz

• p(f) is frequently expressed as a voltage (in
  series) or current density (in parallel)

• en(f) in(f) given in volts/sqrt(hz)
  amps/sqrt(hz)
• To get values of en(f) in(f) Nyquist, Phys
  Rev, Vol 32, 1928, p. 110

Total noise current in cable
11

• Disconnect resistors trapping noise power in
  cable
• Total energy in cable, in frequency band Df is

• Open circuit cable requires current at ends to
  be zero, and voltage at ends to be nodes
• Standing waves (integer number of half-waves)

• In frequency band Df , number of modes is

• Energy equipartition requires that each mode
  (one for voltage, one for current) corresponds to
  energy kT/2

?
from which we get

---------------------------- (11)
Independent of frequency ? white noise
12
Basic electronic components and noise
sources Part III General circuit analysis
primer

• Objective
• To find response of arbitrary circuits to
  arbitrary stimulus in both time and frequency
  domains.
• Use this to get expected response from MDT
  Amp/Shaper to
• calibration pulses injected into drift tubes
• real ion-tail pulses in chambers

• Method - A
• Define ratio of output variable to input
  variable Transfer function H(s)
• Write node and loop equations and solve for
  transfer function
• Delta function response of circuit is just h(t),
  the inverse transform of H(s)
• To get response to other inputs g(t)
• Get transform of g(t) ? G(s)
• Transform of response is ? F(s)G(s)H(s)
• Invert to get f(t)

Simple example Find step response of simple
low-pass filter
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Basic electronic components and noise
sources Part III General circuit analysis
primer

• Objective
• To find response of arbitrary circuits to
  arbitrary stimulus in both time and frequency
  domains.
• Use this to get expected response from MDT
  Amp/Shaper to
• calibration pulses injected into drift tubes
• real ion-tail pulses in chambers

• Method B
• What if method A fails? ? ie the transforms or
  inverse transforms cannot be found in closed form
• Resort to the time domain solution ? Convolution
  integral and use numerical solution if necessary

• Simulation (SPICE)

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General circuit analysis - Homework
An ideal integrator is followed by a 2-pole
RC-CR shaper as follows
Unity gain buffers
C
R
1x
1x
R
C

• Show that transfer function of system is

• a) With delta function input, what do the signals
  look like throughout the circuit?
• b) Is this circuit suitable for use in high
  rate (eg LHC/ATLAS) environment?
• Extra credit part
• c) Replace ideal integrator (1/s) with leaky
  integrator, 1/(sT1) with T15ns
• Same questions as (a) and (b)

15
Part-IV Noise calculations

• Example 1
• What is the rms terminal voltage of the
  following simple circuit?

10k

• Solution
• Add noise current source,
• Solve for circuit transfer function? This
  gives you output voltage density

• set s jw2pjf
• Integrate over frequencies (quadrature)

16

• In this case,

---------------------------- (12)

• Called kT over C noise, or kTC noise (when
  dealing with charge instead of voltage).
• Example (Homework)
• Suppose we want to use an array of 100
  femtofarad capacitors to build an integrated
  voltage waveform recorder in a 3.3Volt CMOS
  process.
• Note that the switches are CMOS devices and
  are actually voltage controlled resistors which
  switch between some finite resistance in the On
  state to near infinite resistance in the Off
  state

• Assume maximum signal swing inside the circuit
  is limited to about half the supply voltage, or
  1.6 volts
• What is the maximum possible dynamic range (in
  bits) of this device? (Dynamic range is max
  signal divided by rms noise).
• If we plan to digitize this signal, should we
  pay more money for a 16 bit ADC, or will a 14-bit
  ADC do the job?

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CMOS components Field effect transistors (nfets)

• In undoped (intrinsic) silicon, electron and
  hole densities are the same
• n-doped (arsenic, phosphorous, antimony,..)
  electron density increases, hole density
  decreases
• p-doped (boron, aluminum, gallium, ..)
  vice-versa
• Strength of doping denoted by sign ? n, n,
  p, p
• sign indicates higher doping, lower resistivity

Conductive gate electrode
Dielectric gate oxide Si02
n source and drain implants
p substrate ( 10kW/sq)

• With Vgate 0, structure is non-conductive
  (back to back diodes)
• Increasing Vgate in positive direction, attracts
  electrons from substrate
• When Vgate gt Vthreshold, channel becomes
  conductive. Conductance increases as Vgate
  increases.
• As Vdrain is made more positive than Vsource,
  current starts to flow
• Voltage gradient appears from drain to source.
• Electric field is strongest near source, weakest
  near drain..

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CMOS components Field effect transistors (nfets)

• In undoped (intrinsic) silicon, electron and
  hole densities are the same
• n-doped (arsenic, phosphorous, antimony,..)
  electron density increases, hole density
  decreases
• p-doped (boron, aluminum, gallium, ..)
  vice-versa
• Strength of doping denoted by sign ? n, n,
  p, p
• sign indicates higher doping, lower resistivity

Conductive (polysilicon) gate electrode
Dielectric gate oxide Si02
n source and drain implants
gate
source
drain
p substrate ( 10kW/sq)

• With Vgate 0, structure is non-conductive
  (back to back diodes)
• Increasing Vgate in positive direction, attracts
  electrons from substrate
• When Vgate gt Vthreshold, channel becomes
  conductive. Conductance increases as Vgate
  increases.
• As Vdrain is made more positive than Vsource,
  current starts to flow
• Voltage gradient appears from drain to source.
• Electric field is strongest near source, weakest
  near drain.
• Channel charge density tilts toward source.
• Drain current increases with Vdrain
• When Vdrain comes within a threshold voltage
  of Vgate, (Vdrain Vgate Vthreshold) current
  saturates
• Saturation region also called pinch-off

19
CMOS components Field effect transistors pfets
nfet
gate
source
drain
p substrate ( 10kW/sq)
n well

• Generally, pfet drain current constant, Kp, is
  about 1/3 that of nfets due to lower hole
  mobility
• For same size transistor at same current, pfet
  transconductance is smaller by sqrt(3)

20
FET properties (simplified model)
Linear, resistor, or triode region
Saturation region

• Drain current properties in saturation region
• Id increases quadradically with Vgs

• Increases linearly with transistor channel
  width, W
• Decreases linearly with transistor gate length, L

• Increases linearly with transistor channel
  width, W
• Decreases linearly with transistor gate length, L

• Definition Transconductance ratio of change
  in drain current per unit change in gate voltage.
  

---------------------------- (14)
21
FET properties (cont)

• Terminal impedances
• Gate No dc current flow, just gate capacitance
  Cgate (of order tens of femtofarads to pf)
• Drain
• Wiggle the drain voltage a little, whats the
  change in drain current?
• Ans no (or very little) change so ?

• Source
• Wiggle the source voltage a little bit.
• This changes Vgs and thus drain current (and
  source current) by (Vgs) x (gm).

• Typical numbers depending on application

• Example
• Idrain 1 ma, L0.5u, W100u

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Some common FET circuits
23
Some common FET circuits cont
E) Fancier differential amplifier

• Boxes Z1 Z2 can be whatever you need
• example
• Z1 is parallel RC
• Z2 is series RC
• Transfer function is

? Implements a Bipolar shaping function (See
table of Laplace transforms)
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Noise in Fets

• Fet channel is resistive and will thus have a
  thermal noise current component, in

• Channel is not a single resistor, but rather a
  series of increasing resistances (from source to
  drain)
• A fudge factor will be needed! (ff 2/3)

en

• Noise current in drain is equivalent to noise
  voltage in gate with

---------------------------- (15)
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Noise in Fets

• HW
• What is the noise voltage density (nV/sqrt(Hz))
  of a 100W resistor?
• How much transconductance is required of a fet
  to have this same noise voltage density ?
• Assuming we have a power budget of 1 ma (drain
  current) for this transistor and that the
  transistor has minimum allowed gate length of L
  0.5 microns, how wide (W) does the transistor
  have to be?
• How much improvement in en do we get by doubling
  the drain current? or the transistor width?

26
Front end amplifiers (eg ATLAS MDT)

• Open loop gain

• Example
• Cstray 500ff
• Gm 0.006
• What is unity gain frequency?

G(f)
f

• Whats the gain at 1 Hz?

27
Front end amplifiers (eg ATLAS MDT)

• Open loop gain

R0

• Whats the gain at 1 Hz?
• Answer 2x109 !!!!
• This cant be right! Actually, gain rarely
  exceeds 100.Why is this?
• Ans Output (drain) impedance of fet is not
  actually infinite same thing for current source

28
Front end amplifiers (eg ATLAS MDT)
To make this a practical amplifier ? use feedback
Transimpedance amplifier

• For high rate environment we want RC to be small
  15 ns is optimal for MDTs (electronics
  chamber simulations)
• Important question is input impedance. In
  general, it is given by

• Wed like it to be
• real or resistive (alternatives are capacitive
  or inductive)
• low ( a hundred W or so)
• as constant over frequency as possible
• HW Questions
• Why the above criteria?
• How might you go about assuring this?
• Second important concept is Sensitivity or
  Peak voltage output per unit charge input
  (typically in mv/fc)
• HW Question What is the Sensitivity (in mv/fc)
  of the above circuit?

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Front end amplifiers (cont)
Now attach this to an ATLAS Muon tube
and add a shaper Question Why do we need the
terminating resistor?

• For extra credit (LOTs of extra credit!)
• Whats the delta function response at preamp
  output, shaper output?
• Characterize system gain in peak shaper signal
  output per unit charge input. (volts/coul or
  mv/fc)
• How might you get the response to the actual
  ion signal from the gas tube? (Dont actually do
  it!)
• What is the rms noise voltage at the shaper
  output produced by the terminating resistor?
• How much charge is this equivalent to
  (equivalent noise charge, or enc)?
• Ans

Hint For the purposes of this exercise, you can
assume input impedance of amplifier is zero.
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MDT-ASD topology
1 of 8 channels
Transimpedance preamps
Signal
Discriminator
(delta response)
Bipolar shaper
LVDS
Dummy
Control logic
Wilkinson ADC
Calibration
DACs
Mode
Deadtime
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MDT-ASD topology
Two transistor current source (Better than single
fet current version)
Vb14 are bias voltages supplied from elsewhere
Source follower
Common gate cascode
Current sink (half of a current mirror)
Common source amplifier
Feedback R C

• Detailed circuit descriptions can be found in the
  following documents
• ATLAS-MUON-2002-003
• http//doc.cern.ch//archive/electronic/cern/others
  /atlnot/Note/muon/muon-2002-003.pdf
• ATLAS-MUON-080
• http//doc.cern.ch/tmp/convert_muon-95-080.pdf
• muon-96-127
• http//doc.cern.ch/cgi-bin/extractFigs.check.sh?ch
  eck/archive/electronic/cern/others/atlnot/Note/mu
  on/muon-96-127.ps.gz

Extra conductance on Hi-Z node to tailor gain vs
frequency, Zin
32
MDT-ASD preamp layout
180u
300u
33
MDT-ASD topology
Shaper differential amplifiers
Vdd
Vref
M5
M5a
M5b
Vb2
M4a
M4
M4b
OUTb
R
OUTa
Z1(s)
M3a
INa
INb
M3
M3b
Z2(s)
M2b
M2c
Vb1
M2a
M2
Fancy differential amplifier (pg 23)
M1
M1a
M1b
M1c
GND
Bias network
34
MDT-ASD topology
Shaper differential amplifiers
35
Summary conclusions

• Analysis/design methodology
• Understand requirements
• Noise, dynamic range,..
• Impedances
• Signal shapes
• etc
• Hand calculations will get you close and/or
  guide design
• Noise contributions of worst offenders
• Transfer functions, response shapes, etc
• Transistor sizing for CMOS circuits
• SPICE modelling
• Vendor SPICE models can be very accurate but
  very complicated
• Produce best analysis at expense of intuitive
  understanding
• To learn more
• Attend IEEE Nuclear Science Symposia and take
  Short course programs in Front End Electronics
  (IEEE NSS 2003 Portland, Oregon, Oct 19-25)

• Bibliography lending library
• Particle Detection with Drift Chambers W.Blum,
  L. Rolandi Springer Verlag, pg 134, 155-158
• Tables of Laplace Transforms Oberhettinger
  Badii, Springer Verlag
• Complex Variables and Laplace Transform for
  Engineers LePage, Dover
• Electronics for the Physicist Delaney, Halsted
  Press
• Noise in Electronic Devices and Systems
  Buckingham, Halsted Press
• Low-Noise Electronic Design Motchenbacher
  Fitchen, Wiley Interscience
• Processing the signals from solid state
  detectors Gatti Manfredi, Nuovo Cimento
• Analog MOS Integrated Circuits for Signal
  Processing Gregorian Temes, Wiley Interscience
• Detector Physics of the ATLAS Precision Muon
  Chambers Viehhauser, PhD thesis, Technical
  University Vienna.
• MDT Performance in a High Rate Background
  Environment Aleksa, Deile, Hessey, Riegler
  ATLAS internal note, 1998