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New England Particle Physics Student Retreat (NEPPSR)

Front End Electronics for Particle DetectionCase study : ATLAS Muon Spectrometer

August 20, 2003John Oliver

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

DisclaimerThis 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 don’t need to memorize this stuff!!

HomeworkThere will be numerous examples given as homework. Go as far with them as you can. We’ll 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)

Vhv

(1 kV)

D(10 mm)

Anode Cathode

x

Q

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

sV

metEvElectrons eee

2

4.0:

sV

metEvionsPositive ionionion

2

5106:

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

A

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• Electrons drift to Anode, ions to Cathode• First the electrons…

In time t, electrons move distance Evwheretvx edriftdrift

through potential tvEV drift

tEvQVQW drift Work done by field is

ttiVW hv )(Work done by battery is

In general hv

drift

V

EvQti

)(

Total signal charge collected in arbitrary time t,

hvV

tVQtq

)()(

-------------------- (1)

-------------------- (2)

constD

vQti drift )(In this example -------------------- (1b)

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Example :

• Q = 1fc , x = 2 mm electron signal current i(t) = 4 nA velocity = E =4*10^4 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, Q*200V/1kV)

Homework : Liquid argon ionization chamber (or calorimeter)• Liquid argon filled gap, horizontal track• e = 0.01 met^2/(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

i(t)

t 50 ns

4 nA

Vhv

(5 kV)

10 mm

What happened to the rest of the ionization charge?

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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 surface[1]• Each primary electron liberates Qtot ~ 2e4 secondary electrons• Must analyze both electron and ion signal response to single primary electron

• Wire radius : r0=25 microns• Tube radius : R= 15 mm• Gas : Ar/C02 (93%/7%)• Vhv = 3080 Volts• Gas gain: G = 2e4• ion = 6e-5 m^2/V-s• e = 0.4 m^2/V-s

Electron signal

• Charge centroid very close to wire short collection time , < 1 ns• i(t)=qelectron * (t)• qelectron= Qtot* V/Vhv =Qtot * (~10V/3080V) ~ (1/3 % ) Qto t~ 130 e

)/ln(

1)(

0rR

V

rrE hv -------------------- (3)

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Ion signal

• Ion velocity

where t0 is a constant of integration given by,

)/ln()())(()(

0rRtr

VtrE

dt

drtv hvion

ion

-------------------- (4)

nsV

rRrt

hvion

11)/ln(

2

1 02

00

-------------------- (6)

• From (1)

hvion V

trEQti

))(()(

2

0

02

02

0

1

)]/[ln()(

tt

t

rrR

VQti hvion

-------------------- (7a)

• Simple diff-e in can be integrated to give r(t)

0

020

2 )()(t

tttrtr

-------------------- (5)

and integrated signal charge :

)ln()/ln(

1)(

0

0

0 t

tt

rRQtqion

-------------------- (7b)

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Pulse properties

• Initial current

nAr

Qi iontot 23

2

1)0(

20

-------------------- (8)

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

msr

RtT 4

2

00max

-------------------- (9)

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

%5)/ln(

)2ln(

2

1

0

rRQ

q

tot

ion -------------------- (10)

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

ion pulse shape

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 20 40 60 80 100

tim e (ns)

no

rmal

ized

cu

rren

t

HW: Go through this analysis to make sure you understand it. It will come in handy some day!

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Basic electronic components & noise sourcesPart – 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 sjj2f

0)()( dtetfsF st

)(tf

dt

tdf )()(sFs

)( Ttf )(sFe sT

t-domain s-domain

definition

time derivative

delay

Delta function

Unit step

exponential

unipolar pulse

bipolar pulse

Tte /

1Ts

T

TteT

t

T

t /)2

1(

3

2

)1(

Ts

Ts

TteT

t / 2)1( Ts

T

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

)(t 1

)(tus

1

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Basic electronic components and noise sourcesPart -II

• Inductor Stores energy in magnetic field E = ½ L i2

Impedance Z(s)= sL Lossless, noiseless

• CapacitorStores energy in electric fieldE = 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 :

1v

and a constraint between voltage and current :

impedancesticcharacteriZI

V0

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).

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• Resistor Electric field pushes conduction electrons through a lattice Dissipates power = I*V Conduction electrons (generally) in thermal equilibrium with environment Noisy Noise characterized by “noise power density” p(f) [watts/hz]

dfftofrangefrequencyinradiatedwattspowerdffp )()(

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

RfifpR

fefp n

n )()()(

)( 22

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

244

22)(

2)(2 nrightnleftn

tot

iiii

in in

½

½

Length L, total time L/v, Impedance Z0

Z0 Z0

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

fc

LR

ifEnergy

cable

n 2

2

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

fc

Ln

cable

2

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

nTkfEnergy

fc

LTkf

c

LR

i

cablecable

n

2

2

2

from which we get

RTke

R

Tki

n

n

4

&

4

}Independent of frequency “white” noise

---------------------------- (11)

• In frequency band f , number of modes is

Ln 2

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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)

H(s)G(s) G(s)H(s)

Simple example

Find step response of simple low-pass filter

C

R

V1 V2

Cs1

CRTwhereTs

Ts

CsR

RsH

11

)(

ssV

1)(1

TtetvTs

TsV /

22 )(1

)(

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

o calibration pulses injected into drift tubeso real ion-tail pulses in chambers

Basic electronic components and noise sourcesPart III : General circuit analysis primer

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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

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

o calibration pulses injected into drift tubeso real ion-tail pulses in chambers

Basic electronic components and noise sourcesPart III : General circuit analysis primer

t

out dthgtV0

)()()(

• Simulation (SPICE)

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General circuit analysis - Homework

An ideal integrator is followed by a 2-pole “RC-CR shaper” as follows

dttf )( 1x1x)(tf

C

C

R

R

2)1( Ts

Ts

s

1

)15( nsCRT

• 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 partc) Replace ideal integrator (1/s) with “leaky” integrator, 1/(sT+1) with T=15ns

• Same questions as (a) and (b)

Unity gain buffers

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Part-IV : Noise calculations

Example # 1

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

Solution1) Add noise current source,

2) Solve for circuit “transfer function” This gives you output voltage density

in

vrms

R C = 1 pf

CRs

R

i

sv

n

n

1

)(

• set s = jjf3) Integrate over frequencies (quadrature)

dCR

R

R

Tkdffvv nrms

0 0 222

222

)1(2

14|)(|

RCxwheredxxC

Tkvrms

0 22

)1(

1

2

14

• In general, such integrals can either be looked up or done by contour integration.

0 2 22

2

2

1

))((

1

2

1

)1(

1 i

i

ixixdx

x

R

kTin

4

10k

(16)

C

kTVrms

• 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?

• In this case,

• At room temperature kT ~ 4e-21 VVrms 63

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

Vin

ADC

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CMOS components : Field effect transistors (nfets)

p substrate (~ 10k/sq)

• 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

n+ n+

Dielectric “gate oxide”: Si02

n+ source and drain implants

Conductive gate electrode

gatesource

drain

• With Vgate = 0, structure is non-conductive (back to back diodes)• Increasing Vgate in positive direction, attracts electrons from substrate• When Vgate > 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)

p substrate (~ 10k/sq)

• 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

n+ n+

Dielectric “gate oxide”: Si02

n+ source and drain implants

Conductive (polysilicon) gate electrode

gatesource

drain

• With Vgate = 0, structure is non-conductive (back to back diodes)• Increasing Vgate in positive direction, attracts electrons from substrate• When Vgate > 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

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CMOS components : Field effect transistors pfets

p substrate (~ 10k/sq)

n+ n+

gatesource

drain

n well

p+ p+

gatesource

drain

• 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)

nfet

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Idrain vs Vds for severalvalues of Vgs

00.20.40.60.8

11.21.4

0 0.5 1 1.5 2 2.5

Vds

Idra

in

Linear, resistor, or triode region

“Saturation” region

2)( thgsd VVI

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

2)( thgsd VVI

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

FET properties (simplified model)

• Definition: “Transconductance” = ratio of change in drain current per unit change in gate voltage.

L

WKI

V

Ig nd

gs

dm

2

2/100:"" VAKvalueTypical n

---------------------------- (14)

2)(2

1thgsnd VV

L

WKI ---------------------------- (13)

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FET properties (con’t)

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, what’s the change in drain current? Ans: no (or very little) change so

d

dsdrain I

VZ

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

md

ss gI

VZ

1

Typical numbers depending on application;

1001

01.001.

source

m

Zk

or

g

Example; Idrain = 1 ma, L=0.5u, W=100u

160

103.6200)10100()10(22 363

s

ndm

Zor

L

WKIg

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Some common FET circuits

d

s

g

A) Source follower

Vin

VoutUsed as (almost) unity gain buffer.Hi-Z in, Lo-Z out.

B) Common source amplifier

d

s

gVin

Vout

Rloadm RgGain

C) Current mirror

d

s

gd

s

g

Iin Iout

inout II

d

s

gd

s

g

D) Differential amplifier

inmout VgI

1gainVoltage

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Some common FET circuits – con’t

d

s

g

F) Common gate or “cascode”

Iin

Used as current buffer.Lo-Z in, Hi-Z out.

1gainCurrent

Iout

E) Fancier differential amplifier

d

s

gd

s

g

Z2

Z1

• “Boxes” Z1 & Z2 can be whatever you need• example:

• Z1 is parallel RC

• Z2 is series RC

• Transfer function is

22

1

)1()(

)()(

sRC

sRC

sZ

sZsH

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

meffective

n gTkR

Tki

4

4

• 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)

mn gTki 3

8

d

s

gVin

Vout

R

inen

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

mn g

Tke

3

8---------------------------- (15)

m

nn g

ie

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Noise in Fets

HW• What is the noise voltage density (nV/sqrt(Hz)) of a 100 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?

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Front end amplifiers (eg ATLAS MDT)

d

s

gVin

Cstray1x

• “Open loop” gain

stray

m

Cs

gsG

)(

• ExampleCstray = 500ffGm = 0.006

• What is “unity gain frequency”?

|G(f)|

f

GHzC

gf

stray

mt

2

2

• What’s the gain at 1 Hz?

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Front end amplifiers (eg ATLAS MDT)

d

s

gVin

Cstray1x

• “Open loop” gain

stray

m

Cs

gsG

)(

GHzC

gf

stray

mt

2

2

• What’s the gain at 1 Hz? • Answer: 2x10^9 !!!! • This can’t 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

• ExampleCstray = 500ffGm = 0.006

• What is “unity gain frequency”?

|G(f)|

f

<100

Ts

G

RCs

Rg

RCs

gsG

stray

m

stray

m

11/1

)( 0

0

0

0

R0

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Front end amplifiers (eg ATLAS MDT)

To make this a practical amplifier use feedback

G(s)

Rf=15k

Cf=1pf

• 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

•We’d like it to be real or resistive (alternatives are capacitive or inductive) low ( a hundred or so) as constant over frequency as possible

• HW Questions: o Why the above criteria? o 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?

Gain

ZZ feedback

in

“Transimpedance” amplifier

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Front end amplifiers (con’t)

Rterm=390

Now attach this to an ATLAS Muon tube

and add a shaperQuestion : Why do we need the terminating resistor?

)1( Ts

T

For extra credit (LOTs of extra credit!)• What’s 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? (Don’t 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:

rmselectronsTR

kTeenc peak

term

000,52

1

peakTCRT

Hint: For the purposes of this exercise, you can assume input impedance of amplifier is zero.

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MDT-ASD topology

Transimpedance preamps

1 of 8 channels

Signal

Dummy

Bipolarshaper

(delta response) Discriminator

WilkinsonADC C

ontr

ol lo

gic

LVDS

Serial string register

CalibrationDACs Mode Deadtime

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MDT-ASD topology

M1

M3

M4

Vdd

IN

OUT

M2

R2C

fVb1

Vb2

Vb3

Vb4

R1

Transimpedance Preamplifier

Detailed circuit descriptions can be found in the following documents• ATLAS-MUON-2002-003http://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-96-127http://doc.cern.ch/cgi-bin/extractFigs.check.sh?check=/archive/electronic/cern/others/atlnot/Note/muon/muon-96-127.ps.gz

Vb[1:4] are bias voltages supplied from elsewhere

Common source amplifier

Source follower

Current sink (half of a current mirror)

Two transistor current source (Better than single fet current version)

Feedback R & C

Extra conductance on Hi-Z node to tailor gain vs frequency, & Zin

Common gate “cascode”

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MDT-ASD preamplayout

180u

300u

(33)

MDT-ASD topology

Z1(s)

Z2(s)

M1

M2

M3a

M4

M5

Vdd

GND

INa INb

OUTb OUTa

Vb1

Vb2

M5a

M4a

M3

M2a

M1a

RVref

M5b

M4b

M3b

M2b

M1b

Bias network

M1c

M2c

Shaper differential amplifiers

“Fancy” differential amplifier(pg 23)

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MDT-ASD topology

Shaper differential amplifiers

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Summary & conclusions

Analysis/design methodology1. Understand requirements

• Noise, dynamic range,..• Impedances• Signal shapes• etc

2. 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

3. SPICE modelling• Vendor SPICE models can be very accurate but very complicated• Produce best analysis at expense of intuitive understanding

To learn moreAttend IEEE Nuclear Science Symposia and take “Short course” programs in

Front End Electronics (IEEE NSS 2003 Portland, Oregon, Oct 19-25)

Bibliography & lending library1) “Particle Detection with Drift Chambers” W.Blum, L. Rolandi Springer Verlag, pg 134, 155-1582) “Tables of Laplace Transforms” Oberhettinger & Badii, Springer Verlag3) “Complex Variables and Laplace Transform for Engineers” LePage, Dover4) “Electronics for the Physicist” Delaney, Halsted Press5) “Noise in Electronic Devices and Systems” Buckingham, Halsted Press6) “Low-Noise Electronic Design” Motchenbacher & Fitchen, Wiley Interscience7) “Processing the signals from solid state detectors” Gatti & Manfredi, Nuovo Cimento8) “Analog MOS Integrated Circuits for Signal Processing” Gregorian & Temes, Wiley Interscience9) “Detector Physics of the ATLAS Precision Muon Chambers” Viehhauser, PhD thesis, Technical

University Vienna.10) “MDT Performance in a High Rate Background Environment” Aleksa, Deile, Hessey, Riegler –

ATLAS internal note, 1998