Using delay lines on a test station for the

Muon ChambersDesign considerations

(A. F. Barbosa, Jul/2003)

Outline

Simple model for the signal time development The delay line method Application to the muon chamber Simulation results Outlook

Simple electrostatic model

In the neighborhood of a wire in a MWPC, the electrostatic field is not very different from the ‘co-axial’ cable case

This is particularly true if ‘s’ is comparable to ‘d’ and both >> wire radius

s

d

The cylindrical geometry(co-axial cable)

The electrostatic field for a wire centered inside a cylindrical surface is well known:

rCV

o

orE 2)( rbCV

o

orV ln)( 2 ab

oCln

2

C = capacitance per unit lengthb = cylinder radiusa = wire radiusr = radial distance

ba < r < b

Particle detection and signal development

Particles interacting with the dielectric (gas molecules) generate ion pairs (e- and ion+) inside the detector volume

The charged particles released in the interactions drift to the corresponding electrodes

Close to the wire surface, the electric field is high enough to accelerate electrons and produce avalanche amplification

We assume that the avalanche charge is ‘point-like’ in order to derive an analytical signal shape

The electric signal Energy conservation allows us to obtain the analytical expression:

Energy acquired by a charged particle while moving in the electrostatic field

Energy lost by the electrostatic field

=

xdEqx

x

.2

1

= 2

1

2

1

u

u

o

u

u

duCVduQ

q = charged released in the avalancheQ = electrodes charge

Signal amplitude In the co-axial cable case, E=E(r) (one-dimensional problem)

Using the field expressions, we may compute:

arq

r

a

r

CV

o

o

o

o

o

o drCV

qqu ln )( 2

12

b

rqr

b

r

CV

o

o

o

o

o

o drCV

qqu ln )( 2

12

Cq

bbq

oququ ln- )()( 2

ln

ln

)()(

boraor

ququ

ro = 15 ma = 10 mb = 1 cm

u(-q) = 0.062 u(+q)

Signal shape (in time) Electrons contribution is negligible For the positive ions, we may assume:

dtdr

PE v

Using the expression for E(r) we find:

2 )( opCV rttr

o

o

o

oo

oo CVrP

ottq t-tu

2

; 1ln )( 2

a = 30 mb = 5 mm = 1.7 x 10-4

Vo = 3000 VP = 1 atm

to =4.5 ns (ro = 60 m)3.125 ns (ro = 50 m)2 ns (ro = 40 m)

Equivalent circuit The detector signal is read necessarily by an electronic circuit The equivalent circuit may be seen as a voltage differentiator or charge

integrator

u(t)

Electronics

Detector

u(t)

Thevenin Equivalent

Out(t)

i(t)

Norton Equivalent

Out(t)

Output signal For the Thevenin equivalent circuit, the transfer function is:

RCiRCi

VV

in

outT

1)(

)( )(

From this we may compute:

RCt-

out u(t)e τ)dτu(t)T(ttV )(

I(t) is the current passing through the detector capacitor:

oab tt

qdtd u(t) CI(t) 1

ln2

The analytical signal shape (RC effect)

0.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6

0.00

0.02

0.04

0.06

0.08

0.10

t0 = 8ns

a = 30 mb = 5 mmr0 = 40 m

V0 = 3000 V

Cathode voltage signal [u(t)]

Ampl

itude

[V]

Time [s]

0.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6

0.00

0.02

0.04

0.06

0.08

t0 = 8ns

a = 30 mb = 5 mmr0 = 40 m

V0 = 3000 V

RC = 10 nsRC = 100 ns

RC = 1 s

RC = Infinite

V out

(t) [

V]Time [s]

The true signal The avalanche may be considered ‘point-

like’ to a good approximation. However, an ionizing particle crossing the

detector leaves charge clusters along its track

E.g.: one M.I.P., in 1cm of Ar/C02 around 40 clusters ( 2 e-/cluster) in one gap (5 mm) we may expect around 40 primary particles, in a rather complex time distribution

The ion mobility () is not really constant Geometry (mechanical precision) affects

the avalanche gain (…)

0.0 5.0x10-8 1.0x10-7 1.5x10-7 2.0x10-7

0.000

0.005

0.010

0.015

0.020

Three 'point-like' clusters signal(RC = 10ns)

V out

(t) [

V]

Time [s]

Finally, the time & space resolution is finite (measured: t 3-4 ns)

The Delay Line Method One delay line cell is an L-C circuit which introduces

an almost constant delay to signal propagation:

)()(

1

11

1 )()(1

2

iLCiTg

LCLCi eAeT

Vin Vout

The main parameters are the cutoff frequency (o), the delay (), and the characteristic impedance (Z)

) ... 3

311)(

o(LCoo

) 2

1

1oC

LCL (Z

o

LCo

1

Z

CL

CZL

ZLC

:yEssentiall

Discrete delay lines Delay line cells may be implemented in cascade, so that one may

associate spatial position with a time measurement

P1 P2 P3

The L-C values are chosen according to the application (bandwidth, noise, count rate, time resolution …)

Application to the Muon Chamber The pad capacitance to ground imposes

a minimum value for C The chamber intrinsic time resolution is

4ns () In order to clearly identify a pad

(separate it from its neighbor) from a time measurement, the time delay between pads should be > 5

The delay line impedance should be as high as possible (in order to have the signal amplitude well above noise)

The band-width has to be large, because very fast signals are foreseen

48.0 47.6 46.1 45.7

47.0 46.9 45.2 44.8

41.8 41.8 40.5 40.5

37.4 37.4 36.7 36.7

47.6 47.4 46.1 45.5

46.3 46.6 45.3 44.5

41.1 41.6 40.2 40.0

36.9 37.1 36.2 36.4

M2R2 pad-ground capacitance values (pF)

The chamber capacitance has to be ‘part’ of the delay line

Preliminary Design The following basic circuit could cope with the requirements:

P1 P2 Pn P31 P32

We start studying it as if the capacitances were all the same, then we compare it with the real design, which incorporates pad capacitances as part of the circuit:

P1 P2 Pn P31 P32

L = 1.6 HC = 40 pF = 8nso = 250 MHzZ = 200

L = 1.6 HC = 40 ± 6.5pF = 8 ± 0.64 ns

o = 250 ± 19 MHz

Z = 200 ± 16

Simulations We assume the detector capacitance (anode to cathode) to be 100pF SPICE is used to simulate signal propagation through the delay line The signal u(t) after traversing the whole delay line is:

0.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6

0.00

0.02

0.04

0.06

0.08

0.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6

0.00

0.02

0.04

0.06

0.08Signal through the whole delay line (96 cells)

u(t)

L = 1.6 nHC = 40 pFZ = 200 Ohm = 8 ns

Ampl

itude

[V]

Time [s]

0.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6

0.0

2.0x10-3

4.0x10-3

6.0x10-3

8.0x10-3

1.0x10-2

1.2x10-20.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6

0.0

2.0x10-3

4.0x10-3

6.0x10-3

8.0x10-3

1.0x10-2

1.2x10-2

Ampl

itude

[V]

Time [s]

Linearity One event is input at each pad, we expect to have a linearly varying time

measurement

0 5 10 15 20 25 30 35

-800-600-400-200

0200400600800

Y = A + B * XA-816B48

Start - Stop (self trigger)

Tim

e [n

s]

Pad #

0 5 10 15 20 25 30 35

0

200

400

600

800

- Constant threshold: 2mV- Simulation time bin: 1ns- Fit error << 1ns

Y = A + B * XA-22B24

Tim

e [n

s]

Start - Stop (external trigger)

Linearity Quality (an example) The simulated non-linearity is best than

what could be expected from a simple model for jitter error

The delay line method actually is known to feature excellent non linearity performance

55Fe

1D PSD

Calibration mask

(high precision)

1600 1800 2000 2200 2400 26000

2000

4000

6000

8000

10000

12000

Co

un

t

Channel

Non-linearity typically < 0.1%

Signal Distortion along the line Due to the reflection and attenuation of high frequencies ( >> o), the

signal is broadened and distorted as it travels through the circuit

0.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6

0.0

2.0x10-3

4.0x10-3

6.0x10-3

8.0x10-3

Delay: 768ns (Threshold 20 mV)

1.23 mV

Signal from the last cell

Signal from the first cell

Ampl

itude

[V]

Time [s]0.0 2.0x10-7 4.0x10-7 6.0x10-7 8.0x10-7 1.0x10-6

from pad #32

from pad #28

from pad #24

from pad #20

from pad #16

from pad #12

from pad #8

from pad #4

Time [s]

Effect of the pad capacitances The pad capacitances are introduced in the circuit, so we may evaluate the

performance

0.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6-1x10-3

0

1x10-3

2x10-3

3x10-3

4x10-3

5x10-3

6x10-3

7x10-3

8x10-3 (signals seen from cell # 1)

Delay line incorporating chamber capacitances

Delay: 730 ns (threshold 20 mV)

1.39 mV

Signal from the last pad

Signal from the first pad

Ampl

itude

[V]

Time [s]

Linearity results The errors in pad position measurement are < cell delay ()

0 5 10 15 20 25 30 35

0

200

400

600

800

Signal seen at cell # 1

Tim

e [n

s]

0 5 10 15 20 25 30 35

-8

-6

-4

-2

0

2

4

6

8

Error = Fit - Measurement (for cell # 1)

Err

or

[ns

]

0 5 10 15 20 25 30 35

0

200

400

600

800

Signal seen at cell # 97

Pad #

Tim

e [n

s]

0 5 10 15 20 25 30 35

-8

-6

-4

-2

0

2

4

6

8

Error = Fit - Measurement (for cell # 97)

Pad #

Err

or

[ns

]

Pre-amplifier A voltage pre-amplifier must be implemented as close as possible to the detector +

delay line, in order to avoid cable capacity losses and distortions The pre-amplifier circuit bandwidth must be matched to the delay line output signal

spectral composition, so that the delay line performance is preserved The following circuit is proposed (it has been separately simulated before coupling to

the delay line circuit):

22K

2K

1.8K

180

70K

10K

1.8K

180 240 50 Load

+12V

0.1F0.1F0.1F

The transistor is BFR 92:- Low noise (2.4 dB @ 500MHz, Ic=2 mA) - Wide band (fT = 5 GHz @ Ic = 14 mA)

Overall performance (pads + delay line + pre-amplifier) The introduction of the pre-amplifier stage does not bring critical

distortions to the signal shape

0.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6

0.0

5.0x10-2

1.0x10-1

1.5x10-1

2.0x10-1

Output signal (pre-amp. effective gain: 37.7)

Volts

Time [s]

0.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6

0.0

2.0x10-3

4.0x10-3

6.0x10-3

signal in cell #97

Volts

0.0 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6

0.0

2.0x10-3

4.0x10-3

6.0x10-3

Input signal in pad #1, cell #1

Volts

Crosstalk(what happens if the induced charge is split between two pads?)

The charge fraction as a function of pad distance has been taken from Ref. LHCb 2000-060 (W. Riegler)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12385

390

395

400

405

410

415

420

425

430

435-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

385

390

395

400

405

410

415

420

425

430

435

Delay line output

Pre-amplifier output

Tim

e [n

s]

Position [mm]

Noise considerations The delay line resistive termination is a source of thermal noise at the pre-

amplifier input

kTRBVth 4

k = 1.38 x 10-23 J/KT = temperature = 300R = 200 B = pre-amp. band width 106

Vth 1V, Ith < 10 nARkTB

thI 4

EMI pickup is also an issue: delay line + pre-amp. must be housed in a Faraday cage.

More detailed noise study may be envisaged.

Outlook The remaining parts of the readout scheme are: amplifier +

discriminator + TDC + PC interface + software The main components are commercially available ICs which have

already been tested A customized solution for TDC + PC Interface + software is

presently being done Most of the parts and components has been ordered Local support is required

Conclusions The fundamental aspects of the delay line technique applied to the

identification of pads in the muon wire chamber have been presented The simulation results show that the method is effective to identify the pad

position for detected events, with reasonably good time resolution Using this method, the chambers may be characterized with cosmic rays,

as it represents a source of homogeneous radiation

(*) The complete test station should also include the measurement of pulse height spectra from the anode wire planes