Using delay lines on a test station for the Muon Chambers

Design 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 d s

The cylindrical geometry (co-axial cable)



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

E

(

r

) 

CV o

2 

o r V

(

r

)  2

CV



o o

ln  

r C

 2  ln  

a o C

= capacitance per unit length

b

= cylinder radius

a

= wire radius

r

= radial distance

b a < 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

x

1 2 

x q



E

.

d



x

= = Energy lost by the electrostatic field 

u u

1  2

Q du

 

CV o u u

1  2

du q

= charged released in the avalanche

Q

= electrodes charge

Signal amplitude

 In the co-axial cable case,

E=E(r)

(one-dimensional problem)  Using the field expressions, we may compute:

u

( 

q

)  

q CV o r o a



CV o

2 

o

1

r dr

 

q

2 

o

ln

r

 

a u

( 

q

) 

u

( 

q

)  -

q

2 

o

ln  

b

 

C q u

( 

q

)  

q CV o r o b



CV o

2 

o

1

r dr



q

2 

o

ln

r

 

b u

(

u

(  

q

)

q

)  ln ln

r r

 

a

 

b r o a

= 15  m = 10  m

b

= 1 cm 

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

Signal shape (in time)

  Electrons contribution is negligible For the positive ions, we may assume: v  

E P



dr dt

 Using the expression for

E(r)

we find:

r

(

t

)  

CV o p



o t



r o

2

u

(

t

) 

-

2

q



o

ln  1 

t t o

 ;

t o



P



o r o



CV o

2

a

= 30  m

b

 = 5 mm = 1.7 x 10

V o P

= 3000 V = 1 atm -4 

t o

= 4.5 ns ( 2 ns (

r o r o

= 60  m) 3.125 ns (

r o

= 50 = 40  m)  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 Detector

Out(t)

Electronics

Out(t) i(t) u(t) u(t)

Norton Equivalent Thevenin Equivalent

Output signal

 For the Thevenin equivalent circuit, the transfer function is:

T

(  ) 

V o u t V in

(  (  ) )  1

i

 

i RC



RC

 From this we may compute:

V out

(

t

)  

u(t)T(t



τ)dτ



u(t)e t RC



I(t)

is the current passing through the detector capacitor:

I(t)



C d dt u(t)

 2 ln

q

 

a t

1 

t o

The analytical signal shape (

RC

effect)

0.10

0.08

0.06

0.04

0.02

0.00

Cathode voltage signal [

u(t)

] t 0 = 8ns a = 30  m b = 5 mm r 0 = 40  m V 0 = 3000 V 0.0

5.0x10

-7 1.0x10

-6 Time [s] 1.5x10

-6 2.0x10

-6 0.08

0.06

0.04

0.02

0.00

RC

= 1  s

RC

= 100 ns

RC

= 10 ns

RC

= Infinite 0.0

t 0 = 8ns a = 30  m b = 5 mm r 0 = 40  m V 0 = 3000 V 5.0x10

-7 1.0x10

-6 Time [s] 1.5x10

-6 2.0x10

-6

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/C0 around 40 clusters (  2  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 (…) 0.020

0.015

0.010

0.005

0.000

0.0

Three 'point-like' clusters signal (

RC

= 10ns) 5.0x10

-8 1.0x10

-7 Time [s] 1.5x10

-7 2.0x10

-7 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:

V in V out T

(  )  1 

i

1 

LC

 1 1   

LC

 2

e



iTg

 1 ( 

LC

) 

A

(  )

e i

 (  )  The main parameters are the cutoff frequency ( 

o

), the delay (  ), and the characteristic impedance (

Z

) 

o

 1

LC Z

 1  1  

o

2

L C



L C (

  

o

)    (   )  1    

o

 1 3  

o

3  ...

 

LC (

  

o

) Essentiall y :  

LC Z



L

 

Z C

 

Z L C

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 M2R2 pad-ground capacitance values (pF) 48.0

47.0

41.8

37.4

47.6

46.3

41.1

36.9

47.6

46.9

41.8

37.4

47.4

46.6

41.6

37.1

46.1

45.2

40.5

36.7

46.1

45.3

40.2

36.2

45.7

44.8

40.5

36.7

45.5

44.5

40.0

36.4

 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

L

= 1.6  H

C

 = 40 pF = 8ns 

o Z

= 250 MHz = 200   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  H

C

= 40 ± 6.5pF

 = 8 ± 0.64 ns 

o Z

= 250 ± 19 MHz = 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 0.08

Signal through the whole delay line (96 cells) 1.0x10

-6 0.06

0.04

0.02

0.00

0.0

5.0x10

-7 1.0x10

-6 Time [s] 1.5x10

-6 L = 1.6 nH C = 40 pF Z = 200 Ohm  = 8 ns 1.5x10

-6 2.0x10

-6

u(t)

0.08

0.06

0.04

0.02

0.00

2.0x10

-6 1.2x10

-2 1.0x10

-2 8.0x10

-3 6.0x10

-3 4.0x10

-3 2.0x10

-3 0.0

0.0

0.0

5.0x10

-7 5.0x10

-7 1.0x10

-6 1.0x10

-6 Time [s] 1.5x10

-6 1.5x10

-6 2.0x10

-6 1.2x10

-2 1.0x10

-2 8.0x10

-3 6.0x10

-3 4.0x10

-3 2.0x10

-3 0.0

2.0x10

-6

Linearity

 One event is input at each pad, we expect to have a linearly varying time measurement 800 600 400 200 0 -200 -400 -600 -800 800 600 400 200 0 Start - Stop (external trigger) Y = A + B * X A -22 B 24 0 5 10 Start - Stop (self trigger) Y = A + B * X A -816 B 48 0 5 10 15 15 Pad # 20 20 - Constant threshold: 2mV - Simulation time bin: 1ns - Fit error << 1ns 25 30 35 25 30 35

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 55 Fe Calibration mask (high precision) 1D PSD 12000 10000 8000 6000 4000 2000 0 1600 1800 2000 2200 Channel 2400 2600 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 8.0x10

-3 6.0x10

-3 4.0x10

-3 2.0x10

-3 0.0

Signal from the first cell 1.23 mV Signal from the last cell Delay: 768ns (Threshold 20 mV) 0.0

5.0x10

-7 1.0x10

-6 Time [s] 1.5x10

-6 2.0x10

-6 0.0

2.0x10

-7 4.0x10

-7 Time [s] 6.0x10

-7 8.0x10

-7 from pad #4 from pad #8 from pad #12 from pad #16 from pad #20 from pad #24 from pad #28 from pad #32 1.0x10

-6

Effect of the pad capacitances

 The pad capacitances are introduced in the circuit, so we may evaluate the performance Delay line incorporating chamber capacitances (signals seen from cell # 1) 8x10 -3 7x10 -3 6x10 -3 5x10 -3 4x10 -3 3x10 -3 2x10 -3 1x10 -3 0 -1x10 -3 0.0

Signal from the first pad 5.0x10

-7 Signal from the last pad 1.0x10

-6 Time [s] 1.39 mV Delay: 730 ns (threshold 20 mV) 1.5x10

-6 2.0x10

-6

Linearity results

 The errors in pad position measurement are < cell delay (  ) 800 600 400 200 0 800 600 400 200 0 Signal seen at cell # 1 0 5 10 15 20 25 30 35 -2 -4 -6 -8 8 2 0 6 4 Signal seen at cell # 97 -2 -4 -6 -8 8 2 0 6 4 0 5 10 15 Pad # 20 25 30 35 Error = Fit - Meas urement (for c ell # 1) 0 5 10 15 20 25 30 35 Error = Fit - Meas urement (for c ell # 97) 0 5 10 15 Pad # 20 25 30 35

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): +12V 22K 1.8K

70K 1.8K

0.1

 F 0.1

 F 0.1

 F The transistor is BFR 92: - Low noise ( (2.4 dB @ 500MHz,

I c

=2 mA) - Wide band

f T

= 5 GHz @

I c

= 14 mA) 2K 180 10K 180 240 50  Load

Overall performance (pads + delay line + pre-amplifier)

 The introduction of the pre-amplifier stage does not bring critical distortions to the signal shape 6.0x10

-3 4.0x10

-3 2.0x10

-3 0.0

6.0x10

-3 4.0x10

-3 2.0x10

-3 0.0

2.0x10

-1 1.5x10

-1 1.0x10

-1 5.0x10

-2 0.0

0.0

0.0

0.0

Input signal in pad #1, cell #1 5.0x10

5.0x10

5.0x10

-7 -7 -7 1.0x10

-6 signal in cell #97 1.5x10

-6 1.0x10

-6 1.5x10

-6 2.0x10

Output signal (pre-amp. effective gain: 37.7) -6 1.0x10

-6 Time [s] 1.5x10

-6 2.0x10

2.0x10

-6 -6

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) 435 -12 430 425 420 415 410 405 400 395 390 385 -12 -10 -10 -8 -8 -6 -6 -4 -2 0 2 -4 -2 0 2 Position [mm] 4 4 6 6 8 Pre-amplifier output Delay line output 8 10 10 12 435 430 425 400 395 390 12 385 420 415 410 405

Noise considerations

 The delay line resistive termination is a source of thermal noise at the pre amplifier input

V th

 4

kTRB k

= 1.38 x 10 -23

J/K T =

temperature = 300

R

= 200 

B

= pre-amp. band width  10 6

I th

 4

kTB R



V th

 1  V,

I th

< 10 nA   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