Using delay lines on a test station for the Muon Chambers

1
Using delay lines on a test station for the Muon
Chambers

• Design considerations
• (A. F. Barbosa, Jul/2003)

2
Outline

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

3
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 gtgt wire radius

4
The cylindrical geometry(co-axial cable)

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

C capacitance per unit length b cylinder
radius a wire radius r radial distance
a lt r lt b
5
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

6
The electric signal

• Energy conservation allows us to obtain the
  analytical expression

7
Signal amplitude

• In the co-axial cable case, EE(r)
  (one-dimensional problem)
• Using the field expressions, we may compute

ro 15 ?m a 10 ?m b 1 cm
?
u(-q) 0.062 u(q)
8
Signal shape (in time)

• Electrons contribution is negligible
• For the positive ions, we may assume

• Using the expression for E(r) we find

9
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

10
Output signal

• For the Thevenin equivalent circuit, the transfer
  function is

• From this we may compute

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

11
The analytical signal shape (RC effect)
12
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
• ()

Finally, the time space resolution is finite
(measured ?t ? 3-4 ns)
13
The Delay Line Method

• One delay line cell is an L-C circuit which
  introduces an almost constant delay to signal
  propagation

14
Discrete delay lines

• Delay line cells may be implemented in cascade,
  so that one may associate spatial position with a
  time measurement

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

15
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 gt 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)
? The chamber capacitance has to be part of the
delay line
16
Preliminary Design

• The following basic circuit could cope with the
  requirements

• L 1.6 ?H
• C 40 pF
• 8ns
• ?o 250 MHz
• Z 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

• L 1.6 ?H
• C 40 6.5pF
• 8 0.64 ns
• ?o 250 19 MHz
• Z 200 16?

17
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

18
Linearity

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

19
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

20
Signal Distortion along the line

• Due to the reflection and attenuation of high
  frequencies (? gtgt ?o), the signal is broadened
  and distorted as it travels through the circuit

21
Effect of the pad capacitances

• The pad capacitances are introduced in the
  circuit, so we may evaluate the performance

22
Linearity results

• The errors in pad position measurement are lt cell
  delay (?)

23
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)

24
Overall performance (pads delay line
pre-amplifier)

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

25
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)

26
Noise considerations

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

k 1.38 x 10-23 J/K T temperature 300 R
200 ? B pre-amp. band width ? 106 ?
Vth ? 1?V, Ith lt 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.

27
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

28
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