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. d s 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

4. b 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 < r < 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. Energy acquired by a charged particle while moving in the electrostatic field Energy lost by the electrostatic field = = q = charged released in the avalanche Q = electrodes charge The electric signal • Energy conservation allows us to obtain the analytical expression:

7. Signal amplitude • In the co-axial cable case, E=E(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. a = 30 m b = 5 mm  = 1.7 x 10-4 Vo = 3000 V P = 1 atm 4.5 ns (ro = 60 m) 3.125 ns (ro = 50 m) 2 ns (ro = 40 m) to = Signal shape (in time) • Electrons contribution is negligible • For the positive ions, we may assume: • Using the expression for E(r) we find:

9. Detector Electronics Out(t) u(t) u(t) Thevenin Equivalent Out(t) i(t) Norton Equivalent 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 main parameters are the cutoff frequency (o), the delay (), and the characteristic impedance (Z) Vin Vout The Delay Line Method • One delay line cell is an L-C circuit which introduces an almost constant delay to signal propagation:

14. P1 P2 P3 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 > 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. P1 P2 Pn P31 P32 P1 P2 Pn P31 P32 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. Calibration mask (high precision) 1D PSD 55Fe Non-linearity typically < 0.1% 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 ( >> 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 < cell delay ()

23. +12V 22K 1.8K 70K 1.8K • The transistor is BFR 92: • Low noise • (2.4 dB @ 500MHz, Ic=2 mA) • - Wide band • (fT = 5 GHz @ Ic = 14 mA) 0.1F 0.1F 0.1F 2K 180 10K 180 240 50 Load 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 10-23J/K T = temperature = 300 R = 200  B = pre-amp. band width  106  Vth 1V, Ith < 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