Good questions:
The total charge from an ionizing event occurs over the drift time for the particular geometry of the chamber. If we integrate the chamber pulse with an integrating ADC over that drift time, we would get something like that shown on slide 22 mentioned in my email. A charge amplifier integrates that same pulse but for a limited time (peaking time or also denoted as tm for measurement time) - similar to an integrator with a continuous reset, thus a time constant. The convolution of these shaping function with the input signal results in the output signal observed at the output of the preamp. Given the peaking time (you can think of it as a sampling interval), a percentage of the total charge is observed. So, for 200 ns (drift time) we get 100% of the charge and at 11 ns we may get about 13% - 15% ( low teens) of the charge.
The gain is not in milivolts but in mV/fC. In that phrase I am just going through the steps of calculating it - (1000mV/400fC)*0.8=2mV/fC.
The peaking time is adjustable so it can be trimmed slightly to fit the requirements for the FDC and for the CDC. However, both chambers can operate with the same peaking time setting.
Simon has run simulations and obtained data from the FDC prototype and 1/5 seems to agree with published data. As the first electrons due to primary ionization move towards the anode wire, most of the avalanche multiplication will occur close to the wire and the + ions will then drift to the cathode strips on both sides of the wire. Tracks occurring far from the wire (corner clipper) will produce a small current signal on the anode wire that is almost symmetric around some peak; extended tracks produce multiple clusters, resulting in a current signal that has a short rise time and a long tail. In the FDC and CDC, the relatively short drift times and high rates, require that we implement a shaping function that has a short peaking time with tail cancellation. As a result, the output signals out of the preamps look symmetrical around the peak (peaking time).
Regards,
Fernando
Mark M. Ito wrote:
Fernando,
I had some questions. Please see the attached PDF file.
-- Mark
Fernando J. Barbosa wrote:
Hall D Electronics:
Hi Elke,
Document 747 on the portal shows the charge deposited on the CDC and FDC detectors. These numbers were first estimated for the Electronics Review in July 2003 and were based on geometrical constructs only. You can find a brief summary on slide 22 (a back-up slide) of my presentation for the Hall D Drift Chamber Review of 6-8 March 2007, document 751. Anyway, these numbers have not changed in years....
For the CDC, the dynamic range is shown to be 100 fC - 3 pC - a factor of 30. Because the charge amplifier has a peaking time of about 11 ns, the dynamic range of the preamp would be about 400 fC for point ionization (~13% of total charge). The gain of the preamp would then be ~ 1000 mV (a reasonable maximum amplitude to expect from a preamplifier) divided by 400 fC times a factor to allow for some headroom before saturation, say 80%. The result is 2 mV/fC.
Similarly for the FDC, the dynamic range for the anodes was estimated to be 300 fC - 3 pC, a factor of 10. For the preamp, 400 fC for point ionization and 2 mV/fC for gain.
For the FDC cathodes, the dynamic range was estimated to be 10 fC - 1 pC, a factor of 100. For the preamp, 133 fC for point ionization and 6 mV/fC for gain. Note that here, the estimate presumed a 1/3 of the charge of the anode on the cathode (charge sharing on adjacent strips). Later, it was decided that this number needed to be changed to 1/5 based on published data. For the preamp, the point ionization was then estimated to be 80 fC and 10 mV/fC for gain.
According to these estimates, the CDC and the FDC anodes require the same gain (2 mV/fC) and the FDC cathodes require x5 gain or 10 mV/fC.
Obviously, this numbers must be updated to reflect the physics events in the detectors. I hope this helps.
Regards,
Fernando