The simulation starts with the generation of an input signal to the electronics according to a Landau distribution, with an added random noise term.(figure)
The timing is supposed to be governed
by a third order CRRC function at the entrance of the comparator. The timewalk
is the moment the CRRC function crosses the threshold (figure).
Only the rising edge is considered (equivalent to Edge Circuitry ON).
The timewalk of each hit thus depends on the deposited
charge and the threshold (figure)
This timewalk is added to a random (within 25 nsec) trigger phase with respect to the clock, in order to simulate the non-synchronised beam in H8. If the charge is above threshold, a "1" is written in the timebin corresponding to the time calculated as described above.
The results reproduce fairly well the behaviour in the testbeam (figure). Compare to data for ABC1, CGT1, CGNT1 (Edge ON 240 V data).
In this figure the centers of the efficiency-TDC distribution can be seen to rise until roughly 3.5 fC (due to the threshold approaching the deposited charge - typically 3 to 4 fC). From 3.5 fC upward, the central TDC value is decaying (due to timewalk, the threshold starts selecting events with high charge, which results in faster discrimination).
