Cathode Pad Electronics

The cathode pads are read-out by AFTER ASIC. One chip has 72 active channels and 4 reference channels for pedestal subtraction. Each channel consists of charge-sensitive preamplifier, pole-zero cancellation of preamplifier decay time, RC2 shaper and 512-cell SCA to store waveform. Amplifier gain, pole-zero time constant and shaping time are programmable. Detailed information is in the manual, but the most relevant slow control settings are summarized in the following tables.

The full range of the AFTER chip and the ADC is ±1V, the gain setting determines what charge that corresponds to, leading to a gain value.

Gain setting	Charge range (fC)	Gain (mV/fC)
0	120	8.333
1	240	4.167
2	360	2.778
3	600	1.667

The peaking time is defined as the time the pulse takes to go from 5% to 100% pulse height. This peaking time translates to other relevant times as shown in the next table.

Illustration of various time characteristics of the filtered AFTER signal

Peaking time (5%-100%)	Fall time (100%-5%)	FWHM	Rise time (50%-100%)	Fall time (100%-50%)
116.7	202.5	158.4	67.59	90.82
200	438.2	311.6	121.3	190.3
505	1194	843	329.2	513.7
993	2351	1689	656.1	1033
1912	4283	3213	1268	1945

Phenomenologically the pulse shape can be described by the function

$f(t)=\left({\frac {t}{k\tau }}\right)^{k}\exp \left(k-{\frac {t}{\tau }}\right)$

Extracting the above mentioned rise and fall times from this formula for different values for the parameter k yields a relatively good match for $k=4$. The resulting numerical relationship between peaking time $t_{r}$ and $\tau$ from this is $t_{r}=3.1365\tau$

The following tables contains the 5%-100% rise times for the different AFTER settings together with the corresponding value for $\tau$.

Time setting	Peaking time (ns)	$\tau$ (ns)
0	116	37.0
1	200	63.8
2	412	131.4
3	505	161.0
4	610	194.5
5	695	221.6
6	912	290.8
7	993	316.6
8	1054	336.0
9	1134	361.5
10	1343	428.2
11	1421	453.1
12	1546	492.9
13	1626	518.4
14	1834	584.7
15	1912	609.6

Reference

File:AFTER MANUAL v2.pdf