TIGER - GEMROC efficiency

Triggerless efficiency

The triggerless efficiency has ben measured with one TIGER and one GEMROC. The acquisition was set in triggerless mode and the TP are generated by the GEMROC itself. The GEMROC generate N TPs after each Frameword received from the chip. The time between the TPs is set by another parameter. This parameter was set to make the TP emission homogeneous with respect to the time.

The data are then decoded and, with a simple script, the efficiency is calculated as the rate between the expected number of test pulse (N times the number of frame-words acquired) and the number of TP registered by the system.

Digital test pulses on 64 channels

TP per frameword	Event Rate (kHz)	Efficency
1	4.8	100%
2	9.8	100%
12	58.6	100%
13	63.4	98%

Both the devices (GEMROC and TIGER) are designed to allow a rate up to 60 kHz per channel (3840 kHz per chip). This measure confirms the performances in the communication between one GEMROC and one TIGER. Efficiency starts to decrease due to bandwidth limit (63 kHz x 64 channels = 4 MHz) of the chip:

• 2 Tx links at 160 MHz (SDR) allow up to 320 Mbit/s
• 4 MHz * 80 bit/hit = 320 Mbit/s

Digital test pulses on one channel

TP per frameword	Event Rate (kHz)	Efficency
20	97.7	100%
22	107	100%
25	122	100%
30	146	100%
35	170	100%
37	180	100%
40	195	90%

In this case, the efficiency starts to decrease when the single channel receives a too high rate. One hit requires between 1-8 us to be processed by the channel, this corresponds to a maximum frequency of 125 kHz - 1 MHz as these results confirm.

Analog test pulses on one channel

TP per frameword	Event Rate (kHz)	Efficency
10	48.8	100%
22	107	100%
25	122	100%
30	146	100%
37	180	100%
38	185	93%

The analogue part of the signal processing does not play a big role for what concerns maximum rate considerations, so these results are very similar to the previous one with digital TP.

I would expect to see some differences if we acquire with the following conditions:

• Signals pile-up (if the input TPs are not homogeneous in time)
• Noisy hits (if input TPs are set to be very small)

Time and Counting TIGER Efficiencies

These efficiencies were measured for each TIGER (for both L1 and L2), in 5 different runs (58 to 62). The different runs differ from the number of TP injected as explained in the table below:

Run Number	Channel injecting the TP	Number of TP Injected
58	20	1
59	10, 20	2
60	10, 15, 20	3
61	5, 10, 15, 20	4
62	5, 10, 15, 20, 25	5

For the runs where more than one channel is used to inject TP (i.e. 59, 60, 61, 62), the efficiency is defined as the product of the single channel efficiencies:

[math]\epsilon_{total} = \prod_{i=0}^{n} \epsilon_{i}[/math]

Time Efficiency (1)

The time efficiency (for each TIGER) is defined as it follows:

[math]\frac{N^{TP~on~time}}{N^{TP~total~ref}}[/math],

where N^{TP on time} is the number of events which are synchronized with the reference TIGER (TIGER 0 for L1 and TIGER 32 for L2), while N^{TP total ref} is the total number of events registered by the reference TIGER.

Counting Efficiency

The counting efficiency (for each TIGER) is defined as it follows:

[math]\frac{N^{TP}}{N^{TP~total}}[/math],

where N^TP is the number of events registered by a TIGER, while N^{TP total} is the total number of events.

Results & Comments

Here is presented a brief summary of the results (NB the summary describes the average behaviour, pathological cases are neglected. For more information, please refer to the .txt files below.):

• if only a TP is injected, the average efficiency is higher than 90%;

• with two TP, the counting efficiency is higher than 85%, while the time efficiency stays above 70%;

• with 3 or more TPs, the average counting efficiency sets above 70%, while the time efficiency drops down even to 30%.

Below, you can find the downloadable .txt files:

• File:Eff Run 58.txt <-- Time and Counting Efficiency referring to Run 58

• File:Eff Run 59.txt <-- Time and Counting Efficiency referring to Run 59

• File:Eff Run 60.txt <-- Time and Counting Efficiency referring to Run 60

• File:Eff Run 61.txt <-- Time and Counting Efficiency referring to Run 61

• File:Eff Run 62.txt <-- Time and Counting Efficiency referring to Run 62

Time Efficiency (2)

In order to understand the time efficiency a little bit better, it was decided to study the distributions of the time differences (ΔT) between each TIGER and its reference (TIGER 0 for L1 TIGERs and 32 for L2 TIGERs). The distributions were studied for all those events for which the reference TIGER had registered an event.

From the ΔT histograms, then, means (μ) and standard deviations (σ) were extracted and plotted as a function of the TIGER ID. In the runs where multiple channels inject a TP, μs and σs are plotted together to appreciate that pathological features are intrinsic to the TIGERs (and are not a channel problem).

Comments & Plots

Below a brief comment about the plots is presented (please refer to the plots themselves for more information):

• where the μs set around zero, the corresponding TIGERs do not present interesting features; though to a more precise analysis, one can notice some of the TIGERs' μs are non-zero, instead they oscillated on the "-1"&"+1" values;

• some TIGERs (e.g. 15 and 70) present interesting features having μs much different than zero; for these TIGERs, one can also notice how the σs are really different (> 200 a.u.) from the typical values (~ 100);

• as a rule of thumb, μs much different from zer0 correspond σs much bigger than 100;

• the problematic features are, as already mentioned, intrinsic to the TIGERs, because they reproduce themselves across the different TP channels.

Below, you can find the downloadable plots (.pdf files):

• 

  μs (above) and σs (below) graphs for Run 58.

• 

  μs (above) and σs (below) graphs for Run 59.

• 

  μs (above) and σs (below) graphs for Run 60.

• 

  μs (above) and σs (below) graphs for Run 61.

• 

  μs (above) and σs (below) graphs for Run 62.