1. LNF PID session 1 December 1st 2009
Estimation of the number of links for the barrel PID D. Breton, C.Beigbeder, J.Maalmi
LNF PID session 1
December 1st 2009

2. Raw calculations (1)…
The calculation of the number of links L for a given subdetector is based on the following parameters:
N: number of channels [channel]
T: trigger rate [events / s]
E: event size [bits / (event x channel)]
R: link baud rate [bits / (link x s)]
The equation giving the minimum number of links with an optimum multiplexing factor and no concern about detector topology is:
L = N x T x E / R
Some of these numbers are common to the whole experiment:
T = 150 k events / s.
R = 2 Gbits / s (conservative)
For barrel PID (focussing DIRC option), numbers are the following:
N = 30,000 channels
E now has to be estimated.

3. Raw calculations (2)…
The calculation of the event size is based on the following parameters:
W: trigger window (specific to barrel PID) [s]
H: hit rate per channel [hits / s /channel]
D: mean number of data bits per hit [bits / hit] (includes data formatting and encapsulation)
The equation giving the event size E is the following:
E = W x H x D
For barrel PID (focussing DIRC option), numbers could be the following with a simple BABAR-like TDC option:
W = 200 ns (reasonable ? … )
H = 100 kHz (Jerry’s guess ... Too optimistic ? …)
D = 32 bits (our guess from BABAR’s experience …)
Which gives for E:
E = 2 E-7 x 1 E+5 x 32 = 6.4 E-1 [bits/ (event x channel)]
Which gives for L:
L = 3 E+4 x 1.5 E+5 x 4.8 E-1 / 2 E+9 = 1.44 link !!!

4. Remarks (1)
Former calculation of the event size is based on the simplest (BABAR-like) option:
We encode the hit arrival with a 100-ps TDC
If we feel like adding the charge information for each hit, D may rise up to 48 bits => factor 1.5 on L.
From what has just been shown, it becomes obvious that our system will be topology driven concerning the number of links with a TDC based solution.
This was already the case in BABAR’s DIRC: 12 readout links each with a payload of 15 to 20% of its capacity.

5. Remarks (2)
The number of links will depend here on our capacity to multiplex the information on the detector.
This very small number of links gives a pleasant (and anyhow necessary) safety factor for all potential increases in the background rate (H), trigger rate (T) or window width (W).

6. Remarks (3)
A solution based on analog memories would require more links.
The main difference sits in the value of D because, in addition to the hit time, a few tens of samples have to be digitized and sent to the ROM, where necessary digital processing has to be performed.
The extra amount of bits, based on discussions with Gary, can be estimated to be 75 samples x 12 bits = 900 bits / hits.
Which would put a factor ~40 on the number of links.
Then the question of the safety factor has to be raised, because we may not be topology driven anymore.
If we don’t want to increase the number of links, digital processing has to be performed in the front-end, which is not optimal from the power and radiation points of view.
More generally, and independently from the solution chosen, what should be the safety factors on:
T: trigger rate [events / s]
W: trigger window (specific to barrel PID) [s]
H: hit rate per channel [hits / s]
W and H are detector specific, whereas T concerns the whole experiment.