1. ETD meeting First estimation of the number of links
needed for the PID readout.
Study of the consequence of the electronics design option of that numbers
On behalf of PID group
Christophe Beigbeder
December 2nd 2009

2. Introduction
A robust and simple TDC based solution (BABAR-like) can be considered as a baseline for the PID readout.
Charge measurement could be added if necessary, at least for PMT aging survey.
There is no obvious use of it for physics up to now.
Could be necessary for discriminator time walk correction
Analog memories are another good solution, which has been proven to be very effective and useful for the characterization benches.
They are the baseline for the TOF electronics ( few channels .Ultra fast pms)
The question is, can we envisage using analog memories for the barrel with the following constraints:
High number of channels => 30,000
High trigger rate => 150 kHz
No T0 for trigger matching => ~ 200 ns window
Little physical space and radiation on the detector
=> limitation of electronics in terms of quantity and « intelligence » on detector
=> limitation of power
Christophe Beigbeder
December 2nd 2009

3. Pros and cons … The positive side of analog memories:
One gets the signal shape, thus all the information!
Capability to apply a digital filter to remove a known noise, if present.
Incredible flexibility to come up with very clever timing schemes (CFD, reference pulse timing, spline interpolations, etc.).
Capability to deal with overlapping pulses, cross-talk, etc.
Capability to deal with unforeseen events.
The negative side:
One gets a lot of samples if:
One doesn’t know where the useful samples do reside
The sample rate is very high compared to the signal shape
As one has to digest the waveforms in real time, not clear how fast the algorithm has to be.
Christophe Beigbeder
December 2nd 2009

4. Back to barrel PID
No T0 for trigger matching => ~ 200 ns time window
If we sample at ~2.5GS/s, we would need 500 samples to cover it (each sample has to be converted into 12 bits by an ADC)
=> totally unreasonable!
Signal from the MAPMT is much shorter (~5 ns useful)
=> we need to tag the position of the signal inside the trigger window with a discriminator/TDC in order to be able to come back for reading the corresponding samples after L1 decision.
If we don’t want this TDC to be very precise (10ns steps), and as we need to cover at least three time steps in order to recover from the digitization uncertainty, we end up with ~75 samples/event.
The whole signal shape is not useful permanently during physics run, mostly for debugging and monitoring purpose
=> Time and Charge could be extracted from samples thanks to digital filtering
=> but this operation is expensive in terms of processing and power if performed by FPGAs on the detector (without forgetting radiation mitigation)
=> it should better be done in the ROM
=> the readout links have to digest the whole sample information
Christophe Beigbeder
December 2nd 2009

5. There is no definitive leadership of TDC/ADC solution as of today
Summary
TDC/ADC solution is the simplest working solution
We already have a 16-channel/100-ps TDC in hand
We need to optimize it for SuperB
We get ~32 bits per hit without charge, 48 bits with charge.
The only difficulty here is the discriminator
Could be power consuming to get the necessary precision
If there is a time walk, charge is necessary for its correction
Could be done on-detector, or in the ROM, or offline …
We have ideas about walk-less solutions => to be tested …
A electronic based on TDC ADC will be Slac on the CRT
Analog memories give a much richer information
but their implementation is trickier, especially with such a high number of channels and no pointing to events’ T0
they would require more computing and power on the detector
if we want to limit the latter, the corresponding dataflow will be significantly higher, thus the number of readout links (factor >> 10)
There is no definitive leadership of TDC/ADC solution as of today
=> we need to farther study the case to make up our minds !
Christophe Beigbeder
December 2nd 2009

6. 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.
Christophe Beigbeder
December 2nd 2009

7. 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 !!!
Christophe Beigbeder
December 2nd 2009

8. 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.
Christophe Beigbeder
December 2nd 2009

9. 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).
Christophe Beigbeder
December 2nd 2009

10. 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.
Christophe Beigbeder
December 2nd 2009