Bandwidth MCH

3 4 5 6 7

Compression factor

Average pad occupancy (%)

Figure 2.12: Zero suppression compression versus occupancy for equidistant clusters of size 3 (blue), 6.5 (red) and 10 (black).

and work of reducing the memory size.

2.4.3.3 Bandwidth MCH

TheMCHis targeting an interaction rate of 100 kHz with 9 % channel occupancy.¹ With a pulse shaping time of 300 ns, the average number of samples above the zero suppression threshold is 10 when the sampling frequency is 10 MHz. The bandwidth available per front-end card is 80 Mb/s, which is shared between the two chips and gives 40 Mb/s per chip.

As described earlier in section 2.4.3, the SAMPA data transmission operates on a packet basis where a packet contains a header of 50 bits and a payload of compressed sample data. The amount of time-bins per packet is programmable up to 1023 bins. If no data is above the zero suppression threshold for the full duration of a packet, the chip would normally send only the header with an empty payload, but it is possible to set the chip to suppress these packets to save bandwidth.

The data rate for each of the possible operations modes of the MCH can be calculated directly, if we assume that there is no noise that creates false clusters.

1Channel occupancy is the fraction of channels that register a hit per interaction.

BWtrigger wo/empty=Hb·fi·Nch·Pocc+ D_b·fi·N_ch·Pocc

(2.3)

BWtrigger w/empty=H_b·fi·N_ch+ D_b·fi·N_ch·Pocc

(2.4)

BWcont wo/empty=H_b·f_pkt·N_ch·(1−(1−Pocc)

fi fpkt) + D_b·fi·N_ch·Pocc

(2.5)

BWcont w/empty=H_b·f_pkt·N_ch+

D_b·f_i·N_ch·P_occ (2.6) WhereBWtrigger wo/emptyin equation (2.3) is the bandwidth needed for trigge-red mode with suppression of empty packets,BWtrigger w/empty in equation (2.4) is the bandwidth needed for triggered mode without suppression of empty packets, BWcont wo/empty in equation (2.5) is the bandwidth needed for continuous mode with suppression of empty packets,BWcont w/empty in equation (2.6) is the band-width needed for continuous mode without suppression of empty packets. BWx

is given in bps. Hb is the 50 bits of the header, fi is the interaction rate, fs is the sampling rate,f_pkt is the packet rate which is the sample rate divided by the programmed length of a time window, Nch is the number of channels,Poccis the occupancy andD_b is the number of bits needed to represent a cluster.

When using zero suppression with run-length encoding to compress the data between the clusters, a time stamp is needed to indicate the position for where the cluster starts in relation to the trigger. An additional word is needed to record how many samples there are in the cluster. This is together encoded into two ten-bit words. In normal zero suppression mode the samples in the cluster themselves are not compressed so the size would be 10 bits for the time stamp plus 10 bits for the cluster size plus 10 bits×10 bits for the cluster itself, for a total of 120 bits. With the cluster sum compression, the samples in the cluster are summed together into a 20-bit word, so the total is then 40 bits.

Table 2.7 present the data-rates per SAMPA for MCH. With the estimated occupancy-rates of 9 %, the only suitable modes are triggered mode with cluster sum compression and suppression of empty packets, or continuous self-triggering mode with cluster sum compression. These estimates assume there is no detector noise.

Mode Cluster Send empty Size of cluster Average packet Data rate Max compression packets (D_b) [bits] length [bits] [Mb/s] occupancy

Triggered None No 120 15 49 7.4 %

Triggered None Yes 120 61 195 0 %

Triggered Cluster sum No 40 8 26 14 %

Triggered Cluster sum Yes 40 54 172 0 %

Continuous None No 120 138 44 8.1 %

Continuous None Yes 120 158 51 6.3 %

Continuous Cluster sum No 40 67 21 20 %

Continuous Cluster sum Yes 40 86 28 18.8 %

Table 2.7: Data rates per SAMPA for MCH. The numbers assume no detector noise.

A drawback of the triggered mode is that the bandwidth usage is more sensitive to noise than the continuous mode. Since there are only a few channels that have data per event, there is a large probability that any noise induced pulses would occur in a channel that would otherwise not have had data for that event. A header would thus also need to be sent, which would otherwise have been suppressed. If we assume that 10 % of the channels will have a cluster of noise for each trigger, then the bandwidth can be calculated as

BWtrigger wo/empty w/noise=Hb·fi·Nch·(Pocc+Pnoise−(Pocc·Pnoise))+

D_b·fi·N_ch·(Pocc+Pnoise) (2.7) and the bandwidth is then increased to 53 Mbps, which is more than the availa-ble bandwidth. Overlap between signal and the noise can be ignored as it amounts to about

P_occ·P_noise·fi

fs

= 0,009% (2.8)

assuming that the noise pulse is only one sample long.

Continuous mode is less affected by noise, as can be seen in equation (2.9), and the bandwidth can be calculated to be 38 Mbps, which is within the available bandwidth. The increase in bandwidth due to noise for continuous mode is 81 % compared to the triggered mode, where the increase is 100 %.

BWcont wo/empty w/noise=H_b·f_pkt·N_ch·

(1−(1−(Pocc+Pnoise−(Pocc·Pnoise)))

fi fpkt) + Db·fi·Nch·(Pocc+Pnoise)

(2.9)

SAMPA chip implementation

This chapter gives a more in-depth description of the implementation of the design, with a focus on the digital implementation. For a more in-depth description of the analogue design, see [28].