LV power cables for iTOP Each boardstack (1/4 module) requires three LV power inputs “RAW1”: 1.87V at 14.5A (mostly for FPGA core) “RAW2”: 3.15V at 13.2A (mostly for IRSX ASIC’s) “RAW3”: 4.33V at 5.1A (mostly for preamplifiers) That is 90.8W (+ 5.2W max for HV power @ 4kV) Total power 384W per module, 6.14kW total PS (3 channels) Patch Point Boardstack 22 – 32 m (4 lengths) 6 wires (10? + 16AWG) for power 3 twisted pairs 24AWG for sense 1.2 m 6 wires (14 + 16AWG) for power Connection scheme: One cable feeds one boardstack, from three power supply channels in E-Hut. No sharing or parallelling. Remote regulation is used to the patch point (1.2 m outside of module, at ECL plumbing area).

Each red curve represents 8 iTOP power cables – routes are approximate, actually will be spread out over ECL/KLM regions

Route lengths: 32.2m, 29.1m, 25.9m, 22.1m 16 cables of each length Typical approximate route – others similar Route lengths: 32.2m, 29.1m, 25.9m, 22.1m 16 cables of each length

Cable power dissipation Resistance of 10AWG is 3.30 mΩ/m Resistance of 16AWG is 12.03 mΩ/m Power in cable is 2 × (14.5A)^2 × (3.30 mΩ/m) + 2 × (13.2A)^2 × (3.30 mΩ/m) + 2 × (5.1A)^2 × (12.03 mΩ/m) = 3.16 W/m Total installed length 1.75 km Total cable power 5.53 kW

Allowable current in cables The allowed (by US National Electrical Code) current in a conductor is determined by the temperature rating of the insulation used, together with a “standard” estimate of temperature rise based on the wiring environment, e.g. number of current carrying conductors in a cable, conduit, raceway, or cable tray. For 10AWG, the basic rating is 40A, reduced by a “derating factor” according to the wiring environment – which is to account for environmental effects on temperature rise, e.g. lack of airflow or presence of adjacent current-carrying conductors. NEC 392.80(A)(1): In cable tray, 10 AWG wire of ≥90 °C rating, in a multiconductor cable rated <2kV, is allowed to carry 40 A (Table 310.15(B)(16)), multiplied by a derating factor 0.8 for 6 (in our case) current-carrying conductors in the cable (Table 310.15(B)(3)(a)), further multiplied by a correction factor for ambient temperature (dependent on adjacent cables in the tray, as well as any other heat sources). I think we can assume (with verification!) the ambient temperature ≤60 °C, which results in a correction factor (Table 310.15(B)(2)(a)) of 0.71. The result of that, is an allowable current of 22.7 A. An alternative approach, perhaps better related to actual safety and reliability, is to measure the temperatures in an actual loaded cable bundle and show that they are well within the ratings. This test is in progress. This approach is recognized (at least for calculated if not for measured temperatures) by NEC 310.15(C). Independent of the above, we have an enquiry in to the manufacturer (Alpha Wire) concerning reliability of the insulation versus operating temperature, and recommended derating from the stated maximum operating temperature (105 °C). Certainly we will not operate at such high a temperature, but the curve of reliability versus temperature is not made clear. There may be no substantial difference between 30 °C and 60 °C, for instance.

Allowable tray loading The NEC provisions on allowable current in multiconductor cables installed in cable tray, are of course subject to compliance with other NEC provisions on cable tray installations, in particular 392.22 on allowable cable loading. 39.22(A)(1)(b) Ladder type cable tray containing any mixture of multiconductor cables (including power, control, and signal cables) all less than 4/0 AWG, the sum of cross-sectional area of all installed cables shall not exceed the maximum allowable cable fill area in column 1 of Table 39.22(A) for the appropriate cable tray width. Table 39.22(A), excerpted In other words, filling to depth > 3.3cm is NOT PERMITTED. I am not so sure we (I mean Belle-II overall, not particularly speaking of iTOP) plan to be in compliance. Tray width, cm Column I allowed fill, cm^2 (NEC) Allowed fill depth after accounting for packing fraction, cm (calculated by Visser, not in NEC!) 30 90 3.31 40 120 45 135 50 150 60 180 75 225 270

Proposed iTOP power cable design 12.3mm OD  UL-1581 Vertical Tray flame test Proposed iTOP power cable design Quote: $6.56 / m @ 3.05 km