Thanks
@MCH for the link, it led me down an interesting Sunday morning rabbit hole!
Clearly some form of active cooling is required for operation for more than a few seconds at high load. To simplify things, we can consider 100W per board and a max temperature rise of 50C (e.g. operation at 70C in 20C ambient air). This is a 1% change in resistance based on the 200ppm/K spec. The airflow required for that is ~6m^3/hr, so 24m^3/hr for four boards at 400W total. Any 80MM PC case fan can easily deliver this, as they usually do 50m^3/hr.
So, getting the heat away using forced air convection will work. But we still need to get it from the board to the air.
This paper gives a value of 100-200W/m^2K for the heat transfer coefficient of the top of a surface mount power device under forced air, and we can probably assume this for the board as a whole. Our board is ~0.01m^2 per side, K is 50, so in principle we can indeed move 100W from the board to the air without a heatsink thanks to its quite large surface area. Whether this will actually allow the chip junction temperatures and other hotspots to be cool enough requires harder maths.
Adding a heatsink would cool the chip tops directly much better, which
this other Vishay paper shows is important, as the thermal conductivity of the resistor material is low compared with the junctions and even the FR4 board material. On the other hand it would restrict airflow to the board top surface, so is possibly more useful for use without a fan.
A version 2 of the board would therefore have:
- Thermal vias under each chip
- 4 layers of copper
- Use of layers 2 and 3 to do the parallel connections between banks
- Exposed copper on the bottom (electrically unconnected)
- Consideration of cheap heatsink sizes in the layout including mounting holes
They're arriving today so I can do some real world testing soon!