Source of voltage for low noise psu

Instead of just a capacitor input filter use a CRC filter, with about equal C values.
The R will drop most of the voltage ripple seen on the first capacitor, so size its dissipation rating accordingly.
Make the R as large as possible without excessive voltage drop and power dissipation.
Of course, route the pcb so the rectifier current pulses are not coupled to the second capacitor.
 
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The modules from LDOVR.com are easy to stack to increase the current capability. I am thinking about a basic toroidal transformer with bridge rectifier and smoothing capacitor. Two stacked modules would be a 2 Amp supply.
 

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The thermal performance seems to me to be the limiting factor in practice - with the DS saying the device's thermal resistance is ~35oC/W I'd not want to dissipate more than 2W in the chip (allows an ambient of 55 degrees) which means you'll want no more than 4V drop to permit the 500mA max output current rating of the device. I rather suspect getting that precise an input voltage won't happen without using a pre-regulator as trafo windings for off-the-shelf units are quite widely spaced (6V, 9V, 12V).
 
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The LDOVR website for the actual board in my attached image shows a board with a small heatsink bonded onto the rear. It also shows details for operating the boards in parallel. I did think that something like an LM350 would do the job of providing a pretty clean voltage to preregulate the supply to the boards.