The main reason for using a DC-->DC converter, in comparison to using your at-home AC-->DC converter with a 12VDC -->120VAC "Inverter" in front is efficiency: converting DC to AC wastes a fairly large amount of power (and maybe needs a noisy fan, to dissapate the "waste heat" being generated in the inverter). Turning around and converting 120VAC into Resmed "DC-Out" is also less efficient than the DC-DC conversion done by my box, or the $85 Resmed original. This saves on battery power overnight, and may also eliminate fan noise from the Inverter.
The "strange thing" about ResMed Power supplies is the fact that they have 3 output wires: "+"24VDC, "-" Ground, plus a sort-of-proprietary +3.3VDC "sense pin" in the middle. The +3.3VDC sense pin needs to have an inline resistor , size 2.7k Ohms, between the +3.3VDC power section and the output cord connector. (They did file a patent concerning their clever use of of the "sense pin" within the ResMed machines, which was designed to determine the +24VDC output power of the corresponding PSU.) 2.7k Ohms corresponds to their own "90 Watt" PSU models.
Part #1: A sacrificial AC-DC power supply for Resmed A10. (Refurbs run about $18 on Ebay.) When it arrives, crack it open and cut the Resmed output cord wires (3) from the Power Supply mainboard, preserving the strain relief and as much wire length as possible. Why? Because the Resmed cable includes a couple of large chokes, which help to reduce electronic "noise". (Dell Laptop power supplies from the "PA-12" Series can be bought for a bit less money, and they have the same connector - but the Dell cords include only one such choke, and it's a lot smaller.)
Part #2: A DC-DC "Boost" Converter, creating regulated 24V output from 11-15V input. I used and recommend this one, which costs $18 as I write this: http://www.ebay.com/itm/Waterproof-DC-1 ... 2574605057. Why? Because your "12V" power sources might be providing power from about 11.8V (deeply discharged) all the way up to 14.4V ("bulk" charging from an RV Converter, or Solar Charge Controller). Most "Variable" and "Doubler" DC converters will vary the output Voltage when the input Voltage changes, we need a "regulator" type.
Part #3: A DC-DC Variable "Buck" Converter, to create 3.3V output from 24V input. I used and recommend one like this, which costs barely $2: http://www.ebay.com/itm/Step-Down-LM259 ... 2405283762. Why? The middle pin of the PSU is required to supply 3.3V, through a 2.7k Ohm resistor. This converter can be an unregulated "variable" model, because it's input will always be regulated 24V.
Part #4: A 2.7k Ohm Resistor, 5% tolerance. Lower quality might also work.
Part #5: A 1000uF Electrostatic Capacitor, rated at 50V Why? I think it helps to protect the Voltage Converter from low-frequency noise emanating from the Resmed VFD. (The cable chokes also play a big role.) This might not be necessary, because the Boost Converter definitely contains a similar "Filter Cap" inside the sealed unit. But I can't ascertain the size within the Boost Converter, and Resmed used a big one across the 24VDC/Ground output legs of their AC-DC Power supply. Note added in 2021: This part appears to be unnecessary, several builders have had success with boxes which don't include it. The Boost Converter filtering is sufficient, all by itself.
Part #6: A "Project Box" capable of containing the components, connectors, and cable stress reliefs. I used this one: http://www.ebay.com/itm/158mm-x-90mm-x- ... 2278707309 With this plastic one, it's easy to drill and cut slots for the strain reliefs on your two cords.
You also need some wire connectors; input wire (I used Low-Voltage landscape cord; 14-2 would be fine); an input cable stress relief for the box entry; and some wire for internal wiring (#16 stranded THHN is fine for this). Here's a picture of my unit:

Ignore all the wire Colors (I didn't have "proper colors" on hand). We have, from the left, two red wire nuts connecting external "+12V" and "Ground" to the input leads of the silver Boost Converter (underneath). Boost Converter +24V output (yellow wire) goes into 5-way push-down wire connector, and Boost Converter "Ground" (black wire) goes into the second connector. Between the two Connectors, we have the Filter Capacitor (with correct Polarity, of course). The small "Buck Converter" (the blue circuit board on top) inputs also connect one wire into each of the 5-way connectors ("+24V", "Boost Converter "-Ground").
The Buck Converter "+ output" goes into the Resistor, and then to the "Middle Pin" wire of the Resmed Cable. (Buck Converter "- Output" is left unconnected, it is wired in common with "- Input" internal to the mini-board.) A wire from the +24V Connector is connected to the Resmed Cable "Inner Cylinder" wire (yellow wire nut), and a wire from the "Ground" Connector is connected to the Resmed Cable "Outer Cylinder" wire.
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Before connecting a Resmed A10 CPAP machine to this Converter Unit, the internal Buck Converter adjustment screw needs to be "tuned" to create 3.3V output, and all 3 voltage values should be verified. You might, as I did, take the unit out to a car (not turned on), and connect the input cable ends to the battery with a jumper cable. You will probably find that 8-12 turns of the adjuster screw are required to bring the output down to 3.3V. After adjusting at the mini-board output contacts, you should also verify that the Resmed connector pins are correct: zero voltage "Outer Cylinder" (i.e., continuity with the vehicle's frame); +24V "Inner Cylinder", and +3.3V "Center Pin".
It's done. Disconnect the jumper cable and close up the box, take it on your next camping trip.