Hcbravesfan,
If you use a 3 wire with ground romex (NM-B) for the purpose of creating 2 circuits what you end up with is a multi wire branch circuit.
With a 3 wire multi wire branch you will have 2 separate circuit,(not 2 dedicated circuits), with a shared neutral conductor.
The 2 hot conductors must be fed from opposite Lines, legs, of the electrical panel.
When a multi wire branch circuit is fed from a single phase, split phase, secondary winding of a transformer only the unbalanced load of the loads connected to each separate circuit will return on the neutral conductor.
Example, if a connected load of exactly 5 amps each is connected to each 120V separate circuit, 0 amps will return on the neutral conductor to the source. The two 5 amp 120V loads are in series with one another.
Example, if 5 amps of load is connected to one 120V separate circuit and 2 amps of load connected to the other separate circuit, then 3 amps (the difference of the two) will return on the neutral. The balanced 2 amps will be in series with one another.
It is obvious why audio equipment should not be fed from separate circuits whether connected together by ICs or not.
Why would you want to series hash from digital equipment right out of the power cord right back into the power supply of an analog preamp or phono preamp.
With true dedicated branch circuits that have their own hot, neutral, and equipment ground conductors the dedicated circuits should be fed from the same Line, leg, from the panel when the equipment is linked together by ICs. I would even go so far to say HDMI cables as well. Though I have not read any info on such regarding HDMI cables..... Must be something out there.
Added note.
Per NEC, the 2008 edition, all multi wire branch circuits shall be fed from a multi pole common trip handle breaker.