Power cable for quiet background

You might experiment with the cord on your CD player first. A lot of people here use Shunyata cords that are designed to quiet digital sources (older ones had the "VX" designation). I've used them myself and found that they made a big difference in the background silence of my system. I didn't like the Shunyata cords on my preamp or amp, though, and felt that on those components the overall sound was more compact and veiled with the Shunyata. Your experience may be very different, of course.

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Never tried Audience, but can recommend Grover Huffman. They do everything you mention and come with a 60 day guaranty and you'll come in under your budget.

$500? Try for a TG audio SLVR or 688. They often show up used here for $2-300. TG has also been re-instituted and is selling new version ( I have not heard the new ones). SLVRs and 688s are absolutely silent and
are great cords in all respects, too. Another cord that is just as silent and also sounds great on my EMM CDSA player is the Stefan Audio Arts Endorphin cord ($379 new, a giant-killer IMHO). See my recent review of a Rudistor headphone amp in the Amp review section for my comments on it.)
The Stefan cord is great on my CDP and Capri preamp too.

Also, check out the Blue Circle BC68 mk2 ... basically a SUPER silent power conditioner and cable.

Also a HUGE TG Audio fan... but the BC68 is quieter... ultra black backgrounds...

Big stage, depth, with great dynamics too... (the BC68 mk2)

May I have a suggestion? A power cord that gives a quieter background means it
has superior shielding against electrical interference. So why don't you contact a
few cable manufacturers and ask them to provide you with the design spec and
the test result of the shielding or noise rejection capability of their cables. Even
the regular coax lab cables like the RG58 and RG59 have design spec, a carefully
designed power cord costing $500 a piece should have even more detailed
design spec and more complete test results. Once you have that information,
selecting the right cable for your requirement should be much easier.