Too late to try that now. Why would it make a difference?
An impedance matching transformer is exactly what Eventide tech support once told me never to use when connecting an unbalanced line with a balanced one.
I'm not sure about balanced line level, but there's no standard output impedance for unbalanced line level audio, but it is typically from 8 to 50 ohms. It's kind of an archaic connectivity that I wish nobody used anymore. If I were Augustus, I would decree that only XLR and AES connections are permissible.
An output of 10k is for an electric guitar. I'm not plugging an electric guitar into active speakers. Standard practice for an RCA connector on a balanced cable ties the shield to the negative conductor, and that is bad. So I would lean towards an unbalanced cable.
The battery backup side may affect the ground and/or hot & neutral, relative to the side that's only surge protected. I was just suggesting possible causes- hard to know if the voltage and other connections aren't checked. If you can move the TV and speakers apart and it fixes the problem, it's basically a free solution.
I'd like to hear the reason for
not using an impedance matching transformer, other than from the standpoint of possible signal degradation. These have been used in recording studios, radio stations and PA systems for decades.
What are you connecting as a source to the speakers and what is the output impedance of that? What is the input impedance of the speakers?
There's a lot of equipment that has 10 KOhm output impedance, not just guitars and even then, not all guitars have that exact impedance. Plus, a lot of guitar amps and effects have extremely high input impedance, in the area of 1 MegOhm. Line level is used to describe variable output from a preamp/receiver/integrated amp preamp section or from a mixer and it's also used when referring to record out signal from any of those, too. Unfortunately, it's not correct when referring to record out.
It would be great if the manufacturers would have actually come up with standards that were more compatible but before ANY of the standards were adopted, there were none, at all. Everyone had their own idea of how things should be connected and what the electrical characteristics should be. That wasted a lot of time for the advancement of audio equipment but the AES and IEEE have made it their mission to standardize everything, as much as possible. The old standards couldn't really be eliminated because so much equipment was out there and still in use, though.
I've been on a campaign to get rid of RCA inputs for a long time- I feel your pain. The problem is that RCA was in the position to get it shoved through at the time and had the money behind their ideas.
Re: the negative tied to the shield- that's going to be hard to separate from the XLR because pin 3 corresponds to the signal - (inverted) and when hardwiring from an RCA to XLR, pin 1 and pin 3 are sometimes connected to the shield. If it hums, pin 1 is disconnected.