Ohm hum from hell

If you have a rack with several units, any one of the units can be causing the ground loop hum problem. You need to isolate all the units from the rack rails (or at least start isolating them one at a time until you find the one causing the problem). "Humfrees" isolating tabs are sold just for this purpose - to insulate the racks from the rack rails. If its just the connection between two units an Ebtech Hum Eliminator will take care of it (and a lot less than the $380). http://www.musiciansfrien...channel-hum-eliminator I used to do amp repair (in Nashville) and customers would come in with ground loop hum problems and the fix many times was not the obvious or suspected problem. BTW, I use a POD X3 (bean type).

It sounds like you've already concluded that the problem is the result of an impedance mismatch, but that seems unlikely, especially given that your guitar has a built-in preamp (which should have a low enough output impedance to drive just about any load).

What's more likely is a wiring problem within the guitar, perhaps a ground wire solder connection that's come loose or was poorly soldered by the manufacturer. If the preamp was added rather than coming with the guitar originally, the technician that installed it may have made a mistake.

You hear the defect when distortion is used simply because you're boosting the gain to achieve the distortion effect. I'd suggest taking the guitar in to a knowledgeable technician and have them check for hum and examine the internal grounding for the pickup enclosures, preamp and tone control wiring. They may be able to add shielding around the electronics, assuming it's not the pickups themselves that are picking up hum.

As for your final question, impedances are not transferred from one unit to another. The guitar sees one load impedance only. The device it's plugged into sees only one load impedance - that of the next device in the chain - and so on. The effects of an impedance mismatch, however (added noise, altered frequency response), will be propagated down the chain.

Agree on using a few guitars and amps to test the offending guitar.... you must isolate the problem before you can solve it. 

Impedance mismatches generally mean poor signal transfer with possibly a substantial signal loss..... compensating for the signal loss requires you to turn things up and that will amplify hum that is in the circuit. 

I too was thinking that the transformers might be isolating stuff and creating the impression that they were a good solution. Those inexpensive in-line transformers aren't the best sounding audio transformers out there, so a more basic solution, as suggested above by shadow may be a good first thing to try.

Here's an illustration of the idea.

I really need to write this up<G>...

First - ground loops, and ground potential differences are NOT a problem, they exist everywhere, and you can't make them go away.

Second - single-ended interfaces, especially inputs, make the problem of noise pickup worse, but once again, they are not the problem, well, I think the world would be a better place without them, but that's cause I'm lazy<G>!

Third - you have to differentiate between different mechanisms for noise couping. And there are a bunch - it can be capacitively or indutively coupled, it can be coupled to the shield or to a signal conductor, etc. And the #1 problem is poorly designed equipment where the noise is allowed inside the case because the manufacturer violated the Pin-1 rule!

Fourth - Ground is not common, and common does not have to be ground. Yeah, makes my head spin too!

Fifth, probably should be first - Safety Ground is there for safety, not noise reduction. NEVER defeat it, not even temporarilly. It's marginal as a trouble-shooting tool, and it's dangerous. If you must break galvinic connections break them on the signal paths. And be wary of any device that claims to do so, the ONLY device that works is a transformer. If you are using it for troubleshooting you can get away with a cheap one, usually, If you are using it as a solution you'll need to spend the money on a good one, or suffer the audible penalty.

Trouble-shooting noise problems is, or can be, complex. So it's generally better to build for noise immunity.

The first step to a low noise system is a clean common reference, and power distribution. Note I say common, not ground. Ground is the final reference point, for safety reasons. Make every path to your reference as short and low impedance as possible.

You'll also need to think through the grounding scheme. There are two camps - single point grounding and mesh grounding. They both work, and they can even be combined, but you have to think it through. Single Point grounding is easier and less expensive, and has become the most common practice, at least in the US.

Power should be fed from a single breaker, or at least one leg. And the leg shouldn't have a lot of noise makers on it.

Balanced output to Balanced input is far and away the best interconnection... assuming the designers didn't do anything dumb - and you can't assume that I'm afraid.

Single-ended output to Balanced input is the second best solution. Wire it with a twisted pair, and connect the shield at the send only for starters. You may need to terminate the shield at the recieve end too in high RF environments.

Note that it is the twist of the signal pair that provides protection from magnetic fields. Shields have no effect at low frequencies.

While it's a bit more work, terminate the shields to the chassis, not the connector. You can, of course, do this only for devices that have a Pin-1 problem, but it's just as easy to start here.

If you are in a high noise environement you might want to modify single-ended sources to impedance balanced sources by adding an impedance between the low conductor and signal common.

Speaking of which - a balanced connection is balanced because the impedance to ground from either conductor is equal. It has nothing to do with the signal, and there is no requirment that both conductors carry a signal, only that each one has the same impedance to ground at the input. This allows the input stage to maximize Common Mode Rejection.

Single-ended source to Single-ended input, or Balanced source to single-ended input should be a last resort!

The worst is Balanced source because now you need to figure out if you need to ground or float the unused pin.

Avoid them and save me some typing<G>!

Other thoughts... impedance matching is not required, and in fact can make matters worse. Modern equipment (except guitars and guitar amplifiers) is designed for voltate transfer, not power transfer, and contrary to popular belief, characteristic impedance does not play a role in typical studio designs.

This is a huge topic - and an interesting one. I only skimmed it, so feel free to ask questions...