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Every musician has fought hum and buzz in their amplifiers from time to time. What causes this nasty problem? How can it be solved? Let's take a look.
The root of the problem is the alternating current nature of our power system. The electricity that squirts out of a wall socket is changing all the time, 60 times per second in the USA and 50 times per second in much of the rest of the world. Unfortunately, that frequency and its harmonics are in the audio range, competing for face time on your sound system or amplifier.
In the 1800's, when electricity was first distributed, it was transmitted as direct current (DC), an unchanging current like that which comes out of a battery. The problem is that it cannot be easily changed in form, from low to high voltage and back, limiting its transmission distance. Alternating current (AC), however, can be easily changed. There was a battle between Edison and George Westinghouse on this topic, but the more efficient AC system won.
So we are stuck with AC power. A DC world would have been much quieter for musicians, but there would be power plants on every street corner.
However, if we are careful with our system connections, we can avoid that hideous buzz. To see how, let's look at what causes the buzz: Ground loops.
Ground loops occur when you can trace a loop in the ground connections between separate pieces of equipment in your band's stage setup. In the picture, we have a typical situation. There is an instrument amplifier, a direct box, a long snake, a PA system, and everything is plugged into the AC mains.
In a perfect world, this setup would present no problems. However, assume you are playing in a club with a restaurant. Your gear is not the only equipment plugged into those AC outlets. In the kitchen, there are refrigerators, ovens, stoves, and various other appliances, each of them switching on and off when needed. Each of them also has some leakage of electric current to its ground wire (that third prong on AC plugs in the USA). Motors and transformers are the main culprits here, and their magnetic fields induce some currents in their ground conductors.
These ground currents flow through the wiring in the wall, between the two sockets pictured. If the outlets are on different branch circuits, then the ground wires can be very long, going to and from the breaker box. These wires are not perfect conductors, and small voltages are actually measurable between the ground pins on adjacent AC wall outlets. (For safety, DO NOT attempt to measure this yourself!) Those voltages ensure that the PA and amplifier shown will have different voltages on their frames. In some cases, those voltages are large enough to sting your lips when you cozy up to the microphone while playing your guitar. Ouch!
When the circuit through the DI box completes the ground loop conduction path, what happens? A current flows around the loop! And that current causes very small voltages to appear in the signal paths as well, sometimes by magnetic induction, sometimes through the poor design of preamp circuits in the PA, or the use of unbalanced signal connections.
That's why you will find a "ground lift" switch on most DI boxes, to break this very ground loop.
To combat ground loops, use balanced XLR connections between your gear on the stage and the PA. On the stage, connect all your equipment to one branch circuit if possible. If that is not possible, be sure each musician's rig is connected to only one outlet, and that the separate rigs are not connected together or touching metal frames. NEVER, NEVER REMOVE THE GROUND PIN FROM ANY POWER CORD PLUG.
For example, my rig is contained all in one rolling rack, with an internal power strip. I need only one AC outlet to run the whole thing. Connecting the amp to one outlet and my effects devices to another would almost certainly cause ground loop noises.
I have an equalizer in that rack that hums to beat the band. That's not a ground loop problem, however, it is just a cheap eq! Got to buy quality to hear quality.
What about cable shielding? Some people recommend disconnecting the cable shield at one end to avoid ground loops. This is permissible on balanced signal cables with XLR connectors, and that is what the ground lift switch on the DI box does, as we discussed above. The signal is carried by opposite polarity signals on the two remaining conductors in the cable. The shield remains connected at one end of the cable, preventing noise from fouling the signal. Breaking the shield path prevents ground loop currents from flowing.
On guitar signal cables (as used with a guitar or bass), the signal is unbalanced, meaning that there is one signal wire and one ground wire. It does absolutely no good to leave the shield hanging at one end of a guitar cable, and can only increase noise (though slightly and probably negligibly). Also, there is zero chance of a ground loop between your amp and guitar because there is no loop!
For keyboards or other equipment powered separately, it's a little more complicated because there may be several devices plugged into different power outlets. There is then the possibility of ground loops when connecting the audio jacks from box to box.
This is a difficult situation because generally all of the audio signals are unbalanced, and you cannot disconnect the shield in such a case. The best prevention is to plug the amp and keyboard into the same AC mains outlet.
Why can't you disconnect the shield? If the cable has only a shield and signal conductor, then the shield conductor is also needed to carry the signal. If you disconnect it, then the signal will flow through whatever ground connection it can find. That connection will likely be through the power mains, and will be noisy.
In summary, buy good quality signal cables, shield connected at both ends. Use balanced connections between the stage and PA. And plug each musician's stage rig into one outlet, if possible.