Electronic – How much power can electrical noise (EMI) produce

The solution was to physically separate the power connections for the audio components. While @Dave mentioned in the comments something about a star ground topology, the problem was that while the ground connections were all centralized, the Vcc connections were also, and shouldn't have been.

In the original design, power was supplied to the entire assembly via a small PCB with header pins for each separate component. Two rows of male header pins, one for 12V DC and one for ground. In this arrangement, all of the noise was being dumped onto the audio components each time the servo motor was actuated. Adding capacitors helped slightly, but certainly not enough.

The main two wires supplying the small power distribution PCB are about 10 cm long. I added a second pair, and created a second power distribution PCB. The original one was used for the servos and receiver, while the new one was used for audio and amplifier. The "Y" split in the power cable ultimately had the effect of keeping the power clean on the audio side.

I also removed the ground connection between the RC receiver and Arduino, though this was unnecessary. Its presence did not add noise, nor did its absence cause triggering problems.

An electrical engineer coworker advised me that it was important to have separate power supplies for motors versus digital components. While this project still only uses one power supply, the solution was to split the power as early as practical, and dedicate each to its respective purpose.

This may be reasonable or not, depending on the environment.

First, you should have reasons to suspect EMI may be a problem, otherwise I wouldn't bother.

Second, you should understand where the source of EMI noise is. If the source is near the device (or the device itself), grounding a back plane via the cable sounds like a good thing to do, provided the device is hand-held and cannot have its own proper grounding.

On the other hand, if the device is operated in a relatively calm (EMI-vise) environment, whereas the cable goes e.g. through a plant with heavy machinery, your ground connection will do more harm than good. The cable shield will effectively act as antenna, picking up all the noise from the plant and delivering it to your device, which would be much better off without it. In this case, you should still ground the cable shield, but not connect it to the device.