Just in general, what constitutes a "ground plane"? Multi-layer PCB's have a ground plane that all grounds are connected to...in pedals and amps, grounds are connected to the chassis. What prevents the grounds from being connected to just a tiny piece of conductive material? I assume there's some kind of physical limit as to how small your grounding plane can be in order to work properly. Does it depend on the size of the signal being grounded?
To be planar, it just has to look like a plane; wide and flat.
To be an effective ground plane, it must have low resistance and low inductance. Resistance is a function of the material properties (resistivity) and the area through which current flows. Inductance is more complex, but one convenient fact is that it can be decreased by increasing the width of a conductor. The interesting thing is that a mostly flat wire will have equal inductance to a round wire of the same diameter. So a 1" wide copper trace on a circuit board will be just as good at reducing inductance as a 1" diameter wire. Pretty cool, especially if you're trying to fit into a small space.
The reason for decreasing resistance and inductance in the ground is that ground is the ideal voltage source/sink. It can supply infinite amps to maintain a zero volt potential. Any resistance or inductance in series with ground will decrease the current that can be supplied by ground, and in stompbox type circuits this can mean pesky oscillation or worse problems.
Thanks earthtonesaudio! So it sounds like the "ideal ground" would be something very wide, but not necessarily very thick? This would keep the area through which the current flows low and therefore keep the resistance low, as well as keep the inductance low by it being very wide. Am I thinking about it correctly?
Lower area means higher resistance, but otherwise you have the general idea. The resistivity of copper is so low that a small area doesn't mess it up that much.