Funny you mention toroids. Both powdered iron mixes and ferrites are available in that shape. Fair-Rite's products are numbered, so be careful not to confuse them with Micrometals'! (Others use alphanumeric designations, e.g. Ferroxcube's 3F3 and etc., TDK's N97 and etc..)
FBs are available anywhere from microscopic (SMT chips well under 0402) to over 6" across. Beads are intended for use on component leads or over cables; the cable kind come pretty large, so somewhere in the 1-3" range they kind of cross over to being toroids for RF and power transformers. But they're all the same thing, just in different heights and diameters, it doesn't matter.
Closed ferrite shapes, like beads, toroids, and ungapped shapes, are not useful under DC bias.
The general purpose is to add impedance, especially at RF, to the conductor or cable. Obviously, an important first step in making a transformer, hence that application as well. For signal applications, this adds damping and high frequency filtering, especially in combination with some capacitors and maybe resistors. This doesn't help much for single power lines (because of saturation), but if the current is equal and opposite (as should be the case for the sum of all conductors in a cable), saturation is avoided and common mode impedance is introduced. This is especially helpful for EMC, dampening the resonances of cables, and to some extent filtering noise (from within the device, or induced on it from ambient sources).
FBs can be used on transistors, usually the input (gate/base) or common (source/emitter) terminals to act to slow down switching speed, or help neutralize unstable impedances (low input resistance tends to result in oscillation in the 10-100MHz range).
Whether applying a FB is right for you, would require a study of just what's oscillating (if anything), and some analysis of whether it'll help at all, or actually make things worse (FBs aren't by any means a miracle).
Tim
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