I simulated this circuit in LTspice IV, to illustrate the phase change from stage to stage.
All such "rings" oscillate at the frequency that gives a 360 degree phase change around the loop, (and the loop gain has to be greater than 1 as well) So if we have 3 stages, the phase progression is 360/3 from each stage, if 4 stages are used, then each stage changes the phase by 360/4, etc.. (assuming all the stages are identical) If two stages are used, each stage has to be an inverting amplifier, i.e. produce a 180 deg phase change. And that won't happen with inductors and capacitors, I don't think, the components must be resistive, or operate at resonance where the circuit is resistive.
EM
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