I have been attempting to analyze the following common source ring oscillator:
I am having some trouble here. Based on my understanding, each stage of the FETs provides 270 degrees of phase shift total. 180 from the inverting common source, and 90 from a pole due to the capacitor. In order to oscillate we need 360 degrees total. With only two stages of the CS FETs, the necessary phase shift for oscillation is there but would be stable at either rail. Why would it still be stable?
Now, at 3 stages, the circuit oscillates provided the gain of each stage is greater than or equal to 2. Can someone explain this as well? I do not understand why it is 2 instead of one, nor can I seem to understand the math behind this.