How can Barkhausen criteria be related with the simplest ring oscillator?

how can Barkhausen criteria be related with the simplest ring oscillator based in inverters ?

barkhausen criterion for oscillator

well, i THINK that it can be applied , u neeed a positive feedback and a beta*A > 1 ,
for a positive feedback u need an odd number of inverting stages and for the gain u may think of the inverter stage as two common source amplifiers (i.e. gain stage) with a unity feedback then the beta*A>1 , then we have oscillation.
if we talk about the three inverter stages ring osc. each of the three stage gives a phase shift of 180 degrees (i.e. total phase shift of 270 degree) therefore we need another 180 degree for +ve feedback , since there r three poles at the o/p of each stage then each of the poles give a freq. dependent phase shift that will reach -270 degree at infinite freuency , and hence we can see that the -180 degree required happens at freq. < inf. therefore osc. ocuurs.
regards.

barkhausen criterion

well since poles ( R & C ) are there then we will have an ideal sine wave copming out and not a pulse . here it shd be perceived in time domain .

what u said is also possible but inverters(bjt + Rc) with decent gain are applied there and o/p can be taken as sine wave.