nrk1 wrote on Nov 20th, 2012, 9:15am:buddypoor wrote on Nov 20th, 2012, 6:43am:Raj, you strictly must discriminate between
(a) linear/harmonic oscillators of at least 2nd order (pole pair in the right s-plane), and
(b) relaxation generators (I avoid the term "oscillator"), which are of 1st order only.
Your circuit belongs to type (b) and there is no equivalence with a negative-resistance concept. OK?
This distinction is correct. But just want to point out that a schmitt trigger is a second order system in the sense that there are two state variables-the capacitor voltage and the state of the schmitt trigger. I think it is not possible to make an oscillator with a single state variable.
You are correct. At least two state variables are needed. It's a mathematical principle that goes beyond EE and can be found in mechanical engineering, civil engineering, etc..
About the relaxation oscillator: its poles are moving back and forth on the s-plane. At the moment the sign changes, the poles are complex, and at that moment in time you could apply the Barkhausen criterion. If it doesn't suffice, the relaxation oscillator will never switch, and the oscillation is stopped.
Considering the naming (generator/oscillator): to my opinion, the circuit produces a stable period and is therefore rightfully called an oscillator. For some 'so called' oscillators on the other hand that can have chaotic states, I'd be more reluctant.