I dont know what you mean by gain>1 and stability. How is this so?
Sorry, I'm not explaining very well. I'm mostly in a brainstorming mode here because I find this a faster way to get to answers.
What I mean is that usually we start up the oscillator with gain>1. This seems to be a necessary condition as Mike suggested (can we find exceptions?). However, it seems to me that Winterstone's latest circuit has gain>1 but is stable for small signals at startup. Then, when the gain saturates, the circuit becomes unstable. This is the opposite of usual oscillators that are unstable at startup and become stable if the gain is reduced below 1.
So, I'm questioning this gain>1 as a sufficient condition, without further qualification about the stability/instability we will find when closing a positive feedback loop. The Nyquist stability rules about "encirclement" seem relevant here to tell us which way it goes.
To me this latest circuit is not a good situation to have for an oscillator because (I think) it can't give stable and reliable oscillations. Gain is greater than one and stable will drive the signal higher, limit the gain and then make it unstable. To me this is undesirable for sufficient conditions for a practical oscillator. I would generally prefer to design a circuit that can start unstable and drive itself into a stable condition. Does that make any sense? I'm basically brainstorming here, because I haven't had time to do simulations on this yet. I have some time now, so I'll write a simulation program for Winterstone's last circuit. Maybe I'll have to change my mind after I do that.
I also do not believe that simply stating "noise" is sufficient for start up for the following reasons:
1. If the noise does not contain the right frequency, it wont start anyway, so 'noise' is under specified.
2. If the noise does contain the right frequency, it starts, but then 'noise' is over specified.
3. Since the "right frequency" is at the heart of it, it makes more sense to simply state the the right frequency has to be present as stimulus at start up.
In theory I think you are correct, but in practice noise is always present at all frequencies. If the oscillator is unstable at startup, then the tiniest noise will eventually get amplified at frequencies where gain>1, and this would generally be sufficient to start most oscillators. But, I'm not opposed to stating the condition in the way you say, since it is simple and all-inclusive and less vulnerable to debate and exceptions.
So what this implies is that there is no real circuit that will fail Barkhausen unless the right frequency is not present, and if the right frequency is not present then many circuits will fail even though analytically they pass the two Barkhausen tests.
Winterstone's circuit appears stable for small signals and it would seem the Barkhausen condtion can be met for some particular amplitudes and conditions. Yet, the instability when the gain is limited seems to be an impediment to making a good oscillation. At small signals the circuit is stable and a signal at the right frequency can get amplified since the gain>1. So, I'm not sure how we want to classify this. Is the crude oscillations we might get with this circuit something we want to classify as a "working oscillator"?.
So to be specific about this other new conditions, i would state it as "having at least the right frequency stimulus present at startup" (other frequencies can of course be present too, but are not necessary but the correct one *IS* necessary). It's a necessary condition and quite succinct.
I agree with that.