I did that, too, (except using impedances) and got the same results I got setting the input voltages equal.I let XC1=XC2+XL1 and I got a real frequency of 7.17kHz.
Don't let us hinder you from taking on this analysis.Staying with the OP's original circuit, one could undertake the "traditional" stability analysis in which the positive feedback path is "broken" and the open loop transfer function [w.r.t the feedback signal] is obtained.
A bode plot of the the open loop TF would then provide some understanding of the closed loop stability - based on gain / phase margins. Of course this might not predict the large scale limit cycle oscillations which are also likely.
As the previous posts indicate the problem arises of characterizing the real op-amp behavior vs an ideal op-amp model.
I have seen that app note before. It's a very good paper. You won't find any LC oscillators there, but the general theory might be applicable (but not to the original circuit).I found this App Note from TI:
http://www.ti.com/sc/docs/apps/msp/journal/aug2000/aug_07.pdf
It's only 5 pages long and seems like it should be pretty readable. I don't have time to read it now, but perhaps tonight before I go to sleep.
I think we are in agreement here. The analysis resulted in an imaginary sinusoidal oscillation frequency, which I conjectured probably meant that the system could not oscillate sinusoidally. As soon as that is said, then the meaning of the 7.17kHz becomes very murky. Someone that understands this stuff well could probably extract useful information from it, but I certainly can't. The simulated output showing that it is a quasi-square wave output supports that and let me to wonder if redoing the analysis under the assumption that you would have a few harmonically related components might yield a real value for the fundamental frequency. I don't know.So in theory the arrangement would not oscillate at any particular sinusoidal frequency. Whilst not conclusive, this makes me wary of the earlier analysis giving an oscillation frequency of j7.17kHz. I also have a conceptual difficulty with an imaginary solution for a notionally real condition for a physical system.
This is very much in keeping with the discussion in the TI App Note I linked previously. That was a good read. Of course, there's only so much that can be put into a five page paper, but I think that overall he chose well what he put in there.The oscillations observed in the simulation by the OP are presumably therefore limit cycle excursions with the op-amp switching between its ± output limits. If the op-amp were ideal I doubt one could justifiably conjecture the existence of oscillations even in that mode.
This sounds pretty close to the 5.033kHz at which the LC series network in the feedback to the non inverting input is resonant.Thanks WBahn,
I've realised my analysis using phase and gain margin based on the inbuilt functions in my Scilab application would be "looking" for the 0dB / 180° [negative feedback mode] transition. With +ve feedback one would look for 0° phase shift at 0dB. The attached Bode plot is for the OP's circuit open loop response showing a highly unstable [0dB / 0°] point at about 5kHz - visible in the attachment. This may give some insight as to why small scale oscillations might fail to occur in practice. A study of the well-known Wien bridge circuit is informative as the latter's open loop response transition is well defined & stable at the critical frequency. The second attachment shows a typical Wien bridge open loop Bode plot with circuit parameters adjusted such that oscillation just initiates. Chalk and cheese.