Analog design of oscillators often proceeds as a feedback problem where the denominator of the second order response is set to zero to produce oscillation. The real part of the pole is designed to lie in the RHP so that the oscillation will start, and most often the amplitude limits at some point where the circuit non-linearities force the real part into the LHP.

But, some designs are not nearly so forgiving, and require some sort of amplitude regulation feedback system. The operation of this is to regulate the real part of the pole back and forth across the imaginary axis to make the amplitude grow or decay.

My problem is that I can't see any tractable way to analyze this. Empirical designs can sometimes be made to work satisfactorily, but sometimes there is just no substitute for a real analytical understanding for how things can be made to work.

Does anyone have any thoughts on this? What look to be the most useful refs on this all seem to be in the IEEE archives, access to which would be, for me, prohibitive since I'm retired.

Appreciate any comments.

Thanks,

Dave

 

The Electrician posted this link to a useful paper some time back ...

https://portail.telecom-bretagne.eu/publi/public/download.jsp?id_publication=6959

Can be referenced back to this thread ....

http://forum.allaboutcircuits.com/showthread.php?t=81678

 

Thanks, t_n_k for the interesting paper. Yes, this is pretty much exactly what I am doing. A linear oscillator operating in the linear range.

Except that I want to regulate the amplitude of the actual oscillation within it's linear range. So, the system response under regulation consists of making the real part of the complex root go back an forth a small amount across the real axis to make the oscillation dampen or grow.

My question is how to design this regulation loop. The feedback portion of the regulation loop is unrelated to the oscillation frequency, pretty much. But, the response of the real part of a root is now a time dependent function. So, I'm stuck really, on how to analyze this.

I can use SPICE to make the design up to a point (essentially empirically), but for some feedback designs, it appears I really need a good analytical model to design the loop compensation role-off.

Any ideas?

Thanks,

Dave

 

Would there be a way to use Middlebrook's GFT in an AC simulation to characterize the system?

Thanks,

Dave