Hello all!  What is large-signal stability and how does one do the analysis?  All the stability analysis in books (mine at least) concentrates on how the small-signal gain interacts...Af=A/(1+AB) where A and B are small-signal gains.

It sounds like to do large-signal stability you might do transient analysis using large signals and at different frequencies.  Maybe there's a rigorous way to do this.

Please clue me in!  

Thanks in advance!!!

Marc

Hi Marc,

Small signal stability analysis will show whether a circuit is stable or not. If not, then this will manifest itself as large signal oscillations.

Circuits such as oscillators are large-signal (and small signal) unstable, and you can do small signal analysis to show positive feedback, or from an RF point of view, one often measures the negative resistance (by means of sparameter analyses) and insures the net negative resistance of the "tank" (LC or xtal etc.) and circuit is negative.

Often in RF amplifier circuits (such as PA's etc.) then the analysis for stability is often measured by calculation of K-factor. K is a function of the two port sparameters S11, S21, S12, S22 and is often calculated in most RF simulators. K>1 means unconditionally stable. K<1 means could be unstable given the certain input/output terminations.

In such circuits as PA's where the S-parameters change depending on how hard (or how large) the signals are driven then you could view then the calculating K based upon large-signal-sparameters is applicable. I guess it is this circumstance you are interested in ? If so i guess some frequency swept transient analyses and some mathematical jiggery pokery are required.....

cheers

alan

Thanks Alan!  I'm not working on RF stuff or anything involving S-parameters.  I did talk to an RF guy just a few moments ago and he suggested something similar to what you are saying.  Basically, apply a big sine wave and do a parametric sweep of frequency.  The freq. range would be chosen to fit the desired operation frequencies.  I don't like the sound of the math jiggery pokery...

So far it sounds like I just do a bunch of large-signal transient analysis and hope I don't see any instabilities.  This doesn't sound that foolproof though.

ACWWong wrote on Apr 26^th, 2006, 3:49pm:

Hi Marc,

Of course one can always do small signal stability analysis around any large signal (DC or transient) operating point. An example is doing stability analysis of an op-amp when the output is at maximum swing.

cheers

aw

Hi Marc,

I would suggest on or both of the following:

1) A large signal transient simulation, and then apply a very narrow spike (unit impulse, or dirac), and show that you do not go off oscillating at any frequency. As the impluse contains an infinite frequency spectrum (obviously depending on how narrow it is) then it should excite any possible frequency of any instability/oscillation.

2) At extremes of large signal operation, run the small signal anaylsis off the tranisent operating points.

Hope this helps

alan

I can't resist chiming in on this one. Stability has always been one of my favorite topics.

I agree with the reviewer. It is always a good idea to check stability with transient simulations. Kick the circuit in as many ways as you can think of and look for unstable behavior that was not predicted by your small signal analysis.

As for a more rigorous approach, large signal stability is essentially the stability of nonlinear systems. If the system were linear, small signal stability would suffice. As I recall from the last class I took on nonlinear systems, there is no one method that suits all systems. However, probably the most rigorous and most general approach is to use Lyapunov functions. You can think of a Lyapunov function as an expression of the total instantaneous energy stored in the system. If, with no independent dynamic sources, the energy always decays with time, the system is stable. Sounds reasonable but I've only seen it used in high level proofs. I've rarely seen it applied to practical circuits.

I usually think of two kinds of large signal instability: the existance of a stable but undesired operating point, and a limit cycle. If an undesired operating point exists, if you kick the system hard enough, it might be sucked into the undesired operating point. An undesired stable operating point can be found by performing small signal stability analysis over a wide range of DC operating points. A latching condition could be an undesired operating point. The limit cycle potential, (a large signal oscillation), can usually be assessed using describing functions. The describing function is a large signal transfer function. It is like a small signal transfer function except that it depends on the amplitude of the input sinusoidal drive. Most text books on nonlinear systems will have a section on describing functions and you could probably find descriptions on the internet. However, if you like, I can try to explain them.

Hope this helps.

-Jess

Hi everybody,

personally I would tend to use Raul's approach and run a couple of transient simulations. Make sure to use square wave input signals and not sine waves, which are much less aggressive. You probably wouldn't see any overshoots, signalling stability issues, with the latter waveforms.

Do not forget to run the same type of simulation for common-mode stability too, people tend to forget this may be an issue.

Finally, regarding the simulation set-up, I wanted to point out that your transient simulation results are strongly dependent on your simulation parameters. The Backward Euler algorithm for example may stabilize unstable circuits, while the trapezoidal algorithm may exhibit numerical oscillations, which are not an indicator for circuit instability. So be careful when chosing your simulation algorithm, as well as the maximum time step and the vertical resolution, which help in attenuating numerical oscillations appearing due to the trapezoidal simulations.

Best,
Paul

Ezra,

You'd better read the manual or relative textbook to find what those parameters stand for? Usually, if a transient analysis fails, we may adjust the tolerance options.


Best regards,
Yawei