Hi,

I am trying to simulating pulling (not locking) between two LC tanks on cadence so not sure if it's possible to run pss to simulate pulling effects and had to revert to transient sims. I run into a lot of trouble, when I do a transient sim especially when w1-w2 = 2e-4*w1. The ppm difference is so small that when I try to plot the dft (even with sufficient resolution), i see the weird spurs closeby (like 3MHz) that are caused due to instantaneous frequency difference which scales linearly with reltol but this blows up simulation time. Is this expected in general or there is a way to avoid this?

PSS will not converge unless there is a purely periodic solution. Generally when simulating coupled oscillators the solution is not periodic and so PSS is not suitable. The only exception is when the coupling between the oscillators is so strong that the oscillators are fully entrained.

-Ken

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Yes. The issue is that the simulation algorithms are reacting to the large signals, meaning that the errors that are created are not independent of the signals, but are being modulated by the signals.

Behzad Razavi published a rather famous rant about this in "A Study of Phase  Noise in CMOS Oscillators" (JSSC 3/96). It is a particular frustration of mine as I came up with a solution to the problem and presented to all of the companies that are producing simulators for analog/RF ICs and they were all uninterested, saying that their customers seemed happy with the accuracy of their DFT results.

As a user it is quite difficult to eliminate this error. I think your best option is to leave reltol to something reasonable and instead shrink maxstep. This should reduce the largest source of this error.

I hesitate to make this recommendation as I find designers can overuse such advice. Normally controlling accuracy using maxstep is a very poor approach, but in this very specific case, it may be your best option.

-Ken

A well-designed transient noise should should shrink the time step in order to render white noise sources properly.  This is one of several reasons I would typically avoid transient noise as a well designed transient noise should be slow. However, as a side effect, if they do shrink the step, it should help with your problem. Even if they are not shrinking the time step, injecting randomness into the system would act to obscure the modulation effects, and so would likely reduce and obscure the beat tone you are seeing.

-Ken

It is just a coincidence. Because you are being plagued by small simulation errors, small seeming inconsequential changes to the circuit or the simulator settings can effect the results in unexpected ways, but I believe you will find them very fragile.

-Ken

It is possible, but I don't know how likely the chances are either way. For me to be able to say with any certainty one way or another I would need to be running simulations myself so that I could do detailed experiments.

The question you are asking is, is it possible that there are patterns in the error made in the simulation that mimic a plausible signal. Yes, that is possible. Is it happening in this case, I have no idea.

-Ken