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Paul Geraedts

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PSS time resolution for PXF
Oct 15^th, 2020, 2:06pm

Ken Kundert wrote on Aug 12^th, 2019, 2:56pm:

PNoise starts with a PXF analysis on the periodically time varying linear representation of the circuit about it periodic operating point, which is used to compute the transfer functions from every noise source to the output.

If I understand correctly, for PXF to come up with accurate noise transfer functions the underlying PSS needs to compute all events along the corresponding transfer paths accurately. If I recall correctly, ~10 time points per crossing would be good. I recently experienced this as a result of not being sufficiently careful in Verilog-A code; When I lower the number of time points per crossing from ~10 down to zero the noise results change in an intriguing way.

So now my question: what makes the PSS time resolution sufficiently accurate for PXF? (What is the theoretical background? What happens when the resolution is not enough?)

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Ken Kundert Global Moderator Offline Posts: 2386 Silicon Valley	Re: PSS time resolution for PXF Reply #1 - Oct 15^th, 2020, 3:34pm 10 points per crossing? Verilog-A? I think you need to be more specific in what you are asking. -Ken
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Paul Geraedts

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Re: PSS time resolution for PXF
Reply #2 - Oct 16^th, 2020, 1:44am

Recently, I investigated an unexpected noise contribution in the noise summary of sample Pnoise output. It brought me to have a closer look at some of my Verilog-A code.

The signal path from this specific noise source to the output flows through this Verilog-A block: from the control input to the output. This control input is sampling another input of the block; i.e. the control input continuously modulates the conductance of the sampling switch inside a voltage window and clips it outside.

It turned out that I had forgotten to bound the step size sufficiently inside this voltage window. When I took care of sufficient time points the noise summary was as expected.

Now my question: what number of time points is sufficient during such a crossing? (I am interested in the theorectical background.)

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Ken Kundert

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Re: PSS time resolution for PXF
Reply #3 - Oct 16^th, 2020, 10:09am

I do not know. �I do know is zero is too few.

Perhaps the way to think about it is to think about how the gain is varying over time. If the simulator only places steps where the block is in saturation, then the apparent gain is zero at all time. But if the simulator places one point in the active region, the gain is nonzero at that point. In between the computed points the simulator interpolates. So presumably the gain as a function of time now looks something like a tent; zero in most places but it peaks up at the point sitting in the active region. If you place more points in the active region you further resolve the shape of the tent. The shape of the tent is the modulation function for the circuit. It describes how much of the input is making it to the output as a function of time. IN otherwords it is the gain as a function of time. So the question becomes, how important is resolving the shape of the modulation function to the performance of your circuit. Presumably with a small number of points you can get a reasonable estimate of the gain, but you might need more if you want to accurately model frequency conversion effects.

If you are using a Verilog-A model, then it would not seem like resolving the shape of the modulation function is all that important because the modulation function of the Verilog-A model will be different from that of the circuit.

-Ken

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Paul Geraedts

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Re: PSS time resolution for PXF
Reply #4 - Oct 16^th, 2020, 12:56pm

The Verilog-A block takes care of only certain post-processing of the output signal of the circuit (double correlated sampling).

In case there was no time point describing the tent the (sampled Pxf) gain was indeed zero (as expected). Strangely enough in that case most (sampled Pnoise) noise contributions were not that much off. Mostly a certain 1/f noise contribution turned out to be much smaller. This noise situation was similar for both zero and 3 time points along the window, but with 3 time points the gain was closer to expectation (but still much off). When going for ~10 time points results were as expected. As if some sort of averaging effect plays a role.

Still somewhat of a riddle to me. Anyhow, thanks for your time Ken!

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Paul Geraedts

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Re: PSS time resolution for PXF
Reply #5 - Oct 16^th, 2020, 2:26pm

Hearing myself made me go back to the data set from that time and have another look. Fortunately one piece of the puzzle is solved now.

What I mentioned about the number of time points scheduled is only true for the voltage window when the signal is sampled to use for the correlated double sampling (I only checked this edge at the time); Not for the voltage window when the reference is sampled (this contained one time point when the other window contained none). I forgot to check that carefully at the time: sloppy. So the white noise is probably only off by sqrt(2). I cannot yet explain why the 1/f noise contribution was smaller and not larger though. Possibly something for a next time.

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