I am trying to put together for myself why dividing a sampled PXF analysis by the slope of the signal translates into jitter.
I understand the units makes sense ([V/V]/[V/S]=[S/V]), but conceptually, i am trying to make sense of it.
I want to start with what exactly a sampled PXF simulation does. I understand the difference between PAC and PXF, but what exactly is a sampled PXF trying to do?
The only definition i found is the following: "sampled analysis tells you the transfer function at a specific time-point in the periodic solution". I am looking for some more words
Sampled PXF gives you the result that you would see at the output of an ideal sampler. For the conversion of sampled voltage to jitter, figure 13 of https://designers-guide.org/analysis/PLLnoise+jitter.pdf might help.
You beat me to it Frank - didn't have a chance to answer this earlier. Saying that it "tells you the transfer function at a specific time-point in the periodic solution" is a bit misleading, so I don't like that way of describing it (it's still computing the time-averaged transfer function, but sampled at an instant in time). This means that you could still see the effect of a signal which is sampled at an earlier point in the period, delayed, and then sampled again later in the period; it's not the instantaneous transfer function around an operating point at an instant in time (that's what using xf in the acnames/actimes options of transient would tell you).
So a good way of thinking about it is that the ideal sampler that sampled pxf introduces is similar to what would happen if you had a subsequent stage in the circuit (e.g. a sample and hold, or something that makes a decision based on the signal you're sampling crossing a threshold) - it means that you can focus on the transfer function effects at the output at that point in time and not worry about the impact in the rest of the period, similar to the fact that noise contributions may have an impact throughout the period, but you are only concerned about the noise around a switching threshold if you're analysing jitter; the output noise during the rest of the period would not impact when the subsequent stage switches.
That may have confused you more, but hopefully it helps!
Hi Andrew, My understanding is that PXF derives the individual transfer functions (TFs) at a node at multiple time instants across the period and then computes the average of all TFs. One of these derived TFs can be the one derived at the time instant where we are interested, e.g. crossing point of the waveform. If I understand your explanation above sampled PXF still uses the time-averaged TF, not the one derived at the time instant of interest, to compute the sampled TF. I am wondering if my understanding is correct. Any further elaboration on sampled PXF is appreciated.
Also, you have mentioned that using xf in the acnames/actimes options of transient results in instantaneous transfer function which is apparently different from sampled PXF result. Would you please comment if my understanding is correct? Thank you for your time.
No, your understanding is incorrect. It does not derive the "individual transfer functions" at each time point and then average the result. The output at a particular time can be dependent on the inputs at earlier times in the period, and that would not happen if it was just a matter of instantaneous transfer functions at a specific time point. It would also be a bit pointless computing the individual transfer functions at each time point only to then sample the result and taking the result at just one time point. Doing what you think it does wouldn't include frequency translation effects, and would end up being the same as what xf with acnames/actimes does, which is to give you the transfer function at the bias point at a specific instant in time.
If you think about PAC (which is a little easier to grasp), it's like running a time-domain analysis with the small-signal source injected into the circuit, but rather than solving the equations of the normal non-linear equations of the devices, it solves the linearised model of the devices at the time-varying operating point (found from the PSS), and because it's linear it uses the same time points that were solved in the PSS. This means that your small signal input is mixing with the large-signal response found in the PSS, and from this you observe the frequency translation. PXF is similar, but in reverse - it computes the transfer function to a given output to each source (rather than injecting an input and computing the response at each node voltage/branch current).
It's a little hard to grasp, and to be honest you probably don't need to worry about this level of detail (and I'm simplifying things in my explanation). The key is that PXF takes into account the frequency translation caused by the non-linear response found during the periodic steady state; using XF at specific times during a period would not do that. Sampling the PXF at a particular time gives you the transfer function, including frequency translation, at that instant in time - it's just like adding an ideal sampler at the output of the circuit and then performing PXF.