HB Analysis on PLL

I rather doubt 50 harmonics would be enough with a divide ratio of 24 - that's only 2 harmonics to represent the VCO output frequency (and you can already see quite a bit of Gibbs effect on the reference clock). However, the first thing I would check is what is going on in the initial transient results (you've saved them). Is the VCO even oscillating? Perhaps it hasn't started properly... (that might explain why the VCO output is flat and the divider output is flat, and also might explain how it managed to converge with rather few harmonics)?

Is there a particular reason why you want to use harmonic balance for this rather than pss with shooting?

Andrew

The VCO is oscillating and the PLL is settling, see below:

I used PSS HB option, behaved similarly. I used PSS Shooting and it gave non-convergence over and over. 

Can you zoom into a couple of periods of the 240MHz (near the end) and show that?

Can you also please show the analysis statements from the bottom of the input.scs (paste them here)?

Andrew

Below is the analysis statements:

----------------------------- 

simulatorOptions options psfversion="1.4.0" reltol=1e-3 vabstol=1e-6 \
iabstol=1e-12 temp=175 tnom=27 scalem=1.0 scale=1.0 gmin=1e-12 \
rforce=1 maxnotes=5 maxwarns=5 digits=5 cols=80 pivrel=1e-3 \
sensfile="../psf/sens.output" checklimitdest=psf
hb hb tstab=10u saveinit=yes oversample=[10] fundfreqs=[(20M)]
+ maxharms=[50] errpreset=moderate annotate=status
modelParameter info what=models where=rawfile
element info what=inst where=rawfile
outputParameter info what=output where=rawfile
designParamVals info what=parameters where=rawfile
primitives info what=primitives where=rawfile
subckts info what=subckts where=rawfile

----------------------------- 

OK, oversample of 10 is probably not particularly helpful here - you might need 2 or 4, but it's rare to need beyond that. I would guess you're going to want at least 200 harmonics to capture the edges with some level of fidelity. I'm not that sure why the i_clk_240MHz should be flat in the time domain output from the hb unless the oscillation has died out completely - it's really hard to tell without seeing the example.

Can you contact customer support?

Andrew

I will contact support...

Just one question: do we need to set an Initial Condition in the oscillator to get oscillation going for the HB? I thought if the HB tan gets going it should be sufficient for the HB?!

No - it's clearly oscillating in the transient phase and that is used to determine the starting point for the harmonic balance solution. It's possible however that the harmonic balance solution is not sufficient to sustain the oscillation - which is why I was suggesting increasing the number of harmonics (50 means that the maximum frequency in the circuit is 1GHz, which is clearly nonsense) might help. Having too few harmonics means that you are trying to represent the solution with just the harmonics you've asked for, and that means that circuit state in the frequency domain doesn't match reality - it may iterate towards the oscillation dying out. I'm guessing a bit here, because I don't know what was going on and haven't seen the log file.

So try increasing the number of harmonics to 200 or 400 to see whether that helps (and reduce oversampling to 2 or 4).

Andrew

Well 1G > 2x480M (> Nyquist) so I expected to see at least one tick of output or VCO within the 1/20MHz period. FYI, I used 200 harmonics with 4 oversampling and it converged buy output and VCO were still stuck at 0. Then I tried 500 harmonics with 2 oversampling and it failed convergence. 

Dear fortune100worse,

I am jumping into your post a bit later...but have been monitoring Andrew's good suggestions...I might add a few comments based on my experiences simulating high Q resonator and ring VCO. Please consider these my comments and not necessarily consistent with Andrew's opinions and suggestions!

fortune100worse said:

Well 1G > 2x480M (> Nyquist) so I expected to see at least one tick of output or VCO within the 1/20MHz period. FYI, I used 200 harmonics with 4 oversampling and it converged buy output and VCO were still stuck at 0. Then I tried 500 harmonics with 2 oversampling and it failed convergence. 

I am not sure of the type of VCO you are attempting to simulate in your PLL simulation. However, higher Q based VCO do require some "special" attention - especially with respect to their start-up and HB convergence behavior. A few comments...

fortune100worse said:

hb hb tstab=10u saveinit=yes oversample=[10] fundfreqs=[(20M)]
+ maxharms=[50] errpreset=moderate annotate=status

1. I noticed you have set your errpreset to "moderate". I would suggest using a value of "conservative" for any VCO based on a relatively high Q resonator (such as an LC or quartz resonator) or one in which the accuracy of the frequency of oscillation is important. to you (i..e., even if your VCO is a ring based VCO). This will likely increase the simulation time somewhat, but it is probably more acceptable than waiting for your existing simulation times and seeing no oscillation from your VCO!

2. From my experience, and especially since your simulation time is 10 us, the default value of the integration timestep defined by your use of an errpreset of "moderate" may not be sufficient to assume start-up. The maximum timestep of your simulation, in turn, sets the bound on the simulator numerical noise which is the mechanism you are using the excite your VCO.and may not be sufficient to assure VCO start-up and convergence in an HB simulation. I recommend forcing a value of maxstep to be 1/100 or 1/200 of the VCO period (or less). Hence, for a 20 MHz based VCO, I might suggest a maxstep of 500 ps or 250 ps or less (1/20 MHz = 50 ns and 50 ns/100 = 500 ps). Check the value your simulation is using in your spectre.out file.

3.  A final thought...are you using  spectre +aps or spectre ++aps? I might also suggest if you are using spectre ++aps, you use +aps. I have seem some cases where, although it reduces simulation time, the difference in accuracy using ++aps in lieu of +aps can be an issue in precision VCO. If you are not using either +aps nor ++aps (and hence using just spectre), the use of +aps will reduce your simulation time signficantly without a significant loss in simulator accuracy.

Anyway, a few thoughts that came to mind to possibly provide some help or insight into your issue...hope they do!

Shawn

Dear fortune100worse,

I am jumping into your post a bit later...but have been monitoring Andrew's good suggestions...I might add a few comments based on my experiences simulating high Q resonator and ring VCO. Please consider these my comments and not necessarily consistent with Andrew's opinions and suggestions!

fortune100worse said:

Well 1G > 2x480M (> Nyquist) so I expected to see at least one tick of output or VCO within the 1/20MHz period. FYI, I used 200 harmonics with 4 oversampling and it converged buy output and VCO were still stuck at 0. Then I tried 500 harmonics with 2 oversampling and it failed convergence. 

I am not sure of the type of VCO you are attempting to simulate in your PLL simulation. However, higher Q based VCO do require some "special" attention - especially with respect to their start-up and HB convergence behavior. A few comments...

fortune100worse said:

hb hb tstab=10u saveinit=yes oversample=[10] fundfreqs=[(20M)]
+ maxharms=[50] errpreset=moderate annotate=status

1. I noticed you have set your errpreset to "moderate". I would suggest using a value of "conservative" for any VCO based on a relatively high Q resonator (such as an LC or quartz resonator) or one in which the accuracy of the frequency of oscillation is important. to you (i..e., even if your VCO is a ring based VCO). This will likely increase the simulation time somewhat, but it is probably more acceptable than waiting for your existing simulation times and seeing no oscillation from your VCO!

2. From my experience, and especially since your simulation time is 10 us, the default value of the integration timestep defined by your use of an errpreset of "moderate" may not be sufficient to assume start-up. The maximum timestep of your simulation, in turn, sets the bound on the simulator numerical noise which is the mechanism you are using the excite your VCO.and may not be sufficient to assure VCO start-up and convergence in an HB simulation. I recommend forcing a value of maxstep to be 1/100 or 1/200 of the VCO period (or less). Hence, for a 20 MHz based VCO, I might suggest a maxstep of 500 ps or 250 ps or less (1/20 MHz = 50 ns and 50 ns/100 = 500 ps). Check the value your simulation is using in your spectre.out file.

3.  A final thought...are you using  spectre +aps or spectre ++aps? I might also suggest if you are using spectre ++aps, you use +aps. I have seem some cases where, although it reduces simulation time, the difference in accuracy using ++aps in lieu of +aps can be an issue in precision VCO. If you are not using either +aps nor ++aps (and hence using just spectre), the use of +aps will reduce your simulation time signficantly without a significant loss in simulator accuracy.

Anyway, a few thoughts that came to mind to possibly provide some help or insight into your issue...hope they do!

Shawn

fortune100worse said:

Well 1G > 2x480M (> Nyquist) so I expected to see at least one tick of output or VCO within the 1/20MHz period. FYI, I used 200 harmonics with 4 oversampling and it converged buy output and VCO were still stuck at 0. Then I tried 500 harmonics with 2 oversampling and it failed convergence. 

From this, I think you have a flawed understanding of the importance of harmonics in a harmonic balance simulator. 

With the shooting approach (Shooting Newton) available in PSS, the simulation solution is essentially a transient (with additional controls to ensure sufficient time steps to guarantee enough spectral accuracy, plus techniques to ensure that the result is periodic and also to accelerate finding the settled steady state). The number of harmonics is an output parameter, and doesn't particularly affect the accuracy of the solution - it just controls how many harmonics you observe in the frequency domain results. Put another way, the analysis will naturally follow the transitions in the output signals (just as transient does) and a high number harmonics simply ensures there are enough points simulated in the period captured in order to ensure that those higher harmonics can be captured with enough fidelity. The solution itself is the time domain simulation and that should handle pretty nonlinear designs. The fact that it doesn't converge is a little odd - but more on that in a moment.

With the harmonic balance approach available either in pss or hb analyses (the engine is the same; it's just the interface to the engine that is different), the solution is a harmonic series in the frequency domain, represented by the number of harmonics you ask for. For a weakly nonlinear system, you can represent the solution with a small vector of complex harmonic components for each node, and so it can be quite efficient. However, it is very important to ask for sufficient harmonics, because all of the energy in the signals at every node and branch current has to completely be contained within the number of harmonics you've asked for. In other words, asking for 2 harmonics of a square wave frequency is going to massively misrepresent that signal and the energy will spread into places it's not supposed to be. That can lead to significant inaccuracy and strange results (quite often you'd see it fail to converge for any reasonable circuit). As with shooting, the harmonic balance analysis is trying to find the settled steady state performance of the circuit and this means that it can predict a solution a long way away from the initial "guess" that it's given (based on the initial transient results), which could be that that the oscillation has died out (maybe). It does do some occasional points in the time domain (it does an inverse Fourier transform from the frequency domain solution, and re-solves at a set of sample points, oversampled if needed, to take into account the nonlinear components in the circuit), but the primary solution is the frequency domain solution as described by the number of harmonics. you've asked for. For this reason, 50 is definitely too few points.

Now, there may be other things going on here (and bear in mind I'm rather blind to your actual circuit):

1. Are you using the oscillator mode of the hb or pss analysis? If so, you should turn it off. A PLL is a driven circuit, not autonomous (i.e. not an oscillator). The fact that it has an oscillator within the circuit is irrelevant, because all that oscillator does is produce a harmonic of the input reference clock - as such, all frequencies should be harmonics of the input frequency (or maybe of a subharmonic of the input frequency - more on that  next). Using oscillator mode on something that isn't an oscillator can lead to non-convergence.
2. How is your divider implemented? It's a divide by 12 - but are there any lower frequencies within the divider? Remember that with both shooting and harmonic balance, every node in the circuit must be an integer multiple of the fundamental frequency - so if it (say) really divided by 16 and then reset when the divider reached a count of 12, then you'd have 15MHz in the circuit - and so your fundamental would need to be 5MHz (as the greatest common divisor of 20MHz and 15MHz). Getting this wrong would almost certainly cause shooting to fail to converge, but with too few harmonics and harmonic balance it might have ended up killing the oscillator and converging with the oscillator not running (bit of a wild guess here though - I could easily be wrong).

Regards,

Andrew

Thanks for your detailed reply. 

I understand well that harmonics count has a much more pronounced effect on the HB analysis as it basically tries to find a weighted combination of the available harmonics to represent all periodic signals within the circuit and if not enough harmonics are specified, then the accuracy of representation can be affected. My point was even with 50 or 200 that I tried, I expected to see at least the DC component of the VCO or PLL outputs (which should be 750mV or VDD/2) but I saw flat out 0v; and this result was with convergence.

I am not using oscillator mode, it is a PLL and it is a driven circuit hence oscillator option is turned off. 

The divider is made of div23 cells (5 of those): two cells are configured as divide by 2 and 1 as divide by 3 hence 2x2x3=12 and 2 are not dividing (or divide by 1). However, you are absolutely right that some unforeseen frequencies within the  divider maybe the root cause, that is what I am currently investigating.

I realised (in the middle of the night, as you do...) that you'd already shown in your responses yesterday that you weren't using oscillator mode. Sorry about that - I was on a bit of a roll when I wrote my last reply!

Andrew

In the meantime, I discovered the feedback divider made of 2/3 dividers was designed to cover a wide range of divide ratios besides the simulated one of 12; this capability caused the feedback divider to produce other frequencies: in this particular simulated case I explained earlier, the feedback divider also produced a 20MHz/3 (6.67MHz) tone. 

After changing fundamental from 20MHz to 20MHz/3 (I exactly put 20M/3 in the entry box); the Shooting method still complained but the HB analysis using oversampling of 10, harmonics count of 120, and very importantly maxperiods of 200 (default appears to be 100), converged and produced the attached picture. Clearly the reference and output are periodic.

I repeated and increased the number of harmonics to 180, 240, and even 600 in HB analysis keeping the over sampling still at 10:  log file reported " WARNING (SPCRTRF-15319" too small number of harmonics in the case of 180 and 240 (also earlier for the 120) but for 600 it didn't (seems like 600 harmonics are sufficient). However, all HB simulations failed convergence (only 120 harmonics converged; 180, 240, 600 all failed). 

HB complained on few signals in the flip-flip cells of the feedback divider coming from a standard cell library; the convergence norm for these signals is about 50 to 100 (so not too big but also not getting any smaller). The waveform of such signals is also attached below. I wonder if these waveforms are not periodic or how the simulator will react to such waveforms?! 

With your new fundamental frequency, 120 harmonics is still too low (that's equivalent to 40 with your older setup with 20MHz fundamental, so even worse than before), and oversample=10 is a crutch - that also indicates that you have insufficient harmonics. Given that convergence is not improving with more harmonics, and that it still doesn't converge with shooting (which I think would be more appropriate), I wonder whether you've really identified the true lowest common frequency.

I can't see from the last plot whether it appears to be periodic or not because it's truncated.

Debugging this kind of thing in the forum is very hard - can you contact customer support?

Andrew

Hi Andrew,

I got the HB converged with 600 and 900 harmonics (4.8GHz and 6GHz), this is more than enough even if I were to do a HBNOISE with >=20 sidebands (please correct me if I am wrong). 

HB converged when I set cmin=3f for 600 harmonics and when I set cmin=4f for 900 harmonics. Obviously I cannot increase cmin arbitrarily because it affects the circuit at some point (which implies a limit on the maximum harmonics I can use).

Now my question to Cadence: how does increasing cmin improve HB convergence at higher harmonics?? How come cmin=3f converged with 600 harmonics but cmin=4f was needed for 900 harmonics?

Dear fortune100worse,

I am sorry I did not respond earlier - but for some reason did receive copies of all your correspondences with Andrew concerning your continual convergence issue! You wrote something in your post of 12 days ago...

fortune100worse said:

The divider is made of div23 cells (5 of those): two cells are configured as divide by 2 and 1 as divide by 3 hence 2x2x3=12 and 2 are not dividing (or divide by 1).

and then...

fortune100worse said:

In the meantime, I discovered the feedback divider made of 2/3 dividers was designed to cover a wide range of divide ratios besides the simulated one of 12; this capability caused the feedback divider to produce other frequencies: in this particular simulated case I explained earlier, the feedback divider also produced a 20MHz/3 (6.67MHz) tone. 

I have  a lot of experience with div23 cells in simulations. I think the reason, indeed, you are experiencing harmonic balance related convergence is that the frequency components in the response are not integrally related due to the nature of the div23 cell. If your end goal is to estimate the steady-state response of your PLL, have you considered performing a standard transient analysis and allowing it to approach staady-state?

This is the approach we use for multi-modulus, LC VCO, based PLL (i.e., contains div23 cells in feedback divider of PLL) with much success. The simulation times to reach steady-stae for loop bandwidths on the order of MHz are quite reasonable for netlists composed even from extracted views of PLL components using spectre X with very conservative levels of post layout optimization. The aperiodic behavior is quite evident in the simulated results and useful to study in Fourier analyses.

Let me know if I can better clarify my comments.

fortune100worse said:

Now my question to Cadence: how does increasing cmin improve HB convergence at higher harmonics?? How come cmin=3f converged with 600 harmonics but cmin=4f was needed for 900 harmonics?

I do not believe the improvement you are observing is a direct result of changing coin. There is a nice discussion of what cmin does in a transient simulation in the On-line support article at URL:

https://support.cadence.com/apex/ArticleAttachmentPortal?id=a1Od0000000nSkmEAE&pageName=ArticleContent

Often, as noted in the article, the use of a larger cmin "masks" model related discontinuities and other simulation artifiacts (for example, ideal transition times limited only by simulator tilmestep). I would consider re-examining your models and other netlist parameters to make sure none of these exist. Even if they do not, I, personally, do not think the HB simulation methodology is well suited for a circuit containing a fractional divider based circuit element and would still suggest the use of a conventional transient analysis. If you want to re-start the simulation close to its steady-state in a second simulation, you might consider saving the simulation state and re-starting to avoid much of the low frequency behavior of the loop and rapidly approach a new steady-state. If you are not familiar with this process, it is also detailed in your spectre manual, or the On-line support article at URL:

Spectre Circuit Simulator Reference -- Other Simulation Topics - Checkpoint - Restart (checkpoint)

I just wanted to add a few of my personal thoughts to, possibly, provide some possible insight and help to you fortune100worse (hope they do!

Shawn

Hi Shawn,

Thanks for your valuable feedback.

My final goal is to avoid lengthy transient noise simulation for checking phase noise and jitter of the PLL. I want to have a converged steady state and do a hbnoise or pnoise. I have done this task before using company internal simulators (Philips, Motorola) without problem, even AFS from BDA did a good job but with Spectre I usually face convergence issues. 

I have checked all signals inside the feedback divider and for the case of reference=20MHz and divide ratio=12; the lowest frequency inside the feedback divider is 20MHz/3 (6.67MHz). 

As with cmin, obviously setting cmin avoids sudden (ultra fast) voltage variations and smooths out such variations which makes it easier to converge. Assuming the same cmin (the same level of smoothing) the simulator should have better time converging with higher harmonics than lower harmonics (am I right here?) so why do I need to increase cmin to get convergence for higher harmonics? That is precisely my question. 

Br, fortune100worse

fortune100worse said:

My final goal is to avoid lengthy transient noise simulation for checking phase noise and jitter of the PLL. I want to have a converged steady state and do a hbnoise or pnoise. I have done this task before using company internal simulators (Philips, Motorola) without problem, even AFS from BDA did a good job but with Spectre I usually face convergence issues.

I'm not sure you're comparing like with like here, as RF simulation technology has very different convergence criteria than (say) transient. Particularly trying to converge a harmonic balance with the very small number of harmonics you were trying to do initially did not make sense for the reasons I outlined at the beginning, and I still think that shooting would be a more appropriate solution here. For a switching circuit it should normally be much easier to obtain an accurate solution and I wouldn't expect such difficulties in convergence either.

I would not expect you to have to use cmin at all here - it's possible that you are just damping down the numerical noise at the higher frequencies - this might be an instability, or it may be some residual inaccuracy if the 480MHz frequency is pretty square - even with 900 harmonics of your 20MHz/3 fundamental, that's only 12 harmonics of 480MHz - which is not very many for a good square wave. For example, 12 harmonics of a square wave (converted back into the time domain) would look like this:

Now, if the square wave is squarer than that (I assume it probably doesn't have anything like that ripple) then there are presumably harmonics beyond the 12/13th harmonics with significant energy. With harmonic balance, it is trying to ensure that the harmonics are balanced into each node, and so the energy from the missing harmonics has to go somewhere - if that energy is significant enough, it causes convergence difficult - some level of filtering might damp that uncertainty down a bit, and that's probably what you're seeing with cmin - it's crutch and this dampening is hiding the true problem, which is that even 900 harmonics are not enough for this (assuming you really have got the fundamental right).

I'm a little surprised that shooting is not converging, because that should capture the entire content of the waveform - but PLL convergence can also be problematic if you have (say) dead bands in the phase detector, or having the wrong fundamental again.

I really would suggest that you contact customer support - trying to figure out what is going wrong without being able to see the data is very hard. Trying to infer what's going on from the results of setting a simulator parameter (cmin) that is probably not wise to use anyway is also not easy - I doubt there is a strong correlation between the value of cmin and the number of harmonics; there's an element of luck (well, it's not really luck) if you are trying to squeeze the energy of lots of harmonics into too few harmonics, which is one fo the downsides of harmonic balance with heavily non-linear circuits; it's always important to ensure you have sufficient harmonics to capture all harmonics with significant energy (not just the harmonics you're interested in). Shooting is (usually) more forgiving because it is closer to a transient and the number of harmonics is just how many you want to observe; shooting is less good though with a highly linear system that can be represented accurately with a small number of harmonics because it doesn't have the dynamic range that harmonic balance does.

Andrew.

Hi Andrew,

I started to play with cmin per advise from Spectre after failing to converge Shooting.

12 Harmonics are more than enough to construct 480MHz VCO output. Why? Because VCOs (oscillators) oscillate at one frequency (given by the Barkhausen criteria); the harmonic distortion in VCOs is rather small, VCOs are not wideband, so few harmonics are sufficient to represent the 480MHz well (see below VCO output with 900 Harmonics comparison between hb_tran and hb_td). However, the VCO output goes to a div2 (240MHz) and then into the feedback divider and those logic cells tend to add a lot more harmonics (Gibb's effect may be more pronounced there or specially in the reference generated by an ideal source with linear edges). 

The PLL uses a dead zone free PFD design (it locks with an intentional small phase difference, ensuring there is no dead zone). Shooting not converging has to do with something else, Shooting fails convergence even with cmin=3f or 4f!