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Easy enough to check the noise floor. As Max suggested, take a tightely coupled pair of lines and deembed to zero length. Then we get an idea of how much the error is.

The "asymptotic estimator" is believed to be used for filling the impedance matrix, with no known exact value. Hence the error (noise of impedance filling) is difficut to ascertain.

I remember EM3DS also provides an example project for the stripeline benchmark problem. But they didn't make any claim regarding "noise floor". So again, the way of characterizing the "noise floor" of an EM field solver has not been standardrized.

Hi loucy,

It is mentioned that EM3DS uses
"asymptotic estimation" (extracting most of the information from a single frequency analysis),to fill MoM matrix...
What is that mean? or How it compute the moments...


Thanks
---manju---

Yes, in EM3DS the asymptotic estimator, has nothing to do with interpolating data - (i.e. Y-parameters). It has to do with the Green kernel estimation and is why it needs a single freq point only to yield correct results. Besides that, in the newer version I have my hands on - there is a rational polinomial fit -- SmartFit that works great either. (The trick here is that there are some cases where the estimator will not yield very accurate results - and the program issues warnings, but one needs to practice a bit to get a good gut feeling about it.)
We ran the thin stripline benchmark and the noise floor seems fine. Whereas in the 2D case there is the analythical solution known (Cohn), for thick metal there is none.
For the thick metal it was difficult to compare the 2.5D with multiple paralel sheets and the full 3D kernel of Em3DS for the formulation ss different but that is not a point in here. What I insist on though is that given that MoM solver is programed thoughtfully and proper port calibration is provided the net noise floor will not pose serious issue- particularly for Manhatan structures. For bends or curvilinear structures it is a different story and the mesher more often than not is more important.
Regards,

In the MoM formulation for shielded circuit, each element of the system matrix is assembled from a few (4?) values defined as infinite sums. the FFT is applied to a truncated version of the infinite sum--that is a summation of finite number of terms. When the number of terms are high (say >2 times the number of cells in the uniform cell size case--not true for EM3DS), one usually throw away the tail which is equal to ("infinite sum" - "finite sum that is calculated"). if you have a good way of calculating the tail, then your finite sum could have fewer terms. I believe that is where the "asymptotic estimator" comes in. However, I don't know the details of their implementation.

Hi Loucy -- With the FFT approach, the number of modes used has almost no effect on speed (at least with Sonnet). We default to 2x the number of cells per side. For example, if using 100 cells per substrate side, the number of modes uesd is 200x200 = 40000. Change to 3x is very easy (-c3 advanced option). Now 300x300 = 90000 modes used. Analysis time and answer are both almost exactly the same. Easy to try, and see for yourself, even in the free version. So the "tail" that is left over in Sonnet is essentially nothing.

Hi Cheng -- You are taking the "It is giving the correct answer" attitude. That is OK, and that is what many people do. However, the main point of several of my posts is that it is much more interesting to take the position that. "It is giving the wrong answer, how much wrong is it, and why?"

For example, the stripline benchmark does not check for noise floor. (If you have found a way to use it to check for noise floor, please let us know!) It checks for error due to subsection size. The output of the stripline benchmark is Zo error versus subsection size. Error due to subsection size is the predominant error in a well designed EM software and ranges from 5% down to 0.1% and lower (we can get results down to 0.01% with Sonnet). If you do not find the error using the stripline benchmark then something is very very wrong.

If you want to check for noise floor, take any pair of tightly coupled lines (the more tightly coupled, the better). Set the reference planes so the result will be zero length. Analyze it. You now have S-parameters for a 4-port zero length coupled line. If port 1 and 2 are the first line, then the correct answer for S11, S13, and S14 is -infinity dB. Because of numerical error your calculated S-parameters will not be -infinity dB. Instead, it is the noise floor of your analysis (for that particular frequency range, subsection size, circuit geometry, etc.)

To say the noise floor is inconsequential is to say that your attempt to measure it failed. Only until you have measured it can you say you are successful. And, as mentioned before, in practice it will cover range of values, depending on the parameters cited in the above paragraph.

Remember, my position is that if you say you have good agreement, you are doing sales. If you say your result has no more than X% error, now you are doing engineering.

There is a nearly exact solution for thick stripline. The attached pdf gives the reference and one example. The solution for thick stripline also has a very firm upper limit for error. That error for the cited case is extremely tiny, much less than the analysis error anyone can possibly expect from an EM analysis. The geometry described is very extreme for planar analysis: 1 mm ground to ground spacing and 0.5 mm metal thickness. This is the range I would normally consider switching to a volume mesher. However, one customer reported trying a volume mesher on it and they saw poor convergence. It might have been the customer though, so feel free to try it for yourself. Any questions, just let me know.

One extra question, Cheng. Can the EM3DS SmartFit (or anyother interpolation in any other tool) fit the entire bandwidth of a 6 resonator filter to very high quality fit with analysis at 4 frequencies? Sonnet can do so easily.

Dr. Rautio -- It is difficult to understand your statement regarding the effect of number of modes on speed.

Performing a 1D FFT on a sequence of 300 numbers certainly takes more time than on 200 numbers--altough it might be difficult to profile. Problems with sveral hundred of cells along one side are comfortable to handle with current PC. Thousands of cells along one side are taking too long. The memory required for the 2DFFT alone can overwhelm the system. I guess we can't test Sonnet Lite with large (say 2048x2048) number of cells. The EM3DS use non-uniform "elementary" cells. To compute the matrix element corresponding to the finest cell, the number of modes required under the "2x number of cells" rule of thumb would be extremely high. For this reason, I believe the "asymptotic estimator" is essential in EM3DS.

One might argue that the task of "assembling" the FFT results into the system matrix dominates the time. This might be true. When the (finest) cell size is small, the number of modes required is high, even the relatively less time-consuming FFT step might be too much. Otherwise if the speed/computing time were almost the same, why can't we use very fine cells in every problem?

Good questions, Loucy. (OK to call me "Jim".)

Actually, you can try it on SonnetLite. Please do so. The FFT takes some memory and SonnetLite is limited to 16 MB. So, with almost no circuit, I decreased the cell size by specifying 1000 cells per box side. (1500x1500 cells required > 16 MB.) You can do this too. Here are the SonnetLite timing statistics:

Frequency: 1 GHz
Circuit requires 5 subsections and 12 MB of memory.
Subsections by level and type:
Level 0:
Staircase: 5
Waveguide mode time: 0.156 seconds.
Fourier transform time: 1 second.
Coupling time: 0 seconds.
Loss time: 0 seconds.
Matrix fill time: 1 second.
Matrix solve time: 0 seconds.
De-embed left box wall:
First de-embedding standard, left box wall: 40 mils length, 18 subsections, about 8 MB.
Time: 0.704 seconds.
Second de-embedding standard, left box wall: 80 mils length, 35 subsections, about 12 MB.
Time: 1 second.
Total time per frequency: 3 seconds.

In otherwords, a 1000x1000 FFT reqires 1 second. (There were only X directed subsections. If there were both X and Y, there would be 3 FFTs, but no increase in memeory.) The calculation of waveguide modes took 0.156 Seconds. For a 1000x1000 FFT, Sonnet (by default) calucates 2000x2000 = 4000000 modes in that 0.156 Seconds. Pretty fast, huh?

If you increase the number of modes (for example, by specifying -c3), the only thing you increase is the 0.156 Seconds of waveguide mode time. Not a big deal. The FFT remains at 1000x1000 and FFT time remains unchanged. I get the impression from your comments that the FFT size for EM3DS increases in this case. If true, that is very inefficient!

What requires time and memory, is if you have lots of subsections. For SonnetLite, matrix solve time is also almost nothing, because of the memory limit. For full Sonnet, 1000 subsections means a 1000x1000 matrix (this is independent of the FFT size and time), and fill time and solve time combined are just a few seconds. When you get up to 20000 subsections, the fill+solve time can be 20 minutes or so (3 GHz PC). If you invoke conformal meshing (on which we have a patent), the subsection count goes down by a factor of 10 to 100, but the matrix fill time goes up a bit. When the subsection count goes down by a factor of 10, the matrix solve time goes down by 10**3 = 1000 times faster. This is pretty serious stuff, don't you agree?

Basically, Sonnet development has been focused exclusively on our planar shielded FFT tool for nearly 23 years. Newcomers simply are not going to catch up to our technology. If this "asymptotic estimator" figures out the tail of the Green's function infinitely faster than we do and they reduce the time for the rest of the Green's funciton to zero, they will gain 0.156 Seconds over Sonnet on a 1000x1000 cell substrate. That is useful only for marketing and only if users never find out how insignificant it really is.

Bottom line: If you have both tools, don't take anybody's word for anything (including me). Think a little bit about it and then run some benchmarks.

---This just in. I tried -c3 option. Now 3000x3000 = 9000000 modes are calcualted. Mode calculation time is now 0.235 Seconds, FFT time is 3 seconds. The FFT time includes inserting all 9000000 modes into the 1000x1000 FFT matrix.

Dr. Rautio,

I am afraid the timing data you presented above does not support your earlier statement. If I read it correctly, it happens to show to the contrary that the size of the FFT, or the number of modes whose contributions are added, does affect the "efficiency". your data indicates that changing the number of cells along each of the x- and y- dimensions from 1000 to 1500 causes the FFT time to increase from 1 second to 3 seconds. In absolute magnitude, both cases are pretty fast indeed. In relative terms, however, an 1.5 increase in cell density costs 3 times longer.

The other timing infos are not directly related to the "asymptotic estimator" of EM3DS, in my view.

Although I do not have the details of EM3DS' implementation, I think its "asymptotic estimator" is addressing the difficulties which Sonnet's Conformal Mesh has solved or is attempting to solve. Depending on the geometry, even 10 times increase in the cell density is not enough. On the other hand, as the cell size decreases, the rule of thumb of "2X number of cells" is not always necessary. One might relax it, to say 0.1X number of cells, if he has a good estimation of the contribution from the "0.1X+1 ~ infinity" modes.

If EM3DS simply repeats implementing the same formulation as Sonnet did, one might not expect it to be faster or more accurate. However, this "asymptotic estimator" is an example of the "new"/different ideas in EM3DS that we donot see in Sonnet.

Hello. Been gone for a day and see that the discussion had shifted (as usual).
Yes, Loucy you are correct - that is pretty much what the estimator is doing and I don't know the implementation either but it is how it works.
To come back to the point of the topic if someone is interested I will prepare a benchmark (EM3DS) over tightly coupled lines with 0 length and will post the data as well as the structure if someone else is to check.
As the discussion shifted - it is not every time the speed that is critical - sometimes using a certain EM modelling technique is simply not appropriate.
In the case of EM3DS, an entire class of devices using BAW resonators is not possible not only in Sonnet, but in any other MoM tool I know about. We been involved in RF MEMS for a good number of years and found results with fraction of percentage error with measured devices that attests well to the techniques being used.
As far as the AWR co-simulation is concerned, it appears that the EM3DS folks been first to do that - at least that's what we been told - not sure about it though.

Rautio, in the pdf file of the thick metal you attached (multiple sheet approach) I did not see timing and cells versus number of sheets. Was this inadvertent ommision or was not in the scope of the study you conducted?

Hi Loucy -- My post was a bit long, so it is easy to mis-read it a little bit. The FFT size is 1000x1000 in both cases. (You need at least SonnetLite Plus to do 1500x1500.) The only thing that is changed between the two cases is the number of waveguide modes that are summed (to get the Green's function). In the first case it is (2x) 2000x2000 = 4 million modes. In the second case (3x) 3000x3000=9 million modes summed. In both cases a 1000x1000 FFT is performed. The listed FFT time includes the time it takes to insert the 4 million (or 9 million) modes into the 1000x1000 FFT array. The time taken for the actual FFT is exactly the same. It is just that in the 9 million mode case, 2 extra seconds were needed to fill the FFT array prior to the transform itself.

The -c3 option (to increase the number of modes included) is almost never used. In fact, it's only practical use is to prove that including more modes makes no difference in the result. Because our mode calculation/FFT is so incredibly fast, there is no need for any kind of estimation and we always use 2x number of cells per side for the number of modes. When it requires only 1 second for a 1000x1000 substrate, why ever do anything esle? (Reducing the number of modes to 0.1x, even with some kind of mode estimation to compensate, seems really scary to me. Sorry!)

The important thing here is that the 1 second needed to calculate modes and do the 1000x1000 FFT is the same regardless of the number of subsections. Most practical circuits have a few thousand subsections. The big ones (where speed up is important) have 10-20 thousand subsections. Such circuits require up to 20 minutes or so for analysis. I suggest that any and all effort expended to improve the 1 second FFT+mode calculation time is seriously just a bit pointless.

By the way, it is a pleasure to have a discussion like this with someone who clearly knows quite a bit more about the shielded EM theory than the average engineer.

Hi Cheng -- Did not see your post when I was making the above post. It has been some time since I did the analyses in the pdf. I looked back at the data and one timing is the 17 sheet model, 32 cells wide took 4m13s. I am not sure what computer I used, might have been my notebook. The 32 sheet, 128 cells wide line took 1h12m per frequency. Most of the time was spent deembedding. Without deembedding, the time was only 15m. The 9 sheet 16 cell wide line was 23 seconds per frequency.

It is really important to do the convergence analysis (when accuracy is an issue). I have seen cases where people do many analyses and select a couple good results (where multiple errors cancel out) and neglect to publish the not-so-good results. This is called "data selection" and it is not ethical. Do not do that. Look for multiple results (not just one good result) that converge to the correct answer as cell size gets smaller and smaller, just like the plot in the pdf. Settle for nothing less.

One problem with this benchmark is that it is lossless. It would be really nice to have a lossy benchmark where side current physically penetrating into the body of the conductor is important. With this lossless model, all the current is surface current, so the hollow tube-like model of thickness should work well, provided you can divide the side current subsections into narrow subsections too (the side current varies strongly from top to bottom).

Because of the extreme thickness dimensions, I fully expect volume meshers can do a better job on this one than surface meshers, but, as I mentioned, the one case I have seen was unexpectedly poor. If anyone can get good results using a volume mesher, please post them. It would be most interesting to see.

Did not know EM3DS does SAW stuff. I will be sure to point it out to people who need to do that. As always, multiple EM tools are needed. One single tool simply is not good enough.

As for AWR cosimulation, if you are talking about using the AWR EMSocket, AWR and Sonnet developed that working together very closely and at our urging. We were the first to offer software for that, plain and simple. If this is what EM3DS people are talking about, they are incorrect.

Hello All,


EM Simulation: A Look under the Hood - Part 2 has been uploaded see below links for more details...


http://www.appwave.com/support/training/webinars.html

http://wcc.webeventservices.com/view/wl/r.htm?e=19797&s=1&k=82AD7146A68092FF4E463FD4082BBE67


EM Simulation: A Look under the Hood - Part 2
In this webinar, we continue our investigation into the inner workings of electromagnetic simulators - specifically EMSight, the moment method simulator built into Microwave Office. Emphasis will be placed on fundamental concepts essential for successful simulations. Topics covered in the webinar are: the importance of the simulation box size, and the proper use of boundary conditions.


---manju---