spiral inductor EM Simulator

embedded spiral inductor

Im trying to simulate spiral inductor.
But I have some problem.
That's I want to know about the relationship of thickness and inductance.
I try Ansfot Ensemble,ADS Momentum,Zeland IE3D.
Does anyone tell which one is better for 3D simulation ?

thanks

Hi I'm working for RFICs and dedicated for Inductor.

If we are talking about inductors dimensions about up to 500X500um
and planar inductors (not multi level),

the best performance(compared to meadurements) reached by
ADS Momemtum -(RF Mode) it is also the quickiest.

Sonnet is very accurate too (but it relatively slow)

IE3D a bit slower that Momentum RF mode and has bit reduced accuracy

(Don't forget to put thick metal model in these 2.5D simulators in order
to achieve the most accurate results especially when you interested in
thickness)

HFSS - is not so slow as you might think, but since his current
distribution(even if you do solve inside metal - which is a Must for high accuracy)
is not so accurate the accuracy is bit reduced.

But all in all the inductance error in all theses tools is not more than 5%
(if you know ,of course, how to set up problem well)

When the the inductor lenght is big the capacitance between inductor traces
become significant Momentum and Sonnet cannot capture this capacitance
since vias have only Z directed current - IE3d and HFSS supposed
to catch this capacitance but till today I haven't seen this happens.

So if you have RFIC application with restriction I've mentioned
the best tool ADS Momentum - Very accurate, Quickest and easy problem
definition.


If you also interested in stacked(multi level) transformers HFSS is the best
in general any 3D structure is better characetrized by the 3D EM tool.

Hope it helps,

Gosha

Hi Gosha -- You have some incorrect information, but the bottom line is that there is no single correct answer to the above question. Which one is best? The answer is a clear Yes...and No to each and every tool you mentioned.

As for thick metal models, these are needed only when the gap is less than about 2 times the metal thickness. (We have explored this in detail, but we always recommend the designer test it for themselves, analyze with, then without thickness and note the difference). You might not be aware of Sonnet's multi-sheet thick metal model, it works very well and has excellent convergence, as has been published in detail in MTT Transactions. It takes into account side currents along the length of the line and line to line capacitance.

As for speed, I can set a problem such that any one of the tools you mentioned will be very fast, or very slow, take your pick. Sonnet has a clear advantage when thickness and high edge current is important. We can also do circular spirals with our conformal meshing, with thickness and edge meshing, in a few minutes for cases that can not be done by either tool (as long as thickness and edge meshing are included).

If you want make Sonnet slow, that is easy too. Just make sure you use a gap and line width that do not fall on a fine underlying uniform mesh. This is a real case that some people have, maybe even need to have. Yup, Sonnet will be slow because of the fine mesh required.

If you are on Sonnet support, and you have a slow problem, send it off to us. This is by far the most common support question. We have gotten really good at speading things up. And if another tool is more appropriate, we won't hesitate to tell you, we have absolutely no desire to pretend we are the proverbial "total solution" (which, of course, does not exist).

I do appreciate you posting your frank comments. Thank you.

GoaGosha: It is interesting to see your comment that IE3D yields reduced accuracy for your simulation. I know RFIC modeling requires very high accuracy especially for the loss. Modeling skill is quite critical. I know two independent validations in BroadCom and Motorola in the last few years proved that IE3D yields the best results. Also, I got comment from some divisions of Triquint that IE3D yields the best accuracy. I would like not to say IE3D would yield the best accuracy for every structure and for every case. However, I would like to let you know many users are getting accurate and consistent results. In case you have accuracy problem on IE3D, please send your test structure to us (support@zeland.com) and we can help you on improving your modeling. Thanks!

Hi myem,


I have used sonnet very extensively for spiral inductor simulation & analysis for
MMIC & RFIC applications...
It is very accurate in most of the cases & it almost matched with the measured data...

Regarding Thickness, I agrre with rautio
"Thick metal option needed only when the gap is less than about 2 times the metal thickness"...

One more tool which is also very popular for designing & analysis of spiral inductors is OEA International SPIRAL...It actally synthesizes spirals from specifications....
**broken link removed**

A design tool set for creating optimal embedded spiral inductor designs in ICs, Hybrids, and PCBs. It integrates together geometry building engine, a 2-D and 3-D field solver for extraction of RCL, and a frequency dependent circuit simulator. Outputs include GDSII, graphical plot file, SPICE models, and S- and Z- parameter files.


regards,
manju

Hi Jim and Jian,

Thank you for your respond.

Jim,

I'm also agree with your claim about thickness.Simply
I assumed that in most today's RFIC the spacing is equal or smaller
than thickness,so you need thick model.

I'm aware of multi sheet model but it is not good for RFIC typical
crosssection in which current are pretty uniform at center and not zero
as this multy level model forces by interior levels.This model practic use
,probably, is in more thicker and wider conductors.

One of things I don't understand in Sonnet why is the current ratio default is zero?
For RFIC as I saw (you can easily see with 2 sheet model) and also
in more bigger crossection it is about 1 or some fraction bigger than ¼.
In fact as I understood the 0 CR is veryyy radical case.

About timing maybe except circular spirals (which I haven't tested) the rectangular
and octagonal inductor simulation are everagely bit slower from other
simulator , WHEN using differntial inductors which have diagonal
parts and some of them touching vias , with or without conformal mesh, the simulation time become much bigger than other tools,because of many
unneeded subsections.

Since we often simulate big structures and need to "scratch" each MB
out of problem memory ,I think after 2 years ,I learned with Sonnet support help how to set porblem to achieve close to minimal simulation time.

Of course there is no general tool approriate for all cases,but if we narrow
application field enough I think there is.

Right now (maybe I wrong) I think the Momentum RF is best ( in terms of:
accuracy,simulation time and easy problem setup) for restrictions
I mentioned.


Jian,

Most of my IE3D comparison was done on many turns (High Inductance)
inductors
(For low inductanes the teststructure parasitics significant
so to avoid deembeding complications whole structure need to be simulated
I couldn't find ideal port setting for the problem ,so later on this year
I probably contact you about this issue).

In this many turns inductors I mostly look on inductance which is not
property of loss. It is hard do to mistake there since teststructe parasitics
are insignificant and return current was via inductor himself (and NOT for instance
through teststructure) this made also very easy problem setup.
In this test I found that IE3D had poorest results (I've used thick model)

For very long inductors all the tools gave not so accurate results and they all missed resonance freq.

One of the question on IE3D , is there ports that may refernced
to other ports without any metalic ,on which potential excited, and which put in layout between desired metals and introduce port parasitics in structure?
In Momentum it is simply reference port ,in Sonnet it is the box.



Jim & Jian

One of the question may be arisen from this letter why don't you have
some RF biased engines which can speed up the simulation moreover
it may reduce inaccuracy which MAY introduced when solving RF problems
with fullwave mode ?
By RF I mean high freqs but relativly lumped devices.



And yes I might be wrong in my conclusions as we all

Thank you,
and looking forward to working with you in order to get best results from your
newest EM solvers.

Hi Gosha -- Many questions! First, on thickness. All the different thickness models have advantages and disadvantages. The sheet current tube-like model now recently introduced on Momentum is nice in that it models the side current as a continuous sheet. However, like all models, it also has disadvantages, and it is important to know about disadvantages as well. In the case of the tube model (which you can also use in HFSS by setting "Do Not Solve Inside"), all current is restricted to the surface. This can be a problem when current diffuses into the metal by skin effect. When skin depth is small compared to the gap, this is no problem. When skin depth is a significant fraction of the gap, then the effective gap width is wider. This makes the effective gap width wider than the phyiscal gap width.

You correctly point out the disadvantage of Sonnet's multi-sheet model, the side current is not modeled as a continuous sheet. If skin depth is small, the side current is effectively modeled as a series of filaments. But, it is also important to understand the advantages, every model has advantages as well. The advantages of the multi-sheet model is that when skin depth is significant (compared to the gap), it can penetrate into the metal and the increase in gap width in properly modeled.

Even without a gap (i.e., single line), this is very important at low frequency when current flows in all the metal of the line. In this case, surface current flow model is completely inappropriate. This happens when the thickness is about one skin depth.

In certain cases, Sonnet does not include the interior subsections on interior sheets. Check emvu to see if it is the case. If you need interior subsections in those cases, contact support.

The multi-sheet model also properly models the variation of currnet along the side. The highest side current is at the top and bottom. There is less current in the middle of the side. A single sheet of current on the side does not model this properly.

We have checked the multi-sheet model carefully for both capacitance (using an exact solution for very thick stripline). It converges very well, with error dropping by about 1/2 each time the number of sheets is doubled and the cell size is cut in half. This result is about 1 year old and was not published in my paper on the multi-sheet model.

Sonnet has no problem with lots of extra layers, that is why we use the multi-sheet model.

Default current ratio is zero because that is what all the other tools force user's to use. Also, it gives the highest loss answer. If the user does not bother to figure out what current ratio is, then, when they build the circuit, they are most likely to find the loss is a little less than what they expected. This is better than finding out it is a little more than expected.

Timing tests for spirals that are designed for Sonnet (i.e, to allow a good representation on the uniform FFT mesh) analyze much faster than others, in cases that customers have told us about. This is especially true for circular spirals that include thickness and edge effect, due to our conformal meshing. If a spiral is designed so that it is difficult for us to analyze, yes, it could be slower.

As for inductance, most tools get inductance pretty well. Q is more difficult. In recent work with IBM Fishkill (which will be published in IEEE Microwave Magazine) we discovered what appears to be a very common measurement error for inductors on silicon. The error does not affect the inductance, only the Q. It makes the Q appear lower. If a user is not aware of the measurement error, he might be tempted to adjust the conductivity of the silicon to compensate. But in doing this, he merely transferrs the measurement error into the analysis. This should be present about half the time (my estimate), but all published data shows good results. So I think there is a problem with at least some of the published data, esp. if the user adjusted the substrate conductivity.

We don't do an RF tool because our niche is accuracy. If we did an RF tool, some users would use it out of range and get a bad fabrication. That is not acceptable. If you really want an RF tool with reduced accuracy, use circuit theory. A good designer can generally come really close with circuit theory.

Got to run now. #20 of my Maxwell lecture is tonight. Had over 100 people last night at the lecture.

GoaGosha:

1. Regarding inductor modeling, high inductance should not be a problem for IE3D. Normally, it should be quite accurate. However, there are something you may want to pay attention. It is the meshing. the rule of thumb for many structures is 20 cells/wavelength. However, for spiral, you may want increase it significantly. The reason is that the current is changing very fast around the turns. Simlar thing is true for MIM capacitors. We normally want the users to create at least 2 cells for the inner most segement of a rectangular spiral. This tip is documented in the manual. I understand that many users may not have time to read it completely.

In fact, Motorola did a benchmark on modeling spiral in 2003. They compared all the EM simulators in the market. All of them gave about the same L value while IE3D yields the best accuracy in Q or R. They informed us.

An ex-engineer of Broadcom informed us in 2004 that they did a benchmark on many EM simulators in the market in Broadcom and IE3D gave them the best results.

IE3d is considered as the golden standard for some engineers in RFMD.

Nevertheless, IE3D is integrated into Intel Corp.'s design flow for RFIC. They are getting excellent results.

If you could not get good results, I would strong suggest you to contact us. You should be able to get excellent results using IE3D, because many others do.

2. Regarding a port reference to another metal, you can use differential ports. Differential ports were implemented into the IE3D more than 10 years ago. You mentioned in your posting that Momentum has a reference port. In my understanding, a reference port is basically the negative port on IE3D. It seems to me you mentioned the reference port can be in a location without a metal. I am sure whether my understanding of your question correctly. A reference port certainly can not be in a spot no metal is there. Apparently, a port is not only related to voltage. It is also related to current. If you have a port referencing to a spot without metal, you will have the voltage while you will not have the current. It will not yield correct results.

Regarding a reference to a wall, first, the wall is not in an true RFIC circuit. Most RF circuits do not have the walls there. We would rather not to have it there because it is not true. Seconldly, you can always define a wall on IE3D and use it as a reference to a port. This feature has been there since IE3D V.7 or V8. I understand many users may overlook it. Anyway, IE3D has so many features there and it is easy to miss one. However, I do suggest users to contact us if they have question or problem. We do offer the best support. Thanks!

Hello everybody, I have a question about IE3D in simuating sprial inductor. I find some problems that I can't figure out. I used the other EM simulators as like Momentum, Ansoft PlanarEM.. etc. When the EM simulator considered the metal thickness, the inductance will down a little. I can figure out this phenomenon, but only IE3D have the different simulation result. The inductance is quite different(if 3.5nH in measured, about 4nH in IE3D simulation, the other simulators simulated around 3.5nH in +/-0.02nH range ) when I grow the metal thickness(about 2um in my spiral indutor design). I have seen the manual(IE3D v10.2) about thickness setup methods, IE3D can calculate cross-section factor automatically. but why the inductance is so different with measurement and the other simulators? I feel like something wrong in my IE3D setup. Would somebody know how to setup in IE3D?

Hi, Richard: Please send me the .geo file at: jian@zeland.com. We can help you. Thanks!

Is there anyone familiar with HFSS in spiral inductor design? I am a novice in this research. I am trying to simulate two design examples in an IEEE letter and another famous Journal. My results are far worse from the published results. For example, one of the published results is a suspended spiral inductor has a peak Q of 70 at 6 GHz, and the corresponding L is 1.35, but my simulation result was only 25 (peak Q) at 2.5GHz with a L of 1.15. I realize the simulation result is a little bit different from the measurement. But it should not be so significant. And normally, the simulation result should be better than the measurement result. Anyway, I am suspecting my simulation setup. When I started the inductor research, I consulted the HFSS new customer support. I did the setup based on her comments and she said no problem. But right now, I do think there is some critical problem. Can anyone give me a guidance?

Frank_001 said:

Is there anyone familiar with HFSS in spiral inductor design? I am a novice in this research. I am trying to simulate two design examples in an IEEE letter and another famous Journal. My results are far worse from the published results. For example, one of the published results is a suspended spiral inductor has a peak Q of 70 at 6 GHz, and the corresponding L is 1.35, but my simulation result was only 25 (peak Q) at 2.5GHz with a L of 1.15. I realize the simulation result is a little bit different from the measurement. But it should not be so significant. And normally, the simulation result should be better than the measurement result. Anyway, I am suspecting my simulation setup. When I started the inductor research, I consulted the HFSS new customer support. I did the setup based on her comments and she said no problem. But right now, I do think there is some critical problem. Can anyone give me a guidance?

Click to expand...

Hi, Frank,

I have almost the same issue, the HFSS simulated results is much worse than measurement (both Q and L), have you figure out why? And I found that not many guys here have the same issue, but get no answers. You'll be highly appreciated if you share your opinions,

Ruri

You might want to read my recent paper:

A potentially significant on-wafer high-frequency measurement calibration error
Rautio, J.C.; Groves, R.;
Microwave Magazine, IEEE
Volume 6, Issue 4, Dec. 2005 Page(s):94 - 100
Digital Object Identifier 10.1109/MMW.2005.1580342

Since I wrote the paper, I have personally visited about half a dozen companies that, on discussion, have one form or another of the problem. It appears to be unexpectedly common.

One thing I mentioned in the paper, but did not provide much detail: While Sonnet gave a much higher Q than the (it turns out bad) measurement, two other EM analyses gave good agreement with the bad measured Q (inductance was OK in all cases). I suspect de-embedding problems. Sonnet is the only tool, as far as I can tell, that has numerically exact de-embedding. But, I can't be sure because (as far as I know, correct me if I am wrong), no other vendor publishes their de-embedding algorithm. That leaves the rest of us guessing, at best.

This measurement problem is particulary dangerous, because you can get an EM analysis to agree with the bad measurement by adjusting the substrate conductivity used in the EM analysis. This inserts the measurement error into the previously good analysis. Now both measurement and analysis are bad!

If you do not have access to IEEE Xplore, I will be glad to email anyone a pdf of the paper on request.

Hi People,

Since the last post my expirience grew a little.
Again I'm talking about inductors dimensions about up to 500X500um
and planar inductors.

The update is that I succeeded (with help of Jian) to get excellent results
(compared to measurements) with IE3D also.

So the summ table so far for me is :
Both Momentum and IE3D have excellent agreement in measuremets
when I use thick model and their best setups - I might say their
results are almost identical in L and Q.
Momentum(RF Mode) is faster, much faster esspecially in new version 2005A.

Sonnet to my expirience, after I spent a loooot of time arranging setups with belief that is the most accurate tool, Q accuracy was lower compare to others (for large L inductors ) .
And again as I mentioned in previous posts time solution is very long
especially for symmetrical inductors.

Jim I know ,as a vendor,you will object some points in my update
But is so far what I have come to.And yes I agree I might be wrong.

Please bare in mind that comparing inductors results it's quite a task.
First of all for being measurement error free I've picked only those inductor which had large L and therefore pad structure parasitics had negligible effect.
Second from those large L inductors I picked one with wide width otherwise
microelectronic process deviation error become significant.

The last one,most interesting, is that 3D planar simulators can
never simulating CONFORMAL passive layer which is common for top
level metal in microelectronic processes - this is very important
for big inductors since they have big self capacitance.
Therefore I had to tune it with capacitor(=correct effective Er).
Only after this tuning I get accurate results.
(For small inductors there is no need for this tuning due to their low self
capacitance)

By the way Jim I'm aware of the paper you mentioned since you presented it to me personnaly.It is not relevant to us since we used other type of callibration standards.

Jim & Jian I don't really know what is percentage of your RFIC clients.
In my humble opnion you might lose this market to Momentum which
RF mode is much faster and has pretty accurate results.

Your answer for making RF mode(=lumped=near field)
is always that - fullwave mode is more accurate.
Clearly for distributed structures , but I'm not sure that for lumped elements
it has the same answer.
Can't it be that fullwave mode indroduce more numerical error
than some lumped/near field mode?

Moreover since for lumped/near field mode you make additional assumptions
you migth discard some initial assumptions to make more accurate lumped solution.

Best Regads,

Gosha

Hi, GoaGosha:

Thank you for your comments.

1. You mentioned that planar EM simualtor can never do the conformal stuff. In fact, IE3D can do it because IE3D can use finite dielectrics and you can model the non-planar structures especially when the non-planar part is not big.

2. Regarding speed, we should have a very fast and robust IE3D coming out very soon for it. Please stay tuned.

Best regards.

Hi, GoaGosha:

In order for the readers of this topic to have an independent judgement, can you please describe more details about your "best setups" in Momentum & IE3D for your spirals? What was the information("help") you obtained from the vendors?

It is relatively easy to "tune" the simulation settings to obtain agreement with one's measurement. If you tell Sonnet beforehand the answers you are looking for, I imagine you can get the same "best agreement" from their answers. So it seems that you have not been fair to Sonnet...

Hi Loucy,

Every tool has it's little nuances when setting the problem.
You should bear in mind all these nuances.
Writing all them down here will be quite a work.


"Help" in IE3D was doing rectangularization option.
This helps to generate straight mesh cells for thick conductor
-> so element currents have always the same direction to real current.
For instance when you have some triangular cell you will have
element current which direction is off by some angle relatively to real current.
Though these element currents has to sum up to real current direction,
it turns out that these diffrences introduce significant error.

About tuning,
I don't understand how you got the idea that I "discriminate" Sonnet.
On the contrary ,as I said, with my believe in Sonnet I spent lot of time
trying to set it correctly. My target is always to get maximum from each EM tool
so for any new project/task I could pick up the correct/best EM tool.

To my best understanding Sonnet problem for cases which I'd described
in 2 posts above is that they have no horizontal current in vias.
It is especially important when you have big with many turns inductors.

Yes I can do 3 and above sheet model in Sonnet for getting horizontal
currents with inner sheets but simualtion times become unpractical,or insufficient memory especially for symmetrical inductors.

Believe me I would always prefer situation when I have
all EM tools giving me accurate solutions.

Regards,


Gosha

Hi, GoaGosha:

Thank you for your comments on IE3D.

Actually, "rectanglization" in IE3D is not for accuracy. It is for efficiency. Meshing a structure into more rectangles makes it more efficient because one rectangule is equivalent to at least 2 triangles. It can reduce the number of unknowns signficantly if it is meshed into more rectangles.

In fact, considering triangles will lead un-nature current flow is a mis-leading concept. In fact, no matter what kind of meshing you have, you can display the vector current distribution on IE3D. You will see the direction of the current is normally always current no matter how the meshing look like (rectangles or triangles of different shapes). The display does not do any tricking. It is display the truely simulated current distribution on the meshing. It is modeling the current's direction and magnitude current unless a triangle is too "singular". If a triangle is too "singular", it will cause un-physical result. What is too "singular"? Basically, when the area of a triangle is approaching 0, it is too "singular". What does such thing happen? It happens when one edge of a triangular cells is about 4 to 5 orders smaller than other edges. I would like to say we can never avoid such a situation. However, it seldomly happens especially with the "contemporary" meshing.

Also, when you use IE3D, you may see some warning message like "... the minimum forced meshing size is 0.123 (<0.5)...". Many people may not try to understand what it means. Basically, it means that "0.5" is some kind of artificial limit. The "0.123" is the minimum distance of two vertices or the specified edge cell size. This minimum value is smaller than the artificial limit of "0.5" and IE3D is giving you a warning on possible singularity. How important is this messsage? In fact, it is not very critical when it is a="0.123" vs. b="0.5". From our experience, only when a is about 3 orders smaller than b, it may cause singularity problem on the radiations (not the s-parameters). Only when a is about 4 to 5 orders smaller than b, it may cause "singular matrix" or incorrect s-parameters. Most of the time, you can ignore this message.

Some people consider that "triangular cells" will create zip-zag current. This is really not a correct concept. Just look at the vector current distribution on IE3D and you will know this is not the case. Triangular cells will predict the correct current and s-parameters unless the triangular cells are too "singular". Best regards.

Actually, at Sonnet, we take the attitude that all EM analyses always give the wrong answer. Then we set about finding out how much wrong and why. This is engineering.

If we take the attitude that the EM analysis is correct, then there is nothing more to do.

So, Sonnet always gives the wrong answer (just like all the other EM analyses). How much wrong? Cut the cell size in half and re-analyze. In Sonnet, almost always the error cuts about in half when you cut the cell size in half. The difference between the two is the error. If you are not sure that the error is cut in half, cut the cell size in half again and make sure the pattern holds.

GoaGosha -- You are worried that Sonnet gives the wrong answer because a via through a single layer has no horizontal current. You are absolutely correct, Sonnet does indeed give the wrong answer! Now, how much wrong? Double the number of dielectric layers the via goes through and make each one half as thick, and cut the cell size in half. Look at the difference between the two results and you have a good estimate of the error. If the analysis takes too long, pick a simple circuit. The percent error for a big circuit is likely to be about the same. This overestimates the error because we have much more than horizontal via current error here. If your gap is less than about twice the metal thickness, metal thickness error will dominate.

As for tuning the analysis to get agreement with measurement...NEVER EVER do this! It is very dangerous. (I think at least a few people are tuning an EM analysis to match measurement, and then they publish but do not mention that they tuned the analysis. This is unethcial.) Read my recent paper written with Rob Groves of IBM Fishskill in IEEE Microwave Magazine:

A potentially significant on-wafer high-frequency measurement calibration error
Rautio, J.C.; Groves, R.;
Microwave Magazine, IEEE
Volume 6, Issue 4, Dec. 2005 Page(s):94 - 100

(mentioned in another thread), go to IEEE Xplore or I will email a pdf on request.

I have seen quite a few good desingers who thought their measured data was good. Then they tune their EM analysis to match the measured data. But the measured data is BAD! Now the measurement error is inserted into the EM analysis!

The only way Rob Groves and I found this problem was by doing a huge number of convergence analyses to check quantitatively Sonnet analysis error sources. We were convinced the problem was analysis error. However, after checking convergence, not one of our ideas for analysis error could explain the difference between measured and cacluated (including doubling the number of sheets for thick metal). Only then did we look at measurement error, and we found it. And it seems quite a few others around the world have this same measurement error. If they tune their analysis, they are inserting this error into the analysis. Don't ever do that. Instead, whatever EM analysis you use, if you suspect analysis error, do a convergence analysis to prove it, or you could be sorry! Do not tune the analysis! You can also estimate the error in your measurement, as described in the paper.

As for pure triangle meshing, I have yet to see such a meshing that gives what I would call a good current distribution. I have seen mixed triangle and rectangle work OK. If anyone has a pure triangle meshing that gives a good current distribution, please post it. We would all love to see it.

P.S. Tuning to analysis data, esp. if checked carefully for convergence so the amount of error is well understood, as in the paper I gave you on conformal passivation modeling, is much less dangerous.

Hi, All:

The beauty of full-wave EM simulation is the fact that it is completely based upon mathematics. Full-wave EM simulation is solving the Maxwell's equation numerically. Maxwell's equations are based upon the Columb's law and some other equivalent laws. The columb's law says that the electric force between 2 point charges is inversely proportional to the square of R where R is the distance between the 2 point charges. This law is based upon measurement. However, it is verified to be very accurate by modern measurements.

A good full-wave EM simulation algorithm should make little assumption in solving the Maxwell's equations. If little assumption is made, it is proven that full-wave EM simulations can yield very accurate results for many general cases. In general, MOM algorithms are proven to be very reliable for planar circuits. However, there are still many factors may affect the accuracy of a simulation. For example, the choice of basis function is critical. As you know, on IE3D, you can choose to use AEC (automatic edge cells) or not to use AEC. If you don't use AEC, you will get much faster results. However, you will lose accuracy. Increasing the meshing density may lead to more accurate results in general. However, if you don't use AEC, the convergence speed will be slow. If you use AEC, normaly it is quite accurate. Also, the choice of AEC parameters may also affect accuracy. We have general guidelines documented in the manual. Those guidelines are based upon our experiences with many testings and convergence studies. For the IE3D 10.x and earlier editions, increasing meshing density may not always lead to a monotonically increasing accuracy due to some other parameters such as port extensions may also affect accuracy. In the IE3D 11, we have the Auto Adjust feature of port extension which will normally lead to higher accuracy with reduced cell size. However, please be informed that complete monotonic convergence may not be true even though the trends are like that.

As it is discussed by people on the EDAboard, metal thickness is quite critical in practical cases. It may not be just the top abd bottom plates. The current on the side surface of a thickness trace may also be very critical in many cases. On IE3D, we don't ignore the vertical current. We also don't ignore the variation of current in the z-direction. We also model the 3D arbitrary current distirbution on a 3D structure. On the side surfaces of a thickness trace, we don't limit the current to be vertical. We assume the current to be flowing horizontally and vertically. Basically, we allow the freedom. How will the current flows is completely determined by solving the Maxwell's equations.

In the past ten more years, many people may have asked me how accurate an IE3D simulation is. I have seldom given them a quantative answer because I know giving a quantative answer can be mis-leading to the users. For some applications, you can get very accurate results. For some applications, the accuracy will be less. I have never given and will never give those comments like that "using IE3D, you will get 0.001% of error while using some other software packages will give you 1% error" because, as you know, this kind of statement can never be true. In stead, I would give users a general guideline how you can obtain accurate results based upon our experiences. For example, based upon our experiences, triangular cells yield similar results to rectangular cells and that is why we claim that triangular cells will not yield incorrect results. Some people look at triangular cells and they may think that it may cause accuracy problem. We have done many tests on it and we know this is not true. In the IE3D manual, we documents a case with a rectangular patch using either pure rectangular meshing or triangular meshing in the Appendix. You will see there is very little difference in the simulation results. There is a very small shift in the resonance frequency and this kind of shifting is more due to meshing because using different meshing density of rectangles can also lead to this kind of shifting.

Again, there are many general rules in obtaining accurate and efficient IE3D EM simulation results. There are 3 most important rules: (1) Try to match your structure to the reality as much as possible (such as using thick trace when the strip is thick). (2) Try to increase the meshing density where the current changes the most. (3) Try to use AEC properly because proper setting of AEC will actuall capture the current density change close to the edges.

Thank you for reading my comments!