difference between 2.5d and 3d
what is the main difference between 2.5D and 3D simulation tools?
Have it something to do with near and farfield calculations? Is for simulations with planar antennas (S11-Calculations) 2.5D good enought?
Is there some difference in calculation method?
Thanks,
AJ
2.5 D are mostly planar structures, ie arbitrary shaped (multiple) layers and only vertical vias. Nothing to do with near/far fields.
Coaxial structures for example are difficult if not impossible to model in 2.5D. Connectors, transition from connectors to planar structures or waveguides, horn antennas etc. usually require 3D simulators.
2.5D simulators are based on the method of moments (MOM) and they can be closed box versions where you cannot analyze antennas or open versions where you can.
3D solvers can be FEM, FDTD, MOM, TLM.
I found a good introduction here:
http://advancedem.com/methods.html
To answer to your question: If you only simulate planar antennas then 2.5D is not only good enough, but it is actually faster and more accurate than 3D!
However, your planar antenna most probably has a transition from coax to planar somewhere and that part is a problem for 2.5D.
I agree, it's basically a problem with drawing the structure (e.g. feeding). Just to add, structures like CPW, inductors where you have problems such as skin effect, current crowding, etc; you really need 3D simulator and solve the inside of the metal. This option can be found in HFSS.
Hi wlcsp
I did not mention skin effect etc. because there is (at least) one MOM planar solver that discretizes inside the metal volume ? EM3DS found on the same web site I mentioned above. They have some examples exactly on inductors! It is still 2.5D because, apart from that, it has the other limitations.
When EM3DS solves inside the conductor, its author is calling it a 3D model. However, the currents (EM3Ds uses volume current to solve inside conductor) are still x-, y- or z-directed, so you might still call it 2.5D. In general, I think people would call a solver 2.5D if it works mainly on stratified background media (i.e. without the metal trace) and uses/models only arbitrary transeversal current and strictly vertical current.
There are several commercial 3D mom softwares, e.g. Feko.
Indeed, that is why I call it 2.5 D or ?planar 3D?, it is just a somewhat more advanced 2.5D solver, using volumetric MOM
The 3D MOM software does not discretize the volume of metals only the surface but they can have arbitrary 3D shapes. They have some metal loss models to appoximate skin effect. Not specifically recommended for planar problems, more for large 3D structures, scattering.
A friend just pointed me to this forum, this is my first posting. Full disclosure, I work for an EM software vendor (Sonnet), however I make at least a reasonable attempt to resist the urge to sell stuff.
I published a short piece on this question in: J. C. Rautio, "Some Comments on Electromagnetic Dimensionality," IEEE MTT-S Newsletter, Winter 1992, pg. 23. It is attached to this posting (it is not copyrighted).
Back when I did my Ph. D., my research was on planar MoM under Roger Harrington at Syracuse. At that time we had 2-D current (X and Y), and 3-D fields. My research was funded by GE Electronics Lab (among others). Back at E-Lab, they looked at the current and called it 2-D. Harrington looked at the fields and called it 3-D. Since my success depended on the good will of both parties and I had just read a book on fractal theory (where fractional dimensionality is explicitly defined), I compromised and called it 2.5-D. As far as I know, this is the first time fractional dimensionality was used in EM.
Almost immediately after completing my disertation, I added Z current (vias), and now we were full 3-D. However, we were restricted to planar dielectric, so to eliminate confusion with volume meshing codes, we call it 3-D planar. However, the term 2.5-D is so sexy, it has taken on a life of its own and is today used almost interchangeably with 3-D planar.
As for edge effect and skin effect (two distinctly very different things), if you want all the details, get a copy of: James C. Rautio and Veysel Demir, "Microstrip Conductor Loss Models for Electromagnetic Analysis," IEEE Transactions on Microwave Theory and Techniques, Vol. 51, No. 3, March 2003, pp. 915 - 921. Go to IEEE Explore or I will email a pdf on request.
Basically edge effect starts when frequency increases so that R is about equal to ωL (per unit length) of a transmission line. In sharp contrast, skin effect happens when the skin depth is much less than the line thickness. Contrary to popular opinion, edge effect has nothing to do with skin effect. Both effects constrict the current flow, increasing loss.
When using a planar MoM code and zero thickness current sheets, the skin effect is included by modifying the Ohms per square as a function of frequency. See my paper for the correct equation. It is not the equation most commonly used. In addition, the fact that current flows (unequally!) on both sides of a planar conductor must also be taken into account.
If you want skin effect to appear directly from Maxwell's equations, then you have to use a meshing that is small (veritcally) compared to skin depth. This is true for both volume and surface meshers. In the case of surface meshers, this means multiple sheets one on top of the other covering the line thickness. Many examples in my paper referenced above. (This is true even for surface meshers that use volume current unless the exponential skin effect taper is explicitly included in the volume current.) For volume meshers, the tetrahedra or cell size must be small with respect to thickness.
To properly represent the edge effect, again for both volume and surface meshing analyses, the mesh must be small with respect to the edge effect. If you have any doubts about how small, try one mesh size, then cut the mesh size in half and look at the current distributions of both results. The skin effect and edge effects generally result in small changes in S-parameters, so look directly at the current distribution to see if you have the edge and/or skin effect present and well represented.
Current crowding is a third distinct loss mechanisim seen in spiral inductors. The B-field of the inductor penetrates the plane of the spiral and pushes the high edge current to one side or another, further increasing the loss. When you have a sufficient mesh, you will clearly see the high edge current switching from one side to the other as you move along the spiral. Effect on S-parameters is very small. Effect on Q can be substantial.
That?s great stuff!
I am glad that a ?heavyweight? like Dr. Rautio joined the forum.
looks like the topic is shifted toward modeling of conductor loss. Is 3D better, or is 2.5D more accurate for this purpose? Let's talk about difference more specifically.
Looking forward to your input.
Fekete -- Thanks for your very kind comment. Please feel free to just call me "Jim". I also answer to "Hey you!"
Loucy-- Actually, both volume and surface meshing can give equally accurate answers. Specifically, if the cell or mesh size is about the same, you should have about the same error. For iterative approaches (like finite elements), this does assume you have complete convergence. Generally you can just look at S-parameter convergence for most cases. However, loss is very sensitive to small errors in S-parameters. Thus, if precise calculation of loss is important, you should check on the current distribution convergence. After all, it is I2R loss, you have got to get the I right! Because most of the loss is in the high edge current, look for a clear well defined high edge current to judge convergence. Once you have that high edge current you can check the data. Volume and surface meshing should come up with essentially the same result.
If you want to get an approximate number for the error, repeat the entire analysis with the mesh cut in half. Compare the results. The difference between the results is typically about equal to the error in the finer mesh result. There are occasional exceptions. To be sure, repeat the analysis again cutting the mesh size in half once more. If the difference between the second and third analyses is about half of the difference between the first and second, you have a number for the error.
As discussed previously in this thread, when you use volume meshing, in order to include skin effect directly from Maxwell's equations, you must make the mesh size small with respect to thickness/skin depth. In surface meshing you must use multiple sheets to represent thick metal. A short-cut around this is described in James C. Rautio, "A Space-Mapped Model of Thick, Tightly Coupled Conductors for Planar Electromagnetic Analysis," IEEE Microwave Magazine, Vol. 5, No. 3, September 2004, pp. 62 - 72, available on IEEE Explore, or I can email you a pdf on request.
SO...which is better for loss, volume or surface meshing? The answer is a clear resounding, "Yes!".
I would add, from my experience, that when using 3D simulators and meshing the volume of the thin metal traces (like for spiral inductors in MICs) it can be a nightmare!
The mesh size has to be very small there to capture well the skin effect, edge effect etc. and then there are relatively large dielectric layers and air spaces (+pml) to be meshed.
Planar simulators cope better with this kind of situations.
No big problems with 3D solvers for simple planar antennas though.
Fekete's experience seems to suggest that 2.5D (more specifically 2.5D/3D MoM with surface mesh) is better. Since MoM can go to a smaller cell size with the same computer resource, Dr. Rautio's comment also hints that 2.5D is better.
Authors of HFSS and EM3DS obviously have a different viewpoint. They think volume mesh is more accurate or even necessary to resolve the "skin effect" etc. (I infer this from EM3DS manual, and I remember reading similar public comment from HFSS).
So the answer is still not so clear to me. Consider for example the microstrip problem, can we neglect the "eddy" current circulating in the vertical planes (xz or yz plane if z is the direction of the stratification)? or is it captured in the 2.5D model where all currents are assumed lying in xy planes? Can we do the same for a coupled line, a spiral?
I couldn't find answer to the above questions in Dr. Rautio's papers cited above. But I think even with infinite number of current sheets, there is still no z-directed current inside the thick conductor. To me, this is the main difference between 2.5D and 3D.
Hi Loucy -- Z directed currents are included in 3-D planar by use of vias attaching the multiple sheets. If the conductor is thick compared to skin depth, there is no current in the interior, so no vias are needed there. In fact, even x/y current is not needed. There is no point in solving for zero, so just leave out the subsections with zero current.
If it is not thick with respect to skin depth, you can include vias everywhere if you like. But don't take my word, or "someone said" word as to if it is needed. Try it with, then without and see what the difference is. This is science, not philosophy. Aristotle died a very long time ago. Do an experiment and test the hypothesis.
We call this an A/B test. Very very common question, "Should I do A or should I do B?" Typically one option will take longer and promise greater accuracy. Try it with one and try it with the other. If there is little difference (compared to your requirements), use the faster one. If there is a big difference, use the more accurate one.
By doing numerous numerical experiments like that, we find that z current is sometimes needed at the edges of thick lines, and the Sonnet thick metal model automatically includes them. However, the current on these vias is very small. Do an example for yourself and look at it. Even though it is small, it is important when the line gets more than a small fraction of a wavelength long, or there is a discontinuity of some kind. It is needed only when current flowing on one surface needs to flow to the other surface. And it does so around the edge of the line, not through the body.
We included vias everywhere at the edges of all lines in my paper on microstrip loss, just in case they were needed.
I'm not sure what "eddy currents" are. Sounds like a term borrowed from the silicon folks referring to the very real current induced in a conducting substrate (which looks nothing like ?eddies?). What it brings to mind to me is little swirls of current going +/- z (vertical) direction on the interior and +/- x or y on the surface. This of course causes a problem where one swirl ends and another starts, you have + and - z current right beside each other. Perhaps we get more very tiny swirls at the interface? You might see this kind of thing in fluid flow (look at pictures of the planet Jupiter), but that is a non-linear chaotic effect. This is not seen in linear EM. Never.
Try this out: Whomever told you about these "eddy currents", see if you can get them to be specific, like, "Just how big are these eddies?" or "Show me a plot of the current distribution with these eddies in it." Maybe they could post an eddy current distribution image? I?d love to see what happens where the + and ? z currents rub up against each other. If they can answer these questions, I'll have some new research areas to go into! Hope I am not offending you, Loucy, but I think the term eddy current in thick conductors may have been invented by an over-enthusiastic, not-so-bright salesperson.
Basically, for both volume meshing and surface meshing, if you have essentially the same mesh size, and the volume meshing is converged so that you get a good edge current (surface meshing tools are typically not iterative and you don?t have to converge), then you should get about the same answer.
That I said before. I will add this now. Here is where I get partisan. For planar circuits, you can analyze roughly the same mesh size much faster (typically 100-1000X) than with volume mesh analysis. If you want to get the volume mesh current distribution to converge to the same level as the surface mesh result, throw in another ten times or more. Don't take my word for it. Try it and see.
In defense of volume meshers, they do a great job on 3-D arbitrary structures. Or even planar structures with some 3-D arbitrary aspect (like a coax connector). They have an important place in the microwave engineer's tool box. It is just that they have been oversold into the planar market. I know entire countries where they are using volume meshers for planar problems...oh those poor people! In my opinion, using a volume mesher on a pure planar circuit is just plain wrong. Even with thick metal. Try it for yourself. I think you will agree. And you can compare any surface mesher and any volume mesher, you will get the same result.
So, which is better for loss? They are both just fine when properly used. Which gives faster results for a given level of error? Surface meshers by far for planar circuits and volume meshers by far for arbitrary structures. Use the tool that is right for the problem.
Just for the sake of argument, let me ask this:
if "z current is sometimes needed at the edges of thick lines", why is it not needed inside the conductor?
It is natural to have currents penetrating inside the conductor along both the vertical and horizontal directions, especially when the width is comparable with the thickness. The convergence studies reported in the papers cited above are with respect to the number of current sheets along the vertical direction. Althought the cell size (in xy plane) is varied, (it appears that) the z-currents are limited to the side walls (surface current) or the first cell including the edge (z-directed volume current basis). (it is not clear whether volume or surface current basis is used in the vias.) So it needs to be justified why the z-directed currents one cell width inside the conductor can be neglected, and the argument falls upon the assertion that "the current on these vias is very small".
This assertion is questionable becasue the z-currents should be of the same magnitude as the transversal currents on the top and bottom surface of the microstrip, especially when the width is comparable with the thickness. (This is clear because if we remove the substrate and the infinite ground, then there is no preference as to which surface should be called top surface or side surface. One might expect that the existance of an infinite ground plane make the current on the top/bottom surface higher, but then the addition of a conductor to the side (as in the coupled line case) would make the current on the side wall higher.) Ignoring all of the transversal currents leads us back to a TEM analysis, which is hardly what we are looking for from a field solver.
Hi Loucy -- Very nice questions.
Our vias are volume current, as described in the Sonnet documentation.
Consider an infinite length uniform transmission line (or at least one that is long compared to wavelength). The "length" is the dimension that is large compared to a wavelength. The width and thickness are << wavelength. Basically, in a uniform transmission line, the currents along the width and thickness must be very small exactly because their size is << wavelength. Doesn't matter what your ground return is.
Let's explore this in more detail. If you look at a plot of Zo or Eeff for thick lossless microstrip, you will see that it is very close to TEM. This is why the microstrip mode is called a "quasi-TEM" mode. In fact a quasi-static analysis of microstrip comes up with almost exactly the right answer over a good share of the useful single mode frequency range.
However, at high frequency, even lossless zero thickness microstrip has large dispersion. I think you will agree that zero thickness microstrip can not support Z-directed (vertical) current. Therefore, Z-directed current does not cause dispersion in this case. In fact, the dispersion is caused by non-TEM E and H fields surrounding the line. The non-TEM fields are caused by the non-uniform dielectric (substrate below, air above).
Lossy transmission lines of any kind do have very large dispersion at low frequency. This is due to series R. The R in series with L (per unit length) causes the circuit theory Zo (=sqrt(L/C)) and velocity of propagation (=1/sqrt(LC)) to become complex and very dispersive at low frequency. But you can get this information out of pure circuit theory which allows only for longitudinal current (lossless substrate case). And you can see it in EM analysis for zero thickness transmission lines...no Z-current at all. (At low frequency this extreme dispersion does not matter: line lengths are such a tiny percentage of wavelength.)
You point out the case of width and thickness being about equal. We found, as described in my paper, that this specific case requires more sheets in order to calculate Zo to the same accuracy. (For volume meshers, it requires a finer mesh.) This is because the fields from the sides of the line contribute more to Zo, and fields from the top and bottom sides contribute less to Zo as compared to the wide case. Makes sense.
Let's look at the lossless case first. Now we don't have to worry about skin depth. In this case, we still find that nearly all the current is still longitudinal. Very easy to check. Select dimensions for a test line. Analyze it with any surface or volume mesh analysis, perfectly lossless. Look at the current. You will see it is nearly all longitudinal. You can do a 2-sheet circuit in SonnetLite (free from www.sonnetsoftware.com). You can view 3-D currents in Version 10. No need to take my word for it. In fact, please don't take my word for it. If it is important to you, try it and see for yourself. Any EM analysis will give pretty much the same answer. If you use an iterative volume mesher, just be sure you have converged the much more sensitive current distribution, not just the S-parameters.
In the lossy case, we need to extend the current distribution inside the conductor. If there were significant Z-directed current, we would have to extend the vias inside. We tried it and looked at the result. No Z-current. So, we don't do that now because we know it isn't there. Doing it would be a waste of time. It is absolutely OK if you think I am wrong. Please try it and see for yourself. Maybe you can find an exception. I would welcome such information. This is the way science works.
What is important in the lossy case, as I said, is that the (longitudinal) current must extend inside the conductor. You can get a very reasonable approximation to the skin depth by making the cell size equal to the skin depth. This extends the current into the condutor uniformly for one skin depth. If you need a better representation of the current, then use a smaller mesh. But that costs more analysis time. Make sure you are getting increased accuracy you need by doing and A/B test. Don't waste hours of analysis time getting accuracy you don't need.
In the case of equal width and thickness, espeically with tightly coupled lines, we find that having the current extend into the body of the line can be important. Keeping it all on the surface results in increased error.
Having said all this, if you or anyone else can provide even one well converged plot of fundamental mode microstrip showing eddy currents swirling around, (along with sufficient information to duplicate the result!) you will have my full attention. A fundamental mode microstrip has width, thickness, and substrate thickness << wavelength. Please do not bother posting a current density plot that still has a lot of numercial noise in it. Anyone can see anything they want in a plot like that, it is like looking at clouds.
Loucy, if you don't mind, can you share with us where you first heard this "eddy current" concept for lossy microstrip? I'd be very interested in finding out where it came from. I guarentee it did not come from capable EM researchers.
Has anyone else been presented with this eddy current concept? Please feel free to share with us where you heard it. Would love to explore it's family tree.
I remember reading the term "eddy current" in a paper on spiral inductor. I couldn't find it at this time, but I will keep an eye on it.
As I remember, the term "eddy current" was used in the paper to describe the current on the surface of conductor, not in the substrate. I think the paper didn't give an reference on the origin of the term "eddy current", and it was not written by a EM researcher.
Thanks Loucy. I have done quite a bit of work with Si RF IC designers over the last few years. In EM, the eddy current term was first used in power transformers (60 Hz AC kind). The massive iron cores would have induced current increasing loss and temperature. This induced current was referred to as eddy currents. To solve the problem, they laminate the cores to open circuit the induced currents.
The term has seen occasional use in Si RF IC design for the current induced in the substrate, physically similar to the AC transformer situation, but laminating the Si substrate is not possible. The conducted current in the Si substrate is fully included in all EM analyses that I know of, both surface and volume meshing. I have never seen a reference to eddy current in a microstrip conductor, probably because it does not exist.
I think using the term eddy current is very misleading because it brings to mind nonlinear chaotic fluid flow effects that simply do not exist in linear EM. To avoid confusion, they should use the term induced current, rather than the cooler sounding but inaccuate eddy current description.
The main problem with volume meshing for planar circuits is you have to mesh the volume. For high accuracy loss in thick conductors, the volume mesh size must be small compared to the thickness at least around the conductor. As circuit complexity increases beyond even the simplest circuit, this quickly becomes an impossible task. Surface meshers have much less trouble, and you typically don't have to worry about converging the current distribution, there is no iteration.
I do not understand why some designers still use volume meshers for pure planar circuits. Maybe it is the only tool they have. But they pay a huge price in analysis time for doing so, and because they typically don't iterate until the current distribution is fully converged, they get a lower accuracy result in addtion to spending all the extra time. A lot of the problems I have seen posted on this forum for volume meshers just don't happen with surface meshers. It is a very very sad situation.
Loucy, I think your comment about EM3DS is not appropriate (or at least not very appropriate). EM3DS is a full-wave 3D solver, using MoM and the "additional" half of the dimensionality is obtained through the derivation of the entire Green's function kernel for the Environment. Once you know that kernel and are able to solve the IE you know every vector quantity in every point of the volume. Nuff said.
Of course, EM3DS does solve the IE assuming 2D currents on metals (if thin), 3D inside metals (if thick) and 3D inside any other dielectric (including lossy metals, vias etc) (for the current there is simply field). We are not able to see the field in arbitrary points of the volume and the reason is that we are normally interested with the transfer and reflection on ports, that is, we don't much care (some of us do) what is the field in the corner of, say, some dielectric or substrate, but we care of what is happening to the I/O bus - that is - the ports. In that respect, EM3DS is a full featured 3D solver and in our lab we are using it as such.
One may argue that the derivation of the kernel is done assuming layered media - that's not the point - because for that media (or for that kind of media) it is a 3D solver. Is it a good approach for say Luneburg lenses? Definetely not - unless one may staircase the lens and live with huge number of cells and approximate the open case etc etc. But for what this solver is intended - it is a full 3D solver. The issue with x-, y-, z-directed currents is irrelevant - solving the IE in ANY coordinate system is just fine as long as you know how to transform - the rank of space is still 3 and we just use different basis, but that's so natural. Reason MR guys use cartesian is because their kernel is derived in that Coord. S, and because their Environment is so described (by constitutive parameters etc) but has nothing to do with the dimensionality.
Our experience with Em3DS is not very big - just a year and half, but we have managed so far in designs that we failed by pure 2.5D engines. One such case was in a tightly packaged structure, with a fence, very close to the structure. We did use the via z-directed approach to emulate what we wanted but we failed for the simple reason current was not z-directed at all (I mean not only z-directed) and we FORCED the engine to think it was - you guess right our results were bogus. We are working on MEMS switches and tunable filters and we found EM3DS very competitive compared to any of the big brothers - FEM and FDTD.
Hence, the discussion - is a certain solver 2.5D or 3D should be considered keeping in mind the entire structure and environment - that is, if you are able to draw the structure in your native editor and solve for it with all 3D stuff and not "assuming" - it is a 3D solver - if not - it is 2.5D etc etc. Certainly EM3DS will fail in a "Generic" dielectric antenna design - but like I said, you won't even be able to draw it in its editor:) apart from the "closed" formulation etc.
It was a great feature added in Em3DS - what they call 2.5D mode. It is just a 2.5D approach assuming thin metals etc. similar to all other 2.5D engines. It is much faster, complements the 3D engine and our designers love to start designs using it. But when it comes to sending the wafer layout to the fab we do use the 3D mode and I am happy even if it takes a night before validation. Here, I agree with Jim Rautio that many times we do not need the "heavy weapons" (3D) and we can obtain better results (I stress better) using 2.5D tool.
A point oft overlooked is the accuracy or what I call a "convergence" of a design.
That is, is it good to use heavy, resource-hungry engine and live with poor convergence, stopping far from optimum for lack of time and resource or is better to "assume" something and use lighter and faster approach (or tool) thus obtaing BETTER overall accuracy. But that's off our topic and I don't want to start that here.
Well, that much for my "hands-on" experience with EM3DS.
My first advice to people starting with EM solvers is to investigate the "native" set-up environment - media, parameters etc, not even looking the engine at that point. This approach often speaks for itself: first because one may see if that is close to the problem in hand and second because if you can draw it (w/o much effort), you will probably be able to solve it. The engine, method etc. comes next.
Regards,
Cheng
Hi Cheng, Are you talking about this sentence that I wrote above:
"However, the currents (EM3Ds uses volume current to solve inside conductor) are still x-, y- or z-directed, so you might still call it 2.5D."?
If this is your objection, go ahead and call it 3D MoM solver. I understand the general arguments of both sides. (Maybe you have noticed that I used the word "might".)
I have to disagree with your advice to people starting with EM solvers (in the last paragraph). To me, you statements imply that the GUI or the geometrical engine is the first thing one should look at. 3D solvers using FEM or FDTD generally comes with a better solid modeler, so you can propably draw the geometry most "close to the problem in hand". But that doesn't mean one should start with learning FEM or FDTD packages.
It is much better to start with getting a general idea on the kinds of problems that can be solved in different EM packages, which means finding out the "features" of the EM engine. This is the reason smart questions such as "difference between 2.5D and 3D simulation tools" are often posted in this forum.
Yes, I took reference by your comment concerning the cartesian current expansion. It is not related at all to the DIMs.
As for your disagreement - well, it is a matter of getting a good fresh look onto the subject and not be bloated by commercials.
The reason one ought to look the set-up (not the gui as you say:)) first is that it will show the sort of "real problems" he/she MAY solve or is best suited to solve. Take ANY of the so called MoM solvers - you won't find ANY fancy 3D solid modeller (with all the blows and whistles) in there because it is useless.
Like I said, it is just a screening where NOT to go at the first place. If it was not for a good reasoning people should have all rush to An$oft and C$T:)
Regards,
Cheng
Added after 3 minutes:
Louce, just missed the last part of your reply. YES, it is in line with what I replied too. I think we say same thing:):)
Regards,
Cheng.