Quick question: why does Q of spiral inductor have a peak?

[rautio]

Re: Quick question: why does Q of spiral inductor have a pea

Hi Jian -- Glad to hear that you might be willing to put some effort into this topic. From your last post, I thought you were backing out. However, keep in mind that I will be inclined to not proceed if you keep saying, "It's accurate, it's accurate!" when our objective is to find the error. Also, you may recall that I wrote that claiming to be an expert or an authority (which you have done again in the above post) is not helpful. Allow me to explain. Many people in the US (and Europe, too), especially of my generation, were brought up to very strongly distrust experts and authority. And I mean VERY strongly. Thus, when you offer being an expert as part of the defense for your viewpoint, it actually makes your case much weaker. If you would like to make a strong case, you should not draw attention to being an expert. You should place your emphasis on data.

As for point #1, when I say the differences appear large, I am pointing out that two people can look at exactly the same data and see two completely different things, and both can be completely 100% correct. This is a very important concept you would do well to realize is often the case. It is my nature to look for differences in data because that is where the interesting research can be done. So I look at your data, or anyone else's data, I look for the differences. The differences between triangle and rectangle meshing results in your plots are quite easy to see. That is something, if I had the software, that I could work with. Trying to find out why those differences are there could be a lot of fun, as well as educational. However, if we look at that data and say it has good agreement, that is the end of the story. Nothing more to do! Soooo boring!

So assuming, we won't rely on telling each other that we're experts, and assuming we're looking for the error, and that we are not successful until we find a reasonably high confidence number for the error, here are the answers to your questions:

1) Purpose? To find the error in inductance at low frequency.

2) For whom? For curiosity primarily, others may find it interesting or even useful, but I consider that secondary. If you want to do something of immediate practicality, you should look elsewhere.

3) What is low freq? Anything where the current density is close to uniform through the volume of the metal. There are two transition frequencies for microstrip loss, as indicated in my paper on microstrip loss. High frequency is above the higher of the two. Low frequency is below the lower of the two.

4) Yes, DC is low frequency. However, DC is a different problem as the ground plane and any sidewalls have no effect on magneto static inductance. Would be interesting to get a result there. If you can do that, please share it with us.

5) What is the converged value? An example is in the pdf I attached previously.

6) Box size? Given in the pdf I attached previously. You should be able to download SonnetLite and look at the two layer file. All the info is in there, too.

7-12) All box boundaries in this case are infinitely thick and perfect conductor. Top and bottom covers can be lossy and of any thickness but are not in this case. Sidewalls are always PEC as I often state.

Extra comment for 10) Yes we can not get perfect PEC walls in measurement. However, all computer modeling is abstraction from reality. Thus all EM analyses always give the wrong answer. We can never build anything exactly as we analyze it. We can only approximate it. Fortunately, in the case of PEC walls and in the case of many other things that we approximate, we can often get really really close. (I think you know this.)

You can do the multi-sheet model manually, it might be interesting to see if you can duplicate what I did in the previously attached pdf.

Just for the record, I will state my top level viewpoint on this matter, even though I have already done so many times. All the different EM tools (and their models, including both tube-like thickness and multi-sheet thickness) have their advantages and disadvantages and a good designer can benefit tremendously from intelligent use of multiple tools and models. And that includes tools from multiple vendors. I will take issue with anyone that seriously suggests anything to the contrary with regard to any of the available models or any of the available EM tools. I do not consider "puffing" (a standard term of the sales trade) to be serious.

 

[jian]

Re: Quick question: why does Q of spiral inductor have a pea

Hi, All:

I don't know what "puffing" is. It must be something not related to a technical discussion. However, a well-known fact tells me that, when frequency is approaching DC, the current is approaching uniform in where the conductivity is the same. If there are conductors of finite conductivity and PEC inside a structure, the current will only go in the PEC and it will not go in the conductors when frequency is going to DC. Basically, the current goes in the least impedance path. When the frequency is approaching DC, the impedance of the path is changing and the current is changing too. The changing current distribution results in changing L when frequency is approaching DC.

All my twelve questions asked in my previous posting are related to the above fact. In some sense, before we get all the information about the conductivity, the size and the thickness of strips, the ground planes and/or the metallic enclosure box, we can’t find a converged value of L when the frequency is approaching DC. That is the point. The uncertainly in L with frequency approaching DC may not very critical to circuit design due to the fact that the impedance is (j*omega*L) and it is what we are concerned. When omega is small, slight difference in L really doesn't have a significant effect on the impedance. More detail discussion is documented in the Appendix BB of the IE3D 11.5 User’s Manual. Interested users can e-mail to me and I can send you a PDF file copy. Regards.

 

[rautio]

Re: Quick question: why does Q of spiral inductor have a pea

"Puffing" is when some one says something like, "Our product is the best!" or something like that. There is no way to prove that it is actually true, and a puffing statement can actually be false with no problem. It is still OK to say. This is very common in sales (in fact, it is expected and almost required), and, to one degree or another, everyone does it. It is accepted practice. Because it is accepted practice, that is something I will not take issue with.

If I read your post correctly, I think you are saying that the current will flow only (or mostly) in the perfect conductor of the box sidewalls and not in the resistive transmission line at very low frequency, and this leaves the inductance entering some kind of non-converging state. Will you please verify that my understanding of your viewpoint is correct?

P.S. The line I analyzed is actually 104 uM wide. Pdf with 100 uM changed to 104 uM is attached. No other changes.

 

[jian]

Re: Quick question: why does Q of spiral inductor have a pea

Hi, James:

I didn't say that current would only flow on PEC but not conductors with finite conductivity at low frequency. I only said that this is the situation when frequency is at DC. However, when frequency is going down and approaching DC, the current distribution is changing on the ground planes (and enclosure if there is any) as well as the strip. Depending upon the difference in the conductivity, the thickness, the size of the ground plane and enclosure, the current distribution will be different. To get the L at very low frequency precisely, we do need to get the information about the metallics in the whole cross-section of the transmission line. Don't you agree on it? Regards.

 

[rautio]

Re: Quick question: why does Q of spiral inductor have a pea

Jian -- I would like to make sure I understand your viewpoint correctly. I think you are saying:

1) In the case that I described above, DC current flows only on the perfect electric conductor (PEC). At DC, no current flows on the finite conductivity conductor. This is because the PEC has zero resistance and the finite conductivity conductor has non-zero resistance. Current flows where there is least impedance. At DC, least impedance means least resistance.

2) As we go lower and lower in frequency, the current changes from flowing on the finite conductivy metal to the PEC metal and as this happens (as we go lower in frequency) the inductance changes too.

If my understanding of your viewpoint is not correct, please provide more detail.

Also, if there is any part of the proposed problem (conductivity, PEC, geometry, etc.) that is not specified well enough to provide a convergent solution, please tell me. I will immediately provide any missing specifications. If there is any other reason we might not get a well-behaved convergent solution, please tell me.

 

[loucy]

Re: Quick question: why does Q of spiral inductor have a pea

The above convergence study is very interesting. Allow me to cut into the exchanges and raise some questions that might be relevant.

1. for transmission line with non-perfect conductor, is there a mathematical proof that there exist a unique fundamental mode?

2. is there a standard/universal way of computing the S-parameters from the current for a transmission line consisting of non-perfect conductor and/or lossy dielectric?

3. for a fixed set of S-parameters, is the equivalent circuit unique? would we get a different inductance value if we follow a procedure different from the one implemented in Sonnet?

The answer to these questions will affect one's opinions on the numerical results reported in the above numerical study.

my 2 cents:
a. convergence study is a good thing to do, not only for academic reason, but also for designer engineers in practical applications.
b. the lack of error standard is a weakness of the MoM formulation itself. there has not be a proof that the MoM procedure would converge as one refines the mesh for general problem. therefore one can expect that different implementations (by different vendors or even the same vendor) could "converge" to a different value. Some problem might not lead to a convergent result at all. It can be imagined that the argument on accuracy will continue until some more fundamental problems of the MoM formulation is resolved.

 

[rautio]

Re: Quick question: why does Q of spiral inductor have a pea

Some perceptive questions Loucy. My answers for what they are worth:

1) For EM, we have the Uniquenes Theorem (see Harrington, among others) that states there is one and only one solution to a completely specified EM problem. For the problem as stated above, it is completely specified and there is only one solution. The solution involves many transmission line modes. However, all but one mode is cut-off so all the cut-off modes become what we call fringing fields. Regardless of what you come up with for inductance, or Zo, or anything else, there is only one field solution. This is one reason it is interesting to look at current distributions. They do not depend on how you specify S-params.

2) There is no universal way to get S-param from an EM solution. There is an exact way to do it in a shielded environment as described in our paper on the unification of SOC and double delay de-embedding recently published in MTT Trans. However, no matter how you get S-params, if you have a good EM analysis and a good way to get S-params, you should be able to get an answer and show some kind of convergence.

3) Given a set of S-params, there are different ways to come up with equivalent circuits, and the results will not be identical. That is why I suggested that we could all use Sonnet's way to do it. Using other ways are fine too, as long as if we compare, we all use the same way. At low frequency, all the ways should come up with answers that are very very close. That is one reason to use low frequency for a test case.

Providing my 2 cents about your 2 cents: Yes, MoM is not guarenteed to converge. That is one reason it is interesting to check convergence. The most valuable checks are to see if MoM converges to the exact answer in exactly known problems, like stripline, thick stripline, and coupled stripline. I have published these tests and I have a nice little spread sheet that has the exact solution programmed up for all but the thick stripline case. I will post it if anyone wants it. Other cases for which there are exact answers are the coupled line de-embedded to zero length. I have never seen Sonnet MoM diverge except in cases where more precision is needed or the de-embedding is experiencing one of the well understood failure mechanisms. Given sufficient numerical precision and valid de-embedding, my experience has been that it always converges.

When we don't have an exact answer it is useful to see if two different tools converge to the same answer. If not, then it becomes interesting to figure out why. That is what I was hoping was going to happen here, but I am starting to have my doubts. Gotta go!

 

[rautio]

Re: Quick question: why does Q of spiral inductor have a pea

I have given Jian a few days to confirm that I understood his viewpoint correctly, but a reply has not been forthcoming. I am guessing he has realized his blunder and I will proceed on that assumption.

We are all human and we all make blunders (myself most certainly included), so, as far as I am concerned, there is and should be no shame there. These things happen, that's all there is to it. Best thing to do is to realize it happened, deal with it, then get on with life.

First, yes, it is true, if you have a perfect electric conductor (PEC) connected in parallel with a lossy conductor at low frequency (and DC), all the current flows in the PEC and that will change the inductance. However, for the problem presented, the current flows down the transmission line, and then the PEC sidewalls of the containing box act as ground current return back to the source (i.e., port). Thus, the lossy conductor is connected in series with the PEC box sidewalls. The complete current flow forms a loop, an ideal and very stable situation for calculating inductance.

The reason I am making this post is because it seems there is an awful lot of "folklore" that is starting to accumulate about RF design. Some of the folklore is correct, but most of it is just plain wrong. I do not want the incorrect low frequency inductance scenario proposed in prior posts to become part of that folklore.

To set the record straight, for the geometry I described, the low frequency inductance (i.e., when current is uniform in the metal of the lossy line) is constant right down to and including DC. All current that flows out on the line from port 1 returns on the PEC sidewalls. It is does not suddenly switch from the lossy line to the PEC sidewalls. It has to flow on both, going down one and coming back on the other.

If people will take the time to think just a little bit, bad ideas will be immediately rejected. All you have to do is imagine building the transmission line and connecting a 1.5V DC battery to it. You will immediately realize how the low frequency current flows.

I shall point out one blunder I made in this thread. I suggested that this problem (low frequency inductance) was of limited practical importance. On this matter I was completely wrong. Note the following article that I spotted while browsing the most recent issue of MTT Trans (I at least glance at every article in every issue of the MTT Trans. when it comes). It seems this problem is of critical importance and has been the subject of extensive research in the VLSI field:

Capture High-Frequency Partial Inductance More Accurately by Gauss Quadrature Integration With Skin-Effect Model
Du, Y.; Dai, W.
Page(s): 1287- 1294

It would still be nice to see inductance, or even resistance, results from any other EM tools for the 200 uM long line at 10 MHz, but I have a feeling that that will not, and perhaps can not, happen.

 

[lagrange]

Re: Quick question: why does Q of spiral inductor have a pea

Hy, all

I would like to add my 2 cent to this very interersting thread.

Apart from the wrong assumption on the low freq behaviour of currents in lossy metals +PEC I think Jean is correct when he states that the tube model can be complete in that there is no need to take into account for the volume currents. In fact, at least in principle, the well known equivaence principle states that the volume fields (and currents) that are inside the metal can be removed provided that a proper set of electric and magnetic equivalent currents is placed on the metal boundary. These two quantity are related by a sort of "surface impedence" and I think that the Jean dissertation on the diffraction angle proves that, when the imaginary part of Er is much grater then its real part the surface impedence can be computed using the plane wave model.

To be more precise I think that to justify this computation of the surface impedence it is also necessary to assume that the metal thikness is quite higher than the skin depth. In fact, even considering the planar model, it is clear that when the two faces of the metal layer are close, there is a coupling between the related currents which is not taken into account by the "scalar" surface impedance. In the planar case one could easely refine the model to include also this coupling effect but I can not see an easy way to generalize this model to an arbitrary geometry. In the general case one should compute a sort of generalized impedence matrix which relates the tangent E to the electrical current impressed on the metal boundary. In principle the computation of this matrix can be done using a volume solver which meshes the metal volume (FEM, FDTD ..) or also using a MoM solver like IE3D. May be that IE3D has done something to address this problem but the lack af details and the fact that Jean speaks only of the normal diffraction to justify his method let me think that this is not the case.

These considerations let me to think that the IE3D tube model can be appropriate (and probably also very efficient) to deal with a thick metal at a high frequency but probably it is not appropriate for the test case proposed by Rautio. In fact at DC the skin depth is infinite and the simple surface impedence model is not applicable.

Of course the last word is left to a the facts (i.e.to the comparison of the results of a simulation with a measurement or better with an analytical data).

 

[jian]

Re: Quick question: why does Q of spiral inductor have a pea

Hi, James:

I think my viewpoint was clearly stated in my last two postings. Everybody can read it and understand it and judge whether what I said is true. There is no need to use the word "blunder" to describe it. Again, such a claim is inappropriate for a technical discussion. For those interested persons, they can read the Appendix BB of IE3D 11.5 manual to be released in a very short time. Well, I am very busy to lead our team to bring out the IE3D 11.5. The IE3D 11.5 will have the FASTA (Full-wave Accelerated Simulation Technology Algorithm) which may solve much bigger structuers using much less computational resources. I hope that all interested users can see it before IMS 2006. Regards.

 

[rautio]

Re: Quick question: why does Q of spiral inductor have a pea

Hi Lagrange -- I agree with your observations. When I commented that skin effect was exact only for a normal plane wave incident on an infinite conducting plane, Jian focused on the normal incidence. I have no problem with the normal incidence. Rather, I wanted to point out that the infinite half plane assumption is violated, as you have detailed so nicely. The approach you describe, by the way, is realated to the equivalence principle and is called the Boundary Element Method and is used in several commercial EM tools. Use of the equivalence principle itself usually includes electric currents impressed on a PMC (perfect magnetic conductor) or magnetic currents impressed on a PEC, or a combination of magnetic and electric currents with zero field in one region.

Jian -- If I understand your position correctly (which you still have not commented on) I am afraid it is indeed a blunder. (A blunder is typically a simple, fundamental mistake, it does not have particularly strong negative conotations. As I said, we all make blunders, I even pointed out and corrected a blunder I had made.) For the stated problem, there is plenty of current in both the lossy conductor as well as in the PEC sidewalls. The current has to flow through both, it can not choose one or the other. In addition the current distribution remains stable and almost completely unchanged (in both the lossy conductor and in the PEC sidewalls) at all frequencies from DC up to the low frequency limit. This means the low frequency inductance is constant and well behaved. All this is in direct contradiction to your statements.

I carefully worded my previous post so that you could back away (or modify) your viewpoint with little loss of credibility provided you realized you had made this mistake. I am very sorry and disappointed to see that you do not realize your error and that you continue to defend and promote a position that is so clearly incorrect and untenable, apparently (inferring from your comments), even in your documentation to your customers.

To All -- I think Jian is a little bit too busy to post results for the problem I suggested. Anyone else care to help out?

 

[jian]

Re: Quick question: why does Q of spiral inductor have a pea

Hi, All:

Well. I think many of you may be interested what my complete view point on Inductance at Low Frequency and DC. Here is the Appendix BB of IE3D 11.5 Manual to be released. Any suggestion, please feel free to contact me at: jian@zeland.com. Regards.

 

[Nonsense]

Re: Quick question: why does Q of spiral inductor have a pea

Hi, James and Jian,

I never expect this post will arouse such an enthusiasm! Two thumbs up!

IE3D and Sonnet, I'll recommend these tools to my boss!

God bless both of you.

 

[lagrange]

Re: Quick question: why does Q of spiral inductor have a pea

Hi Rautio

I am very interested in your thick metal benchmark. As I have told in an other post I made a long time ago I am developing a new 3d EM solver and I am looking forward to apply it on your test case. Unfortunately I am not yet ready to make the test now and there are many things to do before my code is able to address this complex problem.

Hi Jian

Your appendix BB is very intersting but I do not completely agree on your conclusions about the extreme instability of the L parameter.
In my view the crucial point is that your are looking at a planar wave which propagates in a cylindrical structure. In this case, as you said, whith an infinite lossy ground planea and at DC the current must flow uniformly on the whole plane but also the field excitation must extend to the infinite on the transversal section. I think that this condition is very far from a practical situation where we have a local excitation (like a lumped port). In such a real case I am quite convinced that the inductance of the equivalent circuit seen by the lumped port can not be so sensitive to a small variation in the resistivity of a conductor that is situated very far from the excitation.

Added after 2 hours 25 minutes:

Other comments for Jian:

On the other side I Igree that the L parameter seen by an input port depends on all the possibe current paths in the global net and therefore can not be computed looking only on a small portion of the net.
But this is the same as to say that a the electrical responce of a circuit is influenced by those of all its subcircuits and this fact has never been an impediment for the design strategy based on the sub circuit division.

 

[rautio]

Re: Quick question: why does Q of spiral inductor have a pea

Hi Nonsense -- Thanks for your "quick question"! It has certainly turned out to be quite a discussion. Good luck in your efforts. And as always, I do recommend multiple EM tools from multiple vendors if at all possible.

Hi Lagrange -- Good luck with your EM analysis. There is always room for another good tool at the table. If you can provide details to me sometime, I will be happy to consider what might become its advantages and disadvantages. From your postings, I get the impression you might find the topic of analysis error (as opposed to accuracy) as interesting as I do.

As for Jian's appendix, I agree with your comments. But I also point out, even though I am sure you already noticed, the problems Jian discusses in the appendix do not include the problem discussed in this thread. If we start discussing those new problems, the original problem will be left unresolved. The problem discussed in this thread is a thick lossy microstrip surrounded by perfect conductor for all ground current return, and that problem is not even mentioned in Jian's posting. Somehow I had thought he was posting the appendix as justification for not solving that problem. Silly me.

 

[lagrange]

Re: Quick question: why does Q of spiral inductor have a pea

Hi rautio. The code is based on a new method that I have developed and which is quite different from other full wave methods in that it is not in the frequency domain and neither in the time domain but it goes directly to an equivalent crcuit which represents the electromagnetic responce of the analized component. Actually I know of the existence of onother method (PEEC) which follows a similar strategy but I think that it is not full wave or, at least, that only the "not full wave version" of PEEC is effective in handling large problems.
In my method the microwave component can be composed of several parts made of different materials which are subjected to independent analyses and each part produces a different subcircuit with a one to one relation between subcircuits and subvolumes.
The principal merit of this method is that the computation time scales linearly with the problem dimension. To be honest the linear time scaling is limited to the circuit generation while the computation time of the spice-like simulator can increase more quickly. Nevertheless, due to the sparsity of the circuital problem and the fact that my method should produce circuits with much less elements then PEEC I think that it can have meny advantages even when the time of the circuital simulation is taken into account. Furthermore in this comparison it must be considered that the circuital representation fits very well in the typical design flow of the EDA industry which is well accustomed with the spice format.

Yes you are right I am very interested to the error analysis but for the moment, that is fore the present development phase I can address only simple canonical problems. The first test I have done is the computation of the reactance of the TE11 mode of a sphere having a diameter of 20 mm.
The TE11 port covers the whole boundary of the sphere and is looking towards the inside of the sphere. The frequency responce of this reactance has been computed using an open source spicelike simulator (gnucap). I have annexed the related plot where you can see the comparison of the computed versus the analytical curve. Please take care that in this plot the units are wrong: the frequency unit is Hz and not GHz as written while for the y axis unit is ohm (and not dB).

PS I am aware the this description is not sufficient to make a clear picture of what is really done in my method. I hope anyway that it is enough to create some curiosity about it.

 

[loucy]

Re: Quick question: why does Q of spiral inductor have a pea

lagrange -- I think Jian didn't mean that "there is no need to take into account for the volume currents". On the contrary, it is suggested that IE3D has proprietary way of accounting for currents flowing in the internal (volume) of a non-perfect conductor. It appears to be some high order basis but unfortunately Jian is relunctant to give out more details.

 

[rautio]

Re: Quick question: why does Q of spiral inductor have a pea

Hi Loucy -- Glad to see you are part of the audience. Interesting idea, but I am doubtful. If Jian were using some kind of volume current basis function, then he would not need to use the concept of surface impedance. Surface impedance works with surface currents, and does not work with volume currents. The VLSI paper I referenced appears to use a combination of skin effect and volume currents to get the correct low frequency inductance. Would be easy to check for sure, however. Just solve a problem with thick metal and then view the current distribution.

 

[lagrange]

Re: Quick question: why does Q of spiral inductor have a pea

Hi Loucy and Rautio. I also am doubtfull about the possibility that Jian is tring to solve the inner problem. In fact he says that he uses analytical solution and I can not imagin of an analytical solution that is applicable on a general thick metal.
Nevertheless I think that this point doesn't mutter very much. This i s because to me it is quite clear that Jian has no interest at all in the lo freq induttance of the the thick metal. I also thik that the last Jian annex (appendix B) is intended to demonstrate that, due to its supposed high instability, the low freq induttance is not a significant parameter. If I have well interpreted his position he is saying that this is a general truth and therefore (as already pointed out by Rautio) he is using the appendix B to justify the scarse interest in the thichk metal test case. I also would appreciate much more if Jian would taken a different approach tat just to negate the evidence or to hiden the fact that a problem is not very well suited to IE3D with a negation of its relevance.