[SI-LIST] Re: Signal crossing Split plane

  • From: Scott McMorrow <scott@xxxxxxxxxxxxx>
  • To: ch_harrington@xxxxxxxxx
  • Date: Mon, 03 Dec 2007 14:44:09 -0500

Charles,

You said:=20

" if you place your stitching vias (or whatever you call them), close to =
the signal via, they will also define the inductance and impedance of the=
 return path. The inductance of the complete arrangment (signal via, stic=
hing vias/return path) depends almost entirely on the geometry of the via=
s and the distance between the stitching vias and signal via. If you incr=
ease your simulation area without increasing the geometry/position of the=
 stitching vias, then the inductance/impedance of your return path will n=
ot change."

This is only partially true, but it is not the complete story.  Dr Johnso=
n is only partially correct on his treatment of via inductance.  It is go=
od as a 1st approximation, but it does not tell the whole story.  His tre=
atment assumes planar cavities of infinite extent and no full-wave effect=
s occurring between the signal, stitch vias, and planes.  Planes are not =
infinite, and full-wave effects do occur, however, under some conditions =
they can be approximated by the quaint TEM phenomena that we call "induct=
ance".  Any time vias penetrate a planar cavity, a circular parallel plat=
e excitation will occur.  Vias used to stitch the cavity cannot contain a=
ll of the magnetic field and thus some energy propagates into the cavity,=
 depending on the frequency.  The percentage of energy lost to the cavity=
 is frequency dependent, and will resonate and eventually be converted to=
 crosstalk, power system noise, and distortions in the signal as the ener=
gy is re injected in the signal via.  These effects are non-localizable w=
ithout considering the complete planar boundary conditions, and constitut=
e errors in modeling that are dependent on the exact configuration of the=
 planes. Many times these errors are acceptable.  Some times they are not=
=2E  Frequency of operation, desired bandwidth, and required isolation ar=
e determining factors in the acceptability of a particular modeling appro=
ach.

Placement of model launch ports at well-defined signal mode boundaries he=
lps to solve some of the localization problems, but not all of them.  Sig=
nals following vias go through very tricky rabbit holes indeed, and as so=
on as via lengths approach significant fractions of the signal wavelength=
, large amounts of energy can be converted to parallel plate mode excitat=
ion, well before other higher order modes of propagation develop.

Yuriy and I have had many discussions about these things going back 5 or =
6 years now.  I'm quite sure he has an ample grasp on the RF Electromagne=
tic phenomenon.  I've also looked at his application notes and find that =
the are fine for what they are, but in some cases they are quick and dirt=
y.  There's nothing wrong with that!  They serve to show and establish so=
me fundamental points.  Knowing Yuriy, I know that he understands the inh=
erent limitations of the way that he launched into some of the structures=
, and I find his emails quite enlightening as he expands on his thoughts.=



Regards,

Scott

Scott McMorrow
Teraspeed Consulting Group LLC
121 North River Drive
Narragansett, RI 02882
(401) 284-1827 Business
(401) 284-1840 Fax

http://www.teraspeed.com

Teraspeed=AE is the registered service mark of
Teraspeed Consulting Group LLC



Charles Harrington wrote:
> Yuriy,
>   =20
>   if you place your stitching vias (or whatever you call them), close t=
o the signal via, they will also define the inductance and impedance of t=
he return path. The inductance of the complete arrangment (signal via, st=
iching vias/return path) depends almost entirely on the geometry of the v=
ias and the distance between the stitching vias and signal via. If you in=
crease your simulation area without increasing the geometry/position of t=
he stitching vias, then the inductance/impedance of your return path will=
 not change. So your explanation that changing the simulation area automa=
tically changes the impedance of the return path and |S11|, is not correc=
t. If you do not believe me, then contact Dr. Howard Johnson for further =
explanations. In his book (advanced black magic) he has an excellent expl=
anation of the relationship between these stitching vias and the inductan=
ce of the return current of the signal via. This is the only text I know =
that treats these issues in a very
>  practical manner and I think it will be of great help to you. I strong=
ly recommend it to every other person working with via modeling. Note tha=
t the number of stitching vias you use depends on a number of other facto=
rs. From his book, you'll see just a method. You can apply the method to =
your own designs. Don't expect an automatic solution to your problem!
>   Remember, Maxwell never said Ampere is wrong. He said Ampere's circui=
tal law is not complete and then completed it using the displacement curr=
ent term (See J.C. Maxwell - On Physical Lines of Force, 1861). Now, when=
 your stitching vias define the return current path, the conduction curre=
nt is much more greater than the inter-plane displacement currents, such =
that we can use the original form of Ampere's law without any loss of acc=
uracy. Quasi-static methods use this approximation too. It's not that the=
 displacement current is not present. But it is too small to be considere=
d. With that said, you can visualize the discontinuity (considering its r=
eturn paths and traces) as consisting of 2 parts. The closest part (which=
 you beautifully describe as the "near field zone") and the "far-field zo=
ne" - if you allow me to use your words. In the "near field zone", which =
should be less than 3mm for frequencies up to 50 GHz (from my experience)=
 when using typical PCB/package
>  geometries, |S11| (at a given constant frequency) depends almost compl=
etely on the higher order modes excited by the discontinuity. |S11| decre=
ases as the length increases because the higher order modes die off. In t=
he far-field zone, |S11| increases because the higher order modes have co=
mpeltely decayed and other factors now play the deciding role. As you kno=
w, |S11| for a given line length at a givn frequency is constant.=20
>   This is the method I have been using to define the boundaries of both=
 vertical discontinuties(such as via-holes) and horizontal discontinuties=
 (such as bends). And I'm fine with it. I have done many simulations and =
measurements. As I said earlier, I got it from the paper I cited on Nov. =
20. and other publications from these authors. I had problems to accurate=
ly model discontinuties at higher frequencies (up to 77 GHz) years ago. R=
emember it is just a method and you have to take into consideration your =
real design enviroment, if you apply the method proposed in the paper. Do=
n't expect an automatic solution to your problem! As far I know, the term=
 "boundaries of discontinuities" as used in PCB/package design was first =
introduced by these authors. If you have your own method, then you can al=
so use it. But one thing is clear. You have to define these boundaries at=
 your 20 GHz and beyond. If not, your models are not correct and can not =
be validated with measurements. I'm not
>  interested in your tool. Just like Chris, I'm interested in methods or=
 methodology as he calls it.
>   =20
>   Hope this helps
>   =20
>   Best regards
>   Charles
>  =20
> Yuriy Shlepnev <shlepnev@xxxxxxxxxxxxx> wrote:
>   Chris,
>
> I think all definitions of the interconnect models you provided may be
> applicable under different circumstances. It depends on possibility to
> localize discontinuities such as vias and splits for the electromagneti=
c
> analysis. If all discontinuities in you channel can be isolated for the=

> electromagnetic analysis, then the de-compositional analysis you descri=
bed
> in a) and b) can be safely used. If such localization is impossible, th=
e
> system-level model has to be built either on the base of a complete 3D
> electromagnetic analysis of the whole board (possible but not practical=
) or,
> alternatively, the de-compositional model has to be extended with model=
s of
> such structures as parallel planes and splits with all decoupling struc=
tures
> connected to them (hybrid system-level models with transmission planes)=
=2E
> Those structures are the major reasons of non-localizability of
> discontinuities on PCB and in packaging applications.
>
> How to define the boundaries of a discontinuity and localizability. If
> simulation results (S-parameters for instance) are relatively independe=
nt on
> the simulation area size and on the boundary conditions, the discontinu=
ity
> can be isolated for the analysis and a reusable model can be generated
> (otherwise the discontinuity is not localizable). Simple rules based on=
 line
> width/substrate height can be used to define the simulation area in cas=
e of
> localizable discontinuities. Phase reference planes may be shifted towa=
rd
> the discontinuity to make it electrically smaller (for better fitting o=
r
> interpolation). A line segment with a minimal length to prohibit intera=
ction
> through the higher order modes have to be added at the system-level in =
that
> case. This de-compositional technique used in microwave engineering sin=
ce
> 40-s (Levin, Advanced theory of waveguides, 1951) and is the mainstream=
 in
> the microwave system-level analysis tools. The smaller the localizable
> discontinuity the smaller the effective discontinuity area. It provides=
 good
> models even for micron-sized structures up to sub-mm wave frequencies.
>
> Note that dependency of S-parameters on the simulation area sometime ha=
s
> nothing to do with the higher order modes discussed here before, but ra=
ther
> related to parallel planes and to localizability. S-parameters of a sin=
gle
> via without or with a stitching via nearby can show significant depende=
ncy
> from the simulation area simply because of the discontinuity is not
> completely localized and the impedance of a cavity formed by parallel p=
lanes
> may change the |S11| for instance. Increasing the simulation area, one
> increase the inductance of the return path and together with the via
> capacitance to the planes it may be visible as the decrease of |S11| wi=
th
> the increase of the simulation area size (effect observed in the paper =
cited
> below). Such problems may be on the border line between the localizable=
 and
> non-localizable problems and sometime may even require the system-level=

> hybrid models with the transmission planes.
>
> Who has to define the boundaries of discontinuities or minimal length o=
f the
> line segments to connect the discontinuities. Ideally, it has to be the=

> system-level tool that decomposes a channel into transmission lines,
> discontinuities and possibly transmission planes. All mainstream SI too=
ls
> are already based on the decomposition into line segments. It may inclu=
de
> coupling between the lines bases on physical or electrical thresholds. =
The
> same approach has to be used to define what discontinuities may be anal=
yzed
> with a 3D EM tool and what discontinuities require hybrid models. If tw=
o
> discontinuities are too close to each other (physical or electrical cri=
teria
> can be used) - they have to be analyzed in a 3D solver as a whole and s=
o on.
> In addition, a 3D solver has to define sufficient simulation area
> automatically and produce the model that is electrically as small as
> possible. Without such interaction between the system-level tool and a =
3D
> solver you have to follow the recommendations provided by a 3D tool ven=
dor
> and make sure that the discontinuity model is connected in the final de=
sign
> with sufficient line segments. I think that report on the minimal lengt=
h of
> the line segments would be a good feature for an electromagnetic tool.
>
> Best regards,
> Yuriy
>
> Yuriy Shlepnev,
> Simberian Inc.
> www.simberian.com
>
> -----Original Message-----
> From: Chris Cheng [mailto:Chris.Cheng@xxxxxxxx]=20
> Sent: Thursday, November 29, 2007 6:18 PM
> To: ch_harrington@xxxxxxxxx; shlepnev@xxxxxxxxxxxxx
> Cc: SI LIST
> Subject: RE: [SI-LIST] Re: Signal crossing Split plane
>
> Charles and Yuriy,
> I have a philosophical question about modeling these 3D structures.
> It seems both of you agree that the entry ports needs to be back out to=

> certain distant from the structure itself (most likely dimensionally
> compatible to the structure itself). So what is the definition of the
> overall system level interconnect model ?
> One can have the following defintions :
> a) interconnect model (most likely lossy trace model) with length up to=
 the
> extended port location + the 3-D model of the plane cut/via transition =
model
> b) interconnect model (most likely lossy trace model) as report by the
> design data base + the 3-D model of the plane cut/via transition model =
-
> effect of just the extend port length of the interconnect model
> c) the entire interconnect structure is simulation in one gigantic 3D
> structure=20
>
> The combine last two terms of b) is what Roger Harrington used to call
> excess parasitics.=20
> In a PCB interconnect environment, a) and b) for all practical purpose =
are
> the same because the interconnect length >> extended port length. But f=
or
> package model where the entire structures are measured in mm or mils, a=
) and
> b)
> may have significant differences.=20
>
> Should a 3D cad tool report the "excess parasitics" so that users can s=
imply
> use the length report of the design database, then add in the via/plan =
cut
> section anytime he/she encounters such structure ?
> Or should a 3D cad tool be just modeling the true 3D structure but then=
 has
> to warn users to back out the interconnect trace length to account for =
the
> extend port length (which seems to require careful consideration of the=
 3D
> structure on a case by case basis).
> Or, just lump the 3D structure into a gigantic 3D file together with th=
e
> rest of the interconnect and pray that the simulator will converge ?
>
>
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx
> [mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Charles Harrington
> Sent: Wednesday, November 21, 2007 2:57 PM
> To: shlepnev@xxxxxxxxxxxxx
> Cc: sunil_bharadwaz@xxxxxxxxx; 'SI LIST'
> Subject: [SI-LIST] Re: Signal crossing Split plane
>
>
>
> Yuriy,
> I think we really have to end the discussion. I recommend you also
> talk to some experts in this forum about your models. They will tell yo=
u
> exactly what I=12m trying to say and even more.
> I didn=12t even know you have your own software. But I cannot understan=
d why
> you make such claims that your software can compute =13whatever multila=
yered
> geometry=14 and that =13it also automatically defines the boundary of t=
he
> discontinuities=14. You know this is not true. We all know this is not =
true.
> So why do you make such claims? If I ask you, with what degree of accur=
acy
> does your software compute "whatever multilayer geometry" (when compare=
d
> to measurements) and how does it automatically define the boundaries of=

> discontinuities, I know that you will be baffled. So, I don=12t need th=
e
> answers to these questions. However, I'm glad you acknowledge the fact
> that you need about 1mm distance away from the via pad at such higher
> frequencies to get accurate results. Let us leave it there. I will not
> write any more.
> I wish you the best with your models. 25 yrs of experience is quite a l=
ot..
> I respect that. But as you can see, there is still a lot out there to
> learn.
> Best regards
> Charles
>
>
>
> Yuriy Shlepnev wrote: Hi Charles,
>
> Thank you for the reference. I am familiar with this paper as well as w=
ith
> the other publications of this group from Fraunhofer Institute.
> First of all, our 3D full-wave solver allows to build different via-hol=
e
> models. It solves whatever multilayered geometry with ports you put in
> there.
> Second, the solver automatically defines the boundary of the
> discontinuities. See for instance the final model for optimal via-hole =
on
> slide 8 in
> http://www.simberian.com/Papers/OptimalDifViaholesDesign6pPCB.pdf. The
> differential line segment length in that particular example is about 1 =
mm,
> that is sufficient for high-order modes to die even at 30 GHz. Though, =
to
> define the area we use technique different from one described in the pa=
per
> (I hinted details earlier). Lumped ports are often used for the
> preliminary
> optimization of via-holes because of it is quick and it provides good
> approximation (see for instance the final model and comments in the
> presentation mentioned above). Essentially, it ends the discussion.
> If you looked through the app notes on our web page you just saw the ti=
p
> of
> an iceberg. We put about 25 years of research to develop and validate t=
he
> technology. It is well documented on our web site in Downloads/Papers a=
nd
> Presentations areas.
> And, I do not even want to start discuss the definition of ports or
> multimodal decomposition, because of it looks strange to me that after
> reading Collins you still do not understand what it means and how it
> applies
> to the multilayered circuits.
>
> Best regards,
> Yuriy
>
> Yuriy Shlepnev, Ph.D.
> President, Simberian Inc.
> 2326 E Denny Way, Seattle, WA 98122, USA
> Tel/fax +1-206-726-1098
> Cell +1-206-409-2368
> Skype shlepnev
>
> www.simberian.com
>
>
>
>
>
> From: Charles Harrington [mailto:ch_harrington@xxxxxxxxx]
> Sent: Tuesday, November 20, 2007 2:46 PM
> To: shlepnev@xxxxxxxxxxxxx; scott@xxxxxxxxxxxxx
> Cc: sunil_bharadwaz@xxxxxxxxx; 'SI LIST'
> Subject: RE: [SI-LIST] Re: Signal crossing Split plane
>
> Yuriy,
> I agree with some of your views. However, they contradict your via mode=
ls..
> I couldn't reply yesterday, because I was trying search for the referen=
ce
> I
> mentioned, since you needed it. Many other people replied off-line and =
so
> needed the reference. Got it from IEEE Xplore.
>
> A Novel Methodology for Defining the Boundaries of Geometrical
> Discontinuities in Electronic Packages
> Ndip, I.; Reichl, H.; Guttowski, S.;
> Research in Microelectronics and Electronics 2006, Ph. D.
> 12- 15 June 2006 Page(s):193 - 196
>
> You mentioned in your mail that the near field zone as a result of the
> higher-order modes excited at the via expands with frequency and is ver=
y
> small. I agree with you.
> But the question is this. How small is it? How small or big is at 1 GHz=
,
> 10
> GHz, 20 GHz? Have you ever studied it? You have to take this zone into
> consideration when studying vias or any other structures that excite
> higher
> order modes.
> The method proposed in this paper is quite illustrative and useful. I
> understand it this way (Please correct me if I understand it wrongly):
> These higher-order modes (e.g., TE, TM...) are characteristics of the
> trace
> or transmission line and they die exponentially away from the point of
> excitation, i.e., the via-trace interface. S-parameters, like other
> network
> parameters, give us the relation between input and output signals. Now,=
 to
> obtain S11, for example, you need to get the ratio of the reflected and=

> input signals. Both signals must be of the same "type". We can not
> directly
> compare cars and aeroplanes, though both are used for transportation. Y=
ou
> know your input signal (e.g., a transverse electromagnetic wave), becau=
se
> you excited it at the port. At discontinuities, an infinite order of
> given
> higher-order modes can be excited. The orders or strength of the excite=
d
> modes differ from one discontinuity to another, although the modes can =
be
> the same. So, there is no way you can know all the orders of the
> higher-order modes excited and how they interact. Now if you place your=

> ports quite close to the point of excitation of these modes, then your
> S-parameters must be wrong. Why? In this case, to obtain S11, you need =
to
> obtain the ratio of the unknown higher-order modes and your known excit=
ed
> transverse electromagnetic wave at the port. That's why in most 3D
> full-wave
> solvers, it is recommended that ports should be placed far away from th=
e
> discontinuities, so as to enable these higher-order modes to die. When
> they
> die, then you can easily define your S-parameters which will then be th=
e
> ratio of the input signal you know (transverse electromagnetic wave) an=
d
> the
> reflected signal you know (transverse electromagnetic wave). To define =
the
> points where these modes die or have attenuated substantially, these
> authors
> argued that near the discontinuity, the imaginary part of the Poynting
> vector describes the reactive energy associated with these higher-order=

> modes. So they studied this imaginary part and used it to define the po=
int
> where the modes die. I think they mentioned that only at a distance of
> about
> 1mm away from the via-trace interface, at 20 GHz (or may be 30 GHz) may=

> you
> place your ports, to get correct results. Certainly, this depends on th=
e
> via
> geometry and trace type. But I find the results very helpful and can be=

> used
> as a base for further experiments. You can get the details from the pap=
er..
> Unfortunately in your case, you compare what you don't know (reflected
> signal) and what you know (excited input signal). In your via models,
> neither did you define the required distance away from the via-trace
> interface needed for these modes to die nor did you follow the advice
> given
> in full-wave solvers to be far way from the via-trace interface. You
> considered the via just as the barrel and the pads at 20 GHz and beyond=
=2E
> That's why I mentioned yesterday that your via models are not correct a=
nd
> your S-parameter results are misleading. If you wish to study only the
> behaivor of the barrel alone at lower frequencies (for what ever reason=
 -
> but not for realistic designs), then you don't even need a field solver=
=2E
> You
> can get formulas from good SI texts like that of Horward Johnson or fro=
m
> papers.
> At first I was also making the same mistakes as you are making right no=
w.
> I
> had a lot of difficulties to correlate my simulation and measurement
> results. So I learnt a lot from this paper, from Professor C. Balanis
> (Advanced engineering electromagnetics) and from Professor R. Collins
> (Field
> theory of guided waves). I think these references will be good for you.=

> You
> need all three of them.
> There are also a lot of points that you need to modify in your models.
> It's ridiculous when you talk of -30 dB attenuation of higher-order mod=
es..
> Which higher-order mode? Which order of this mode? Basic electromagneti=
c
> theory teaches us that an infinite order of a given higher-order mode c=
an
> be
> excited at any discontinuity. An interaction between makes matters wors=
t.
> So
> how do you separate the different orders of the modes and tell which on=
e
> attenuates by -30 dB? Are the modes propagating or evanescent? Never us=
e
> rule of thumbs that have no base. I supposed you meant attenuation of t=
he
> fundamental mode which is propagating.
> I don't know anything about the lumped ports you use. All I know is tha=
t
> some lumped ports in some field solvers assume perfect H boundary
> conditions
> on the sides. Consequently, depending you may not even capture stray
> fields.
> So you can even get the worst results with lumped ports.
> You can only shift your reference S-parameters plane and get accurate
> results if your model captured all the necessary field behavior. But yo=
u
> can
> not simulate the via and traces differently and then do some
> post-processing
> or circuit modeling afterwards and expect to get correct results at hig=
her
> frequencies. The traces too are part of the "via effect" at least, at t=
he
> frequencies you are interested in (20 GHz and beyond), because the stor=
ed
> higher-order modes give rise to additional inductances and capacitances=
=2E
> These inductances and capacitances can not be captured if you analyze t=
he
> vias separately from their traces.
> Finally, the theory of multi-modal decomposition means different things=
 to
> different electrical engineers. So I don't know what you mean. If you m=
ean
> that different parts of a system can be analyzed separately and then pu=
t
> together, then it's true that it has been done for decades now. But the=

> question is this. How do you bring the different parts together in the
> case
> where there are discontinuities like vias? How do you define the via? H=
ow
> small or big is your near field zone? I bet you, we have not yet
> understood
> this type of decomposition and it has not been done, or at least publis=
hed
> for decades. Whenever we have to deal with vias and other discontinuiti=
es
> at
> higher frequencies, straight-forward modeling can not be used.
> Please Yuryi, don't get me wrong. I'm not trying to highlight on your
> errors. I have mine too, like any body else. No one is perfect. I'm jus=
t
> trying to raise the point that we need to be careful when modeling vias=
 at
> your frequencies. I agree with most of the points you made, but disagre=
e
> on
> the ones stated above. We learn from each other when we exchange ideas
> about
> such fundamental issues that affect our modeling results. I think that =
is
> one of the reasons why Ray and his team set up this forum.
>
> Best regards.
> Charles
>
>
>
>
>
>
>
>
> Yuriy Shlepnev wrote:
> Charles,
>
> I am sorry that the simulation examples were not helpful to you. I will=

> appreciate if you send me the reference you mentioned - I am preparing =
to
> be
> shocked:)
>
> You are absolutely right, the via-holes are not just pads and barrels a=
nd
> there is no one solution that covers all possible cases. Analysis of
> different vias has to be done in different ways. Transition to the trac=
es
> have to be almost always included in the final model for analysis of
> multi-gigabit channels. Moreover sometime the via-hole problem cannot b=
e
> solved locally and require analysis of parallel plane structures with a=
ll
> decoupling structures attached (see technical presentation #1 at
> http://www.simberian.com/Presentations.php for more details on differen=
t
> structures).
>
> Considering the ports and excitation. Analysis of via-holes with lumped=

> ports provides just rough idea about the via-hole behavior. It is simil=
ar
> to
> what you would see from a differential probe attached to the pads of th=
e
> via-holes. Transition to traces and transmission line or wave-ports hav=
e
> to
> be used for the final extraction of S-parameters for the system-level
> analysis (I am sorry that you missed this part in app notes). Note that=
 it
> is possible only for the localizable via-holes or via-holes not coupled=
 to
> parallel planes in general. Such t-line ports have to be positioned at =
a
> distance from the via-hole that guaranties that the high-order modes ar=
e
> attenuated substantially (for practical applications we usually use -30=
 dB
> threshold at the highest frequency of interest). After such analysis, t=
he
> phase reference planes of S-parameters can be safely shifted closer to =
the
> via-hole at the position where t-lines are still continuous to preserve=

> causality (to the edges of anti-pads for instance). Such transformation=

> does
> not affect the near field or high order modes around the via-holes and =
the
> final model can be safely connected with the transmission line segments=
 in
> a
> system-level solver. Though, the model have to be used with transmissio=
n
> line segments with length not less than in the electromagnetic analysis=

> (to
> avoid the near-field interaction between the vias and possible
> discontinuities). This technique called the multi-modal de-compositiona=
l
> analysis and used in microwave engineering for decades at frequencies e=
ven
> higher than 20 GHz.
> Note, that in typical PCB trace the cut-off frequencies for high-order
> modes
> are extremely high. 10 mil trace on 10 mil dielectric with dielectric
> constant 4.2 have cut-off frequency about 120 GHz, and the cross-over w=
ith
> the surface TM mode may happen only at 200 GHz. Before 120 GHz the
> high-order modes are evanescent and essentially form the via-hole near
> field. This near-field zone is expanding with the frequency, but at 20 =
GHz
> the area is still relatively small. Thus S-parameters only for the
> dominant
> modes can be safely extracted and used as the via-hole model.
> Cases when via-hole excite the non-evanescent parallel-plane modes and
> planes are not stitched close to the via-hole cannot be solved locally
>
> =3D=3D=3D message truncated =3D=3D=3D
>
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> List archives are viewable at:    =20
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To unsubscribe from si-list:
si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field

or to administer your membership from a web page, go to:
//www.freelists.org/webpage/si-list

For help:
si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field


List technical documents are available at:
                http://www.si-list.net

List archives are viewable at:     
                //www.freelists.org/archives/si-list
or at our remote archives:
                http://groups.yahoo.com/group/si-list/messages
Old (prior to June 6, 2001) list archives are viewable at:
                http://www.qsl.net/wb6tpu
  

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