[SI-LIST] Re: Via stub math help needed....

  • From: Vinu Arumugham <vinu@xxxxxxxxx>
  • To: si-list@xxxxxxxxxxxxx
  • Date: Thu, 12 Jan 2012 14:22:12 -0800

It seems to me that the via (thru and stub) can be modeled with segments 
of loaded transmission lines.
The anti-pads usually provide periodic loading causing the transmission 
line impedance and prop. delay to be altered as below:

This change in impedance and delay will appear as an Er change even 
though the actual Er of the material is unaltered.

A fully loaded multi-drop backplane bus transmission line will have a 
lower impedance and higher prop. delay than when it is lightly loaded. 
We don't usually attribute that to an Er change. Same for the via.

Thanks,
Vinu



On 01/12/2012 01:41 PM, Scott McMorrow wrote:
> Bert and Ralph
> There are layered-anisotropic variations in Er for many materials,
> especially those that include fiberglass weave.  However, Er does not
> change with non-TEM modes or different TEM modes (stripline, via-coaxial,
> circular cavity ... etc).  Different propagation modes merely concentrate
> the field in different directions and select a different set of localized
> material characteristics.
>
> I've read the papers and seen the claim that the dielectric constant of
> layered fiberglass material is higher for propagation through a via, due to
> the direction of the field, however, I've not seen a systematic study of
> this. (Adjustment of material Er(effective) to obtain a match to modeling
> does not constitute proof.)  My experience for launch vias with coaxial
> ground rings has been that the resonance computed by full wave solvers
> matches measurements quite well in a multitude of materials, if the
> dielectric has been characterized correctly.  I find that most of the
> mis-correlations that I've seen are due to improper material
> characterization.  I do not discount the possibility of a higher localized
> Er region around a via in some measurements, its just that I find little
> evidence for fiberglass being the sole culprit. In many cases I've found
> that mismatch in stub resonance could be easily accounted for by adding the
> correct amount of soldermask to the bottom pad in modeling.  In other cases
> I've found that material variations between layers were not correctly
> modeled.
>
> As a thought experiment, take a section of a PCB with a via along the
> z-axis that is fully surrounded by a coaxial metal wall.  Calculate the
> average Er from top to bottom, and then calculate it radially out.  The
> volume of material is the same.  The composition of the material is the
> same.  Thus the average Er is the same.  The only way to come up with a
> higher Er for the radial direction is to conclude that somehow  the
> drilling process selectively removes more epoxy than fiberglass from the
> mixture.  There are layered variations as we travel down the via passing
> through fiberglass rich, and then epoxy rich layers.  But I see no reason
> why they would not average out.  I can make a case that individual pairs of
> signal and ground vias can have Er variation, just as I can for traces, but
> I cannot come up with any reason why the Er would not average out in the
> limit.
>
> There is one other potential reason why a via could have a higher localized
> average Er.  But it has nothing to do with the fiberglass itself.  I will
> probably use it as a topic for next year's DesignCon paper, as a follow up
> to the paper I'm involved with this year.
>
>
> regards,
>
> Scott
>
>
> On Thu, Jan 12, 2012 at 3:51 PM, Lambert Simonovich<
> bertsimonovich@xxxxxxxxxx>  wrote:
>
>> Ralph,
>> When building your 3D model, you should also take into account the
>> anisotopic factor of the material. I.E. Dkx-y can be 15-20% higher than
>> Dkz. Since conventional FR4 type laminates are fabricated with a weave of
>> glass fiber yarns and resin, they are
>> anisotropic in nature. Because of this, the dielectric constant value
>> depends on the direction of the electric fields. In a multi-layer PCB with
>> vias,
>> there are effectively two directions of electric fields. The one we are
>> most familiar with has the electric fields running perpendicular to the
>> surface of the PCB -as is the case of stripline traces. The dielectric
>> constant,
>> designated asDkz in this case, is normally the bulk value of the
>> dielectric specified by the laminate manufacturer's data sheet. The other
>> case has the electric fields
>> running parallel to the surface of the PCB, as is the case when a signal
>> propagates through a differential via structure.
>>
>> I know for a fact that HFSS allows you to have a different value for Dkx-y
>> vs Dkz, and when you take this into account, from my experience, it agrees
>> quite well with measured results. I don't know about the 3D tools you
>> mentioned though.
>>
>>
>> -Bert Simonovich
>>
>>
>> ________________________________
>>   From: Ralph Wilson<ralph.wilson@xxxxxxxxxxxxxxxxxx>
>> To: Antonis Orphanou<aorphanou@xxxxxxxxxxxxxxxxx>
>> Cc: "si-list@xxxxxxxxxxxxx"<si-list@xxxxxxxxxxxxx>
>> Sent: Thursday, January 12, 2012 3:13:54 PM
>> Subject: [SI-LIST] Re: Via stub math help needed....
>>
>> Antonis,
>>
>> With this, I disagree.  Based on other feedback I've gotten, and looking
>> at some of the cross references and reference papers, since the via
>> does not meet the TEM conditions of a typical transmission line, the
>> Dk associated with the PWB stackup is not appropriate to use.  Calculating
>> an "effective" Dk using one of several methods gets me close (3D
>> simulations
>> are the best).  Due to the non-TEM boundary conditions (pads, anti-pads,
>> orthogonal
>> reference planes, etc.), the "effective" Dk can be 4x the FR4 Dk.  This
>> causes
>> the delay to be twice that of a stripline in the same material, and leads
>> to the x2 factor in the null frequency.
>>
>> Ralph
>>
>> On 1/12/2012 1:52 PM, Antonis Orphanou wrote:
>>> The first resonant frequency occurs at half and not a full wavelength.
>>> In your calculation/formulation you assume full wavelength and this is
>> why you are a factor of 2 off.
>>>
>>>
>>>
>>> -----Original Message-----
>>> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
>> On Behalf Of Beal, Weston
>>> Sent: Thursday, January 12, 2012 11:41 AM
>>> To: Ralph Wilson; si-list@xxxxxxxxxxxxx
>>> Subject: [SI-LIST] Re: Via stub math help needed....
>>>
>>> Ralph,
>>>
>>> Your calculation assumes TEM propagation. This happens on uniform
>> transmission lines, line long traces or coaxial cables. The via is not
>> uniform long enough to support at TEM field propagation. It really is a 3-D
>> geometry that needs to be analyzed as such. A 3-D field solver should give
>> the most accurate results. Some good calculations based on the analysis of
>> the 3-D geometry as HyperLynx does can give a reasonable answer very
>> quickly.
>>> Weston
>>>
>>>
>>> -----Original Message-----
>>> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
>> On Behalf Of Ralph Wilson
>>> Sent: Thursday, January 12, 2012 4:24 AM
>>> To: si-list@xxxxxxxxxxxxx
>>> Subject: [SI-LIST] Via stub math help needed....
>>>
>>> All,
>>>
>>> While working on some SERDES nets, specifically trying to quantify the
>> effects of some via stubs, I ran across something that has me stymied.  I
>> expect a null in S21 where the stub length (delay, actually) is 1/4
>> wavelength. However, the simulations are showing a null at half the
>> frequency I predict.  I've subsequently run the via model through several
>> different tools, and although the null frequency varies a little bit due to
>> modeling / parasitic issue, they all come up with a null frequency roughly
>> half of what my "math" predicts.  So my fundamental question is where is my
>> theory or my math wrong?
>>> Null frequency = 1/wavelength = 1 / (4 x via-stub-delay)
>>>
>>> via-stub-delay = d / s, where d = distance (length of stub) and
>>>        s = wave propagation speed
>>>
>>> s = c / sqrt(Dk), where c = 299,792,458 m/s, or
>>>        c = 299,792,458 m/s x 1/0.0254 in/m x 1E-9 s/ns = 11.8 in/ns
>>>
>>> So, if I pick a via stub length of 80 mils in FR4 with a Dk of 4...
>>>
>>> s = 11.8 in/ns x 1/sqrt(4) = 5.9 in/ns
>>> via-stub-delay = 80 mils x 1/5.9 ns/in x 1E-3 in/mil = 0.0136 ns
>>>
>>> Hence, the predicted null frequency = 1 / (4 x 0.0136 ns) = 18.44 GHz
>>>
>>> However, all of my simulation tools (Hyperlynx, IE3D, CST MWS) show a
>> null in the range of 9-10 GHz.  Digging deeper, they show the via delay to
>> be in the range of 27 ps rather than the 13.6 that my math shows.
>>> What gives?  Why is my delay calculation off by (roughly) a factor of 2?
>>> Is the lumped capacitance of the via stub somehow affecting the
>> propagation delay in the via stub? That's somehow mixing t-line theory with
>> lumped model approximations... I'm at a loss.
>>> Thanks for any insight.
>>> Ralph Wilson
>>> Alcatel-Lucent
>>>
>>>
>>>
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>



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