[SI-LIST] Re: Via stub math help needed....
- From: Vinu Arumugham <vinu@xxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Thu, 12 Jan 2012 14:32:57 -0800
(With the equations in text this time...)
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:
Zo(eff) = Zo / (sqrt(1 + Cd/Co))
Tpd(eff) = Tpd * (sqrt(1 + Cd/Co))
where Cd is the extra capacitance per unit length.
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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