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

  • From: Lambert Simonovich <bertsimonovich@xxxxxxxxxx>
  • To: Ralph Wilson <ralph.wilson@xxxxxxxxxxxxxxxxxx>
  • Date: Thu, 12 Jan 2012 12:51:03 -0800 (PST)

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 manufacturerâ??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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