[SI-LIST] Re: Via stub math help needed....
- From: Lambert Simonovich <bertsimonovich@xxxxxxxxxx>
- To: Ralph Wilson <ralph.wilson@xxxxxxxxxxxxxxxxxx>, "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
- Date: Thu, 12 Jan 2012 06:17:27 -0800 (PST)
Ralph,
The additional delay in the via stub is due to the additional distributed
fringe field capacitance between the via barrel or inner layer pads to the
clearance holes (anti-pads) of the planes. This results in a higher effective
dielectric constant (Dkeff) due to the excess distributed capacitance. You can
estimate Dkeff based on the via barrel to anti-pad geometry. Once you have
determined Dkeff, then the resonant frequency can be predicted by the following
formula:
fo = c/(4*sqrt(Dkeff)*stub_len)
where c = 1.18E10 sec/in and stub_len is in inches
For more information, I invite you to visit my web site and download a copy of
a white paper titled, "Method of Modeling Differential Vias"
-Bert
________________________________
From: Ralph Wilson <ralph.wilson@xxxxxxxxxxxxxxxxxx>
To: si-list@xxxxxxxxxxxxx
Sent: Thursday, January 12, 2012 7:24:26 AM
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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