Hi Aaditya,
There is no simple relationship between S21 phase and Dk for interconnects
in general.
The simplest case to understand the dependency is the plane wave in
dielectric. Assuming normalization of S-parameters to the impedance of the
plane wave in dielectric (generalized normalization), the exact expression
for the transmission phase in this case is
arg(S21)=Im(-i*2*PI*frq*sqrt(eps*mu)*L), were frq is frequency, L is
distance, mu is permeability and eps is complex permittivity (Dk is the real
part of it normalized to permittivity of free space). As you can see, in the
simplest case increase of Dk will cause the increase in phase of S21
proportional to square root of Dk. Increase of phase or slowdown of the wave
is the effect of dielectric polarization. That defines general dependency in
all other cases.
If we discuss a segment of strip line, Dk defines slowdown of the waves
similar to the plane wave. Though, even in this simplest case, conductor
dispersion (skin and roughness effects) and reflections will also contribute
to the phase change with the frequency. Group delay (negative derivative of
phase) can show it clearly as the dispersion. In cases of t-lines with
inhomogeneous dielectric, such as microstrip lines, high-frequency
dispersion (concentration of electric field in dielectric with larger Dk)
will define the phase in addition to the dielectric dispersion and
reflections. S-parameters normalization to the characteristic impedance of
the t-line can remove the effect of reflections.
The dependency of the transmission phase on Dk for interconnects in general
is the same as for a segment of t-line plus effects of discontinuities
(launches, vias, transitions). Only good models of interconnects can
realistically capture the dependency of the transmission phase on dielectric
and conductor dispersion and effect of discontinuities. Same is applicable
for the extraction of Dk from the transmission phase.
Best regards,
Yuriy
Yuriy Shlepnev, Ph.D.
President, Simberian Inc.
3030 S Torrey Pines Dr. Las Vegas, NV 89146, USA
Office +1-702-876-2882; Fax +1-702-482-7903
Cell +1-206-409-2368; Virtual +1-408-627-7706
Skype: shlepnev
www.simberian.com
Simbeor - Accurate, Productive and Cost-Effective Electromagnetic Signal
Integrity Software
2010 and 2011 DesignVision Award Winner, 2015 Best In Design&Test Finalist
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Aaditya K
Sent: Sunday, July 12, 2015 1:01 PM
To: si-list
Subject: [SI-LIST] Dependence of Dk on S21 Phase
Hello Experts,
I am trying to understand S21 phase plot's dependence on Dk, could you
please explain me how does this happen?
Thanks
Aaditya
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