[SI-LIST] Re: dispersion and group velocity
- From: "Antonis Orphanou" <orphanou@xxxxxxxxxxxx>
- To: "shlepnev@xxxxxxxxxxxxx" <shlepnev@xxxxxxxxxxxxx>, "ankit.wangoo@xxxxxxxxx" <ankit.wangoo@xxxxxxxxx>, "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
- Date: Wed, 6 Mar 2013 00:06:57 +0000
At the end of the day dispersion will be a function of the propagation constant
of your line. The reactive part of the propagation constant is a function not
only of the dielectric but also of the permeability and the conductivity
properties of the line. In our cases we mostly concentrate on the loss tangent.
For very low loss systems the reactive part of the propagation constant is
simply: g=j*w*sqrt(mu*eps') which points towards a linear phase dispersion-less
system. Now as the loss increases the reactive part of the propagation constant
requires more terms in the taylor expansion.
For some loss in the system, the reactive propagation constant becomes a
function of wmega and wmega^2 and you can see how loss slowly introduces
dispersion. What I define as loss, is the imaginary part of the dielectric,
eps=eps' + j*eps". Permeability is rather constant.
Another way to look at this is to consider the following:
In the expression:
D(t)=eps*E(t)
Consider eps as a linear operator describing an LTI system. That will require:
eps(t) = e0 + e1*d/dt + e2*d^2/dt^2 + e3*d^3/dt^3 ....
In frequency domain then that becomes: eps(w)=e0 + j*e1*w -e2*w^2 +... =
e'(w^2, w^4,..) + j*e"(w,w^3...), with tanDelta=e"/e'
Depending on the loss more or less terms will need to be assumed to physically
describe the problem proving the dispersion dependency on the loss tangent.
Thanks
Antonis.
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Yuriy Shlepnev
Sent: Tuesday, March 05, 2013 2:45 PM
To: ankit.wangoo@xxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: dispersion and group velocity
Ankit,
Yes, there will be dispersion in a transmission line even if permittivity is
not changing with the frequency.
There will be dispersion related to per unit length inductance change due to
the skin-effect.
In addition, in structures with inhomogeneous dielectric, there will be
high-frequency dispersion caused by concentration of fields in dielectric
with larger permittivity (or with smaller losses) at high frequencies. This
effect can be observed in microstrip structures as a growth (or flatness) of
group delay starting from 5-10 GHz. In cases when dielectric has
permittivity that decreases with frequency (typical for FR4), the observed
group delay may stay flat at high frequencies in microstrip structures -
this can be misinterpreted as the absence of dispersion. Note, that
concentration of fields in media with larger permittivity at high
frequencies causes on only the dispersion, but also difference in losses (in
dielectric part). The effects can be accounted only with a full-wave
analysis of a cross-section with inhomogeneous dielectrics.
Finally, a material with constant permittivity is not physical.
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
Skype: Shlepnev
www.simberian.com
Simbeor - Accurate, Fast, Easy and Affordable Electromagnetic Signal
Integrity Software
2010 and 2011 DesignVision Award Winner
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Ankit wangoo
Sent: Monday, March 04, 2013 7:54 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] dispersion and group velocity
Hi
Is dispersion bound to happen due to propagation constant being depended on
freq specially phase constant?Or it is solely because of permittivity of the
material changes with Freq.
Can we have dispersion when permittivity is constant?
regards
Ankit
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