[SI-LIST] Re: Relationship between loss tangent and dielectric constant's frequency dependence
- From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
- To: "'Neo'" <neoflash2008@xxxxxxxxx>, "'List Si'" <si-list@xxxxxxxxxxxxx>
- Date: Wed, 31 Mar 2010 08:07:42 -0700
Neo,
As was already mentioned here, the real and imaginary parts of permittivity
are related by Kramers-Kronig (K-K) relation
http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relation This is the
most general relation.
Unfortunately, it is practically impossible to verify the K-K relation on a
few measured points typically available for dielectric constant (DK) and
loss tangent (LT). The relation can be verified (or used to derive one part
from another) only in case if one part is known analytically for instance
from DC to infinite frequency or if one part is described with sufficient
number of frequency points and have well defined asymptotic behavior at DC
and infinity. This is typically not the case as the dielectric behavior is
becoming more complex at higher frequencies.
So, what is the alternative if you have just a few measurements of DK and LT
for an FR-4 or similar laminate material?
Some dielectrics have more specific relations between the real and imaginary
parts that may be useful to restore one part from another or construct
complete frequency-domain behavior from one of a few measurements.
Glass or quarts for instance can be effectively described as a one-pole
Debye model in microwave frequency band. Such models can be constructed with
measurement of DK and LT at just one frequency and knowledge of the pole
relaxation frequency (two frequency points must be used if the relaxation
frequency is not known).
Generalization of one-pole Debye model is a model with multiple Debye poles.
Any PCB dielectric can be described as a multi-pole Debye model with
sufficient number of measurement points. 4-10 poles may be required for a
broad-band description of PCB laminate (see effect of the number of points
on S-parameters in App Note 2008_06 at
http://www.simberian.com/AppNotes.php). Such model can be constructed by
fitting the measured dielectric parameters or by fitting the magnitude and
phase of a generalized modal transmission coefficients as done in our
DesignCon2010 paper (available together with the presentation at
http://www.simberian.com/AppNotes.php - #2010_01).
Causal wideband Debye model (also known as Djordjevic-Sarkar) is the
generalization of the multi-pole Debye model and is very convenient to
describe some types of high-loss dielectrics - see Eric Bogatin's paper from
DesignCon2010 with excellent explanation of how the model works.
Best regards,
Yuriy Shlepnev
www.simberian.com
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Neo
Sent: Tuesday, March 30, 2010 7:24 PM
To: List Si
Subject: [SI-LIST] Relationship between loss tangent and dielectric
constant's frequency dependence
Hi,
This email's title is a bit long but it is exactly a question annoying me.=
I'm trying to find out whether there is a proven relationship between a
dielectric material's real part and imaginary part. Imaginary part is
dielectric loss tangent. And real part is the dielectric constant.=
For a material like FR4 or Rogers, their dielectric constants all change
over frequency. And their loss tangents are also different.=
Is there any inner relationship between the value of loss tangent and how
the dielectric constant (real part) changes over frequency?
Thanks,Neo
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