[SI-LIST] Re: (no subject)
- From: Steven_McKinney@xxxxxxxx
- To: steven.corey@xxxxxxxxxxxxxx
- Date: Wed, 11 Dec 2002 16:39:44 -0600
A question about the methodology you are taking in order say whether the
permittivity changes with frequency:
Are you considering a complex permittivity??
In the dialogue that I have seen, I have not seen anything mentioned about
the imaginary part of the complex permittivity, only the real or absolute
permittivity. Since you are considering lossy mediums such as FR-4, then
you must consider the complex permittivitiy, not just the real part which
would be a lossless case.
The complex permittivity of a medium is e = e' - je"
The imaginary part of e (e") accounts for loss in a medium due to dampening
of the vibrating dipole moments and provides a measure of power loss in the
medium. This is where your frequency dependancy comes in, a.k.a. loss
tangent (tan(delta)).
The loss tangent has a frequency dependancy by the relation of dielectric
dampening (w*e").
Loss tangent is the ratio of e"/e' which will produce tan(delta) =
(sigma)/(w)*(e) where
e = eo*er. This incorporates the conductivity of the medium, the frequency
of propagation, and absolute permittivity.
The end result is that you end up with a permittivity of e = e'(1-
j*tan(delta))
This result is a frequency dependant permittivity that incorporates the
ohmic losses as well as dampening.
-Steve
-----Original Message-----
From: Steve Corey [mailto:steven.corey@xxxxxxxxxxxxxx]
Sent: Wednesday, December 11, 2002 1:37 PM
Cc: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: (no subject)
Or perhaps take this approach, since as the modeling guy I always resort
to equations:
v = c/sqrt(er)
v is the velocity of the wave, c is the speed of light in a vacuum, and
we assume that the relative permeability is unity for simplicity.
Now, if we have already settled that v can vary with frequency, and
hopefully we can agree that c doesn not vary with frequency, that leaves
only er to vary with frequency. If er is constant, so is v.
If this doesn't seem authoritative enough, consult any undergraduate
physics book or electromagnetics book published over the past 100 years.
It will tell you that er varies with frequency. I find it a good
practice to consult such books prior to posting, since half the time the
person who wrote the book is lurking on this list.
-- Steve
Scott McMorrow wrote:
> Justin,
>
> You are just plain wrong here about FR4. It is a highly non-linear
> material that does have significant changes in Er across frequency that
> have been characterized in the peer reviewed engineering literature for
> at least 20 years. Dielectric losses and changes in Er are linked by
> causality as Steve Corey wrote a few days ago, and has been well
> discussed in the professional and academic journals. The latest issue
> of IEEE Transactions on Advanced Packaging, which includes papers from
> last years EPEP, has several papers on just this subject.
>
> For FR-4, non-uniform dielectric properties throughout the material tend
> mask the effects of frequency dependent Er (or velocity of propagation)
> changes. (i.e. - you get more impedance variation due to material
> variation than due to Er changes across frequency.) For low loss
> materials, such as Real Air, the dielectric loss and Er does change,
> based upon the relative humidity. Pure air, however, does have a flat
> frequency response and extremely low losses.
>
> As for broadband, just launch a gaussian pulse down a microstrip or
> stripline trace on an FR4 substrate and see what you receive at the far
> end. After you subtract out the effects of variable skin depth
> penetration at different frequency (due to the finite conductivity of
> the conductor) you will find that there is still pulse distortion due to
> Er variation.
>
> Finally, I would refer you to the material data sheets for many
> different vendors versions of FR4, where you will find that the measured
> Er does truly vary with frequncy, tending to lower at the higher
> frequencies. Since the velocity of propagation of an electromagnetic
> wave in a dielectric media is proportional to the square root of the Er,
> I would expect an accompanying dispersion of any broadband signal across
> the entire frequency band, with an accompanying change in Impedance.
>
> regards,
>
> scott
>
>
--
-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Modeling Company."
http://www.tdasystems.com
email: steven.corey@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax: (503) 246-2282
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