[SI-LIST] Re: Dispersion
- From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
- To: si-list <si-list@xxxxxxxxxxxxx>
- Date: Sat, 14 Dec 2002 20:06:03 -0800
List members -- I am resending for the second time, since the list
server seems to be eating my posts. If at some point it decides to
regurgitate the originals, my apologies in advance...
***
Craig -- I think we both agree. As Xin Wu pointed out earlier in this
thread, if we step away from physical materials and go to pure
mathematics, we can come up with a system that is causal, lossless, and
dispersive. Your perfectly conducting waveguide built with a lossless
dielectric and lossless conductors is a good example. For the same
reason, we can also come up with a non-physical "material" that is
causal, lossless, and dispersive.
Simplified in the interest of brevity, the Kramers-Kronig relationships
are derived under the assumption that free space (with its purely real,
constant permittivity) is the only lossless "material", and it is
therefore used as the limiting case. This is not overly restrictive if
we are discussing physical materials, since it follows directly from the
second law of thermodynamics -- interaction with matter always increases
entropy. It has also stood the test of time to some extent, since it
still stands today as postulated independently by the two originators in
1926 and 1927.
Based on this assumption (and the assumption of linearity), if we
analyze the permittivity of any physical material, it will be lossy and
it will be dispersive. I'm sure we both agree on this point. The more
interesting part is that via the Hilbert transform, the real part of the
permittivity completely determines the imaginary part, and vice versa.
-- Steve
-------------------------------------------
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
-------------------------------------------
C Deibele wrote:
> Jeff,
>
> You bring up some very good points -- The real definition of dispersion is
> the
> fact that the phase velocity (omega divided by k) is different than the group
> velocity (d omega / dk). When the phase velocity is different from the group
> velocity, an impulse "disperses" or gets "fatter" when looked in the time
> domain.
>
> In fact, even though I don't like the textbook in general, Jackson's book
> "Classical Electrodynamics" has a great theoretical treatment of the subject
> that can be fairly well understood even with a cursory overview.
>
> Dispersion, in general, has absolutely nothing to do with losses. For
> example, a waveguide (here I mean a pipe, circular or rectangular), is
> absolutely dispersive. the phase velocity is different from the group
> velocity.
>
> Regarding loss -- when the loss varies w.r.t. frequency, this causes
> dispersion. While the loss variance may be accounted for in any myriad of
> techniques, the end result is dispersion.
>
> In fact, I've designed lots of equalizers to rid systems of dispersive
> properties.
>
> I agree, if a material is lossy, it is dispersive. This is easy to measure
> in
> the laboratory. Take a short piece of coax and put in a *great* square wave,
> and measure the rise time on a scope. Now, take a 100 meter section of coax
> and insert it in place of the short piece. The rise time measurement will be
> *much* worse. This is an effect of dispersion.
>
> In essence, lossy implies dispersive. but dispersive does _not_ imply lossy.
>
> A perfectly conducting waveguide is a great example of this property.
>
> And yes, knobbing is perfectly legal. While this isn't the perfect
> definition
> for measuring the dispersion, one can see the phase dispersive qualities.
> The
> magnitude is also very important. So, one has to consider the bandwidth of
> the source -- and relate that back to the measurement.
>
> So, if one corrects the magnitude to be flat, and corrects the "knobbed"
> phase
> to be flat, the system is absolutely non-dispersive.
>
> Craig
>
>
>
>>===== Original Message From "Loyer, Jeff" <jeff.loyer@xxxxxxxxx> =====
>>This part of the thread (discussion of dispersion) began when I asked the
>>
> question below. It seems that we are back to the original question.
>
>>ORIGINAL QUESTION:
>>When you use the term "dispersive", are you talking about losses (resistive,
>>
> skin effect, dielectric), or about differences in phase velocities (page 170
> of Pozar's book)? I've heard others refer to loss effects as dispersive and
> have had
>
>>confusion as a result. Are both uses of the term "dispersive" correct?
>>
>>The explanation of how to measure dispersion (S21 magnitude) implies you
>>
> believe "dispersion" and what I would have termed "effects of conductor and
> dielectric losses" are the same. I have trouble with that, since stripline
> insertion loss
>
>>magnitude definitely varies with F, and that effect is explained without
>>
> dispersion. I believe "dispersion" is a separate effect than conductor and
> dielectric losses. The only tie between them that I've heard of is that
> Steve
> Corey (who I am
>
>>loath to contradict) stated "if a material is dispersive, it is also lossy".
>>
> It may be that the converse holds (if a material is lossy, it is also
> dispersive), but I believe the 2 effects are separate (even if one can't
> occur
> without the other).
>
>>Maybe Steve would clarify this?
>>
>>I couldn't follow the explanation of "knobbing" electrical delays until S21
>>
> phase is flat. Is that legal? ;-)
>
>>Jeff Loyer
>>
>
> Craig Deibele
> Spallation Neutron Source
> 701 Scarboro Road
> Room 301 MS 6473
> Oak Ridge, TN 37830
> mailto:deibele@xxxxxxx
> office: +1 865.574.1969 cell: +1 865.719.4381 fax: +1 865.241.6739
>
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