[SI-LIST] Re: Dispersion
- From: C Deibele <deibele@xxxxxxx>
- To: "Loyer, Jeff" <jeff.loyer@xxxxxxxxx>
- Date: Thu, 12 Dec 2002 10:00:22 -0500
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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