[SI-LIST] Re: Dispersion

  • From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
  • To: si-list <si-list@xxxxxxxxxxxxx>
  • Date: Mon, 16 Dec 2002 10:00:27 -0800

Craig -- You're correct that geometry can cause dispersion.  This was 
covered earlier in this thread -- that permittivity varying with 
position can cause dispersion.

Regarding lossless transmission lines, they can't be fabricated from 
real materials.  And since materials are generally taken in classical 
electromagnetics to approach transparency at high frequency, those 
required to build an attenuator with constant loss at all frequencies 
can be safely assumed to not exist as well.  So while the attenuator may 
be simple on paper, it can't be fabricated.

Of course I don't want to come off as an ideologue by implying that 
everyone should always use lossy models based on thermodynamic 
considerations.  On the contrary, we encourage our customers to use 
lossless models whenever possible.

My purpose for making my original statement about the relationship 
between loss and dispersion was in the framework of people working on 
FR4 and other dielectrics that they consider lossy enough to model as 
lossy.  Anyone who has tried to code up a time-domain model for such 
materials quickly finds out that if they ignore the relationship between 
the real and imaginary parts of the permittivity, they get noncausal 
results.  My experience is that many SI engineers are unaware of the 
relationship.

You're right, we've strayed away from the original questions in the 
thread and are now into perfectly conducting materials and behavior at 
infinite frequency.  If there's additional ground to cover, we should 
probably consider discussing it off-list.

   -- 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:

> Even circuitry adds dispersion -- I did an example, privately for someone,
> where I had a simple transmission line (lossless in this example) and 
> put a short circuited
> stub in the middle of it.  The resonance causes dispersion.
> 
> This brings up some wonderful questions about matching circuits....but I'll
> leave that for another day.
> 
> I don't know if I agree, that physical materials are always dispersive. 
>  Do you think
> that superconductors are dispersive?  In all honesty, I've measured so 
> many properties
> of them, but I don't know if I've ever taken the time to measure its 
> dispersiveness.  I am
> guessing it is pretty damn small, given the fact that I can make 
> superconducting cavities
> with Q's on the order of 10^10, when copper is on the order of 40 x 10^3.
> 
> The notion that dispersion implies loss is nonsensical.
> 
> Even the notion that loss implies dispersion is nonsensical.  A simple 
> attenuator
> is, for example, dispersionless and lossy.
> 
> I think I am going beyond the initial question though.  The answer to 
> the original
> question is most likely, "It depends."
> 
> Craig
> 
> 
> 
> Steve Corey wrote:
> 
> 
>>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
>>-------------------------------------------
>> 
>>
>>
> 



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