RE: [SI-LIST] : A basic question

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From: Daniel, Erik S. (Daniel.Erik@mayo.edu)
Date: Fri Mar 17 2000 - 05:55:48 PST


Jim-

For a transmission line (i.e., a structure in which the cross-section is
constant along the direction of propagation), it is impossible to change C
without changing either L or er. Therefore, Pd=(LC)^(1/2) and velocity =
c/(er)^(1/2) are forced to be true. Moreover,

     Pd=(LC)^(1/2) = (length/c)*(er)^(1/2)
                   
In a more complicated 3D structure, it is more difficult to see, but it is
is still true that any attempt to change C or L independent of the other
results in an effective change in dielectric constant or the length of the
path taken by the signal, so again, the relationships between delay and
propagation velocity hold. For example, consider adding a lumped
capacitance at a point on a transmission line to increase delay. Two
possible physical methods of doing this would be to increase the dielectric
constant in the transmission line at this particular point, or to "wire in"
an extra capacitor component. In the first case, er is changed, and in the
second, the effetive propagation length is changed.

                                        - Erik

==================================================================
Erik Daniel, Ph.D. Mayo Foundation
Voice: (507) 284-1634 Guggenheim 1011B
Fax: (507) 284-9171 200 First Street SW
E-mail: daniel.erik@mayo.edu Rochester, MN 55905
==================================================================

>
> SI List:
>
> I have a question about the relationship between Z and Pd
> (prop. delay). The
> equations used for these two are :
> Z=(L/C)^(1/2)
> and
> Pd=(LC)^(1/2)
> I guess my question has to do with Pd. How can we equate Pd
> to both the
> above equation and the fact that the speed of light is
> C/((er)1/2)? Which
> says that prop. delay is just a function of the dielectric
> constant (or the
> material that light is propagating through).
> Can I really reduce C, without increasing L, and thus reduce
> the Pd of an
> interconnect? If I can't then the Pd=(LC)^(1/2) has problems.
> If I can then
> how does it align with light's speed being just a function of
> the medium
> it's traveling through?
>
> regards,
> Jim
>
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