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Have the S-parameters of a coax with truncated inner been derrived?

Question asked by drkirkby on Jul 28, 2013
Latest reply on Aug 2, 2013 by drkirkby
Consider a coaxial cable which has an outer conductor "O" of infinite length, but an inner coductor "I" of some finite lenght, as I've tried to show with ASCIII graphics below. I've had quite a few beers tonight, so don't fancy my chances trying to draw this in a graphics package!!! 


Have the S-parameters looking into the left hand side ever been derrived theoertically, and published? If so, does anyone have a reference? 

Clearly such a structure would be relatively easy to make as a calibration standard *IF* the properties could be derrived theoretically. I can imagine it is the sort of structure someone might have thought to solve, and I can imagine it might be possible to arrive at a sollution. I might also postulate it would involve Bessel functions an be non-trivial to derrive. 

Even more useful would be the case if the inner was tructated, but supported by a dielectric D, as in 


It would of course be fairly easy evualate the S-parameters numerically with a 3D EM solver such as Agilent's EMPro or Ansys's HFSS, but I wonder if anyone has a theoretical solution to either of these structures? 


Edited by: drkirkby on Jul 28, 2013 10:48 PM