Sorry if this is a little off-top, but hopefully not too much.
Would anyone know if there is an exact analytical solution to the
capacitance per metre (and/or the related impedance) of a coaxial
cable consisting of two concentric dielectrics? Rather than just
having one dielectric between the inner and the outer, this would have
two dielectics, both coaxial with each other. This has a high-degree
of circular symmetry, so I can't help but feel an analytical solution
might exist, but I don't know of one, and maths was never my best
subject. Anyone care to try to derrive one ???
I'm asssuming the radius of the inner conductor is r1, the radius of
the inner dielectric r2, and the radius of the outer conductor is r3.
The permittivity of the inner dielectric is Er1 and of the outer
dielectric Er2.
Does anyone know of any structure (coax, microstrip or whatever) that
has an ***exact*** analytical solution when there are multiple
dielectrics?
I would like to verify some numerical code of mine that computes the
impedance of arbitrary transmission lines
http://atlc.sourceforge.net/
Despite doing extensive testing on single dielectrics (i.e. the error
on normal coax is under 0.2%), I've not managed to do any significant
testing with multiple dielectrics. I'd particulary like to analyse
this twin dielectric coax.
--
"The day Microsoft makes something that doesn't suck is probably
the day they start making vacuum cleaners." -Ernst Jan Plugge.
Dr. David Kirkby,
Senior Research Fellow,
Department of Medical Physics,
University College London,
11-20 Capper St, London, WC1E 6JA.
Website: http://www.medphys.ucl.ac.uk/~davek
Author of 'atlc' http://atlc.sourceforge.net/
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