Microwaves101 created the topic: Coax dielectric loss

This question came from Dave... any help is appreciated! - Steve

I’ve just been doing some analysis to determine how dielectric loss distributed through the dielectric heats up the centre conductor compared with the loss assumed concentrated at the centre conductor (as it is for resistive loss). I get a figure of exactly 1/2, which is the same ratio as a parallel plate arrangement, regardless of cable geometry.

Can anyone confirm my findings, and does this indicate dielectric loss heats up the centre conductor only half as much as the loss would if concentrated at the centre conductor for any TEM transmission line type (including stripline), that is to say it is another thing that is invariant under a conformal transformation?

When I say “heats up”, I mean the centre conductor temperature rise over the outer temperature. It doesn’t matter what temperature the outer jacket is held at, the only assumption in that sense being that the dielectric loss doesn’t vary with temperature. I guess it does, but that makes the analysis a lot more complicated.

Calculus may not help where structures aren’t analytic. I’m thinking there may be a way to prove the result by showing the distributed and centre conductor loss models require the same difficult part of the solution, which cancels in the ratio.

Please share this problem. I note that a line in Harlan Howe’s Stripline book suggests dielectric loss is concentrated around the centre conductor, and is more accurately modelled by supposing it is lumped with centre conductor loss. I have doubts this is correct. Put it this way, although it is true that dielectric loss concentrates around a small conductor, particularly at sharp edges, the heat flux is just as willing to spread away from the small conductor, and especially its sharp edges.

It would be very interesting to find out whether my assertion is true. I can’t remember any analysis on the subject, and the result is so basic, and of a kind I would have expected to have been established decades ago.