Field Analysis of Transmission Line with Finite Conductivity

[chingkui]

In all the source I have read about, EM field analysis of Transmission Lines always assume the conductor is perfect (infinite conductivity), and that simplify a lot the analysis, since there can be no field inside the conductor and that gives much easier boundary condition, which allows us to get standing wave solution for each cross section.
What if we allow finite conductivity in the conductor (e.g. Parallel Plate Transmission Line with finite conductivity and lossy dielectric in between)? Have anyone seen a field analysis of such situation? I know the simplest approach would be using circuit method for analyzing this general condition, but I want to use Maxwell Eq to get a EM field analysis which would be more convincing (at least to me) and beautiful. I have had a hard time thinking of how to make that works when we throw out the simple boundary condition that comes with perfect conductor.
Have anyone done this or seen someone else done this before? Any reference? Thank you.

 

[ZapperZ]

In all the source I have read about, EM field analysis of Transmission Lines always assume the conductor is perfect (infinite conductivity), and that simplify a lot the analysis, since there can be no field inside the conductor and that gives much easier boundary condition, which allows us to get standing wave solution for each cross section.
What if we allow finite conductivity in the conductor (e.g. Parallel Plate Transmission Line with finite conductivity and lossy dielectric in between)? Have anyone seen a field analysis of such situation? I know the simplest approach would be using circuit method for analyzing this general condition, but I want to use Maxwell Eq to get a EM field analysis which would be more convincing (at least to me) and beautiful. I have had a hard time thinking of how to make that works when we throw out the simple boundary condition that comes with perfect conductor.
Have anyone done this or seen someone else done this before? Any reference? Thank you.

I work with people who does this all the time in designing accelerating structures. Unfortunately, I don't have that much of an expertise in this area other than what I have gathered.

Unless I'm mistaken, modelling codes such as Microwave Studio can in fact incorporate such finite conductivity walls. Most often, one tries to find the Q factor from this. As you can imagine, these are extremely tedious numerical computation.

If you are willing to wait, I'll try to forward this question to someone who should have a more intelligent response to this question when I get into work tomorrow.

Zz.

 

[chingkui]

Thank you very much, I certainly would be interested to learn more.
Do you know if finite conductivity wall is allowed, then all we could do is to numerically simulate that? Even if the cross section is highly symmetric (e.g. parallel plate, coaxial, etc), numerical computation is needed?
I am particularly interested in whether it is possible to write down the solutions in simple functions such as sin, cos, exp or some other types of infinite series?
Thank you.

 

[ZapperZ]

OK. It appears that due to the major snow storm here yesterday, a lot of people are taking an unplanned day off today, so I am not seeing the usual suspects in this morning.

Looking around at the various texts that I have, you may want to take a look at David Pozar text "Microwave Enginnering", 2nd Ed. (Wiley). In Chapter 2, he discussed in detail Transmission line theory. He of course started out with lossless transmission line, but in Section 2.7, he discussed lossy transmission lines, but under the approximation that the loss is small (if not, having a transmission line would be "of little practical value").

This may or may not be what you're looking for, since from my impression, you want to solve the lossy case starting from Maxwell equations and the boundary condition. I still think that solving the general case like that is not trivial and may not produce closed form solutions.

And a correction on my statement about Microwave Studio being able to do such a thing. I've just been informed that Microwave Studio CANNOT solve lossy boundary conditions. However, it can still be used to get the field distribution for the lossless situation and THEN, from the output, do a post-processing to include some form of perturbation to account for the lossy boundaries. So that's why I thought initially that Microwave Studio can do such a thing, but it can't. I was told that no commercially available software can solve lossy boundary condition. It appears that one has to set up the codes oneself to do this.

Zz.