NEC-LIST:Rectangular transmission lines

Dear NEC-lister,

Duncan Baker recently made a post to NEC-list requesting information on
rectangular transmission lines. I believe that I can help with that
request.

This is a venerable problem and can be solved both accurately and
approximately by conformal transformation. The exact solution is in
terms of elliptic integrals. The approximate solution relies on the
corners being far enough apart for them to be considered isolated, with
the sections in between modelled as parallel plate lines; it therefore
works best for low impedance lines. A conformal transformation solution
to the problem of an isolated corner (in the form of the excess capacity
which results from making a right angle bend in a parallel plate
transmission line) was obtained in the Nineteenth Century where there
was interest in the problem of the excess capacity at the bend in the
bottom corners of Leyden jars. That solution is to be found in Jeans'
book.

Some more contemporary references are the following:

Y A Omar and C F Miller, "Characteristic impedance of rectangular
coaxial transmission lines", Trans AIEE, vol 71 (Communications and
Electronics, pt 1), pp 81-89, January 1952.

T-S Chen, "Determination of the capacitance, inductance and
characteristic impedance of rectangular transmission lines", IRE Trans
MTT, vol MTT-8, pp 510-519, September 1960.

G M Anderson, "The calculation of the electrical capacitance of coaxial
cylinders of rectangualr cross-section", Trans AIEE, vol 69, Pt 2, pp
728-731, 1950.

J J Skiles and T J Higgins, "Determination of the characteristic
impedance of UHF coaxial rectangular transmission lines", Proc. Nat'l
Electronics Conference, vol 10, pp 97-100, 1954.

Later I obtained a solution to a sub-species of this problem myself
numerically using finite difference methods. The reference is:

H E Green, "The characteristic impedance of square coaxial line", IEEE
Trans MTT, vol MTT-11, pp 554-555, November 1963.

The bibliography of this paper also contains the four references listed
above. Later I gave a more extended version of the use of finite
difference techniques to solve this and a range of other similar
problems in:

H E Green, "The numerical solution of transmission line problems",
Advances in Microwaves, vol 2, chap. 6, pp 327-393, Academic Press, New
York, 1967 (Editor Leo Young).

If anyone is interested in higher order modes in these sorts of lines, a
good reference is:

L Gruner, "Higher order modes in square coaxial lines", IEEE Trans MTT,
vol MTT-31, pp 770-772, September 1983.

In a later paper of which I was a co-author, it was shown how (some of)
Gruner's results could be obtained using the transverse resonance
technique, subject to the approximation that that corners can be treated
as isolated. The reference is:

H E Green and J D Cashman, "Higher order modes in polygonal transmission
lines", IEEE Trans MTT, vol MTT-33, pp67-69, January 1985.

In doing this we made use of data on E-plane bends in rectangualr
waveguide (which is equally applicable to the parallel plate line case)
which is contained in Marcuvitz' "Waveguide Handbook" on pp 316-318.

I hope that the above is a satisfactory answer to Duncan's request.

Harry E. Green,
Adjunct Research Professor,
Institute for Telecommunications Research,
University of South Australia

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