Selected References

1. H. A. Wheeler, "Formulas for the skin effect", Proc. IRE, Vol. 30, No. 9, September 1942, pp. 412-4124
2. Stanislaw Rosloniec, Algorithms For Computer-Aided Design of Linear Microwave Circuits, Archtech House, 1990
3. John Karahask, Transmission Lines and Filter Networks, MacMillan, 1950, New York
4. Robert Colin, Foundations for Microwave Engineering, McGraw-Hill, Inc. 1966, page 81.
5. Ruel V. Churchill and James Ward Brown, Complex Variables and Applications, 4th ed., McGraw-Hill, Inc., 1984, New York. This book includes an appendix with a catalog of conformal transformations of regions. A transform which is most useful for coax lines with offset center conductor may be found here.

Comments

Coaxial transmission lines are almost always used in a frequency region where only the transverse electric magnetic (TEM) mode will propagate. Several texts give an approximate formula for the cutoff frequency for the lowest order TE mode but most do not provide details on the exact calculation. The general solution can be found by following the texts on circular waveguides but recognizing that we have a boundary condition imposed by the center conductor which is different than the boundary condition imposed by a hollow pipe. Wcalc uses a numerical iteration to find the constants which satisfy the boundary conditions to in theory provide an exact solution.

Known Issues

1. The TE10 cutoff calculation is based on c=0 (center conductor is not offset from center). If anyone cares to offer a suggestion on how to solve for the TE10 cutoff frequency when c is not zero, please let me know.