Wcalc Coaxial Transmission Line Model
H. A. Wheeler, "Formulas for the skin effect", Proc. IRE,
Vol. 30, No. 9, September 1942, pp. 412-4124
Algorithms For Computer-Aided Design of Linear Microwave Circuits,
Archtech House, 1990
Transmission Lines and Filter Networks,
MacMillan, 1950, New York
Foundations for Microwave Engineering,
McGraw-Hill, Inc. 1966, page 81.
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.
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.
- 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.