Analysis of Coaxial Line Discontinuities by Boundary Relaxation

Discontinuities in coaxial lines may in general be represented in equivalent networks by lumped capacitances. The calculation of discontinuity capacitance is possible by means of mode-matching techniques for very simple discontinuities; for more complex cases, direct numerical methods are preferable. A new numerical technique is presented for solving the field problem in a region bounded on two sides by infinitely extending coaxial lines. The approach used is to define operators by means of which the potentials at a given cross-sectional plane of the coaxial line are related to potentials at another plane. The problem of a discontinuity region between two infinitely long lines is thereby converted into a finite problem with prescribed boundary operators in place of boundary values. Standard methods may be used to solve the problem in a finite region. Subsequent reformulation of the discontinuity capacitance in terms of stored energy permits calculation of this capacitance from the potential values in only a minimal region. The resulting computer programs are at least an order of magnitude faster than previously published ones.