Bounds for capacities in microwave filter problems.

Complementary (maximum and minimum) variational principles are used to obtain upper and lower bounds for capacities in microwave filter problems. The results are illustrated by calculations for a periodic system of cylindrical rods between two parallel ground planes.
In this paper we shall study the boundary value problems which arise when a periodic system of cylindrical rods lies between two parallel ground planes. Such systems are used in certain microwave filters.
The basic problem is to determine the capacitance of the system when either the odd or even mode is excited. The odd mode gives rise to a Dirichlet problem and the even mode gives rise to a mixed boundary value problem. Approximate solutions for the fields in these eases have been obtained by Richmond (1923) using a conformal transformation method, by Chisholm (1956) using a stationary (variational) principle, and by Cristal (1964) using a numerical method for the appropriate integral equation. An alternative approach to the problem is pointed out in this paper. It is based on the theory of maximum-minimum (complementary) variational principles, and leads to both upper and lower bounds for the capacitance. [ABSTRACT FROM AUTHOR]