Studies on the Mode Frequencies of a System of Coupled Resonators

Abstract

The mode frequency distribution of a coupled resonant system is investigated from the view point of equivalent circuit. Explicit expression for the mode frequencies can be conveniently obtained by transformation to normal coordinates, which can be effected with the help of a suitable matrix. It is shown that for a system possessing symmetry in space, this transformation matrix can be easily determined from space geometry considerations.

An expression for the mode frequencies is derived for a system with cyclic symmetry, a specific example of which is a cylindrical magnetron, with or without cathode. This expression, applicable to a system with complete symmetry, can be used for a priori prediction of mode spectrum if all the electric and magnetic coupling coefficients are known. In view of the difficulties of determining these coefficients, the expression is used to study the functional dependence of the mode frequencies on the coupling parameters and a posteriori curve fitting. Mode spectra are computed for various assumed relations between the coupling coefficients. Comparison of these results with the theoretical and experimental mode spectra of cylindrical magnetrons, available in literatures, by means of curve fitting, determines these coefficients and also justifies the validity of the analysis.

Expression suitable for estimation of mode spectrum of a system with incomplete symmetry, as in a rising sun magnetron, is derived and similar studies are made for this system.