Abstract :
The storage field of diaphragms in wave guides is usually described in terms of higher-order evanescent waves. Yet a rectangular wave guide may be thought of as a strip transmission line, which is continuously stub-supported at both edges, and one would not normally describe the storage field of a condenser or coil shunted across the line, in terms of evanescent waves. A straightforward calculation of capacitance or inductance using some quasi-stationary method, such as the Schwarz-Christoffel transformation is usually all that is required. Why, then, should it be necessary to wrestle with an infinity of higher-order waves in the case of diaphragms in wave guides? In fact there is no such necessity. All the higher-order evanescent waves, or at any rate all those of order greater than a certain small number, possess cut-off frequencies large compared with the frequency at which the guide is operated. The effect of these higher-order waves may therefore be calculated as though the frequency were zero. This means that higher-order waves are substantially the same as those occurring in a certain electro- or magneto-static problem. Provided this associated static problem can be recognizedand solved by some straightforward method not involving high-order waves, a mathematically- simple and physically direct approach to calculation of shunt admittance is available. This technique has been developed for four simple problems, namely, capacitive and inductive diaphragms in strip transmission lines and rectangular wave guides. Calculation of the shunt admittance at a sudden change in section of a strip transmission line is used to illustrate the power of a combination of the quasi-stationary method and Babinet´s principle for electromagnetism. A result is obtained which is valid even when the cross-sectional dimension is comparable with, or greater than, a wavelength. Finally a list of known reactances of diaphragms in wave guides is given together with equivalent circuits.
