A contribution to the theory of probes in waveguides

An account is given of some of the difficulties which beset the calculation of the impedance of the finite-size probe in a waveguide. In the particular case of a probe completely spanning a rectangular guide and fed by a coaxial line, a solution is set up in which the line is represented by an arbitrary loading impedance terminating the probe. An integral equation for the current in the probe is solved by a Fourier series in the waveguide modes, and an approximate summation of the double series involved is achieved using Poisson´s formula. An expression is derived for the probe impedance from which an equivalent circuit with determinate parameters is obtained. The quasi-static antenna solution is derived as a limiting case for small probe radius, and an interpretation is attempted of the physical significance of the individual terms in the expression for the inductance of an inductive post in waveguide. This is a particular case of the probe for which the solution is well known but for which the meaning of the formula is not too clear.