Analysis of longitudinal slot in a rectangular waveguide using image series and Chebyshev-Toeplitz algorithm

The internal admittance of a radiating longitudinal slot in the broadwall of rectangular waveguide, required in analyses such as Method of Moments, has been evaluated by considering the images of the slot in waveguide walls. The contribution from this set of infinite images has been evaluated using simple closed form expressions for mutual coupling between slot and its image. The convergence of the series is accelerated using Chebyshev-Toeplitz algorithm. The resonant length calculated using this simple and accurate analysis is shown to be in close agreement with measured results and with other theoretical results. The analysis given here can be extended to include other slot aperture distributions with edge condition in the transverse direction or for rounded end slots. This analysis is useful in the efficient design of waveguide slot arrays.