Taking into account the edge condition in the problem of scattering from the circular aperture in circular-to-rectangular and rectangular-to-rectangular waveguide junctions

An integral equation for the equivalent magnetic current sheet at the centred circular aperture of a diaphragm in a transverse plane of circular-to-rectangular and rectangular-to-rectangular waveguide junctions is approximately solved by Galerkin´s method. A basis of weighted Jacobi polynomials which satisfy the edge condition is used for the magnetic current. The results are graphically compared with formulas derived from the variational theory given in the Waveguide Handbook (McGraw Hill, New York, 1951)