Formulation for numerical solution of radiation and transmission from arbitrary apertures

A solution is offered to the general problem of a waveguide coupled to an arbitrary region through a rectangular aperture of arbitrary dimensions. An equivalence principle is used to reduce the original problem to two canonical problems, one for each side of the aperture. The only coupling is through the aperture, whose characteristics can be expressed by one aperture admittance matrix for each region. Application of the boundary conditions (the continuity of the tangential electric and magnetic fields) results in an integral equation, which can then be solved numerically for determining the equivalent magnetic current, which in turn is related to the tangential component of the electric field in the aperture. A moment method is then used to reduce the integral equation to a matrix equation to compute the current coefficients. The procedure is illustrated by considering the radiation from a waveguide fed aperture. Quantities computed are the transmission coefficient, the equivalent magnetic currents, and the gain pattern.