A theoretical model for the radiation characteristics of the tapered slot antenna is presented. The theory presented is valid for antennas having an arbitrary and smooth taper shape. The model adequately predicts the pattern dependence on the structural parameters of the antenna such as its length, the taper shape, the dielectric substrate and its thickness. The antenna is modelled as a tapered slot radiating in the presence of a conducting half-plane. The electric field distribution in the tapered slot is determined by effecting a stepped approximation to the continuous taper. Data on a uniform slot line is used to determine the slot field distribution in the stepped model. The uniform slot line is solved by the spectral Galerkin\u27s meth...