Useful coordinate transformations for antenna applications

General coordinate transformations which are commonly encountered in many antenna applications are presented. Neither the feed coordinates nor the far-field pattern coordinates in general coincide with the antenna coordinates. Transformations discussed allow one to relate the spherical and Cartesian components of one system to the spherical and Cartesian compoents of the other system. In particular, attempts are made to use unified notations to assist the reader in a straightforward application of the transformations.