A theory of antenna array conformal to surfaces of revolution

For a conformal array of nonparallel radiators the classical array theory fails to offer a convenient way for calculating the array pattern and its cross-polarized counterpart. This study shows that under a wide range of conditions, these patterns can be simply obtained from the array space factor by partial differentiation. The scalar space factor of an array, therefore, can be considered as a generating function for the array patterns for both the principal and the cross-polarized fields in a vector form. To illustrate the theory, arc arrays of uniformly spaced dipoles and slots are treated. The analysis is extended to the case of conical arrays.