Derivation of source fields from power density distributions

This work demonstrates a technique of deriving the phase relation between spherical wave modes which combine to realize a desired antenna design power distribution. Beginning with the power density expansion described in Keith et al. (2001), it is shown that a field distribution can be determined from the power density modes. The paper reviews the power density modes and demonstrates how a set of nonlinear equations is obtained from the expansion. A procedure for solving the nonlinear equation set is introduced. The paper demonstrates the procedure with a few simple examples. With these examples, a few interesting characteristics of the solutions are revealed.