Inverse-source algorithm for antenna-field transformations using the weak form of the combined-source condition

Inverse equivalent-source algorithms for antenna-field transformations are particularly powerful and robust if they work with directive sources that radiate primarily from the source region towards the field observation locations. Such directive behaviour can for example be achieved by employing an additional integral equation that explicitly imposes a null-field condition (known also as a Love condition) in the original source region of the antenna. An approximate null-field condition can be achieved in the form of an impedance-boundary condition, which is also known as the combined-source condition. In this work, the combined-source condition is utilized in a weak form, and the directivity of the expansion sources is further increased by shifting the source points into complex space. This inverse-source algorithm is formulated and used for near-field to far-field transformations of measured antenna fields. The results are discussed and compared to those achieved with the corresponding strong-form algorithm.