**Authors:** Thomas F. Eibert

**Source:** FERMAT, Volume 19, Communication 12, Jan-Feb., 2017

**Abstract:** Inverse equivalent source solutions are powerful approaches for antenna field transformations and they provide in particular very detailed diagnostic insight into the radiation behaviour of the considered antenna. Commonly such techniques work with electric and/or magnetic surface current densities, where the field observation equations are sometimes augmented by a null-field condition for the region external to the Huygens surface. The surface current densities obtained with such a null-field condition are known as Love currents and they are directly linked to the tangential electric and magnetic fields on the Huygens surface. Also, it is clear that these currents radiate in general (for convex surfaces) only away from the antenna under test (AUT) and are, therefore, very suitable for antenna diagnostics. As an approximate and inexpensive alternative to the null-field condition, we propose to work with directive surface sources, which are obtained by an impedance boundary condition linking electric and magnetic surface currents densities and by shifting the equivalent surface current densities into complex space. These directive sources are integrated into the fast irregular antenna field transformation algorithm which achieves low numerical solution complexity by utilizing multilevel fast multipole like principles. Field transformation results based on real measurement data are investigated to illustrate the performance of the directive surface sources.

**Index Terms:** antenna measurement, near-field measurement, field transformation, antenna diagnostic, integral equation, fast multipole method

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