Array pattern synthesis with null field constraints in the near-field region

Many of the available array synthesis procedures require the prescription of both amplitude and phase of the sought pattern and therefore can be labelled as field synthesis procedures, in contrast to the power synthesis ones, in which only the field amplitude is prescribed. If the array is formed by equal elements with a fixed geometry, only the excitations must be determined. The aim of this work is to find an efficient solution to array power synthesis involving null field constraints in the near-field (NF) region. Null field constraints in the near-field are introduced in the synthesis process to avoid the interaction between the array and the surrounding environment and to prevent electromagnetic (EM) compatibility troubles. The null field constraints are imposed on the spherical surface enclosing the considered volume. In fact, as a consequence of the uniqueness theorem, if the tangential components of the EM field on a closed surface external to the sources are zero, the field is null in the enclosed volume. It is clear that the number of constraints can be remarkably reduced by imposing the annulment of the field tangential components at the sampling points fixed by the nonredundant field representation on a spherical surface external to the sources (see Bucci, O.M. et al., Atti Fondazione "G. Ronchi", vol.54, p.311-21, 1999).