Development of 2-D Generalized Tri-Focal Rotman Lens Beamforming Network to Excite Conformal Phased Arrays of Antennas for General Near/Far-Field Multi-Beam Radiations

In this paper, we present a general closed-form solution of trifocal Rotman lens beamforming network (TFRL-BFN) design to excite a conformal phased array of antennas for multibeam radiations. This TFRL-BFN is a two-dimensional (2-D) configuration and is realizable in a dielectric substrate sandwiched by a pair of metal parallel-plates. In the development, instead of employing the geometric optic (GO) ray paths external to the Rotman lens to form an equal-phase wavefront by equal path lengths for directional beam radiation, we consider the phase need of antenna array excitation as the design target of TFRL-BFN. As a result, the TFRL-BFN concept can be extended to treat conformal arrays of antennas with well-planned excitation schemes, ranging from conventional near- and far-field focus multibeam radiations, as well as multibeam with shaped patterns. Basic theoretical concepts and foundations are presented with simulation and measurement examples to demonstrate the phase production characteristics of this TFRL-BFN. When used to feed a conformal array of antennas, the resulting radiation characteristics validate this TFRL-BFN generalization concept's feasibility.