Synthesis of Shaped-Beam Radiation Patterns at Millimeter-Waves Using Transmit Arrays

Transmit arrays have been mostly used for beam collimation applications, either with fixed or scanning beam capability. But transmit arrays can also be used to synthesize power radiation patterns complying with power pattern templates. A new analytical formulation is presented here to obtain a phase-only correction function corresponding to a given power template. The transmit-array transforms the known power radiation pattern of the primary source into a desired output power pattern. The proposed formulation, specialized for axial-symmetric structures, is based on geometrical optics and provides the solution directly from the evaluation of two closed-form first-order differential equations. As a proof of concept, a sec(2) with a roll-off at 45 degrees is defined as the target power pattern, at the 30 GHz Ka-band. A 10.8 dBi radiation pattern with the circular polarization is used to illuminate a 180 mm x 180 mm transmit array with 60 mm focal distance. Previously designed 3.35 mm thick phase-delay unit cells are used as an example to implement the calculated phase distribution over the transmitarray aperture. The measured antenna radiation pattern matches quite well the template, with a steep fall of the radiation at the roll-off angle and low cross-polarization. This validates the concept, the formulation, and the fabricated prototype.