Bi-Mode Foster’s Equivalent Circuit of Arbitrary Planar Periodic Structures and its Application to Design Polarization Controller Devices

Foster’s equivalent circuit for 2-D planar periodic structures (PPSs) that exhibit an arbitrary geometry is presented for first time in this article. The proposed four-port network shows an invariant circuit topology to the PPS geometry and is completely comprised of invariant-frequency lumped elements. The circuit is the simplest in terms of number of elements within the bimode bandwidth for a certain geometry, and its topology makes it possible both a standardized process to obtain the equivalent circuit of an arbitrary geometry and the use of the circuit theory to design a multitude of devices. To perform a validation, the equivalent circuit of two different PPSs (a rotated dipole and a defected slotted ring) has been obtained and analyzed in single-layer and multilayer configurations. The circuit is also used as a tool to develop elliptical to linear (or circular) polarization converters. One of the designs presented at 20 GHz (in transmission) converts an incident elliptical polarization of axial ratio 5 and tilted $\varphi = 20^{\circ }$ into a purely linear vertical polarization of $\text {XP} \lt - 30$ dB, with near-zero reflections and insertion loss better than 0.1 dB. The designed device is also manufactured and tested, and the measurements are in good agreement with simulations.