  A Fosters equivalent circuit for 2-D Planar Periodic Structures (PPSs) that
exhibit an arbitrary geometry is presented for first time in this paper. The
proposed 4-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 bi-mode 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) have been obtained and analyzed in single and
multi-layer 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 20 deg into a purely linear vertical
polarization of XP<-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.
