Dispersive analysis of 1D–periodic leaky–wave antennas through full-wave simulations of truncated structures

Bloch analysis of one-dimensional periodic electromagnetic structures are often obtained by cascading two-port equivalent circuits derived by simulating a single, isolated cell of the structure, thus neglecting the mutual coupling among cells which occurs in a periodic environment. By simulating truncated structures made of a suitable, finite number of cells such mutual coupling can be correctly modeled; however, spurious solutions are then introduced, that are shown here to be related to nonuniqueness of certain root-extraction operations in the complex plane. A simple automatic method is proposed to avoid such spurious solutions, while testing the convergence of the analysis by increasing the number of simulated cells. In particular, the approach is applied to accurately characterize the dispersive features ofa a leaky-wave antenna based on a periodically loaded microstrip. Results for phase and leakage constants are validated against those obtained with full-wave MoM simulations which rigorously take into account all mutual coupling effects through the use of periodic Green's functions.