On the input impedance of probe-fed electromagnetic bandgap antennas based on lattice modes

The impedance of a coaxial probe, feeding an Electromagnetic Bandgap (EBG) structure conceived for radiation shaping, is studied from the theoretical and numerical viewpoints. The EBG medium is a square arrangement of dielectric cylinders placed in a parallel-plate waveguide, where a suitable lattice mode is excited. A semi-analytical model is developed and used to derive an approximate, closed-form expression of the probe resistance. The model is based on a modal expansion in Floquet harmonics, on which a current distribution is projected according to the Lorentz reciprocity theorem to derive the amplitude of lattice modes propagating right above the bandgap along lattice axes. The dependence of probe impedance on lattice parameters is then investigated with the numerical simulations of a finite-element method, which is also used to validate the developed model. A broad set of parametric analyses is presented, showing that the reactive part weakly depends on probe position, cylinder radius and permittivity, while the heights of probe and parallel-plate waveguide play a major role in determining the resonance condition. As to the probe resistance, it decreases with cylinder radius and permittivity and decreases with probe and waveguide heights. The derived analytical formula correctly reproduces such functional dependences and its calculation is immediate, revealing its usefulness in antenna design. Matching issues are heuristically and experimentally approached by examples, demonstrating that the proposed work can be effectively employed to improve the electrical performance of EBG antennas with an embedded source.