Modal study of electrically small patch antennas on dielectric, magnetic and reactive impedance metamaterial substrates

A modal comparative study of patch antennas over a normal, high permittivity, high permeability and artificial substrates, respectively, is presented. It is based on the theory of characteristic modes. It is shown using some defined metrics that a magnetic substrate offers a significant bandwidth enlargement for the first active modes, and a dielectric substrate presents the opposite effect. This agrees with previously published works based on analytical approaches. An expression for the modal quality factor without defining particular excitation is presented and computed for the studied cases in order to approve these conclusions. Furthermore, numerical results demonstrate that a reactive impedance substrate presents a similar response to a conventional magnetic substrate when associated to a patch antenna near to the resonance. The modal currents are computed using a numerical method. Therefore, this analysis is suitable for electrically small antennas or structures presenting non canonical geometries and arbitrary shapes such as metamaterial inclusions.