Closed-form formulas of input impedance and axial ratio of a circular patch with perturbation segments

We present a simple and useful closed-form expression to compute antenna input impedance and the axial ratio of a circular patch antenna with perturbation segments. The closed-form expression is obtained by applying the cavity perturbation theory on antenna equivalent circuits that represent the resonant behaviors of two degenerated modes in the antenna. In particular, we exclude the assumption that equal resistance occurs between two modes and include the perturbation shape parameters in the proposed formulas, which results in a more accurate prediction of the antenna input impedance and axial ratio. The validity of the proposed equations is demonstrated by comparing the analytical results to full-wave simulations and measurements.