Active impedance based on the cavity model of a circular microstrip antenna element for an infinite planar array antenna

We propose an active impedance formula based on a cavity model of a circular microstrip antenna element for an infinite array antenna. The active impedance is rigorously evaluated from the self-impedance of an element antenna and mutual impedances between element antennas. However, for large array antennas, this method takes a lot of time for calculating the active impedance. Generally, in these cases, active impedances have been evaluated by employing the periodic structures of the infinite array antennas as an approximation of the investigated array antennas. For microstrip antenna elements, the active impedance formulas have been developed by employing the Galerkin´s method which leads to the current distribution on the patches. However, this method has numerical disadvantages where several modes need to be taken into account. We analytically obtain the active impedance formula constructed with equivalent magnetic current sources based on the cavity model. In this formula, the active impedance can be calculated rapidly and analytically compared with the conventional methods because this formula has a closed form. Also we confirm its validity.