$Q$-Factor and Bandwidth of Periodic Antenna Arrays Over Ground Plane

In this letter, the Q-factor expression for periodic arrays over a ground plane is determined in terms of the electric current density within the array's unit cell. The expression accounts for the exact shape of the array element. The Q-factor formula includes integration only over a volume of an element in a unit cell and can thus be efficiently implemented numerically. The examples show good agreement between the proposed Q-factor, the full-wave-calculated tuned fractional bandwidth, and the input-impedance-based formula by Yaghjian and Best (IEEE Trans. Antennas Propag., vol. 53, no. 4, pp. 1298-1324, Apr. 2005) for the array of tilted dipoles and the loops array.