Computation of the Q limits for arbitrary-shaped antennas using characteristic modes

Fundamental limits on the Q-factor for arbitrary-shaped PEC antennas are presented using the theory of characteristic modes. A formula for computing the Q of an arbitrary-shaped PEC antenna with an impressed current mode is derived, and is used to find minimum-Q bounds. It is shown that minimum bounds on small antenna Q can be determined simply through an eigenmode analysis of the Method of Moments impedance matrix representing the antenna geometry. The presented Q limits are then compared with those in the literature for several common geometries.