Computation of the $Q$ Limits for Arbitrary-Shaped Antennas Using Characteristic Modes

In this paper, we present an efficient and direct method for computing the lower bound on Q for arbitrary-shaped, perfectly conducting antenna geometries. We begin by deriving a new formula for Q based on the currents induced on the antenna/scatterer and the method of moments (MoM) impedance matrix [Z]. We then use this formula in conjunction with the theory of characteristic modes to find lower bounds on arbitrary-shaped electrically small antennas (ESAs). Current distributions that yield the minimum possible Q are also given, providing for a powerful insight into the physical factors that affect Q, and offer guidelines for improving the ESA designs constricted to arbitrary physical volumes. Several supporting examples are investigated, and appropriate comparisons to the literature are given to demonstrate the flexibility and effectiveness of our approach.