Lower Bounds on the Q of Electrically Small Dipole Antennas

General expressions are obtained for the lower bounds on the quality factor (Q) of electrically small electric- and magnetic-dipole antennas confined to an arbitrarily shaped volume V and excited by general sources or by global electric-current sources alone. The lower-bound expressions depend only on the direction of the dipole moment with respect to V , the electrical size of V , and the static electric and magnetic polarizabilities per unit volume of hypothetical perfectly electrically conducting and perfectly magnetically conducting volumes V . The lower bounds are obtained directly from the electromagnetic field expressions for Q with the help of current equivalence principles and the uncoupling of Maxwell´s equations for electrically small volumes into quasi-electrostatic and quasi-magnetostatic fields.