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.