Antenna Q for small antennas with radiation constraints and perturbations

Lower bounds on antenna Q for small antennas have recently been formulated as an optimization problem. The approach includes antennas modeled with electric and magnetic currents. We show here that constraints on the direction of radiation can increase antenna Q. We also investigate what happens to antenna Q lower bounds for electric dipole antennas when the maximal radiation increases in the presence of a small superimposed magnetic dipole. Such radiation perturbations can be caused by feeding and in coupling between currents. Magneticdipole perturbation yields a new lower antenna Q bound, that is lower than the pure electric dipole bound on antenna Q.