Stored energies for electric and magnetic currents with applications to Q for small antennas

Fundamental limitations restrict the bandwidth of electrically small antennas. A method to obtain such limitations is based on stored electric and magnetic energies. Vandenbosch recently proposed a set of integral expression for the stored energies. These expressions provide a method to determine optimal currents and physical bounds on antennas for maximal bandwidth and desired radiated fields. In the present paper, we generalize the expressions for the stored energies to include magnetic sources for small structures. We give an expression for the antenna Q for electrically small shapes. Examples for small spheres are tested and the results agree with the published results.