The Measurable Q Factor and Observable Energies of Radiating Structures

New expressions are derived to calculate the Q factor of a radiating device. The resulting relations link Q based on the frequency change of the input impedance at the input port (Q
_X
, Q
_Z
) with expressions based solely on the current distribution on an radiating device. The question of which energies of a radiating system are observable is reviewed, and then the proposed Q factor as defined in this paper is physical. The derivation is based on potential theory rather than fields. This approach hence automatically eliminates all divergent integrals associated with electromagnetic energies in infinite space. The new formulas allow us to study the radiation Q factor for antennas without feeding (through e.g., characteristic modes) as well as fed by an arbitrary number of ports. The new technique can easily be implemented in any numerical software dealing with current densities. To present the merits of proposed technique, three canonical antennas are studied. Numerical examples show excellent agreement between the measurable Q
_Z
derived from input impedance and the new expressions.