Energy Storage and Radiation $Q$ of Infinite Planar Dipole Phased Arrays

The exact stored energy, radiated power, and radiation quality factor of infinite planar phased arrays of dipole elements are presented for configurations in free space, over a ground plane, and on a grounded dielectric substrate. Radiated power and stored electric and magnetic energies are evaluated in terms of the two-dimensional spectral domain Floquet mode series representation of the element current. Characteristics of the radiated power and stored energies are clearly identified from propagating and evanescent spectra. In the presence of a ground plane, the dominant (0, 0) Floquet mode contributes to the stored energy, but not in the free-space case. Standard array configurations are analyzed, and the Q results are compared with impedance-derived values available by independent calculation.