Fundamental Limits on Substructure Dielectric Resonator Antennas

Abstract

We show theoretically that the characteristic modes of dielectric resonator antennas (DRAs) must be capacitive in the low frequency limit and that as a consequence of this constraint and the Poincaré Separation Theorem, the modes of any DRA consisting of partial elements of an encompassing super-structure with the same spatial material properties cannot resonate at a lower frequency than the encompassing structure. Thus, design techniques relying on complex sub-structures to miniaturize the antenna, including topology optimization and meandered windings, cannot apply to DRAs. Due to the capacitive nature of the DRA modes, it is also shown that the Q factor of any DRA sub-structure will be bounded from below by that of the super-structure at frequencies below the first self-resonance of the super-structure. We demonstrate these bounding relations with numerical examples.