Fundamental Limits on Substructure Dielectric Resonator Antennas

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.