Fundamental Limits on Substructure Dielectric Resonator Antennas

TL;DR

This paper establishes fundamental theoretical limits on the miniaturization of dielectric resonator antennas, showing that their modes are capacitive at low frequencies and that sub-structures cannot resonate below the super-structure's frequency, constraining design approaches.

Contribution

It provides a theoretical framework demonstrating that dielectric resonator antennas cannot be miniaturized below certain limits using complex sub-structures, due to their capacitive mode nature and the Poincaré Separation Theorem.

Findings

Modes of DRAs are capacitive at low frequencies.

Sub-structures cannot resonate below the super-structure's frequency.

Q factor of sub-structures is bounded by that of the super-structure.

Abstract

We show theoretically that the characteristic modes of dielectric resonator antennas (DRAs) must be capacitive in the low frequency limit, and show that as a consequence of this constraint and the Poincar\'{e} Separation Theorem, the modes of any DRA consisting of partial elements of an encompassing super-structure cannot resonate at a frequency that is lower than that of 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.