Optimal Composition of Modal Currents For Minimal Quality Factor Q

TL;DR

This paper presents a method to determine the optimal current distribution on arbitrarily shaped small antennas to approach the theoretical lower bound of the quality factor Q, using modal decomposition and matrix-based calculations.

Contribution

It introduces a straightforward numerical approach to find optimal currents for minimal Q on complex shapes, utilizing modal analysis and matrix representations of electromagnetic operators.

Findings

Optimal currents approach the lower bound of Q for various shapes.

Modal decomposition guides the selection and combination of modes.

Results demonstrate significant Q reduction and physical insights into antenna design.

Abstract

This work describes a powerful, yet simple, procedure how to acquire a current approaching the lower bound of quality factor Q. This optimal current can be determined for an arbitrarily shaped electrically small radiator made of a perfect conductor. Quality factor Q is evaluated by Vandenbosch's relations yielding stored electromagnetic energy as a function of the source current density. All calculations are based on a matrix representation of the integro-differential operators. This approach simplifies the entire development and results in a straightforward numerical evaluation. The optimal current is represented in a basis of modal currents suitable for solving the optimization problem so that the minimum is approached by either one mode tuned to the resonance, or, by two properly combined modes. An overview of which modes should be selected and how they should be combined is provided and results concerning rectangular plate, spherical shell and fractal shapes of varying geometrical complexity are presented. The reduction of quality factor Q and the G/Q ratio are studied and, thanks to the modal decomposition, the physical interpretation of the results is discussed in conjunction with the limitations of the proposed procedure.