Optimal Composition of Modal Currents for Minimal Quality Factor $Q$

Abstract

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.

Minimization of Antenna Quality Factor

“…[21]. This is, however, well-aligned with recent attempts utilizing, e.g., characteristic modes, [20]. With respect to those modal approaches, this method can be understood in the same way -as a method combining modes.…”

“…1b. The spherical shell is considered in Section V-C as the third example, being a representative of canonical bodies which are solvable analytically [20]. The spherical shell is of great interest here as it possesses the highest degree of symmetry in R 3 .…”

Tradeoff Between Antenna Efficiency and Q-Factor

“…9 and it is immediately seen that the Pareto fronts sweep a broad range of dissipation factor and radiation Q-factor values. Notice that the ends of the Pareto fronts corresponding with minimum Q-factor are already known: the optimal current for Ω A = × /2, R s1 = 1 Ω is depicted in [54] and the optimal current for partial control and PEC is depicted in [20].…”

Accurate and Efficient Evaluation of Characteristic Modes

“…While memorydemanding, MoM represents operators as matrices (notably the impedance matrix [1]) allowing for direct inversion and modal decompositions [3]. The latter option is becoming increasingly popular, mainly due to characteristic mode (CM) decomposition [4], a leading formalism in antenna shape and feeding synthesis [5], [6], determination of optimal currents [7], [8], and performance evaluation [9].…”