Optimal Currents on Arbitrarily Shaped Surfaces

Abstract

An optimization problem has been formulated to find a resonant current extremizing various antenna parameters. The method is presented on, but not limited to, particular cases of gain $G$, quality factor $Q$, gain to quality factor ratio $G/Q$, and radiation efficiency $\eta$ of canonical shapes with conduction losses explicitly included. The Rao-Wilton-Glisson basis representation is used to simplify the underlying algebra while still allowing surface current regions of arbitrary shape to be treated. By switching to another basis generated by a specific eigenvalue problem, it is finally shown that the optimal current can, in principle, be found as a combination of a few eigenmodes. The presented method constitutes a general framework in which the antenna parameters, expressed as bilinear forms, can automatically be extremized.Comment: 13 pages, 18 figures, IEEE Transactions on Antennas and Propagation 65, 201

Upper bounds on absorption and scattering

“…Expressing unknown currents in a finite dimensional basis, the finite dimensional matrix operators governing quantities of interest may be readily calculated using the tools developed for solving integral equation problems [23], i.e., using the method of moments [24]. Problems in antenna theory solved in this way include maximization of directive gain [25,26,27], maximization of radiation efficiency [28,26,29], minimization of Q-factor (analogous to maximizing bandwidth) [30,31], and the trade-off between these parameters [32,27].…”

State‐space models and stored electromagnetic energy for antennas in dispersive and heterogeneous media

“…The results produced by the state‐space method seem to be reliable and produce similar values as Brune circuit synthesis [ Gustafsson and Jonsson , ] and differentiation of the input impedance for single resonance cases. However, the main advantage over other contemporary methods is that the state‐space model is written as a quadratic form in the current and hence enables fast and effective use in antenna current optimization to determine physical bounds [ Gustafsson and Nordebo , ; Cismasu and Gustafsson , ; Gustafsson et al , , , ; Capek et al , ; Jelinek and Capek , ].…”

“…The stored energy (2) can also be expressed in the current density on the antenna structure [Geyi, 2003b;Vandenbosch, 2010Vandenbosch, , 2013Gustafsson and Jonsson, 2015a, see Figure 1c]. This simplifies the evaluation of stored energy and enables antenna current optimization [Gustafsson et al, 2012;Gustafsson and Nordebo, 2013;Gustafsson et al, 2016;Capek et al, 2017;Jelinek and Capek, 2017]. The main drawbacks with (2) are possible coordinate dependence [Yaghjian and Best, 2005;Gustafsson and Jonsson, 2015a] and negative stored energies [Yaghjian and Best, 2005;Gustafsson et al, 2012].…”

Physical Bounds and Radiation Modes for MIMO Antennas

“…Current optimization has been utilized to construct fundamental bounds on many different antenna parameters previously, such as, Q, directivity, and efficiency [12], [14], [15], [16], [17]. By controlling the current density in the full design space of the antenna an optimal solution can be reached for that configuration.…”