This paper presents a study of transmission through arrays of periodic sub-wavelength apertures. Fundamental limitations for this phenomenon are formulated as a sum rule, relating the transmission coefficient over a bandwidth to the static polarizability. The sum rule is rigorously derived for arbitrary periodic apertures in thin screens. By this sum rule we establish a physical bound on the transmission bandwidth which is verified numerically for a number of aperture array designs. We utilize the sum rule to design and optimize sub-wavelength frequency selective surfaces with a bandwidth close to the physically attainable. Finally, we verify the sum rule and simulations by measurements of an array of horseshoe-shaped slots milled in aluminum foil.

In this paper, we study optimization of multi-tone signals for wireless power transfer (WPT) systems. We investigate different non-linear energy harvesting models. Two of them are adopted to optimize the multi-tone signal according to the channel state information available at the transmitter. We show that a second-order polynomial curve-fitting model can be utilized to optimize the multi-tone signal for any RF energy harvester design. We consider both single-antenna and multi-antenna WPT systems. In-band co-existing communication links are also considered in this work by imposing a constraint on the received power at the nearby information receiver to prevent its RF front end from saturation. We emphasize the importance of imposing such constraint by explaining how inter-modulation products, due to saturation, can cause high interference at the information receiver in the case of multi-tone signals. The multi-tone optimization problem is formulated as a non-convex linearly constrained quadratic program. Two globally optimal solution approaches using mixed-integer linear programming and finite branch-and-bound techniques are proposed to solve the problem. The achieved improvement resulting from applying both solution methods to the multi-tone optimization problem is highlighted through simulations and comparisons with other solutions existing in the literature.

In this paper, the Q-factor expression for periodic arrays over a ground plane is determined in terms of the electric current density within the array's unit cell. The expression accounts for the exact shape of the array element. The Q-factor formula includes integration only over a volume of an element in a unit cell, and can thus be efficiently implemented numerically. The examples show good agreement between the proposed Q-factor, the full-wave-calculated tuned fractional bandwidth, and the input-impedance-based formula by Yaghjian and Best (2005) for the array of tilted dipoles and the loops array.

We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modelling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.

Quadratically constrained quadratic programming (QCQP) can be used to determine the best Q-factor for small antennas with constraints on the antenna efficiency. Constraints on the total directivity and a given front-to-back ratio can also be expressed as QCQP. Such problems are non-convex and hence challenging to solve. Their solution gives the best Q-factor available for any antenna within the considered volume. Thus, solutions to this type of problems provide a tool, which before the design can predict the best possible antenna performance within a given volume of a device. It is hence important to investigate methods to solve this class of QCQP problems. In this paper we compare and investigate two relaxation methods, the Lagrangian dual and semidefinite relaxation, to estimate lower bounds on the Q-factor. The former method is here reduced to solving a generalized eigenvalue-problem. Properties of the different relaxation methods are illustrated and compared. We focus in this paper on the Q-factor and its relation to efficiency, as expressed by the dissipation factor. However, these tools also apply to a larger class of problems including constraints on the directivity and other far-field conditions.

Direction‐of‐arrival (DoA) estimation accuracy can be degraded due to installation effects, such as platform reflections, diffraction from metal edges, and reflections and refraction in the radome. To analyze these effects, this paper starts with a definition of the term installation error related to DoA estimation. Thereafter, we present a postprocessing method, which can be used to determine the DoA estimation accuracy for installed antennas. By computing synthetic signals from the installed far‐field data, it is possible to analyze the installation errors described above, in addition to analyzing array model errors. The method formulation is general, thus allowing generic array configurations, installation configurations, and direction‐finding algorithms to be studied. The use of the presented method is demonstrated by a case study of a wideband four‐quadrant array. In this case study, we investigate the installation errors due to a single‐shell radome. Thereafter, the effects of platform reflections are also analyzed, for an antenna placement in the tail of a fighter aircraft. Simulation results are presented for both the monopulse and the MUltiple SIgnal Classification direction‐finding algorithms.

Pareto-front optimization of antenna properties based on the stored energy approach are investigated in this paper with different methods. The goal is to study how bandwidth through the Q-factor depend on antenna design constraints. We consider two main methods, semi-definite relaxation and a dual-eigenvalue based method, applying them to the same optimization problem. The semi-definite relaxation methods tend to be easier to formulate and to solve than the eigenvalue-based method. The cost of the semi-definite relaxation comes in terms of a memory-intensive solution method.

In this paper we investigate a method to determine the best available bandwidth for small embedded antennas. The available bandwidth depend both on the size and the position within a device, but also on the ohmic losses in the structure. Here we use that solutions to a non-convex optimization problem to predict the available bandwidth for a range of surface resistances. The optimization problem utilizes stored energies, and it is phrased as a current optimization problem. We illustrate the method by comparing the results with embedded antennas in a small IoT terminal. We show that an optimized embedded come rather close to the bounds.

Considerable time is often spent optimizing antennas to meet specific design metrics. Rarely, however, are the resulting antenna designs compared to rigorous physical bounds on those metrics. Here, we study the performance of optimized planar meander line antennas with respect to such bounds. Results show that these simple structures meet the lower bound on the radiation quality factor (Q-factor) (maximizing single-resonance fractional bandwidth) but are far from reaching the associated physical bounds for efficiency. The relative performance of other canonical antenna designs is comparable in similar ways, and the quantitative results are connected to intuitions from small antenna design, physical bounds, and matching network design.

A wideband switched beam antenna array system operating from 2 to 5 GHz is presented. It is comprised of a 4 × 1 Vivaldi antenna elements and a 4 × 4 Butler matrix beamformer driven by a digitally controlled double-pole four-throw RF switch. The Butler matrix is implemented on a multilayer structure, using 90° hybrid couplers and 45° phase shifters. For the design of the coupler and phase shifter, we propose a unified methodology applied, but not limited, to elliptically shaped geometries. The multilayer realization enables us to avoid microstrip crossing and supports wideband operation of the beamforming network. To realize the Butler matrix, we introduce a step-by-step and stage-by-stage design methodology that enables accurate balance of the output weights at the antenna ports to achieve a stable beamforming performance. In this paper, we use a Vivaldi antenna element in a linear four-element array, since such element supports wideband and wide-scan angle operation. A soft condition in the form of corrugations is implemented around the periphery of the array, in order to reduce the edge effects. This technique improved the gain, the sidelobes, and helped to obtain back radiation suppression. Finally, impedance loading was also utilized in the two edge elements of the array to improve the active impedance. The proposed system of the Butler matrix in conjunction with the constructed array can be utilized as a common RF front end in a wideband air interface for a small cell 5G application and beyond as it is capable to simultaneously cover all the commercial bands from 2 to 5 GHz.