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.

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.

The quality of small array antennas in airborne monopulse systems can be significantly reduced by the radome. We therefore present a convex optimization approach to minimize radome effects in monopulse arrays. This is achieved by using active element patterns in the optimization to determine the excitation weights. Simulation results for a BoR array with 48 elements and an extended hemispherical radome are presented. We demonstrate that it is possible to reduce the side-lobe level by 3.5 dB by taking radome effects into account in the optimization. This approach also results in an increased gain, particularly at large scan angles. Furthermore, the presented approach allows the monopulse slope to be indirectly specified as a design parameter. It is shown that the trade-off between the monopulse slope coefficient and the side-lobe level is approximately linear.

The four-quadrant monopulse array is widely used for direction of arrival (DOA) estimation. Errors in the angle estimate are introduced when installing the array on a platform, due to unwanted reflections in the platform, as well as reflection and refraction in the radome. These installation effects are captured in the installed element patterns, which can be computed using a number of computational electromagnetics methods. In this paper, we demonstrate that the error introduced in the DOA estimate can be determined from the installed element patterns. To illustrate how the method is used, we present results for two cases: (a) BoR-array without radome and (b) BoR-array with an extended hemispherical radome. The presented method can be applied for any installation configuration, as long as the installed element patterns can be computed.

A dual-band rectenna for radio frequency (RF) energy harvesting is presented in this letter. The proposed antenna has two concentric square patches electrically connected with a small microstrip line connection. Four ports are located in the inner patch. The configuration of the ports enables a differential field sampling scheme and dual polarization. The antenna operates for the WiFi frequency bands of 2.4 and 5.5 GHz with 7.52 and 7.26 dBi gain, respectively, for each frequency. A full-wave Greinacher voltage doubler rectifier for each polarization has been employed for RF-to-dc conversion. The proposed novel topology utilizes the differential field sampling for each polarization and quadruples the overall output voltage by the rectification process. The differential output voltage source from the rectenna can directly act as a power source as typically electronics require differential source for their operation.

This letter presents a method to evaluate the static electric polarizability of 2-D infinitely periodic metal patch arrays with dielectric substrate. Static polarizabilities are used in several design applications for periodic structures such as estimation of the bandwidth limitations for frequency-selective structures or prediction of the radiation properties for antenna arrays. The main features of the proposed method are its numerical efficiency and a deep insight into the physics of the fields interacting with the structure. We provide derivation and analysis of the method, and its verification against two another commercial solver-based approaches for various structure geometries. Additionally, we suggest the guidelines for applying the method to bandwidth optimization of frequency-selective structures and illustrate this with an example.

In this paper we determine the trade-off between the Q-factor and partial (super) directivity for linear arrays of dipoles. The dipoles are densely spaced in a one or two wavelength long array. We compare the bound for port-feed dipoles with the current optimization approach, with optimal currents on the whole dipole area, and also with an enclosing plate. It is interesting to note that port-feed dipoles are close to the optimal current dipoles in the endfire case, for sufficiently many dipoles in the array, for a wide range of directivities. We also show that the optimization problem for the 'optimal current' and 'the port-feed' cases are very similar and that the Pareto-front (trade-off curve) can be obtained and compared for the different cases.

The reaction theorem is applied to antenna coupling problems. It is shown that the reaction theorem can be used to calculate the mutual impedance between antennas, when the electromagnetic fields are known on a plane that separates the two antennas in two disjoint regions. We also show that coupling paths between the antennas can be visualized on the separation plane, by using intermediate results from the reaction theorem. The coupling paths are visualized based on the fields generated by each of the two antennas, and only take into account the energy that is actually transfered between the antennas. The visualization of coupling paths is useful for understanding how the coupling between the antennas is distributed in space.