This paper 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, capped dipole antenna, 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.

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

Utilization of fast surrogate models has become a viable alternative to direct handling of full-wave electromagnetic (EM) simulations in EM-driven design. Their purpose is to alleviate the difficulties related to high computational cost of multiple simulations required by the common numerical procedures such as parametric optimization or uncertainty quantification. Yet, conventional data-driven (or approximation) modeling techniques are severely affected by the curse of dimensionality. This is a serious limitation when it comes to modeling of highly nonlinear antenna characteristics. In practice, general-purpose surrogates can be rendered for the structures described by a few parameters within limited ranges thereof, which is grossly insufficient from the utility point of view. This paper proposes a novel modeling approach involving variable-fidelity EM simulations incorporated into the recently reported nested kriging modeling framework. Combining the information contained in the densely sampled low- and sparsely sampled high-fidelity models is realized using co-kriging. The resulting surrogate exhibits the predictive power comparable to the model constructed using exclusively high-fidelity data while offering significantly reduced setup cost. The advantages over conventional surrogates are pronounced even further. The presented modeling procedure is demonstrated using two antenna examples and further validated through the application case studies.

/pdf/antenna-modeling-using-variable-fidelity-em-simulations-and-2qa0wtxjqk.pdf

Antenna Modeling Using Variable-Fidelity EM Simulations and Constrained Co-Kriging

Design of contemporary antenna structures needs to account for several and often conflicting objectives. These are pertinent to both electrical and field properties of the antenna but also its geometry (e.g., footprint minimization). For practical reasons, especially to facilitate efficient optimization, single-objective formulations are most often employed, through either a priori preference articulation, objective aggregation, or casting all but one (primary) objective into constraints. Notwithstanding, the knowledge of the best possible design trade-offs provides a more comprehensive insight into the properties of the antenna structure at hand. Genuine multi-objective optimization is a proper way of acquiring such data, typically rendered in the form of a Pareto set that represents the mentioned trade-off solutions. In antenna design, the fundamental challenge is high computational cost of multi-objective optimization, normally carried out using population-based metaheuristic algorithms. In most practical cases, the use of reliable, yet costly, full-wave electromagnetic models is imperative to ensure evaluation reliability, which makes conventional multi-objective optimization procedures prohibitively expensive. The employment of fast surrogates (or metamodels) can alleviate these difficulties, yet, construction of metamodels faces considerable challenges by itself, mostly related to the curse of dimensionality. This work proposes a novel surrogate-assisted approach to multi-objective optimization, where the data-driven model is only rendered in a small region spanned by the selected principal components of the extreme Pareto-optimal design set obtained using local search routines. The region is limited in terms of parameter ranges but also dimensionality, yet contains the majority of Pareto front, therefore surrogate construction therein does not incur considerable costs. The typical cost of identifying the Pareto set is just a few hundred of full-wave analyses of the antenna under design. Our technique is validated using two antenna examples (a planar Yagi and an ultra-wideband monopole antenna) and favorably compared to state-of-the-art surrogate-assisted multi-objective optimization methods.

/pdf/fast-multi-objective-optimization-of-antenna-structures-by-aey4rqjykp.pdf

Fast Multi-Objective Optimization of Antenna Structures by Means of Data-Driven Surrogates and Dimensionality Reduction

This article utilizes a topology optimization approach to design planar multilayer transitions between substrate integrated waveguides (SIWs) and rectangular waveguides (RWGs). The optimization problem is formulated based on the modal field analyses and Maxwell’s equations in the time domain solved by the finite-difference time-domain (FDTD) method. We present a time-domain boundary condition based on the Klein–Gordon equation to split traveling waves at homogeneous waveguide ports. We employ the boundary condition to compute portal quantities and to devise an adjoint-field system that enabled an efficient computation of the objective function gradient. We solve design problems that include more than 105 000 design variables by using less than 400 solutions of Maxwell’s equations. Moreover, a new formulation that effectively combats the development of in-band resonances in the design is presented. The transition configuration allows the direct mount of conventional RWG sections on the circuit board and aims to cover the entire K-band. The guiding structure of the optimized transition requires blind vias, which is realized by a simple and cost-efficient technique. In addition, the transition is optimized for three different setups that can be used to provide different field polarizations. The proposed transitions show less than 1-dB insertion loss and around 15-dB return loss over the frequency interval 18–28 GHz. Several prototypes are fabricated with an excellent match between the simulation and measurement results.

Multilayer Topology Optimization of Wideband SIW-to-Waveguide Transitions

Precise tuning of geometry parameters is an important consideration in the design of modern microwave passive components. It is mandatory due to limitations of theoretical design methods unable to quantify certain phenomena that are important for the operation and performance of the devices (e.g., strong cross-coupling effects in miniaturized layouts). Consequently, the initial designs obtained using analytical or equivalent network models require further adjustment. For reliability reasons, it has to be conducted using electromagnetic (EM) simulation tools, which entails considerable computational expenses whenever conventional numerical optimization algorithms are employed. Accelerating EM-driven design procedures is therefore highly desirable. This work discusses a surrogate-based algorithm for fast design closure and dimension scaling of miniaturized microwave passives. Our approach involves a small database of previously obtained designs as well as two metamodels, an inverse one, employed to yield a high-quality initial design, and the forward surrogate that provides predictions of the system sensitivities. The second model is constructed at the level of response features, which enables a more accurate gradient estimation and leads to improved reliability and a faster convergence of the optimization process. The presented technique is validated using two compact microstrip couplers and benchmarked against the state-of-the-art warm-start optimization frameworks.

https://www.mdpi.com/2079-9292/10/1/10/pdf

Fast Design Closure of Compact Microwave Components by Means of Feature-Based Metamodels

We present an approach to design from scratch planar microwave antennas for the purpose of ultra-wideband (UWB) near-field sensing. Up to about 120 000 design variables associated with square grids on planar substrates are subject to design, and a numerical optimization algorithm decides, after around 200 iterations, for each edge in the grid whether it should consist of metal or a dielectric. The antenna layouts produced with this approach show UWB impedance matching properties and near-field coupling coefficients that are flat over a much wider frequency range than a standard UWB antenna. The properties of the optimized antennas are successfully cross-verified with a commercial software and, for one of the designs, also validated experimentally. We demonstrate that an antenna optimized in this way shows a high sensitivity when used for near-field detection of a phantom with dielectric properties representative of muscle tissue.

Robin Augustine

Papers

Topology Optimization of Planar Antennas for Wideband Near-Field Coupling