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This paper presents the design, optimization, and calibration of multivariable resonators for microwave dielectric sensors. An optimization technique for the circular complementary split ring resonator (CC-SRR) and square complementary split ring resonator (SC-SRR) is presented to achieve the required transmission response in a precise manner. The optimized resonators are manufactured using a standard photolithographic technique and measured for fabrication tolerance. The fabricated sensor is presented for the high-resolution characterization of dielectric substrates and oil samples. A three-dimensional dielectric container is attached to the sensor and acts as a pool for the sample under test (SUT). In the presented technique, the dielectric substrates and oil samples can interact directly with the electromagnetic (EM) field emitted from the resonator. For the sake of sensor calibration, a relation between the relative permittivity of the dielectric samples and the resonant frequency of the sensor is established in the form of an inverse regression model. Comparisons with state-of-the-art sensors indicate the superiority of the presented design in terms of oil characterization reliability. The significant technical contributions of this work include the employment of the rigorous optimization of geometry parameters of the sensor, leading to its superior performance, and the development and application of the inverse-model-based calibration procedure., Competing Interests: The authors declare no conflict of interest.

Small size has become a crucial prerequisite in the design of modern microwave components. Miniaturized devices are essential for a number of application areas, including wireless communications, 5G/6G technology, wearable devices, or the internet of things. Notwithstanding, size reduction generally degrades the electrical performance of microwave systems. Therefore, trade-off solutions have to be sought that represent acceptable compromises between the ability to meet the design targets and physical compactness. From an optimization perspective, this poses a constrained task, which is computationally expensive because a reliable evaluation of microwave components has to rely on full-wave electromagnetic analysis. Furthermore, due to its constrained nature, size reduction is a multimodal problem, i.e., the results are highly dependent on the initial design. Thus, utilization of global search algorithms is advisable in principle, yet, often undoable in practice because of the associated computational expenses, especially when using nature-inspired procedures. This paper introduces a novel technique for globalized miniaturization of microwave components. Our technique starts by identifying the feasible region boundary, and by constructing a dimensionality-reduced surrogate model therein. Global optimization of the metamodel is followed by EM-driven local tuning. Application of the domain-confined surrogate ensures low cost of the entire procedure, further reduced by the incorporation of variable-fidelity EM simulations. Our framework is validated using two microstrip couplers, and compared to nature-inspired optimization, as well as gradient-based size reduction. The results indicate superior miniaturization rates and low running cost, which make the presented algorithm a potential candidate for efficient simulation-based design of compact structures., (© 2022. The Author(s).)

A generalised shape-preserving response prediction (generalised SPRP or GSPRP) methodology for low-cost and accurate modelling of microwave structures is discussed. The GSPRP method predicts the response of a high-fidelity electromagnetic-simulated model (e.g. S-parameters against frequency) using sets of characteristic points and translation vectors obtained from underlying low-fidelity model responses. Unlike the original SPRP technique, which uses a limited number of training points at restricted locations, GSPSP can utilise an arbitrary number of training points, which are handled through Kriging interpolation applied to model a set of characteristic points corresponding to the entire training set. This increases the flexibility of SPRP and allows us to improve the modelling accuracy if more training points are available. At the same time, the GSPRP inherits the main advantage of SPRP: good prediction accuracy without using a large amount of data, which is in contrast to conventional approximation techniques. This is ensured as the locations of the characteristic points are easy to model. The proposed technique is demonstrated through a comprehensive numerical study as well as comparison with other modelling techniques. Application examples are also given. [ABSTRACT FROM AUTHOR]

In this study, the authors propose a robust and computationally efficient algorithm for simulation-driven design optimisation of microwave structures. Our technique exploits variable-fidelity electromagnetic models of the structure under consideration. The low-fidelity model is optimised using its local response surface approximation surrogates. The high-fidelity model is refined by space mapping with polynomial interpolation of the low-fidelity model data used as an underlying coarse model. Our algorithm is carefully developed to minimise the number of evaluations of both the low- and high-fidelity model in the optimisation process. The operation and efficiency of the approach is demonstrated through design of a microstrip filter, a double-ring antenna and an ultra-wideband monopole antenna. A comparison with other design approaches, including the direct high-fidelity model optimisation, is also presented. [ABSTRACT FROM AUTHOR]

Space mapping (SM) has been used in microwave engineering for some 17 years and demonstrated as one of the most efficient simulation-driven design techniques available to date. By exploiting a fast and physically based surrogate model, SM allows rapid optimisation of an electromagnetic-simulated structure of interest (fine model). Several variations of SM algorithms have been proposed including input, output, implicit and frequency SM, as well as recently introduced tuning space mapping (TSM). However, TSM is an invasive technique that requires modification to the designable structure under consideration (i.e. the 'cutting' and inserting of the tuning ports). Here, for the first time, a comparative study of various SM and TSM algorithms is carried out. Advantages and disadvantages of these techniques are discussed and illustrated through design examples. Recommendations for potential users of SM and TSM are given. [ABSTRACT FROM AUTHOR]

To date, space mapping remains one of the most efficient design optimisation methodologies in microwave engineering. Still, its performance depends on the underlying surrogate model, in particular, its approximation and generalisation capabilities. By proper selection of the space mapping transformations and their parameters, a trade-off between these can be obtained. Often, this is done by trial and error that may lead to excessive computational overhead and poor quality of the optimisation outcome. In this study, an adaptively constrained parameter extraction is introduced. Based on convergence results for space mapping algorithms, it allows us to automatically find the approximation-generalisation trade-off through the adjustment of the surrogate model parameter space. Improved performance of the space mapping algorithm is obtained both in terms of convergence properties and the quality of the optimised design. Algorithm convergence is additionally improved by constraining the surrogate optimisation process. The authors' technique is validated using several microwave design problems. [ABSTRACT FROM AUTHOR]

Tuning space mapping (TSM) with embedded tuning elements is a recent development in space mapping technology. The process allows efficient design optimisation of microwave components by substituting sections in an electromagnetic model with corresponding sections of designable equivalent elements. Available parameters of these elements are subsequently tuned and their optimal values are 'translated' into relevant changes in the original structure's design variables. Although the TSM optimisation process typically requires only a few iterations to complete, the simulation of the structure with a number of co-calibrated ports (required for subsequent insertion of the tuning elements) can be substantially longer than that of the original structure. This results in substantial computational overhead of the design process. Here, the authors review a fast TSM algorithm that exploits a reduced structure with significantly fewer co-calibrated ports for creating the tuning model and allows us to obtain dramatic reduction of the computational cost of the optimisation process. In a design framework, the fast TSM as well as other TSM methods are implemented and automated in space mapping framework (SMF) software. Comprehensive verification and comparison with the standard TSM are provided through several examples of microstrip filters. [ABSTRACT FROM AUTHOR]

Space mapping (SM) is one of the most popular surrogate-based optimization techniques in microwave engineering. The most critical component in SM is the low-fidelity (or coarse) model -- a physically-based representation of the structure being optimized (high-fidelity or fine model), typically evaluated using CPU-intensive electromagnetic (EM) simulation. The coarse model should be fast and reasonably accurate. A popular choice for the coarse models are equivalent circuits, which are computationally cheap, but not always accurate, and in many cases even not available, limiting the practical range of applications of SM. Relatively accurate coarse models that are available for all structures can be obtained through coarsely-discretized EM simulations. Unfortunately, such models are typically computationally too expensive to be efficiently used in SM algorithms. Here, a study of SM algorithms with coarsely-discretized EM coarse models is presented. More specifically, novel and efficient parameter extraction and surrogate optimization schemes are proposed that make the use of coarsely-discretized EM models feasible for SM algorithms. Robustness of our approach is demonstrated through the design of three microstrip filters and one double annular ring antenna. [ABSTRACT FROM AUTHOR]

An efficient technique for fast design optimisation of microwave structures is discussed. The approach is based on the recently introduced shape-preserving response prediction method (SPRP). SPRP allows us to estimate the response of the computationally expensive structure under consideration using the properly selected set of characteristic points of the physically based coarse model response. Here, the coarse model is implemented in the same electromagnetic solver as the one that evaluated the original structure, but coarse discretisation is used. It is demonstrated that the presented technique yields a satisfactory design after two or three evaluations of the original structure. The efficiency of this approach is illustrated through the design optimisation of a double annular ring antenna and two microstrip filters. Comparison with the direct EM-simulation-based optimisation of the fine model is also given. [ABSTRACT FROM AUTHOR]