Efficient Design Optimization of Microwave Structures Using Adjoint Sensitivity

Passive resonators have been widely used in MRI to manipulate RF field distributions. However, optimizing these structures using full-wave electromagnetic (EM) simulations is computationally prohibitive, particularly for massive-element passive resonator arrays with many degrees of freedom. While EM and RF circuit co-simulation methods have previously been applied to RF coil design, this work presents a co-simulation framework specifically tailored for the analysis and optimization of passive resonators. The framework performs a single full-wave EM simulation in which the resonator's lumped components are replaced by ports, followed by circuit-level computations to evaluate arbitrary capacitor/inductor configurations. This allows integration with a genetic algorithm to rapidly optimize the resonator parameters to enhance B1 fields in a targeted region of interest. The proposed method was validated across three scenarios of increasing complexity: (1) a single-loop passive resonator on a spherical phantom, (2) a two-loop array on a cylindrical phantom, and (3) a two-loop array on a human head model. In all cases, the co-simulation results showed excellent agreement with full-wave EM simulations, with relative errors below 1%. The genetic-algorithm-driven optimization, involving tens of thousands of capacitor combinations, completed in under 5 minutes-whereas equivalent full-wave EM sweeps would require an impractically long computation time. To the best of our knowledge, this work represents the first systematic extension of the co-simulation methodology to passive resonator design, enabling fast, accurate, and scalable optimization. The approach significantly reduces computational burden while preserving full-wave accuracy, making it a powerful tool for passive RF structure development in MRI.

We inferred the effective sheath width using the cutoff probe and incorporating a full-wave three-dimensional electromagnetic (EM) simulation. The EM simulation reproduced the experimentally obtained plasma-sheath resonance (PSR) on the microwave transmission (S21) spectrum well. The PSR frequency has a one-to-one correspondence with the width of the vacuum layer assumed to be the effective sheath in the EM simulation model. The sheath width was estimated by matching the S21 spectra of the experiment and the EM simulation for different widths of the sheath. We found that the inferred sheath widths quantitatively and qualitatively agree with the sheath width measured by incorporating an equivalent circuit model. These results demonstrate the excellent potential of the cutoff probe for inferring the effective sheath width from its experimental spectrum data.

Accurate responses of antennas, in many cases, can be obtained only with discrete full-wave electromagnetic (EM) simulations. Therefore, contemporary antenna design strongly relies on these EM simulations. On the other hand, direct use of high-fidelity EM simulations in the design process, particularly for automated parameter optimization, often results in prohibitive computational costs. In this chapter, we illustrate how the designs of various antennas can be obtained efficiently using an automated surrogate-based optimization (SBO) methodology. The SBO techniques considered here include the adaptive design specification technique, variable-fidelity simulation-driven optimization, and shape-preserving response prediction. The essence of these techniques resides in shifting the optimization burden to a fast surrogate of the antenna structure, and using coarse-discretization EM models to configure the surrogate. A properly created and handled surrogate serves as a reliable prediction tool allowing satisfactory designs to be obtained at the cost of a few simulations of the high-fidelity antenna model. We also demonstrate the effect of the coarse-discretization model fidelity on the final design quality and the computational cost of the design process. Finally, we give an example of automatic management of the coarse model quality. Recommendations concerning the application of specific SBO techniques to antenna design are also presented.

Electromagnetic (EM) simulators have already become established in the design of a variety of electromagnetic devices, such as MMICs (monolithic microwave integrated circuits), antennas, shields, electromechanical machines, and magnetic circuits. Such broad applicability results from the fact that the EM simulators are software packages for numerically solving the Maxwell’s fundamental electromagnetic field equations; for the same reason, and unlike some of the other simulators, they are independent of technology, models, foundry, and other such ephemeral considerations. Although designers have long carried out electromagnetic analysis of RF components and packages where necessary, the availability of commercial EM simulators1’2 since 1989 has made this task much more common, rapid, and easier. This development parallels the concurrent development of multi-chip module (MCM) technology for high-speed digital systems, as well as the front-ends of radio-frequency (RF) systems, such as receivers, transponders, transceivers, synthesizers, and transmit-receive modules. MCMs are a modern method of electronic packaging and integration that has the advantages of low-cost, compact size, and reliability. At low speeds/frequencies, the analysis, design, simulation, layout, and verification, of MCMs requires a number of software tools for computer-aided design (CAD), including process simulators, device simulators, circuit simulators, thermal simulators, and system simulators. For high-speed and RF MCMs, the design requirements make an additional CAD tool, namely EM simulator, indispensable.

The presence of the uncertainties introduced in the fabrication processes lead to inherent randomness in physical dimensions of microwave components. As such, it is of particular importance to perform statistical analysis and yield optimization before putting a component into production. As electromagnetic (EM)-based adjoint sensitivity techniques have become commercially available these years, it is possible to perform direct yield optimization using full-wave EM simulators. However, the requirement of intensive simulations to cover the entire statistic of possible outcomes makes direct yield optimization computationally prohibitive. In this paper, we propose to apply parallel computation, which is a powerful tool to speed up full-wave EM simulations, to yield optimization of microwave components. With parallel computation technique, the total yield optimization time is significantly reduced compared with the conventional sequential yield optimization method. The proposed technique is demonstrated by a four-pole waveguide filter.

Multiobjective optimization is one of the key challenges in engineering design process. Since the answer to such problem is not unique, a set of evenly distributed solutions is particularly important for a designer. The Directed Search Domain (DSD) method is a numerical optimization approach that has proven to be efficient enough to tackle such optimization problems. In this paper, we propose two modifications to the DSD approach which make the solution algorithm simpler for program implementation. These modifications are related to the control of the search domain and reformulation of the appropriate single objective optimization problem. As a result, the computational efficiency of the method is increased due to the lower number of objective function evaluations. The capabilities of the new approach are demonstrated on a set of test cases.

Yield-driven optimization is important in microwave design due to the uncertainties introduced in the manufacturing process. For the first time, we extend in this paper the use of polynomial chaos (PC) approach from electromagnetic (EM)-based yield estimation to EM-based yield optimization of microwave structures. We first formulate a novel objective function for yield-driven EM optimization. By incorporating the PC coefficients into the formulation, the objective function is analytically related to yield optimization variables, which are the nominal point. We then derive the sensitivity formulas of the PC coefficients with respect to the nominal point, following which we derive the sensitivities of the optimization objective function with respect to yield optimization variables. These sensitivities are then used in gradient-based optimization algorithms to find the optimal yield solution iteratively. The proposed objective function requires fewer EM simulations to provide reliable yield representation than that in the conventional Monte Carlo-based yield optimization approach. As a result, the number of EM simulations required to find the update direction and suitable step size for the change of the nominal point is reduced at each iteration of optimization. This allows the proposed approach to achieve similar yield increase using much fewer EM simulations or greater yield increase using similar number of EM simulations compared to the conventional yield optimization approach. The advantages of our proposed approach are demonstrated by yield-driven EM optimization of three waveguide filter examples.

Purpose Development of techniques for expedited design optimization of complex and numerically expensive electromagnetic (EM) simulation models of antenna structures validated both numerically and experimentally. The paper aims to discuss these issues. Design/methodology/approach The optimization task is performed using a technique that combines gradient search with adjoint sensitivities, trust region framework, as well as EM simulation models with various levels of fidelity (coarse, medium and fine). Adaptive procedure for switching between the models of increasing accuracy in the course of the optimization process is implemented. Numerical and experimental case studies are provided to validate correctness of the design approach. Findings Appropriate combination of suitable design optimization algorithm embedded in a trust region framework, as well as model selection techniques, allows for considerable reduction of the antenna optimization cost compared to conventional methods. Research limitations/implications The study demonstrates feasibility of EM-simulation-driven design optimization of antennas at low computational cost. The presented techniques reach beyond the common design approaches based on direct optimization of EM models using conventional gradient-based or derivative-free methods, particularly in terms of reliability and reduction of the computational costs of the design processes. Originality/value Simulation-driven design optimization of contemporary antenna structures is very challenging when high-fidelity EM simulations are utilized for performance utilization of structure at hand. The proposed variable-fidelity optimization technique with adjoint sensitivity and trust regions permits rapid optimization of numerically demanding antenna designs (here, dielectric resonator antenna and compact monopole), which cannot be achieved when conventional methods are of use. The design cost of proposed strategy is up to 60 percent lower than direct optimization exploiting adjoint sensitivities. Experimental validation of the results is also provided.

In this research, the design and practical realization of microstrip Band-Stop (BS) filter using FR-4 substrate is presented. FR-4 is low-cost substrate with varying dielectric constant, especially at higher frequencies. Therefore, the measurement of FR-4 dielectric constant based on open resonant cavity method is used. Various samples of Printed Circuit Boards (PCB) were used for measurement. The results acquired from measurements of PCBs were different for each piece of PCB. Finally, it turned out that precision of measurement method is dependent on geometric dimensions of PCBs. Obtained frequency dependent dielectric constant improves accuracy of mathematical model of BS filter created in MATLAB. This model also includes attenuation losses in both copper and substrate materials. For verification of filter model created in MATLAB, scattering parameters of various filter models were compared with scattering parameters of same models obtained from full-wave Electro-Magnetic (EM) simulator. One of these BS filter configurations was practically realized. Scattering parameters of MATLAB filter models, filter models created in full-wave EM simulator and practically realized BS filter are in very good agreement.

Microstrip circuits form the backbone of modern high-frequency communication systems, offering compact and efficient solutions for signal processing and transmission. However, the design of these circuits is challenging due to the intricate interplay of electromagnetic (EM) parameters, material properties, and circuit dimensions. Traditional EM simulation methods, while accurate, are computationally intensive and time-consuming, limiting their applicability for rapid prototyping and optimization. To address these challenges, this study integrates deep learning techniques with electromagnetic simulations to enhance microstrip circuit design efficiency. A Recurrent Neural Network (RNN)-based framework is proposed to predict the frequency-dependent behavior of microstrip circuits, leveraging temporal data from iterative EM simulations. The RNN model is trained on a diverse dataset of simulated circuit configurations, capturing the relationships between physical parameters, design constraints, and performance metrics. The proposed approach significantly reduces computational overhead by approximating the results of full-wave EM simulations while maintaining high accuracy. Validation against benchmark EM simulation tools shows that the RNN model achieves over 95% prediction accuracy with a 70% reduction in simulation time. Additionally, this framework enables real-time optimization of circuit designs, accelerating the iterative design process without compromising performance.

Full-wave electromagnetic (EM) simulation models are ubiquitous in carrying out design closure of antenna structures. Yet, EM-based design is expensive due to a large number of analyses necessary to yield an optimized design. Computational savings can be achieved using, for example, adjoint sensitivities, surrogate-assisted procedures, design space dimensionality reduction, or similar sophisticated means. In this article, a simple modification of a rudimentary trust-region-embedded gradient search with numerical derivatives is proposed for reduced-cost optimization of input characteristics of wideband antennas. The approach exploits information and history of relative changes of the design (as compared with the trust region size) during algorithm iterations to control the updates of components of the antenna response Jacobian, specifically, to execute them only if necessary. It is demonstrated that the proposed framework may lead to over 50% savings over the reference algorithm with only minor degradation of the design quality, specifically, up to 0.3 dB (or <3%). Numerical results are supported by experimental validation of the optimized antenna designs. The presented algorithm can be utilized as a stand-alone optimization routine or as a building block of surrogate-assisted procedures.

This article tackles the generalized synthesis of antenna arrays using two-order deep learning. Existing deep learning-assisted antenna synthesis approaches mainly rely on model training using electromagnetic (EM) simulation data, and hence feature limited generalization ability and the need for a huge amount of EM simulations. The proposed two-order deep learning method uses the first-order model to learn the generic features of radiation patterns from the data efficiently generated by applying conventional array factors. After that, the second-order model learns from EM simulations to capture the detailed pattern variations due to concrete coupling effects in the case of a specific array arrangement with different operating frequencies, radiation structures, and feeding schemes. Therefore, the two-order DL model can predict the radiation patterns of a series of antenna arrays while reducing the needed amount of EM simulation data. Implementation is carried out on a series of patch antenna arrays to verify the feasibility and robustness of the proposed approach. The validation includes conditions for the array operating at arbitrary new frequencies, with modified radiation structures or new feeding schemes. The results show that the proposed two-order model provides a prediction accuracy of about 84 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> for a series of 1 × 4 antenna arrays, clearly outperforming the existing regular one-order DL model, which obtains around 65 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> with the same EM simulation data. The proposed method reveals a promising direction for applying deep learning to assist the design and analysis of antenna arrays.

This paper studies the accuracy and limitations of different electromagnetic (EM) simulation approaches for dielectric radar benchmark targets. In comparison to perfect electric conductors (PEC), dielectric targets are much more complex from an EM point of view. However, dielectric materials are widely used for modern aircraft and unmanned aerial vehicles (UAVs). Apart from that, EM simulation tools nowadays play an important role in the design of aerial vehicles and radar systems. In order to evaluate the accuracy and performance of different EM simulation approaches, the results obtained using Physical Optics in combination with a ray tracing approach are compared to full-wave reference data.

This study proposes an antenna simulation framework powered by graphics processing units (GPUs) based on an open-source electromagnetic (EM) simulation software (gprMax) for machine learning applications of antenna design and optimization. Furthermore, it compares the simulation results with those obtained through commercial EM software. The proposed software framework for machine learning and surrogate model applications will produce antenna data sets consisting of a large number of antenna simulation results using GPUs. Although machine learning methods can attain the optimum solutions for many problems, they are known to be data-hungry and require a great deal of samples for the training stage of the algorithms. However, producing a sufficient number of training samples in EM applications within a limited time is challenging due to the high computational complexity of EM simulations. Therefore, GPUs are utilized in this study to simulate a large number of antennas with predefined or random antenna shape parameters to produce data sets. Moreover, this study also compares various machine learning and deep learning models in terms of antenna parameter estimation performance. This study demonstrates that an entry-level GPU substantially outperforms a high-end CPU in terms of computational performance, while a high-end gaming GPU can achieve around 18 times more computational performance compared to a high-end CPU. Moreover, it is shown that the open-source EM simulation software can deliver similar results to those obtained via commercial software in the simulation of microstrip antennas when the spatial resolution of the simulations is sufficiently fine.

A robust and computationally efficient technique for microwave design optimization is presented. Our approach exploits variable-fidelity electromagnetic (EM) simulation models and adjoint sensitivities. The low-fidelity EM model correction is realized by means of space mapping (SM). In the optimization process, the SM parameters are optimized together with the design itself, which allows us to keep the number of both low- and high-fidelity simulations at low levels. The algorithm is demonstrated using two examples. Experimental validation is also provided.