Full-wave Electromagnetic Simulation Research Articles

Broadband Enhancement of Magneto-Optical Effects in Hybrid Waveguide-Plasmonic Surfaces for Sensing.

Conventional magnetophotonic nanostructures typically function within narrow wavelength and incident angle ranges, where resonance is observed and magneto-optical (MO) effects are amplified. Expanding these operational ranges may allow for improved applications, including in (bio)sensing devices. In this study, we describe a hybrid magnetoplasmonic waveguide grating (HMPWG) in which the coupling of plasmonic resonances and waveguide modes leads to enhanced MO effects and sensitivity, according to full-wave electromagnetic simulations. High transverse magneto-optical Kerr effect (TMOKE) signals were observed for the full range of wavelengths and angles investigated, i.e., for θinc ≥ 1° and 500 nm ≤ λ ≤ 850 nm. As a proof-of-concept we verified that using the HMPWG nanostructure with an aqueous solution as superstrate one may obtain a sensitivity in variation of the refractive index unit (RIU) of S = 166°/RIU and S = 230 nm/RIU in angle and wavelength interrogation modes, respectively. Upon comparing with conventional magnetoplasmonic gratings, which only enable excitation of plasmonic resonances, we demonstrate that HMPWG nanostructures can be further optimized to reach not only high sensitivity but also high resolution in sensing and biosensing.

An ultra-wideband antenna design optimization for biomedical applications using artificial neural networks

This paper presents an innovative method based on Artificial Neural Networks (ANN) for optimizing the design of microstrip antennas using HFSS software. The method leverages a dataset generated from comprehensive full-wave electromagnetic simulations to accurately predict antenna performance. In the ANN model, coefficients of reflection as input parameter, and five output parameters representing key geometrical variables of the antenna are utilized. The study demonstrates how ANNs effectively predict these variables, thereby enhancing design efficiency and significantly reducing the computational time required for antenna optimization. By providing a robust and efficient framework, the results highlight the promising potential of ANNs in optimizing antenna designs for diverse applications, including medical and wireless communication systems. Specifically, the proposed Ultra-Wideband (UWB) antenna operates over a frequency range from 5.17 GHz to 7.02 GHz and maintains an S11 value of -20.49 dB at 5.8 GHz within the Industrial, Scientific, and Medical (ISM) bands. This research contributes valuable insights into advancing electromagnetic performance through efficient antenna design methodologies.

Variable data structures and customized deep learning surrogates for computationally efficient and reliable characterization of buried objects

In this study, in order to characterize the buried object via deep-learning-based surrogate modeling approach, 3-D full-wave electromagnetic simulations of a GPR model have been used. The task is to independently predict characteristic parameters of a buried object of diverse radii allocated at different positions (depth and lateral position) in various dispersive subsurface media. This study has analyzed variable data structures (raw B-scans, extracted features, consecutive A-scans) with respect to computational cost and accuracy of surrogates. The usage of raw B-scan data and the applications for processing steps on B-scan profiles in the context of object characterization incur high computational cost so it can be a challenging issue. The proposed surrogate model referred to as the deep regression network (DRN) is utilized for time frequency spectrogram (TFS) of consecutive A-scans. DRN is developed with the main aim being computationally efficient (about 13 times acceleration) compared to conventional network models using B-scan images (2D data). DRN with TFS is favorably benchmarked to the state-of-the-art regression techniques. The experimental results obtained for the proposed model and second-best model, CNN-1D show mean absolute and relative error rates of 3.6 mm, 11.8 mm and 4.7%, 11.6% respectively. For the sake of supplementary verification under realistic scenarios, it is also applied for scenarios involving noisy data. Furthermore, the proposed surrogate modeling approach is validated using measurement data, which is indicative of suitability of the approach to handle physical measurements as data sources.

MetaPhyNet: intelligent design of large-scale metasurfaces based on physics-driven neural network

Abstract Metasurface has garnered extensive attention across multiple disciplines owing to its profound capability in electromagnetic (EM) manipulations. To determine its EM characteristics accurately, full-wave simulations are essential. These simulations necessitate significant amounts of time and memory resources, hindering the efficiency of the design process. In this article, we propose MetaPhyNet, a novel physics-driven neural network based on temporal coupled-mode theory (CMT) to address the challenges of low efficiency and high memory consumption in large-scale metasurface design. In the proposed approach, a surrogate model is developed to achieve rapid prediction of the EM responses of ultra-large-scale metasurfaces. In comparison with the full-wave EM simulation, the proposed model reduces the simulation time of the ultra-large-scale metasurface by up to two orders of magnitude and the memory consumption by more than two orders of magnitude. Our proposed approach aims to enhance the efficiency and intelligence in metasurface design by leveraging the principles of CMT within a neural network framework. Through this innovative integration of physics-based modeling and machine learning, we seek to achieve significant advancements in the design efficiency of metasurfaces. We apply the proposed model to optimize the design of two metasurface absorbers to showcase the effectiveness of our proposed approach. Simulations and experimental results are provided to demonstrate the value and impact of our approach in addressing existing challenges in full-wave EM simulation-based design optimizations of metasurfaces.

Multibeam Wideband Transmit Beamforming Using 2D Sparse FIR Trapezoidal Filters

A low-complexity multibeam wideband transmit beamformer using a 2D sparse FIR filter design capable of multiple beams is proposed as a digital building block for fully digital beamformers. The 2D sparse FIR filter has multiple trapezoid-shaped passbands pertaining to wideband beams aimed at particular directions. The proposed multibeam digital beamformer drives a uniform linear array of wideband antenna elements to achieve the wideband multibeam transmit-mode signals desired by the communication system. The 2D sparse FIR filter is designed to be optimal in the minimax sense using convex optimization techniques. Full-wave electromagnetic simulations using real antenna models confirm that the proposed wideband transmit beamformer can achieve multibeam transmission in the 1.3–2.8 GHz frequency range, with more than 70% fractional bandwidth. Furthermore, the adoption of the wideband transmit multibeam beamformer leads to a significant reduction in digital arithmetic (computational) complexity compared with previously reported wideband transmit beamformers of similar transfer function type, without deteriorating beam directionality and causing increases in the side-lobe level. The proposed sparse 2D FIR multibeam beamformer architecture is well-suited for both sub-6 GHz (legacy) band transmit beamforming, frequency range three (FR3) beamforming up to 28 GHz, and mmWave operation for emerging 5G/6G applications.

Planar non-contact microwave sensor for the detection of aqueous organic and inorganic samples

In this study, a planar microwave sensor was proposed and manufactured with the aim of detecting and categorizing concentrations of various organic substances, including methanol (CH3OH), ethanol (CH3CH2OH), and 1-butanol (CH3CH2CH2CH2OH), as well as inorganic substances such as sodium carbonate (Na2CO3), potassium carbonate (K2CO3), and sodium hydroxide (NaOH). Throughout the sensor's development, a configuration incorporating a microstrip line and a rectangular patch with a central circular aperture was employed. Full-wave electromagnetic simulation software was utilized to analyze the performance of the sensor in terms of reflection coefficients. The sensor was fabricated using a PCB material with defined properties, which included a dielectric constant of 4.3, a loss tangent of 0.025, and a thickness of 1.6 mm. The reflection coefficient (S11) was measured and analyzed using principal component analysis (PCA) to identify correlations between the classification groups and concentrations of organic and inorganic samples. Additionally, the equivalent circuit has been extracted and modeled to describe the operating mechanism of the microwave sensor. The simulation and measurement results indicate that the sensor is a suitable candidate for the detection and classification of water samples containing CH3OH, CH3CH2OH, CH3CH2CH2CH2OH, Na2CO3, K2CO3, and NaOH. The proposed microwave sensor features a surface area of 29 × 18 mm², leading to a noteworthy reduction in surface utilization compared to other breath biosensors designed for measurement purposes.

Dual-Channel Transverse Fields Radiofrequency Coils for 1.5 T Magnetic Resonance Imaging.

This theoretical study presents the design and analytical/numerical optimization of novel dual-channel transverse fields radiofrequency (RF) surface coils for 1.5 T Magnetic Resonance Imaging (MRI). The research explores a planar setup with two channels on a row with aligned spatial orientation of the RF coils, aiming to solve a common design drawback of single-channel transverse field RF coils: the reduced Field Of View (FOV) along the direction of the RF field. A significant challenge in this design is the efficient decoupling of two sets of transverse field RF coils to prevent mutual interference. Our modeling approach integrates thin wire theoretical modeling, magnetostatic computation for strip conductor coils, and their full-wave electromagnetic simulation. Key findings at 64 MHz demonstrate that strategic geometric placement among the two-channel RF coil and the introduction of geometrical asymmetry in the design of the individual RF coils does minimize the mutual inductance, paving the way for effective dual-channel MRI applications. This decoupling approach allows to enhance the FOV, providing a theoretical framework for the development of optimized dual-channel transverse field RF coil configurations. The current design was validated with full-wave numerical study at 64 MHz (1H, 1.5 T), has the potential to be extended at lower or higher frequencies, and the presence of lossy samples needs to be considered in the latter case.

Machine-learning-based global optimization of microwave passives with variable-fidelity EM models and response features

Maximizing microwave passive component performance demands precise parameter tuning, particularly as modern circuits grow increasingly intricate. Yet, achieving this often requires a comprehensive approach due to their complex geometries and miniaturized structures. However, the computational burden of optimizing these components via full-wave electromagnetic (EM) simulations is substantial. EM analysis remains crucial for circuit reliability, but the expense of conducting rudimentary EM-driven global optimization by means of popular bio-inspired algorithms is impractical. Similarly, nonlinear system characteristics pose challenges for surrogate-assisted methods. This paper introduces an innovative technique leveraging variable-fidelity EM simulations and response feature technology within a kriging-based machine-learning framework for cost-effective global parameter tuning of microwave passives. The efficiency of this approach stems from performing most operations at the low-fidelity simulation level and regularizing the objective function landscape through the response feature method. The primary prediction tool is a co-kriging surrogate, while a particle swarm optimizer, guided by predicted objective function improvements, handles the search process. Rigorous validation demonstrates the proposed framework's competitive efficacy in design quality and computational cost, typically requiring only sixty high-fidelity EM analyses, juxtaposed with various state-of-the-art benchmark methods. These benchmarks encompass nature-inspired algorithms, gradient search, and machine learning techniques directly interacting with the circuit's frequency characteristics.

Two bits dual-band switchable terahertz absorber enabled by composite graphene and vanadium dioxide metamaterials

This article presents the design of a 2-bit dual-band switchable terahertz absorber using a stacked combination of graphene and vanadium dioxide (VO2) metamaterials. For the first time, the proposed absorber design offers four switchable states by controlling the conductivity of graphene and VO2 metamaterial layers. The lower absorption band is produced by the graphene metamaterial, whereas the upper band is implemented by the VO2 metamaterial pattern. The structure shows two absorption bands (State 11) at 0.745–0.775 THz and 2.3–5.63 THz, when the Fermi graphene level of graphene is 0.2 eV and the VO2 is in the metallic phase. The lower absorption band is turned off, while keeping the upper band (State 01), when the graphene Fermi level is 0 eV and the VO2 layer is in the metallic phase. The upper absorption band is turned off, while preserving the lower absorption band (State 10) by switching the VO2 into the insulator phase and keeping the graphene Fermi level at 0.2 eV. Finally, both of the absorption bands are turned off by setting the graphene Fermi level to 0 eV and switching the VO2 into the insulating phase. Equivalent circuit modelling analysis and full-wave electromagnetic simulations are used to explain the operation principle of the proposed absorber. Very good agreement is obtained between the theoretical analysis and the simulations confirming the presented design principle for the 2-bit switchable absorber.

Design circular polarized antenna at ISM band for WBAN using parasitic elements

This work represents a single layer wide band circular polarized (CP) antenna with broadside high gain. The antenna configuration comprises an elliptical patch serving as the main radiating element, accompanied by eight parasitic components positioned on the same plane as the patch. This setup demonstrates an enhancement in the antenna's bandwidth and gain in the broadside direction compared to conventional antennas. A detailed analysis of the significant modes, using the characteristic mode analysis (CMA) approach, has been employed to optimize the antenna. This optimization has resulted in a notable increase in the 3-dB axial ratio (AR) bandwidth and radiation gain in the broadside direction, attributed to the presence of extra harmonics and the improved aperture efficiency of the parasitic elements. The significant modes are excited via a full-wave electromagnetic (EM) simulation, utilizing a 50 Ω coaxial feed line in the primary antenna. Furthermore, the proposed antenna's functionality is examined through an analysis based on an equivalent circuit model (ECM). To demonstrate the feasibility of the design approach, an antenna prototype is fabricated on a low-cost FR4 material, occupying an overall volume of 0.58λo×0.58λo×0.030λo (λo is the center operating. frequency). The measured results demonstrate that the suggested antenna operates within a frequency band ranging from 5485 to 6130 MHz for |S11| −10 dB, and the 3-dB axial ratio ranges from 5680 to 5900 MHz. Moreover, the fabricated antenna demonstrates a high gain radiation of 7–7.05 dBi cover the ISM band for biomedical applications.

Design of a binary programmable transmitarray based on phase change material for beam steering applications in D-band

This paper introduces the design of a reconfigurable transmitarray operating within the D-band frequency range (110–170 GHz). The transmitarray unit cell is composed of three metal layers and two quartz dielectric substrates. It achieves a 1-bit phase shift resolution through the alternating states of two innovative switches integrated into the active transmitting patch of the unit cell. To address the challenge of miniaturization in the D-band, compact switches compatible with the proposed unit cell dimensions are introduced. These switches are constructed using phase change materials (PCM) that change between amorphous and crystalline states when exposed to heat. The paper includes a full-wave simulation of the unit cell, demonstrating an insertion loss below 1.5 dB across a wide frequency band of 27%. Additionally, a 10 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes $$\\end{document} 10 elements transmitarray is synthesized using a numerical tool and its theoretical results are compared to full-wave electromagnetic simulations for validation purposes. The results indicate that by incorporating the proposed switches into the unit cell, the transmitarray achieves promising reconfiguration capabilities within the D-band. Moreover, the paper presents the architecture of a command line designed to bias the PCM switches. Notably, this command line represents a novel approach, as it enables individual biasing of each PCM switch using direct current (DC). The influence of these command lines on the transmitarray’s performance is thoroughly investigated. Although there is a compromise in the 1-dB gain bandwidth, the overall behavior of the transmitarray remains encouraging.

Using the CLEAN Method in Three-Dimensional Polarimetric ISAR Imaging Based on Volumetric Scattering Points

We developed a new technique for generating three-dimensional monostatic inverse synthetic aperture radar (ISAR) images using various types of polarimetric information on targets. To remove clutter around a target, we adopted the CLEAN method, in which only the main signals were reconstructed using an iterative algorithm. We conducted a simulation as follows: electric field data that were subjected to polarimetric scattering were obtained for the target using a full-wave electromagnetic analysis simulator. The linear polarization data of a 2 × 2 matrix were compressed into the linear to circular polarization data of a 2 × 1 matrix using the Jones vector based on circular polarization. On the grounds of the post-processed data, inverse Fourier transform was carried out to map scattering points to the spatial domain, after which the CLEAN method was used to retain only the primary scattering points.

On Accelerated Metaheuristic-Based Electromagnetic-Driven Design Optimization of Antenna Structures Using Response Features

Development of present-day antenna systems is an intricate and multi-step process requiring, among others, meticulous tuning of designable (mainly geometry) parameters. Concerning the latter, the most reliable approach is rigorous numerical optimization, which tends to be resource-intensive in terms of computing due to involving full-wave electromagnetic (EM) simulations. The cost-related issues are particularly pronounced whenever global optimization is necessary, typically carried out using nature-inspired algorithms. Although capable of escaping from local optima, population-based algorithms exhibit poor computational efficiency, to the extent of being hardly feasible when directly handling EM simulation models. A popular mitigation approach involves surrogate modeling techniques, facilitating the search process by replacing costly EM analyses with a fast metamodel. Yet, surrogate-assisted procedures feature complex implementations, and their range of applicability is limited in terms of design space dimensionality that can be efficiently handled. Rendering reliable surrogates is additionally encumbered by highly nonlinear antenna characteristics. This paper investigates potential benefits of employing problem-relevant knowledge in the form of response features into nature-inspired antenna optimization. As demonstrated in the recent literature, re-formulating the design task with the use of appropriately selected characteristic locations of the antenna responses permits flattening the functional landscape of the objective function, leading to faster convergence of optimization procedures. Here, we apply this concept to nature-inspired global optimization of multi-band antenna structures, and demonstrate its relevance, both in terms of accelerating the search process but also improving its reliability. The advantages of feature-based nature-inspired optimization are corroborated through comprehensive (based on three antenna structures) comparisons with a population-based search involving conventional (e.g., minimax) design problem formulation.

A systematic approach for the development of wide band band pass filters using resonators

In this paper, for the first time a novel and systematic approach is presented to construct a wideband Band Pass Filters (BPFs) with high selectivity and stopband response. Two BPFs (Filter I and Filter II) were built on a Taconic (TLX-9) substrate using semi-circular tapered coupled lines, Defected Microstrip Structures (DMSs), Defected Ground Structures (DGS), and Stepped Impedance Resonators (SIRs). The precision of the design procedure is confirmed through 3-D full wave Electro-Magnetic (EM) simulation software where two wideband filters were designed for L, S, and C-bands. Additionally, parametric analysis has been done to evaluate the performance of both wideband filters with key features such as return loss, insertion loss, Band Width (BW), selectivity, and stopband response. Even-odd mode analysis has been implemented using the ABCD matrix that acts as a source for mathematical analysis of Filter I. Eventually, two wideband filters have been fabricated and tested for their effectiveness, and the measured results of two wideband filters are in line with the simulated ones with slight deviations due to fabrication tolerances and connector losses. The prototyped Filter I functions as a bandpass in the frequency range of 2.4 GHz to 4.8 GHz with a maximum insertion loss of 0.85 dB and return loss of 19.5 dB thereby providing 64% Fractional Band Width (FBW). Near 19 dB rejection is observed in the lower and upper stopband regions with BW (stopbands) greater than 2 GHz. Moreover, Filter II is also fabricated and tested. The experimental return loss of 20 dB and insertion loss (maximum) of 0.73 dB over the passband (1.9 GHz to 3.4 GHz) were found with 0.7 Selectivity Factor (SF). More than 20 dB attenuation of stopbands (lower and upper) was achieved. Thus, the fabricated wideband BPFs operate in L, S, and C-bands for radars, satellite and long-distance radio communications, and military telemetry applications.

WLAN monopole antenna design by Siamese convolutional neural network and KNN exploiting Gaussian process

In the process of antenna design, surrogate models can generally be used, but modeling requires a large number of samples. Although full wave electromagnetic simulation software can handle this task, obtaining a large number of samples is time-consuming, however too small number of sample may lead to lower accuracy of the trained surrogate model. Inspired by semi-supervised learning methods, this paper uses Siamese convolutional neural networks (SCNN) and K-nearest neighbor (KNN) algorithms to generate highly reliable virtual samples and expand the training sample set, further improving the accuracy and robustness of the surrogate model by exploiting Gaussian process (GP) models. The proposed method is named SCNN-KNN-GP, which is used for the design of WLAN dual band monopole antennas. Moreover, the relationships between the performance of the proposed model and the increased number of virtual samples and the coefficient of the KNN are studied, resulting in a more excellent surrogate model structure.

Optimization Assisted by Neural Network-Based Machine Learning in Electromagnetic Applications

We introduce an optimization assisted by a neural network (ONN) predictor to the electromagnetic community. ONN belongs to the class of the surrogate model-based optimization approaches, and approximates the objective function using a non-linear approximator – neural network. We provide a comprehensive description of the ONN algorithm and the details of its mathematical formulations. We apply ONN to optimize three popular benchmark functions and compare its performance with some commonly used optimization algorithms, namely particle swarm optimization, genetic algorithm, and Bayesian optimization. For the first time, we demonstrate ONN’s applicability and effectiveness in antenna design problems by optimizing a six-element Yagi-Uda antenna and by solving a challenging ten-dimensional dual-band slotted patch antenna constrained optimization problem. To achieve this, ONN is linked with a full-wave electromagnetic simulation solver through an application user interface. The optimized slotted patch is fabricated and measured to demonstrate how ONN can be part of the full antenna design process. Our empirical results indicate that ONN requires less objective function evaluations to reach the same qualitative point and reaches better optimal points for the same number of iterations for the studied benchmark functions and antenna optimization problems compared to the aforementioned baseline optimization algorithms.

The effect of frequency (64-498MHz) on specific absorption rate adjacent to metallic orthopedic screws in MRI: A numerical simulation study.

The imaging of patients with implanted electrically-conductive devices via magnetic resonance imaging at ultra-high fields is hampered by uncertainties relating to the potential for inducing tissue heating adjacent to the implant due to coupling of energy from the incident electromagnetic field into the implant. Existing data in the peer-reviewed literature of comparisons across field strengths of tissue heating and its surrogate, the specific absorption rate (SAR), is scarce and contradictory, leading to further doubts pertaining to the safety of imaging patients with such devices. The radiofrequency-induced SAR adjacent to orthopedic screws of varying length and at frequencies of 64 to 498MHz was investigated via full-wave electromagnetic simulations, to provide an accurate comparison of SAR across MRI field strengths. Dipole antennas were used for RF transmission to achieve a uniform electric field tangential to the screws located 120mm above the antenna midpoints, embedded in a bone-mimicking material. The input power to the antennas was constrained to achieve the following targets without the screw present: (i) E=100V/m, (ii) B1 + =2 μT, and (iii) global-average-SAR=3.2W/kg. Simulations were performed with a spatial resolution of 0.2mm in the volume surrounding the screws, resulting in 76-137 MCells, noting the maximum 1g-averaged SAR value in each case. Simulations were repeated at 128 and 297MHz for screws embedded in muscle tissue. The peak SAR, occurring at the resonant screw length, substantially increased as the frequency decreased when the input power to the dipole antenna was constrained to achieve constant electric field in background tissue at the screws' locations. A similar pattern was observed when constraining input power to achieve constant B1 + and global-average-SAR. The dielectric properties of the tissue in which the screws were embedded dominated the SAR comparisons between 297 and 128MHz. The study design allowed for a direct comparison to be performed of SAR across frequencies and implant lengths without the confounding effect of variable incident electric field. Lower frequencies produced substantially larger SAR values for implants approaching the resonant length for the worst-case uniform incident electric field along the screws' length. The data may inform risk-benefit assessments for imaging patients with orthopedic implants at the new clinical field strength of 7Tesla.

Polarization-insensitive graphene-based THz rasorber with ATA characteristics

This paper presents a polarization-insensitive rasorber implemented with absorption-transmission-absorption (ATA) characteristics over three consecutive frequency ranges in the terahertz (THz) band. The proposed rasorber is made of a two-layer periodic structure. These two layers are separated by a spacer made of glass substrate. The unit cells of the top layer have a modified swastika geometry metallization, which is loaded with graphene strips to make it lossy and provide dual-band absorption. In the bottom plane frequency selective surface (FSS), a square ring is engraved on the metal layer to obtain bandpass characteristics between two stopbands provided by the top layer. The designed rasorber works in the THz frequency range. It provides wideband absorption with a from to THz with a fractional bandwidth (BW) of around An in-band transmission window is designed with a in the frequency of to THz provides a large BW of GHz () for THz communication. Within this transmission band, the lowest insertion loss of is obtained at 0.686 THz. It provides the absorption of more than in both the lower band ( THz, BW) and the higher band ( THz, BW). The simulated response of the designed rasorber using a full-wave electromagnetic simulator and calculated through ECM are found to be in good agreement.

Systematic methods for the synthesis of equidistant MIMO arrays

Abstract. Finding a feasible antenna arrangement for multiple input multiple output (MIMO) arrays to serve a specific purpose is a first crucial step towards a successful MIMO radar system design. Design methods to synthesize uniformly weighted and equidistant MIMO arrays are proposed and investigated. The methods can be used to gain a design foundation for 1D or 2D arrays without software tools or programming effort. Since the presented approach does not consider electromagnetic fields, electromagnetic full-wave simulations might be required additionally. The method is based on sequentially copying and displacing antenna groups with the help of a number scheme. A nomenclature is proposed to classify the degrees of freedom in the design procedure. If the antennas are aligned to a uniform grid, a polynomial representation of the array can be chosen alternatively. This method is beneficial when redundancies of a produced array and where they appear must be analyzed. A new design problem arises when an array is to consist of only transceiving antennas, which can be analyzed with polynomial multiplication. One strategy to find a suitable MIMO array consisting of transceiver elements is given and evaluated.

Analytical equivalent circuit modeling and analysis of complex BGA for 3D silicon-interposer packaging

Through analyzing different cross-sections of the complex ball grid array (CBGA) sandwiched by silicon interposers, various distributed capacitances of the CBGA and the significance of the CBGA's coplanar capacitances are revealed. From the analyses, the composition of the CBGA's capacitance is found to have similarity with that of the coplanar waveguide's capacitance. Based on the electric-field coupling mechanism of the coplanar waveguide, geometrical analysis of the CBGA, and analysis of multiconductor transmission lines, analytical equations are derived to allow accurate modeling the equivalent circuit of the CBGA for 3D silicon-interposer packaging. The modeled equivalent circuit of the CBGA is validated with the full wave electromagnetic simulation, and it is demonstrated to have a good accuracy up to 40 GHz. Moreover, the CBGA structure can be further optimized for impedance matching with the guidance of the derived analytical equations.