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Numerical Methods and Measurements in Antennas and Propagation

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A special issue of Electronics (ISSN 2079-9292). This special issue belongs to the section "Microwave and Wireless Communications".

Deadline for manuscript submissions: closed (15 February 2022) | Viewed by 41785

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Special Issue Editors

Prof. Dr. Enrique A. Navarro-Camba

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Guest Editor

IRTIC Institute/ETSE, Universitat de Valencia, 46100 Burjassot (Valencia), Spain
Interests: numerical methods and measurements in electromagnetics; antennas; and propagation

Prof. Dr. Nagula Sangary

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Guest Editor

Centre for Intelligent Antenna and Radio Systems (CIARS), University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada
Interests: antennas; EM numerical simulation; wireless communication

Special Issue Information

Dear Colleagues,

In wireless communications systems, the antennas perform two very important functions, adapt the signal that leaves the transmission lines of devices to free space, and direct the radiation of microwave energy in the desired directions of space. Antennas also allow spatial multiplexing of the signal to give greater capacity to wireless transmissions to accommodate the multitude of users and devices, which is critical for the wireless internet (Internet of Things - IoT). From the first cellular deployments, 2G, 3G, 4G to current 5G deployment and the emerging satellite communications, all systems depend on the development of new antennas. The antennas are passive devices whose proper design would relax the requirement of front-end elements . An improvement on antenna gain reduces the gain requirement on the transmitter RF Power-Amplifier, which is a complex active device. Similarly, on the receiver side, it can reduce the stringent noise figure requirement of the Low-Noise-Amplifier.

Design and analysis of antennas involve the resolution of Maxwell's equations with complex boundary conditions, and in many cases, numerical techniques are the only option. Since the end of the 80s, there has been a strong development of numerical techniques in parallel with the growth of the computational capacity of computers. Firstly, the application of the Finite Elements Method (FEM) and Finite Differences, which already had a long tradition in the analysis of mechanical structures. Then the Boundary Element Method, (BEM), Transmission Line Matrix (TLM) and finally, a new numerical technique emerged especially and specifically to solve Maxwell's equations, FDTD or Finite Differences in the Time Domain. All these techniques with their variants were applied to the design, analysis and development of microwave devices and antennas.

Experimental characterization of antennas is a sophisticated task that requires highly specific installations depending on the type of measurement, the dimensions of the antenna relative to the wavelength, and the frequency of measurement. In this special issue the topics of interest include, but are not limited to:

Techniques FDTD, TLM, FEM, BEM and their variants in the numerical modeling of antennas.
Advanced techniques for numerical modeling of antennas.
Antenna measurement systems in near field with transformation to far field.
Compact Range measurement systems.
Advanced Antenna measurement systems.
Phased Array Antenna systems.

Prof. Dr. Enrique A. Navarro-Camba
Prof. Dr. Nagula Sangary
Guest Editors

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Electronics is an international peer-reviewed open access semimonthly journal published by MDPI.

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Published Papers (13 papers)

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Research

24 pages, 3793 KiB

Open AccessArticle

Thermal Evaluation of a Micro-Coaxial Antenna Set to Treat Bone Tumors: Design, Parametric FEM Modeling and Evaluation in Multilayer Phantom and Ex Vivo Porcine Tissue

by Texar Javier Ramírez-Guzmán, Citlalli Jessica Trujillo-Romero, Raquel Martínez-Valdez, Lorenzo Leija-Salas, Arturo Vera-Hernández, Genaro Rico-Martínez, Rocío Ortega-Palacios and Josefina Gutiérrez-Martínez

Electronics 2021, 10(18), 2289; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics10182289 - 17 Sep 2021

Cited by 9 | Viewed by 2274

Abstract

Bone cancer is rare in adults, the most affected persons by this disease are young people and children. The common treatments for bone cancer are surgery, chemotherapy, and targeted therapies; however, all of them have side-effects that decrease the patient’s quality of life. Thermotherapy is one of the most promising treatments for bone cancer; its main goal is to increase the tumor temperature to kill cancerous cells. Although some micro-coaxial antennas have been used to treat bone tumors, most of them are designed to treat soft tissue. Therefore, the purpose of this work is to analyze the thermal behavior of four micro-coaxial antennas specifically designed to generate thermal ablation in bone tissue to treat bone tumors, at 2.45 GHz. The proposed antennas were the metal-tip monopole (MTM), the choked metal-tip monopole (CMTM), the double slot (DS) and the choked double slot (CDS). The design and optimization of the antennas by using the Finite Element Method (FEM) allow to predict the optimal antenna dimensions and their performance when they are in contact with the affected biological tissues (bone, muscle, and fat). In the FEM model, a maximum power transmission was selected as the main parameter to choose the optimum antenna design, i.e., a Standing Wave Ratio (SWR) value around 1.2–1.5. The four optimized antennas were constructed and experimentally evaluated. The evaluation was carried out in multilayer phantoms (fat, muscle, cortical, and cancellous bone) and ex vivo porcine tissue at different insertion depths of the antennas. To fully evaluate the antennas performance, the standing wave ratio (SWR), power loss, temperature profiles, and thermal distributions were analyzed. In the experimentation, the four antennas were able to reach ablation temperatures (>60 °C) and the highest reached SWR was 1.7; the MTM (power loss around 16%) and the CDS (power loss around 6.4%) antennas presented the lowest SWR values depending on the antenna insertion depth, either in multilayer tissue phantom or in ex vivo tissue. These proposed antennas allow to obtain ablation temperatures with an input power of 5 W after 5 min of treatment; these values are lower than the ones reported in the literature. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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10 pages, 768 KiB

Open AccessArticle

Analysis of an Inhomogeneous Circularly Polarized Hollow Dielectric Resonator Antenna Using Perturbation Theory

by Neetu Sehrawat, Binod Kumar Kanaujia, Anshul Agarwal and Gaurav Varshney

Electronics 2021, 10(18), 2273; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics10182273 - 16 Sep 2021

Viewed by 1440

Abstract

The perturbation approach is presented here for the first time for the analysis of an inhomogeneous circularly polarized rectangular dielectric resonator (DR) antenna (DRA). The inhomogeneous permittivity is created by perturbing a rectangle-shaped region of different material inside the rectangular dielectric resonator antenna [...] Read more.

{TE}_{111}^{x}

, and

{TE}_{111}^{y}

, are excited simultaneously for achieving circular polarization. A simple expression for the calculation of the resonant frequency and optimal axial ratio point for a circularly polarized (CP) inhomogeneous RDRA is presented here. Theoretical results obtained from the proposed theory are compared with theoretical, simulated, and experimental data available in the literature. The proposed analysis results show optimal axial ratio point calculations within a 1% range of the simulated and experimental data, which is better than the previous transverse transmission line reported method, having an error of approximately 4%. The advantages, accuracy, and simplicity of perturbation theory for DR are discussed in detail. The proposed theory can be easily extended for higher order modes and other shapes of material perturbation and anisotropic DRAs. The proposed technique will help in incorporation of the perturbation in the DR so that CP radiation can be obtained in an easy way. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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27 pages, 5827 KiB

Open AccessArticle

Design & Optimization of Large Cylindrical Radomes with Subcell and Non-Orthogonal FDTD Meshes Combined with Genetic Algorithms

by Enrique A. Navarro, Jorge A. Portí, Alfonso Salinas, Enrique Navarro-Modesto, Sergio Toledo-Redondo and Jesús Fornieles

Electronics 2021, 10(18), 2263; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics10182263 - 15 Sep 2021

Cited by 3 | Viewed by 1946

Abstract

The word radome is a contraction of radar and dome. The function of radomes is to protect antennas from atmospheric agents. Radomes are closed structures that protect the antennas from environmental factors such as wind, rain, ice, sand, and ultraviolet rays, among others. The radomes are passive structures that introduce return losses, and whose proper design would relax the requirement of complex front-end elements such as amplifiers. The radome consists mostly in a thin dielectric curved shape cover and sometimes needs to be tuned using metal inserts to cancel the capacitive performance of the dielectric. Radomes are in the near field region of the antennas and a full wave analysis of the antenna with the radome is the best approach to analyze its performance. A major numerical problem is the full wave modeling of a large radome-antenna-array system, as optimization of the radome parameters minimize return losses. In the present work, the finite difference time domain (FDTD) combined with a genetic algorithm is used to find the optimal radome for a large radome-antenna-array system. FDTD uses general curvilinear coordinates and sub-cell features as a thin dielectric slab approach and a thin wire approach. Both approximations are generally required if a problem of practical electrical size is to be solved using a manageable number of cells and time steps in FDTD inside a repetitive optimization loop. These approaches are used in the full wave analysis of a large array of crossed dipoles covered with a thin and cylindrical dielectric radome. The radome dielectric has a thickness of ~λ/10 at its central operating frequency. To reduce return loss a thin helical wire is introduced in the radome, whose diameter is ~0.0017λ and the spacing between each turn is ~0.3λ. The genetic algorithm was implemented to find the best parameters to minimize return losses. The inclusion of a helical wire reduces return losses by ~10 dB, however some minor changes of radiation pattern could distort the performance of the whole radome-array-antenna system. A further analysis shows that desired specifications of the system are preserved. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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19 pages, 6651 KiB

Open AccessArticle

Design and Study of a Wide-Band Printed Circuit Board Near-Field Probe

by Pedro A. Martinez, Enrique A. Navarro, Jorge Victoria, Adrian Suarez, Jose Torres, Antonio Alcarria, Joaquin Perez, Andrea Amaro, Abraham Menendez and Jesus Soret

Electronics 2021, 10(18), 2201; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics10182201 - 09 Sep 2021

Cited by 10 | Viewed by 4311

Abstract

Magnetic near-field probes (NFP) represent a suitable tool to measure the magnetic field level from a small electromagnetic interference (EMI) source. This kind of antenna is useful as a magnetic field probe for pre-compliance EMC measurements or debugging tasks since the user can scan a printed circuit board (PCB) looking for locations with strong magnetic fields. When a strong H-field point is found, the designer should check the PCB layout and components placement in that area to detect if this could result in an EMI source. This contribution focuses on analyzing the performance of an easy to build and low-cost H-field NFP designed and manufactured using a standard PCB stack-up. Thereby, the frequency range and sensitivity of the NFP-PCB are analyzed through a Finite Element Method (FEM) simulation model that makes it possible to evaluate its sensibility and effective frequency range. The numerical results obtained with the FEM models are validated against measurements to verify the design and performance of our NFP. The FEM model reproduces the experimental procedure, which is used to evaluate the performance of the NFP in terms of sensitivity by means of the simulated near-field distribution. The NFP-PCB has almost a flat response from 180 MHz to 6 GHz, with an almost perfect concordance between numerical and experimental S21 results. The numerical results show an average transmission loss of −27.9 dB by considering the flat response bandwidth, whereas the experimental one is −29.7 dB. Finally, the designed NFP is compared to two high-quality commercial probes in order to analyze its performance. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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22 pages, 3818 KiB

Open AccessArticle

A New Approach to the Modeling of Anisotropic Media with the Transmission Line Matrix Method

by Jorge A. Portí, Alfonso Salinas, Enrique A. Navarro, Jesús Rodríguez-Camacho, Jesús Fornieles and Sergio Toledo-Redondo

Electronics 2021, 10(17), 2071; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics10172071 - 27 Aug 2021

Cited by 2 | Viewed by 1680

Abstract

A reformulation of the Transmission Line Matrix (TLM) method is presented to model non-dispersive anisotropic media. Two TLM-based solutions to solve this problem can already be found in the literature, each one with an interesting feature. One can be considered a more conceptual approach, close to the TLM fundamentals, which identifies each TLM in Maxwell’s equations with a specific line. But this simplicity is achieved at the expense of an increase in the memory storage requirements of a general situation. The second existing solution is a more powerful and general formulation that avoids this increase in memory storage. However, it is based on signal processing techniques and considerably deviates from the original TLM method, which may complicate its dissemination in the scientific community. The reformulation presented in this work exploits the benefits of both methods. On the one hand, it maintains the direct and conceptual approach of the original TLM, which may help to better understand it, allowing for its future use and improvement by other authors. On the other hand, the proposal includes an optimized treatment of the signals stored at the stub lines in order to limit the requirement of memory storage to only one accumulative term per field component, as in the original TLM versions used for isotropic media. The good behavior of the proposed algorithm when applied to anisotropic media is shown by its application to different situations involving diagonal and off-diagonal tensor properties. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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11 pages, 418 KiB

Open AccessArticle

On the Accurate Numerical Analysis of the Propagation Through Dielectric Frequency-Selective Surfaces Using a Vectorial Modal Method

by Ángela Coves and Ángel A. San-Blas

Electronics 2021, 10(7), 766; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics10070766 - 24 Mar 2021

Cited by 1 | Viewed by 1402

Abstract

In this work, we focus on the numerical analysis of the propagation of plane-waves in one-dimensional periodic lossy dielectric media, which constitute the building block of dielectric frequency-selective surfaces (DFSSs). To this end, a full-vectorial modal method was used, in which discontinuities of some components of the electromagnetic fields have to be evaluated, and we propose a numerical improvement in the evaluation of some integrals appearing in the developed formulation. Some confusion may exist in the evaluation of the cited integrals due to the discontinuous nature of the dielectric function and its transverse gradient. Therefore, some considerations are given in order to solve these integrals accurately for the general case of a relative dielectric permittivity function defined as a sum of lossy dielectric slabs. We particularize our study to a dielectric frequency-selective surface (DFSS), for which the periodic dielectric medium can be defined as constant functions inside an homogeneous region, whose contours define the discontinuities. Thus, the relative dielectric permittivity can be expressed in terms of the Heaviside or step function. In this way, the above-mentioned integrals can be correctly evaluated in the discontinuity, obtaining good results with the employed vectorial modal method for both the propagation constant and the electromagnetic fields obtained in the periodic dielectric medium constituting the DFSS. These results are compared with those obtained with a less accurate evaluation of the cited integrals, when an approximation made by other authors is used. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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26 pages, 22766 KiB

Open AccessArticle

Numerical Study of Extremely Wideband-Modified Biconical Radiation Structures for Electronic Support Measures Application

by Chen Wu and Janaka Elangage

Electronics 2021, 10(4), 369; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics10040369 - 03 Feb 2021

Cited by 1 | Viewed by 2276

Abstract

Using the finite difference time domain (FD-TD) method, this paper studies radiation structures that can have multiple tunable frequency bands between 0.4 GHz and 4 GHz, a fixed band in [3.97, 5.36] GHz and an extremely wideband from 6.14 GHz to 68.27 GHz, where a frequency band is defined by the voltage standing wave ratio (VSWR) less than or equal to two. The base radiation structure has a modified-biconical antenna configuration, called base MBA, and is fed by a square-coaxial line with characteristic impedance close to 50 ohms. A dielectric ring and an outer dielectric cover are used between the two modified cones to enlarge the frequency band and strengthen the structure. An equal number of metallic-rings can be stacked at both circular-ends of cones in the base MBA to tune the positions of the frequency bands that are lower than 4 GHz and to alter their vertical polarization (V-pol) patterns. However, compared with those of the base MBA, these stacked metallic rings do not make significant changes to the VSWR in the [3.97, 5.36] GHz and [6.14, 28.27] GHz bands and the radiation patterns in the [6.14, 28.27] GHz band. The simulation results show that the base MBA and its metallic-ring-loaded versions all have V-pol radiation characteristics at all frequency bands and have donut-shaped omnidirectional patterns only when the wavelength is bigger than the length of the structure. When the wavelength is less than the size of the radiation structure, the donut shape is modified with ripples on the V-pol radiation pattern. Sometimes deep notches could be observed when MBAs operated at the higher end of the extremely wideband. A 0.2 mm cube was used to construct the antenna structures with the consideration of using the 3D metal/dielectric printer technology to build the antennas in the future. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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20 pages, 9915 KiB

Open AccessArticle

UWB-Printed Rectangular-Based Monopole Antenna for Biological Tissue Analysis

by Andrea Martínez-Lozano, Carolina Blanco-Angulo, Héctor García-Martínez, Roberto Gutiérrez-Mazón, Germán Torregrosa-Penalva, Ernesto Ávila-Navarro and José María Sabater-Navarro

Electronics 2021, 10(3), 304; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics10030304 - 27 Jan 2021

Cited by 23 | Viewed by 3491

Abstract

This paper presents the design of a printed step-type monopole antenna for biological tissue analysis and medical imaging applications in the microwave frequency range. The design starts from a very simple and widely known rectangular monopole antenna, and different modifications to the antenna geometry are made in order to increase the bandwidth. The antenna dimensions are optimized by means of a parametric analysis of each dimension using a 3-D electromagnetic simulator based on the finite element method. The optimized antenna, with final dimensions of 40 × 36 mm², is manufactured onto a low-cost FR4 (fiber glass epoxy) substrate. The characteristics of the antenna have been measured inside an anechoic chamber, obtaining an omnidirectional radiation pattern and a working frequency range between 2.7 GHz and 11.4 GHz, which covers the UWB frequencies and enables the use of the antenna in medical imaging applications. Finally, the behaviour of four of these antennas located around a realistic breast model, made with biocompatible materials, has been analysed with the electromagnetic simulator, obtaining good results and demonstrating the usefulness of the designed antenna in the proposed application. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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30 pages, 11389 KiB

Open AccessArticle

Analyze the FMCW Waveform Skin Return of Moving Objects in the Presence of Stationary Hidden Objects Using Numerical Models

by Taiwen Tang, Chen Wu and Janaka Elangage

Electronics 2021, 10(1), 28; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics10010028 - 28 Dec 2020

Cited by 4 | Viewed by 4418

Abstract

In this paper, a high-performance antenna array system model is presented to analyze moving-object-skin-returns and track them in the presence of stationary objects using frequency modulated continuous wave (FMCW). The main features of the paper are bonding the aspects of antenna array and electromagnetic (EM) wave multi-skin-return modeling and simulation (M&S) with the aspects of algorithm and measurement/tracking system architecture. The M&S aspect models both phase and amplitude of the signal waveform from a transmitter to the signal processing in a receiver. In the algorithm aspect, a novel scheme for FMCW signal processing is introduced by combining time- and frequency-domain methods, including a vector moving target indication filter and a vector direct current canceller in time-domain, and a constant false alarm rate detector and a mono-pulse digital beamforming angle tracker in frequency-domain. In addition, unlike previous designs of using M × N fast Fourier transform (FFT) for an M × N array, only four FFTs are used, which tremendously save time and space in hardware. With the presented model, the detection of the moving-target-skin-return in stationary objects under a noisy environment is feasible. Therefore, to track long range and high-speed objects, the proposed technique is promising. Using a scenario having (1) a target with 17 dBm² radar cross section (RCS) at about 40 km range with 5.936 Mach speed and 11.6 dB post processing signal to noise ratio, and (2) a strong stationary clutter with 37 dBm² RCS located at the proximity of the target, it demonstrates that the root-mean-square errors of range, angle, and Doppler measurements are about 26 m, 0.68 degree, and 1100 Hz, respectively. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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12 pages, 3258 KiB

Open AccessArticle

Ultra-Wideband Low-Cost High-Efficiency Cavity-Backed Compound Spiral Antenna

by Charl Baard, Yulang Liu and Natalia Nikolova

Electronics 2020, 9(9), 1399; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics9091399 - 28 Aug 2020

Cited by 7 | Viewed by 7986

Abstract

A low-cost high-efficiency ultra-wideband (UWB) cavity-backed spiral antenna is proposed. It employs an equiangular spiral enclosed by an Archimedean spiral and it is fed through a tapered microstrip balun. A center-raised cylindrical absorber-free cavity backs the spiral to minimize the backward radiation without decreasing the efficiency. The cavity is designed to ensure an impedance bandwidth exceeding 16:1 ratio (from 350 MHz to 5.5 GHz). Simulated and measured results are presented and compared, demonstrating competitive performance in terms of impedance bandwidth and efficiency. Time–domain measurements indicate fidelity of 0.62 at boresight. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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9 pages, 1240 KiB

Open AccessFeature PaperArticle

Reduction of the Line-of-Sight Equivalence Principle

by Nagula Sangary and Natalia Nikolova

Electronics 2020, 9(8), 1278; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics9081278 - 09 Aug 2020

Viewed by 2105

Abstract

An improvement to the line-of-sight (LoS) approximation of the equivalence principle used in far-field computations is presented. In the original LoS approximation of the equivalence principle, the integral equation uses only the surface currents on the LoS surface, as well as the edge currents on the contour of the LoS surface, which is the replacement of the surface integrals over the shadow part of the surface. Here, we show that the integration over one type of surface current on the LoS surface and edge currents is sufficient, which reduces the resources required for the LoS radiation pattern computations by half. The proposed theory is a rigorous analysis of Love’s Equivalence theory with an introduction of the point-of-symmetry concept. The proposed method makes use of the vector-potential field representation to derive the improved LoS equivalence principle. The proposed approach is validated with the calculation of the far-field radiation pattern of a patch antenna using the Finite Difference Time Domain (FDTD) simulations. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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16 pages, 2463 KiB

Open AccessArticle

Heat Transfer Study in Breast Tumor Phantom during Microwave Ablation: Modeling and Experimental Results for Three Different Antennas

by Rocío Ortega-Palacios, Citlalli Jessica Trujillo-Romero, Mario Francisco Jesús Cepeda-Rubio, Lorenzo Leija and Arturo Vera Hernández

Electronics 2020, 9(3), 535; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics9030535 - 24 Mar 2020

Cited by 16 | Viewed by 3597

Abstract

It is worldwide known that the most common type of cancer among women is breast cancer. Traditional procedures involve surgery, chemotherapy and radiation therapy; however, these treatments are invasive and have serious side effects. For this reason, minimally invasive thermal treatments like microwave ablation are being considered. In this study, thermal behavior of three types of slot-coaxial antennas for breast cancer microwave ablation is presented. By using finite element method (FEM), all antennas were modeled to estimate the heat transfer in breast tumor tissue surrounded by healthy breast tissue. Experimentation was carried out by using the antennas inserted inside sphere-shaped-tumor phantoms with two different diameters, 1.0 and 1.5 cm. A microwave radiation system was used to apply microwave energy to each designed antenna, which were located into the phantom. A non-interfering thermometry system was used to measure the temperature increase during the experimentation. Temperature increases, recorded by the thermal sensors placed inside the tumor phantom surrounded by healthy breast phantom, were used to validate the FEM models. The results conclude that, in all the cases, after 240 s, the three types of coaxial slot antenna reached the temperature needed produce hyperthermia of the tumor volume considered in this paper. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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18 pages, 4138 KiB

Open AccessEditor’s ChoiceArticle

Method of Moments Based on Equivalent Periodic Problem and FFT with NURBS Surfaces for Analysis of Multilayer Periodic Structures

by Rafael Florencio, Álvaro Somolinos, Iván González and Felipe Cátedra

Electronics 2020, 9(2), 234; https://0-doi-org.brum.beds.ac.uk/10.3390/electronics9020234 - 31 Jan 2020

Cited by 3 | Viewed by 2505

Abstract

In this paper, an efficient technique of computation of method of moments (MM) matrix entries for multilayer periodic structures with NURBS surface and Bézier patches modelling is proposed. An approximation in terms of constant pulses of generalized rooftop basis functions (BFs) defined on Bézier patches is proposed. This approximation leads discrete convolutions instead of usual continuous convolution between Green’s functions and BFs obtained by the direct mixed potential integral equation (MPIE) approach. An equivalent periodic problem (EPP) which contains the original problem is proposed to transform the discrete convolutions in discrete cyclic convolutions. The resultant discrete cyclic convolutions are computed by efficiently using the Fast Fourier Transform (FFT) procedure. The performance of the proposed method and direct computation of the MM entries are compared for phases of reflection coefficient. The proposed method is between 9 and 50 times faster than the direct computation for phase errors less than 1 deg. The proposed method exhibits a behaviour of CPU time consumption of O(N_bLog10N_b) as the number N_b of BFs increases. This behaviour provides significant CPU time savings with respect to the expected behaviour of O(N_b²) provided by the direct computation of the MM matrix entries. Full article

(This article belongs to the Special Issue Numerical Methods and Measurements in Antennas and Propagation)

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