The core structure of transformers and reactors is subject to stress and high-frequency excitation during operation. The core structure is made of laminated silicon steel sheets, which are subject to magnetostrictive strain under alternating magnetic fields. To investigate the comprehensive magnetic properties of oriented silicon steel sheets under the influence of harmonics and stress, this paper builds a magnetic property measurement system for electrical steel and investigates the magnetization and magnetostriction characteristics of oriented silicon steel sheets of type 30SQGD105 under working frequency, harmonic and applied stress conditions. The results show that the effects of harmonics and stress on the hysteresis characteristics of the silicon steel sheet are small, and the effects on the magnetostriction characteristics are large.

Pulmonary edema assessment is a key factor in monitoring and guiding the treatment of critically ill patients. To date, the methods available at the bedside to estimate the physiological correlation of pulmonary edema and extravascular pulmonary fluid are often unreliable or require invasive measurements. The aim of this article is to develop an imaging method of reliably assessing pulmonary edema by utilizing functional electrical impedance tomography. In this article, the Split-Bregman algorithm is used to solve the Total Variation (TV) minimization problem in EIT image reconstruction. A thorax model is constructed according to CT images of rats. Through simulation and experiment, the proposed method improves the quality of reconstructed image significantly compared with existing methods. A pulmonary edema experiment in rats is also carried out. The development of pulmonary edema is analyzed numerically through EIT images.

An optimization method utilizing a multistage genetic algorithm (MS-GA) and considering parameter variations has been proposed to obtain optimal design of one-dimensional dielectric bandgap(1D D-EBG) structures with a few periods in small packaging power distribution networks. One-dimensional finite method (1D FEM) is used to improve computational efficiency and iteration speed. MS-GA consists of 3 stages: In stage 1, the population was initialized by Hamming distance, and the fitness was calculated to determine the number of EBG period. In stage 2, genetic manipulation and sensitivity analysis were used to improve local search ability and obtain preliminary results. In stage 3, cubic spline interpolation and local integral were used to reconstruct the fitness evaluation function considering parameter deviation, adjust the results and obtain the optimal parameters. Three optimized target frequency bands with center frequencies of 2.4 GHz, 3.5 GHz and 28 GHz were optimized, and Pearson coefficient was used to analyze the correlation between the parameters to better understand the influence of parameter deviation on the optimization results. The achieved results meet the optimization object within the allowable range of parameter errors, and the parameter constraints were successfully met for all three designs, with their final dimensions below 20 mm. Three-dimensional full-wave simulation software was used to simulate and analyze the stopband bands, and the simulation results were consistent with the calculation results.

A general theory of a passive multi-port system is presented, incorporating an arbitrary number of feed and load ports. The result is a nonlinear equation system, in which the solution variables are the load admittances, connected to the load ports. The solution ensures impedance match at all feed ports at one particular frequency. It is also shown how this theory can be applied to adaptive and reconfigurable antennas, by using switches to include or exclude some of the load admittances. If, by open state of a switch, the corresponding load admittance is excluded, then the nonlinear equation system is simplified. In general, one load admittance per feed port is required to obtain complex conjugate impedance match. Then, the admittance has a real and an imaginary part, where the real part relates to a resistor, adding loss to the system. It is shown how loss-less matching can be obtained by using two, purely reactive admittances per feed port.

To address the problems of torque ripple, vibration, and noise generated by cogging torque in a dual-stator single-rotor axial magnetic field permanent magnet motor, this article adopts an unequal thickness pole structure to reduce cogging torque. At first, the process of cogging torque generation is analyzed, followed by an examination of the mathematical formulation of cogging torque using the energy technique and the Fourier decomposition method. Then, the impacts of several pole optimization approaches on cogging torque reduction are then compared, and the findings are investigated using the finite element method to demonstrate the efficiency of the optimization method. The results show that the optimization effect of unequal thickness pole structure is the best. Lastly, the optimized motor's air-gap flux density, counter-electromotive force, harmonic content, and rotor mechanical strength were compared and studied to demonstrate that the unequal-thickness structure used in this research can increase motor performance. Finally, based on the determined motor parameters, experimental study of the prototype was carried out to verify the correctness of the motor structure and analysis.

Advancement in radar component technology has led to a reduction in the size, weight, and power consumption of radar systems. Experimental radar systems can now be integrated onto smaller, maneuverable platforms, such as small unmanned aerial vehicles (sUAVs). Integration onto rotor-based sUAVs enables data collection over novel synthetic apertures which can be optimized for different scenarios. The design, simulation, and experimentation of a light-weight, ultra-wideband synthetic aperture radar (SAR) is presented here that will be used for the detection of obscured surface targets. The approach outlined herein uses 3-dimensional (3-D) imagery to vertically resolve clutter from the target. A vertical-grid aperture is presented which yields vertical resolution. Point spread functions are derived for both linear and vertical-grid apertures. The analytical expressions are verified using simulations. Finally, experimental data is used to form 3-D imagery and demonstrate the importance of vertical resolution in the discrimination between scatterers above the ground, as well as clutter mitigation.

The paper represents a rigorous solution to the problem of diffraction of a normally incident plane electromagnetic wave by a circular hole in a perfectly conducting screen of arbitrary thickness, obtained using the eigenmode technique with allowance for the presence of a plane dielectric layer on a thick substrate behind the screen, which can play a part of a radiation detector. The main goal of the work is to describe the effect of diffractionlensless focusing in circular apertures and to determine the conditions of its appearance in the near zone of small holes, when its radius, the thickness of a screen and a dielectric layer are of the order of the wavelength.

A new non-singular fast terminal Sensor-less sliding mode control algorithm (INFTSMC) for IPMSM based on an improved extended sliding mode disturbance observer (IESMDO) is constructed to address the problem of degraded control performance of IPMSM because of uncertainties. Firstly, a mathematical model of IPMSM under parametric ingestion is developed, and a new control law for the speed loop is designed. Then, an improved non-singular fast terminal sliding mode speed controller (INFTSMC) based on a novel extended sliding mode disturbance observer (IESMDO) is designed, where an improved super-twisting control law is designed to speed up convergence, while IESMDO can accurately observe the unknown perturbed part F of the system in real-time relative to the sliding mode disturbance observer (SMO). Finally, high-order square root cubature Kalman-filter (CKF) combined with an adaptive estimator is proposed to accurately estimate the speed and rotor position of the motor in real-time. Through simulations and semi-physical experiments with PI and traditional NFTSMC, it is verified that the algorithm has better transient steady-state performance when external disturbances and parameter perturbation are added externally to the motor, which is conducive to improve the control effect of IPMSM.

The present paper proposes a novel technique to reduce the peak side lobe ratio (PSLR) in the time waveform of the synthetic aperture radar (SAR) pulse. The dependence of the instantaneous frequency on the time over the SAR pulse duration is formulated as an arbitrarily shaped piecewise linear (PWL) curve. The slopes of the linear segments of this curve are optimized to get the minimum PSLR of the received radar echo at the output of the SAR receiver. The particle swarm optimization (PSO) method is used to optimize the shape of the time-frequency curve to achieve the dual-objective of minimizing the PSLR of the received SAR echo and to realize the required pulse compression ratio (PCR). The slopes of the linear segments of the time-frequency curve are the control parameters that determine the position of each particle in the swarm. The proposed method can be considered as an optimized form of non-linear frequency modulation (NLFM) for SAR pulse compression. It is known that the conventional NLFM using second-order time-frequency curve results in a PSLR of -18 dB. The proposed method results in a PSLR of -45.6 dB and achieves a range resolution of 1.4 m. The developed PSO algorithm is shown to be computationally efficient and its iterations are fastly convergent such that a few iterations are enough to arrive at the steady state of the cost function. Finally, a SAR transceiver is proposed as a software-defined radio (SDR) in which the proposed SAR pulse compression technique is employed in the transmitter to generate the transmitted pulse and in the receiver to construct the transfer function of the matched filter (MF).

This article demonstrates the design development, fabrication, and testing of an off-set edge-fed monopole hybrid fractal antenna for ultra-wideband (UWB) applications at a design frequency of 3.2 GHz. The proposed monopole antenna is compact 38.12 mm × 38.42 mm, slotted, and uses a combination of two numbers of Koch plus Minkowski hybrid fractal technology. Antenna resonates at four frequencies i.e. quad tuned (3.2 GHz, 4.94 GHz, 7.21 GHz, and 10.10 GHz). The reflection coefficient, S₁₁ < -10 dB obtained for the excellent UWB fractional bandwidth 119.55% (2.85 GHz to 11.32 GHz) is more than the standard FCC bandwidth (3.1 GHz-10.6 GHz). The antenna has gained 6.73 dBi at 3.49 GHz, 5.91 dBi at 5.52 GHz, 8.26 dBi at 6.81 GHz, and 8.02 dBi at 10 GHz with a maximum radiation efficiency of 89.81%. The main feature of the proposed work is that the antenna is circularly polarized in frequency bands 3.14 GHz-3.30 GHz (Axial ratio: 1.61 dB) and 9.07 GHz-9.45 GHz (Axial ratio: 2 dB) and elsewhere linearly polarized. A total of 16.37% antenna size miniaturization has been achieved with excellent UWB and S₁₁ performance. The measured and simulated reflection coefficients are found in good agreement. Therefore the fabricated and tested antenna is well suitable for Wi-Max (3.3/3.5/5.5 GHz), ISM (5.725-5.875 GHz), WLAN (3.6/4.9/5.0/5.9 GHz), military band applications (radio location, fixed-satellite and mobile-satellite, S-band, C-band and X-band satellite communications, etc.), aeronautical radio navigation, radio astronomy, ITU-8, Sub-6 GHz band, and Radar applications.

This work examines the effects of high frequency radio transmission on the human body. A magnetic point source is used to generate a signal that is transmitted through the human body at a specified distance. The study was conducted to evaluate the health effects of exposure to high frequency radiation, in relation to current density, induced electric field and specific absorption rate at frequencies of 6.78 MHz and 13.56 MHz. The results for both an equivalent cylinder and a realistic human body model were compared. The analytical method presumes a sinusoidal current distribution along the cylinder and introduces the approximations of field integrals. The numerical simulations by the commercial software FEKO confirmed the analytical results depicted in the paper. The study shows that maximum differences between the results of the proposed analytical model and human model (regardless being realistic or cylinder) are less than 10%. This is convenient because analytical methods can ensure fast estimations of the exposure standard limitations.

Parallel computing for the three-dimensional spatial spectral volume integral equation method is presented for the computation of electromagnetic scattering by finite dielectric scatterers in a layered medium. The first part exploits the Gabor-frame expansion to compute the Gabor coefficients of scatterers in a parellel manner. The second part concerns the decomposition and restructuring of the matrix-vector product of this spatial spectral volume integral equation into (partially) independent components to enable parallel computing. Both capitalize on the hardware to reduce the computation time by shared-memory parallelism. Numerical experiments in the form of solving electrically large scattering problems, namely volumes up to 1300 cubic wavelengths, in combination with a large number of finite scatterers show a significant reduction in wall-clock time owing to parallel computing, while maintaining accuracy.

This research paper introduces a novel dual-band single-polarized (DBSP) series-fed center-fed open stub (SFCFOS) Binomial Antenna Array synthesis technique to improve side lobe levels (SLL) and better isolation for the use in Airborne Synthetic Aperture Radars (AIR-SARs). The antenna utilizes a shared-aperture array (SAA) architecture, operating in both X and Ku-bands with center frequencies of 9.3 and 13.265 GHz with a frequency ratio of 1:1.426. The SAA consists of a 7-element linear array of square microstrip patches for the X/Ku-band. The inter-element spacing between patches is set at 0.7λ to meet the ±25˚ scan range requirements. The X-band (9.3 GHz) frequency is ideal for soil moisture estimation in agricultural areas, while the Ku-band (13.265 GHz) is suitable for applications in snow-covered regions, cold areas, and disaster monitoring. To validate the antenna design, a prototype is fabricated and tested for S-parameters, radiation characteristics, and gain measurements. The size of the shared-aperture antenna is 200 mm × 50 mm × 0.787 mm. The measured results of the prototype align well with the simulated ones, exhibiting excellent radiation performance and high isolation. The bandwidth of 1.07% (X-band) and 1.5% (Ku-Band) and return loss of 25 dB/-15.7 dB at 9.3/13.265 GHz are achieved. The measured isolation is -45 dB which provides a large signal separation at X/Ku-bands. The antenna design shows a side-lobe level (SLL) of -39.5 dB at E-Plane (φ=0˚) and -17.9 dB for H-plane (φ=90˚) for the X-band and -35 dB at φ=0˚-19 dB for H-plane (φ=90˚) for the Ku-band. Additionally, it achieves high gain values of 12.8 dBi for the X-band and 13.2 dBi for the Ku-band. This research presents the first reported shared-aperture X/Ku-band single polarized planar array with binomial amplitude distribution synthesis technique, which holds significant value for AIR-SAR applications. All the measured results were in line with simulated ones and matched reasonably well.

In plantation areas, soil conditions affect the crop's quality. One of the crucial elements in the soil for plant survival is soil water content (SWC). Radar system has advantages that can be implemented for measuring SWC in plantation areas. A radar system operates by utilizing electromagnetic waves to obtain the dielectric characteristics of the soil. However, the presence of tea plants has become an obstacle to the radar wave propagation toward the soil layer. Reflected signal, which is influenced by the presence of vegetation, makes the estimation of SWC inaccurate. Consequently, the estimation of SWC needs to consider the vegetation's effect. This study uses an FMCW radar system, which operates at a frequency of 24 GHz. A layer medium propagation model is proposed in this study to prove the relationship between the reflected signal and the SWC. The reflection coefficient extracted from the radar signal is used to estimate the SWC. The vegetation propagation constant was obtained from the average field measurement results. The gravimetric method is used to validate the SWC estimation in vegetation's presence using the radar system. The results of the field experiments showed that the proposed method succeeded in estimating the SWC by considering the presence of vegetation with an average error of 3.57%. The proposed method has the potential to be applied to plantation areas.

The article presents a multiband symmetrically placed two elements, inverted-F multiple inputs multiple outputs (MIMO) antenna for wireless LAN (WLAN), Industrial, Society and Medical (ISM) band, S-/C-band applications. Decoupling (S₁₂ < -15 dB) between the two antenna elements of MIMO antenna is improved by introducing metallic vias at the top ends of the patch. The MIMO antenna has been fabricated and measured on a piece of low-cost, low-profile, FR-4 substrate. A combination of parasitic loading of 4-units (quadruplet) of square-split ring resonators (SRRs) and complementary split ring resonator (CSRR) cells have been used to achieve quad-bands for lower than -10 dB total active reflection coefficients and additionally to improve isolation between antenna elements. The paper also presents the tabularized and graphical investigations of the analyzed and measured resultant MIMO parameters like; envelope correlation coefficient (ECC), diversity gain (DG), total active reflection coefficients (TARC), MIMO-VSWR (voltage standing wave ratio), channel capacity loss (CCL), etc. and are found approximately close to each other with small acceptable errors. The other important parameters (reflection coefficients, radiation pattern, E-plane and H-plane polar plots, electric field vector (E) distribution, and current density vector (J) distribution) of the proposed antenna were also demonstrated and measured using a vector network analyzer (Agilent N5247A VNA) and 18 GHz Anechoic chamber in the microwave research laboratory. The MIMO (1×2) antenna is best suitable for Bluetooth/WLAN/Wi-Fi (2.45-2.57 GHz) and ISM band, FIXED, MOBILE, RADIO Location, Amateur & Amateur-satellite service (2.45 GHz) within impedance bandwidth (S₁₁ < -10 dB) from 2.45-2.57 GHz lower band, and n46 (5.40-5.49 GHz) upper band.

An efficient method for designing narrow beams having minimum peak side lobe level (PSLL) and maintaining power efficiency (reducing active elements) for 5G/6G base stations with large antenna arrays is proposed. To ensure high efficiency in a multi-dimensional complex nonlinear optimization problem with several constraints thinning of antenna of antenna arrays is considered. For performing exhaustive search on the large number of feasible solutions a novel algorithm named discrete cat swarm optimization (DCSO) is usedand is a binary adaptation of real-valued cat swarm optimization (CSO). To testify the efficiency of DCSO a set of standard benchmarked multimodal functions are used. The proposed algorithmsexhibit heuristic nature, so the stability of the proposed method has been authenticated by using statistical test. Later the algorithm is applied to the optimization of a large planar antenna array (PAA) of size 10×20 (200 elements) to suppress the PSLL. Furthermore, the results of the synthesis are compared with literature marking low PSLL and convergence speed as pointers. The comparative results delineate the superiority of the DCSO over the existing discrete versioned traditional algorithms with respect to solution accuracy and speed of convergence. DCSO introducesa higher degree of flexibility to the field of binary-valued thinned antenna array synthesis problems.

The uniform geometrical theory of diffraction (UTD) calculating edge diffraction, creeping diffraction, and reflection, has been widely used to predict the shadowing problems for the beyond 5th generation. The limitation of the previous work, which only discussed the relationship between edge diffraction and reflection in the lit region, has motivated the analysis of the difference between creeping diffraction and edge diffraction in the shadowed region. In this paper, as the difference between creeping diffraction and edge diffraction from a dielectric circular cylinder and an absorber screen, respectively, a novel additional term is derived based on the UTD in the shadowed region. In addition, a uniform additional term using the Fock-type integral is proposed to unify the formulations in the lit and shadowed regions. The proposed uniform additional term is validated by the UTD and exact solutions of a dielectric circular cylinder at millimeter-wave or sub-terahertz bands. From the discussion of the results, the proposal can not only unify the formulations in the lit and shadowed regions but also eliminate the fictitious interference. Through the proposal, we can separate the contribution of the shadowed Fresnel zone number (FZ) and boundary conditions (i.e., the surface impedance and polarization). The frequency characteristics of the shadowed FZ and boundary conditions are analyzed and simulated near a shadow boundary at a high frequency (10 GHz-100 GHz). The results imply that there is almost no dependency (less than 1 dB) on boundary conditions in the lit region while there are few dependencies (more than 1 dB) on boundary conditions in the shadowed region. This work attempts to unify three different propagation mechanisms, i.e., reflection, edge diffraction, and creeping diffraction, by using one formula.

Dynamic Inductive Wireless Power Transfer (DIWPT), used for charging and powering electric vehicles (EVs), has been presented lately as a solution for increasing the distance range of electric vehicles and reducing the utilization of heavy and bulky battery systems. In most DIWPT designs, the voltage induced by the movement of the receiving coil over a time-varying magnetic field is neglected and never quantified. In this work, a simplified phasor expression for the total induced voltage on a coil that is moving in a sinusoidal time-variant magnetic vector field is developed. If no rotation is observed in the coil, a 90˚ out of phase voltage component proportional to the speed of the coil is added to the induced voltage that would be calculated if the coil was stationary. The phase of this voltage component is delayed or advanced with respect to the stationary induced voltage, according to whether the coil is moving into or out of a region of higher magnetic flux. Then, under some assumptions on the geometry of inductive coil configurations, it is possible to estimate the minimum induction frequency for which the quasi-stationary approximation can be considered. The resulting frequency value for a representative geometry is calculated, indicating that, for automotive applications, the relative error in the induced voltage is actually negligible, except in the vicinity of the points of zero-crossing in the magnetic flux, where the absolute value of the induced voltage is low anyway.

This paper presents an in-depth review of the performance improvement of antennas using metasurface. Metasurface is a periodic arrangement of perfect electric conductors (PECs) on a metal-backed dielectric substrate that do not exist in nature and are able to manipulate the behavior of electromagnetic (EM) waves incident on it. The manipulations of EM waves improve the performances in terms of impedance bandwidth, gain, size, specific absorption rate (SAR), radar-cross-section (RCS), and polarization conversions. Consequently, numerous recent works on metasurface-inspired antenna design and their theoretical perspectives on performance enhancements are discussed. By adopting the discussed theories, novel metasurfaces are developed and proposed that analyze impedance-bandwidth enhancement, gain enhancement and SAR reduction. For designing the metasurfaces, initially a conventional rectangular unit cell (CRUC) is theoretically developed using transmission line model at 2.45 GHz. Following that, the CRUC-based metasurface is incorporated with a monopole antenna, which enhanced the impedance-bandwidth from 140 MHz to 320 MHz and the gain from 2.5 dB to 7.4 dB. On the body, the presence of the metasurface retains all the performances as free space, with a reduced 1 g SAR of 0.034 and 10 g SAR of 0.024 W/Kg.

In this paper, a novel frock shaped four-port MIMO antenna is designed, and experimental results were verified for UWB applications. The four elements are placed orthogonal to each other to reduce mutual coupling. The proposed novel-shaped antenna is derived from a circular patch antenna. A series of modifications were made on a circular patch antenna to get desired single novelly shaped radiator. Inserting decoupling stubs in the Plus form between MIMO elements lessened mutual coupling. The entire designing procedure of the proposed four-port antenna was carried out by Characteristic Mode Analysis. The proposed model is printed on an Fr-4 substrate with dimensions of 40x40x1.6 mm³. This novel 4-port antenna is well-operated in the UWB range from 2.8 GHz to 11.4 GHz and bandwidth of 8.6 GHz. The novel shape radiators with good decoupling stubs produce a high impedance bandwidth of as 121.8%, radiation efficiency of 91%, high isolation 26 dB, and a gain of 6 dB in the operating band. The diversity parameters are enveloped correlation coefficient (ECC) less than 0.0011, diversity gain (DG) very near 10 dB, capacity channel loss of 0.28 bp/s/Hz, and mean effective gain of -3.1 dB. The experimental results of the antenna are verified with simulated ones and got good agreement between fabricated and simulated results.

Computation of the magnetic field generated by permanent magnets is essential in the design and optimization of a wide range of applications. However, the existing methods to calculate the magnetic field can be time-consuming or ungeneralised. In this research, a deep learning-based fast-computed and generalised model of three-dimensional (3D) magnetic field is studied. The volumetric deep neural network model (V-Net) which consists of a contracting part to learn the geometrical context and an expanding part to enable the concise localization was applied. We synthetically generated the ground truth datasets from permanent magnets of different 3D shapes to train the V-Net. The accuracy and efficiency of this deep learning model are validated. Predicting on 50 random samples, the V-Net took 4.6 s with a GPU T4 and 23.2 s with the CPU whereas the others took a few hundreds to thousands of seconds. Therefore, the deep learning model can be potentially utilised to replace the other methods in the computation and study of the magnetic field for the design and optimization of magnetic devices (the codes used in this research are published openly in https://github.com/vantainguyen/3D_V-Net_MagneticField).

This paper presents a stabilized scheme that solves the wave propagation problem in a general bianisotropic, stratified medium. The method utilizes the concept of propagators, i.e., the wave propagation operators that map the total tangential electric and magnetic fields from one plane in the slab to another. The scheme transforms the propagator approach into a scattering matrix form, where a spectral decomposition of the propagator enables separation of the exponentially growing and decaying terms in order to obtain a well-conditioned formulation. Multilayer structures can be handled in a stable manner using the dissipative property of the Redheffer star product for cascading scattering matrices. The reflection and transmission dyadics for a general bianisotropic medium with an isotropic half space on both sides of the slab are presented in a coordinate-independent dyadic notation, as well as the reflection dyadic for a bianisotropic slab with perfect electric conductor backing (PEC). Several numerical examples that illustrate the performance of the stabilized algorithm are presented.

In this article, a planar compact grounded coplanar waveguide (GCPW)-fed 4-element multiple-input multiple-output (MIMO) antenna array with a defected ground structure (DGS) is demonstrated for fifth generation (5G) millimeter-wave (mmWave) communication. Each element of GCPW-fed mmWave MIMO antenna array contains a deformed pentagon-shaped radiating patch etched with a pair of identical circular slots in top surface and a DGS in bottom surface. To maintain low design complexity and compactness, a DGS is introduced and formed by embedding dual asymmetrical inverted T-shaped slots in the partial ground plane which enhance the gain and bandwidth of the antenna. The equivalent circuit model of the proposed DGS loaded GCPW-fed antenna is realized and presented. The proposed 4-element mmWave MIMO antenna array is realized by arranging the 4 identical antenna elements horizontally in a row with a distinct gap without any decoupling structure. It has the size of 1.02λ × 3.86λ × 0.021λ (at 25.66 GHz) and exhibits the measured bandwidth of 49.62% (25.30-42.0 GHz) with a peak gain of 12.02 dBi. Furthermore, the envelope correlation coefficient (ECC) < 0.0014, isolation > 24 dB between antenna elements, and channel capacity loss (CCL) < 0.29 bits/sec/Hz of the mmWave MIMO antenna array are attained over the entire mmWave frequency band.

Wide bandwidth compact rectangular and equilateral triangular microstrip antennas employing slots cut bow-tie shape ground plane profile are proposed. Amongst all the designs, patch employing three rectangular slots cut bow-tie shape ground plane yields optimum results. Using the rectangular patch, against conventional ground plane design, increase in bandwidth by 20%, resonance frequency, substrate thickness, and patch area reduction by 32%, 0.034λ_g, and 61.12%, are respectively achieved. In equilateral triangular patch design, a three rectangular slots cut bow-tie shape ground plane configuration shows bandwidth increase by 30%, and substrate thickness, fundamental mode frequency, and patch size reduction by 0.027λ_g, 16.4%, and 36.28%, respectively. Proposed designs exhibit broadside radiation pattern with broadside gain of above 5 dBi.

This paper proposes a method of independent control over each passband in a high performance triple bandpass filter, which is an essential requirement in the field of microwave communication systems. Individual techniques are presented here to control the excited modes that are responsible for the generation of triple passbands based on substrate integrated waveguide loaded with semi-circular mushroom resonators. Initially, a circular substrate integrated waveguide (CSIW) loaded with two cascaded semi-circular mushroom resonators (ScMRs) with distinct modifications and orientations in the schematic is employed to generate three passbands. The fundamental mode and next higher order mode of the entire resonator structure are utilized to generate three passbands, and distinct techniques of mode perturbations and variation in coupling strength are introduced to independently control the excited modes. Subsequently, the methods established to control the excited modes are employed to independently control the center frequencies (CFs) of three passbands. All those methods established to control the CFs of the three passbands are verified with experimental results which show good agreement with the simulated ones.

Powerline communication (PLC) noise is the main cause of reduced performance and reliability of the communication channel. The major source of these noise bursts, which distort and degrade the communication signal, is the arbitrary plugging in and unplugging of electric devices from the electrical network. It is therefore important to perform statistical modelling of the PLC noise characteristics to enable the development and optimisation of reliable PLC systems. This paper presents the Variational Bayesian (VB) Gaussian Mixture (GM) modelling of the amplitude distribution of the indoor broadband PLC noise. In the proposed model, a fully Bayesian treatment is employed where the parameters of the GM model are assumed to be random variables. Consequently, prior distributions over the parameters are introduced. The VB criterion is used to determine the optimal number of components where the Bayesian information criterion emerges as a limiting case. To find the parameters of the GM components, the variational-expectation maximisation algorithm is employed. Measurements from different indoor PLC environments are then used to validate the model. Thereafter, performance analysis is carried out, and the VB framework is compared to the Maximum Likelihood (ML) estimate method. It is observed that while the ML model performs better when the amplitude distribution contains multiple peaks, the VB framework offers high accuracy and good generalization to the measured data and is thus effective in modelling the amplitude distribution of the PLC noise.

The backscattering of electromagnetic waves incident on a rotating metallic wind turbine (WT) is analyzed by using the Physical Optics method. The model developed is general and allows the computation of the spectral Doppler shift of the backscattered waves. All the parameters involved are taken into account, relative to incident wave direction, wind horizontal direction, WT geometric and electromagnetic properties. Numerical computations are carried out for various cases and presented relative to a search radar.

The near and far field EM responses over layered media have long been exploited in diversified applications such as remote sensing, monitoring and communication. In this work, we utilize the near field dependence of the EM fields of a three layered structure resembling air-sea ice-sea water to estimate the thickness and dispersion characteristics of sea ice using deep learning technique. We explore two key methods of field measurement termed as the fixed and scaled sweep methods. In the fixed radial sweep method, the receiver distance and height from the source are kept constant, and in the scaled sweep method both the receiver distance and height are set as a scaled function of the operating wavelength. A synthetic training dataset has been generated (using analytical computation and FEM simulation) in the low MHz band, which is used to train a deep learning model. The model is tested on different test datasets with frequencies inside, below and above the training limits. Even though the fixed sweep method is simpler to implement, the scaled sweep appears to perform better across the wide range of test frequency, both in and outside the training range. When the test frequency is inside the training range, the percentage errors for thickness, dielectric constant, and loss tangent were found to be <2%, <10%, and <5%, respectively, for the fixed radial sweep, whereas for the scaled sweep the percentage error is < 1% for all three measurement parameters. When the test frequency deviates further from the training range, the percentage error gradually increases. Later, we investigate the problem of determining sea ice thickness assuming a priori knowledge of sea ice dielectric parameters, and results show that the model estimates the thickness of the sea ice bulk with error as low as 0.1%.

This paper presents a novel theoretical and numerical approach for an infinitesimal current source (ICS) located in a planar isotropic multilayer medium. Using the mixed-potential integral equation (MPIE) formulation for depicting the electromagnetic disturbance created by the ICS, a detailed definition of Green's functions of Lorenz potentials and fields is provided in this paper. The proposed Green's functions are valid for the considered multilayer isotropic medium, which can have arbitrary layer parameters. This paper also analyzes two commonly observed special cases of the multilayer medium - the multilayer soil including air and the multilayer lossless dielectric - and the proposed equations are modified to meet the requirements of the medium. Green's functions can be obtained from the systems of linear equations proposed in this study. In comparison to other approaches, the advantage of the proposed procedure is that the solutions of the equations are immediately obtained in any field layer of the multilayer medium. In addition, the proposed system of linear equations can be solved easily using well-known numerical computation methods. Furthermore, this paper offers an alternative way of obtaining Green's functions, which are closed-form expressions for the kernels of spectral-domain Green's functions.

The equation of motion for a test particle moving in given fixed external fields is analyzed and compared to the corresponding equation of motion derived from the Darwin Lagrangian for a system of interacting charged particles. The two approaches agree as long as the part of the electric field that arises from the partial time derivative of the vector potential is taken into account. It is, however, only via the Darwin approach that the origin of this field can be understood as arising from a breakdown of the test particle approximation. Applying the formalism to an electron moving outside a long solenoid results in a classical analog of the Aharonov-Bohm effect.

A 3D printing and printed circuit board (PCB) hybrid fabricated modularized dual-stopband artificial magnetic conductor (AMC)-loaded filtering antenna is proposed for an X-band high-power radar system.By loading low-cost microstrip AMCs of different frequency responses into a waveguide slot array, we achieve a modularized filtering antenna whose frequency response can be simply controlled by replacing different AMCs. The waveguide slot array only works as a fixture to host different AMCs to achieve various filtering antenna frequency responses. The interchangeable modularized design helps to reduce the difficulty and cost of component fabrication by eliminating the need for complex resonant cavities inside the waveguide filtering antenna, which is time-efficient at the stage of product prototyping when numerous iterations are needed on a trial-and-error base. A dual-stopband filtering antenna is designed and fabricated in the X-band to verify the design concept. The passband covers 9.25-10.6 GHz with the passband gain greater than 10 dBi. The antenna radiates frequency-dependent scanning beams in the passband. The stopbands are 8.1-9 GHz and 10.75-11.5 GHz, and the out-of-band rejection is larger than 35 dB. The proposed design concept provides a different thought to achieve a low-cost filtering antenna by using interchangeable modularized components. The fabricated antenna prototype is a capable candidate for high-power airborne radar applications.

A dual frequency dual circularly polarized cross-slot waveguide array working at 4.9 GHz and 5.8 GHz is proposed for wireless communication/airborne weather radar applications. Different from the traditional cross-slotted waveguide antenna, to improve space utilization, two sets of cross-slots are slit on both sides of the longitudinal axis of the waveguide's E-plane to realize dual-frequency operation. When the antenna operates in the TE₁₀ mode, the cross-slots on each side radiate left-handed and right-handed circularly polarized electromagnetic waves at two different frequencies, respectively. To suppress grating lobes, phase perturbation structures are periodically loaded in the waveguide to tune the propagation phase constant, thereby changing the effective electric spacing between radiating elements while keeping the antenna a compact physical aperture. The proposed grating lobe suppression method avoids the dielectric loss caused by dielectric loading, eliminates the need for complex array arrangement, and achieves the grating lobe suppression at dual frequencies simultaneously. The metallic 3D printing technology, selective laser melting (SLM), is used to fabricate the antenna in one piece in one run using aluminum alloy. The proposed antenna has gains of 10 dBic and 14.5 dBic with 47% and 69% aperture efficiencies at 4.9 GHz and 5.8 GHz, respectively. It is a capable candidate for air-to-ground (ATG) communication applications.

This paper presents a new scheme to implement the iterative physical optics (IPO) approximation with edge diffraction for the scattering from large perfectly-conducting objects, for which, multiple reflections occur. The use of the electric field integral equation (EFIE) discretized by the Galerkin method of moments (MoM) with Rao-Wilton-Glisson basis functions leads to solving a linear system. The characteristic basis function method (CBFM) needs to invert the self-impedance sub-matrices to calculate the primary basis functions (PBFs). To accelerate this stage, these sub-linear systems are directly solved from the physical optics (PO) approximation. In addition, to improve the precision of PO, the EFIE-PO self-impedance matrix is derived analytically. This avoids to apply the magnetic field integral equation (MFIE), for which its principal value is related to PO. Numerical results showed that the resulting algorithm, CBFM-PO, predicts inherently the edge diffraction. A domain decomposition method is able to split up the geometry into blocks, for which either the PO or a LU decomposition is applied according to the sub-geometry. To accelerate the coupling steps, the adaptive cross approximation (ACA) is also implemented, and the resulting method is tested on different targets having a curvature and producing multiple reflections. The numerical results show that EFIE-CBFM-PO is more accurate than the conventional EFIE-CBFM-POJ (based on Jakobus et al. work), specially for objects with curvature.

The advantage of the canonical filter theory approach to design inductive power transfer (IPT) systems is that values for the coupled resonator elements are readily calculated from scaled canonical filter prototypes with specific frequency response characteristics. For example, Butterworth bandpass filter prototypes can be used to synthesize resonant-coupled IPT systems with critically-coupled frequency response characteristics. In this work, we analyze two canonical filter prototype structures: one prototype has series matching elements at the ports, and the other prototype has shunt matching elements at the ports. Equations are provided to transform the networks into coupled resonator structures that implement IPT links with a transmitter, receiver, and multiple repeater coils. The filter methodology for IPT link synthesis also provides an easy framework to evaluate design trade-offs. An example of comparing resonator inductor sizes for both the series and shunt matching topologies is shown for IPT links operating in ISM frequency bands of 6.78 MHz, 13.56 MHz, 27.12 MHz, and 40.68 MHz. Experimental results are shown for four different IPT examples that were designed using filter synthesis methods.

This article presents the performance of a hexagonal split-ring resonator (H-SRR) antenna in the 2.4/5.2 GHz bands and evaluation of channel capacity for single-input multiple-output (SIMO) and multiple-input single-output (MISO) systems. The proposed antenna consists of two hexagonal-shaped split-ring resonators for dual-band operation with higher gain and metallic loadings between the rings to achieve a wide impedance bandwidth. Impedance modeling of the proposed antennas confirms the role of conductance and inductance of metallic loading for enhancing the antenna characteristics, and thus, the fabricated H-SRR antenna achieves dual-band features with improved impedance bandwidth of 50%/76% and a gain of 2.32/2.57 dB at 2.4/5.2 GHz frequency bands. The performance of the hexagonal SRR antenna is then investigated for space diversity applications in the 1×3 SIMO and 3×1 MISO systems with circular SRR antennas. In linear and spherical arrangements of the antennas, the channel capacity is found in the range of 2.7 to 4.8 Mbps at the 2.4/5.2 GHz bands, which also confirms its dependency on the number of antennas as well as on the placement of antennas.

A flat lens made of a negative index (NI) metamaterial (MTM) focuses the diverging light waves with sub-wavelength resolution. However, to achieve tight 3-D focusing, one needs to realize a 3-D MTM with azimuthal and elevation focusing. In this work, a polarization-insensitive, wide-incident angle 3-D MTM showing an NI band of 0.34 THz (37%) centered at 0.92 THz is realized. A flat lens designed out of the proposed 3-D NI MTM shows sub-wavelength spot sizes of 0.48λ₁ and 0.39λ₂ for cylindrical electromagnetic (EM) waves emanating out of an electric dipole source, at 0.9 THz and 0.95 THz respectively. Also, the sub-wavelength focusing features of the NI flat slab are verified along non-symmetric planes by tilting the dipole source for different angles. It is also found that the finite flat slab configurations efficiently transfer EM beams for long conveyance lengths at NI frequencies. Thus, the realized flat slab configurations are useful for 3-D focusing requirements in optical trapping and imaging, and they are also useful for reducing the transmission losses associated with beam divergences.

To overcome electronic device dependence on energy storage medium, current research proposes a novel multiband circularly polarized (CP), microstrip patch antenna with a voltage multiplier rectifier circuit for wireless energy harvesting. The proposed antenna is designed with a dimension of 50 mm × 50 mm × 0.16 mm (0.80λ × 0.80λ × 0.028λ). Its annular slot and slits on a circular patch along with a defective ground plane result in a miniaturized, circularly polarized, and multiband response with resonance peaks at 6.3 GHz, 7.4 GHz, and 9.1 GHz, respectively. The voltage multiplier rectifier circuit is designed, optimized, and integrated with the antenna for RF signals to DC power conversion in order to energize low-power sensors-based application modules. The simulated multiband antenna resonates at three frequencies of 6.3 GHz, 7.4 GHz and 9.1 GHz with obtained -10 dB impedance bandwidths of 282 MHz (6.276 GHz-6.549 GHz), 178 MHz (7.348 GHz-7.526 GHz), and 81 MHz (9.136 GHz-9.217 GHz), gain of 6.3 dBi, 10.28 dBi, and 7.9 dBi and axial ratio bandwidth of (6.297 GHz-6.302 GHz), (7.783 GHz-7.411 GHz) and (9.256 GHz-9.473 GHz), respectively. The prototype is fabricated, and its resonance peaks are observed at 6.2 GHz, 7.8 GHz and 9.3 GHz with impedance bandwidth of 195 MHz, 206 MHz and 230 MHz and gain of 6.3 dBi, 9.6 dBi, and 7.4 dBi, respectively. The rectifier circuit is analyzed over the power range -20 dBm to 20 dBm and exhibits an increase in the DC output power significantly with a maximum measured efficiency of 53.34% at a frequency of 7.4 GHz with an associated load resistance of 1 kΩ.

The great technological development, the increase in the number of factories, and the large population growth led to an increase in the demand for the consumption of electric energy that we get from traditional methods (fossil fuels). Moreover, the global shortage in fossil fuel sources and their high costs, the global financial and economic crisis, and the harmful emissions it causes for the environment have made researchers look for electrical energy from alternative and environmentally friendly sources. As a renewable energy, solar energy is considered one of the most important sources of electrical energy today because it is easy to obtain at a low cost. However, this type of energy suffers from low efficiency and is greatly affected by changing weather conditions. To address this problem, several techniques have been proposed by research groups, and MPPT is one of those techniques that has been frequently used in recent years to extract maximum power from solar panels despite the instability in weather conditions. This technique can also generate pulses to control the DC-DC boost converter to provide a certain level of voltage. In this paper, three algorithms, namely Perturbation and Observation (P&O), Fuzzy Logic Controller (FLC), and Particle Swarm Optimization (PSO) are modified and applied in the MPPT technology to control the duty cycle of a DC-DC converter. The photovoltaic system consisting of MPPT technology, solar panels, and a DC-DC boost converter was simulated using MATLAB/Simulink. The performances of the three algorithms were compared to determine the best one that guarantees the highest efficiency under multiple test conditions. The simulation results show that PSO was a better performer than others with (99.32%, 97.02%, and 98.33%, respectively).

Among several noninvasive diagnostic modalities used for identifying and assessing breast cancer, a recently proposed digitized frequency-modulated thermal wave imaging (DFMTWI) has emerged as a widely applied active thermographic technique. DFMTWI has demonstrated its capabilities for early diagnosis and quantitative evaluation of breast cancer by exhibiting better pulse compression properties. This approach delivers better depth resolution and sensitivity than standard thermographic techniques. The current research illustrates the novel analytical model for the pulse compression favorable DFMTWI technique for the quantitative estimation of breast cancer. Using Green's function approach, an analytical model has been solved by considering the multilayer Pennes bioheat transfer equation with adiabatic boundary conditions and a constant initial condition. The conventional thermographic techniques (such as Lock-in Thermography (LT) and Pulse Thermography (PT)) are also solved with a similar approach as followed for DFMTWI. The results obtained for the proposed DFMTWI and the conventional LT and PT thermographic techniques are then compared and validated with the numerical results obtained from the numerical simulation considering the correlation coefficient as a figure of merit for early-stage breast cancer diagnosis.

In this paper, we propose a design methodology for waveguide applicators to maximize microwave power deposition into human tissues. The optimized applicators can be used in the experimental studies of the biological effects of exposure to electromagnetic radiation in the frequency range from 6 GHz to 100 GHz. The design methodology relies on the provision of reflectionless matching of a dissipative waveguide load, achieved by employing a matching network based on a quarter-wave transformer prototype. The prototype is synthesized by knowledge of the voltage standing wave ratio (VSWR) evaluated in the unmatched loaded waveguide. A key difference from the conventional synthesis procedure is that in our design approach, the characteristic impedance of the first transformer section is given, and we have to not only determine the characteristic impedances of the remaining sections, but also establish the output load. A solution of this synthesis problem and the process of converting the transformer prototype into a waveguide structure are described. The physical structure can be implemented according to provided sample models of waveguide WR137 applicators employing symmetric inductive or capacitive posts. The matched waveguide applicators are easy to manufacture, and according to the results from computational simulations, they demonstrate superior performance compared to the unmatched waveguides. Limitations of our designs (narrow bandwidth, dependence on the type of tissues encountered, limited potential for miniaturization) are discussed.

In this paper, a new formula for calculating the self-inductance of a thin conical sheet inductor is given. The presented work is derived in a semi-analytical form based on the complete elliptic integrals of the first, second, and third kind plus a term to be solved numerically. The analytical formula is obtained in the special case when the thin conical sheet inductor is degenerated into a thin wall cylinder. The validation of the presented formulas is done by triple, double, single integration and by the semi-analytical formula. These self-inductance calculations of the thin conical sheet inductors can be especially useful in broadband RF applications and wireless power transfer systems where conical inductors have been used.

Many static and rotating electric energy converters make use of inductive coils as filters, reactive loads or exciters, where a sudden variation of the magnetizing current can produce severe overvoltage with potential subsequent insulation damage. In some applications the overvoltage is the result of a superposition of travelling voltage waves in a supplying line. Traditional tools for studying such phenomena are based on ordinary differential equations that can heavily handle variable parameters, especially if they change according to the rapidity of the observed overvoltage. In this paper the transient voltage distribution in the excitation winding of a salient pole synchronous generator is simulated by solving the problem entirely in the frequency domain, i.e., without any use of the traditional ordinary differential equations solvers. Thismakesit possible to tune the parameters of a simplified electric model to the frequency response of the studied winding. It is shown that for highly inductive windings a single transmission line model with frequency dependent parameters can reproduce voltage transients very accurately, in a broad interval of frequency, relevant for power electronics and electromagnetic compatibility applications. Furthermore, the paper presents the experimental setup which has been needed for generating the fast varying voltage edges.

In passive radar systems, target echoes are submerged in the sidelobes of the static clutter, which includes multiple reflection echoes from the objects located in the operating environment of the considered system. This undesired part of the collected signals degrades the detector performances. Consequently, the reduction of the static clutter contribution is essential to ensuring an efficient operation of passive radars. In the literature, many algorithms and methods have been proposed for clutter suppression, where a good quality of the received signals is required to ensure an efficient clutter suppression. These methods require a considerable amount of data to operate which increases the complexity and the calculation load of the algorithms. In this paper, an important contribution is brought by simultaneously improving the signals quality and reducing the calculation load in the static clutter suppression process. Since the static clutter can be considered as time-invariant, the proposed approach exploits the specific architecture of the DVB-T signals to provide a noise reduction in the receiving channels by averaging the received signals after being split into symbols. Three different methods are proposed to examine the efficiency of the proposed approach. The performances of the proposed approach are validated through a set of simulations and verified using real data.

The aim of the next-generation 5G wireless network is to provide high data rates, low latency, increased network capacity and improved quality of surface (QoS) for wireless communication and internet of things (IoT). The millimetric wave communication is a promising technique with the capability of providing multi-gigabit transmission rate, network flexibility and cost-effectiveness for 5G backhauling. Smart antennas are a critical requirement for the success of millimetric wave communication system, and these antennas have the capability to form a high gain beam in desired direction and a null towards interfering signal. Directional beam-forming mitigates the high path loss associated with millimetric communication & improve signal to interference noise ratio. This article presents comparative analysis, effectiveness, and current limitations of various beam steering techniques for 5G networks based on some figures of merit with the aim of highlighting areas of improvements for each beam steering technique.

In this paper, the Wiener-Hopf technique is used to analyze the plane wave diffraction rigorously by a semi-infinite parallel-plate waveguide with five-layer material loading for E polarization. Introducing the Fourier transform of the unknown scattered field and applying boundary conditions in the transform domain, the problem is formulated in terms of the simultaneous Wiener-Hopf equations satisfied by unknown spectral functions. The Wiener-Hopf equations are solved exactly via the factorization and decomposition procedures leading to exact and approximate solutions. Taking the Fourier inverse of the solution in the transform domain, the scattered field in the real space is explicitly derived. For the region inside the waveguide, the scattered field is expressed in terms of the waveguide TE modes, whereas the field outside the waveguide is evaluated asymptotically with the aid of the saddle point method leading to a far field expression. Numerical examples of the radar cross section (RCS) are presented for various physical parameters and farfield scattering characteristics of the waveguide are discussed in detail.

An original application of stopband (SB) type negative group delay (NGD) electronic function is introduced. The unfamiliar SB-NGD circuit is designed with RLC-network lumped passive topology. The SB-NGD circuit is exploited to operate as a true-time delay (TTD) device for smart dual-beam phased array design. The two-port passive topology for designing an SB-NGD circuit constituted by an RLC-network is described. The theory and design method of the employed SB-NGD passive circuit are detailed. The microwave theory of the SB-NGD topology is elaborated from S-matrix modelling. The SB-NGD canonical form is innovatively introduced in function of the expected specifications. The synthesis design equations allowing to determine the R, L and C component values in function of the NGD specifications are formulated. The SB-NGD behavior is verified by comparison of calculated and simulated S-parameters from two different proofs-of-concept (POC). Illustrative results with a very good agreement showing SB-NGD behavior are observed around the arbitrarily chosen central frequencies f₁ = 0.7 GHz and f₂ = 1 GHz over a bandwidth of 50 MHz. The design principle of TTD-based smart dual-beam is described. The dual-band SB-NGD circuit is designed to operate as a dual-band TTD device with fixed delays at t₁(f₁) = 357 ps and t₂(f₂) = 875 ps, respectively. A radiation pattern showing the smart dual-beam steering operating system at f₁ and f₂ frequencies is discussed.

This paper presents an alternative solution for detecting breast cancer through planar antennas. The designed antenna electric parameters are the best gain for tiny radiation elements, along with the suitable characteristic impedance and bandwidth focusing on a specific application. Antennas are deployed nowadays to provide access to the detection of malignant tumors. That solution coexists with those in the hospitals (X-ray Mammography, Biopsy, Ultrasound, and Tomography), as breast cancer is a worldwide health concern because many women die yearly. Unfortunately, none of these methods are efficient as microwave imaging techniques. In terms of rapidity, efficiency, sensitivity, and accuracy, a small microstrip patch antenna operating at the Industrial, Scientific, Medical (ISM) band (5.72-5.82 GHz) is proposed in this paper for early breast tumor screening. Designed from the High-Frequency Structure Simulator (HFSS), the rectangular microstrip patch-antenna of 12x12x1 mm³, etched on an FR4 HTG-175 dielectric material (relative permittivity of 4.4 and 0.02 of loss tangent) has been simulated, prototyped, and experimentally measured with ZVA50 Vector Network Analyzer (VNA). The defective ground structure technique has been used to achieve the goals of the final prototype. The proposed antenna has 51.22 dB of return loss, 230 MHz of bandwidth, with a radiation efficiency of 82% and a gain of 1.45 dBi at the resonance frequency of 5.73 GHz. Simulation results have been well-concluded through different tumor positions on the breast to take comprehensive precautions. Furthermore, a comparison with other antenna designs has been made. Due to the available laboratory equipment, the suggested work focused on the research part.

A rigorous solution is presented for description of the plane electromagnetic wave diffraction by two parallel slots in a perfectly conducting screen of finite thickness, placed before a dielectric layer, operating as a receiver of radiation in the near zone. The field in this layer is studied for the case of small obstacle dimensions being of the order of the wavelength. It is shown that the best spatial resolution of images from two slots in a dielectric layer is reached together with their optimal focusing, which can be determined by the method proposed earlier for one-slot diffraction.

This paper presents the mathematical formulation for the generalized closed-form expressions to calculate sideband power (P_SR) of a nonuniform period time modulated array (NTMA) antenna with volumetric geometry by using pulse shifting strategy. For the arbitrary array geometry, the generalized expression of P_SR is obtained by considering the universal omnidirectional element pattern in the form sin^aθ|cosθ|^b, a > -1, b > -1/2. Then, corresponding to different array structures such as linear, planar, and volumetric ones, the derived expression is simplified for different element patterns with possible combination of `a' and `b'. Through representative numerical results it is demonstrated that the obtained simplified expressions without hypergeometric function are useful to accurately calculate the amount of power losses due to sideband radiations with significantly less time than the conventional numerical integration (NI) method.

Coupling coefficient is a key parameter for the coil design of wireless power transfer (WPT) systems. The accurate calculation of coupling coefficient is an important theoretical basis for optimizing the coil structure and improving the transmission efficiency in WPT systems. In this paper, the magnetic flux density distribution of rectangular spiral coils with double magnetic shielding is studied, and an analytical model of coupling coefficient between arbitrarily positioned rectangular spiral coils is established. First, the incident magnetic flux density is obtained based on the dual Fourier transformation and the relationship between the magnetic flux density and magnetic vector potential. Second, the reflected magnetic flux density in the region of the receiving coil is solved by using Poisson's equation, Laplace's equation and boundary conditions. Finally, the formula for the coupling coefficient between rectangular spiral coils is derived by the spatial frame transformation method and the integral method. The calculation results agree well with the finite element simulation value and experimental measurements, which verifies the correctness of the calculation formula of the coupling coefficient.