Current Equations Research Articles

Conical annular patch antenna for dual band operation on airborne vehicles

An annular patch antenna operating in both TM04 and TM05 modes and conformed to a conical surface is proposed for airborne applications. Dual-slot loading is done to obtain a high gain linearly polarized broadside radiation pattern in both the modes of operation by introduction of additional equivalent magnetic currents. Cavity model analysis of a conical annular patch antenna is carried out and is further extended to obtain the multiport network modeling (MNM) of the dual-slot loaded conical annular patch antenna. Additional control over directivity and side lobe level can be achieved by variation in ratio of slot lengths. The effect of curvature on the antenna performance is studied using MNM. The antenna produces a gain of 9.26 and 8.83 dBi in X-band frequencies of 9.838 and 10.323 GHz respectively.

Manipulation of lasing modes in a circular-side octagonal microcavity laser with a spatially distributed current injection.

We propose and demonstrate a circular-side octagonal microcavity (COM) semiconductor laser with a spatially distributed current injection for manipulating the lasing modes. There are two types of high-quality-factor whispering-gallery (WG) modes with distinct field patterns in a COM: the four-bounced quadrilateral modes and the eight-bounced octagonal modes. By designing two separated p-electrodes, the COM laser is divided into two regions that are pumped independently to select specific modes for lasing. The two types of WG modes lase simultaneously when the two regions are injected with equivalent currents. Degeneracy removal of the quadrilateral modes is observed in both simulation and experiment when the two regions are injected with inequivalent currents. The quadrilateral modes are suppressed when one of the two regions is un-injected or biased with a negative current, and single-octagonal-mode lasing is realized. The results show that the lasing modes can be efficiently manipulated with the spatially distributed current injection considering the distinct field patterns of different WG modes in the microcavities, which can promote the practical application of the microcavity lasers.

New insights into the mechanisms underlying biochar-assisted sustained high-efficient co-digestion: Reducing thermodynamic constraints and enhancing extracellular electron transfer flux

To clarify the roles of biochar in the anaerobic co-digestion of waste activated sludge (WAS) and food waste (FW), batch tests were conducted coupled with thermodynamics, extracellular electron transfer flux and microbial community analysis. Compared with the control group, biochar significantly facilitated the co-digestion at three periods, but its sustainable facilitation was mainly in the syntrophic methanogenesis of volatile fatty acids (VFAs). The thermodynamic analysis confirmed that biochar could alleviate limitations imposed by high hydrogen partial pressure during interspecies hydrogen transfer (IHT), the thermodynamic windows was expanded 137% and 92% in the syntrophic methanogenesis of acetate and propionate, respectively. Meanwhile, due to the redox capacity of biochar (4.85 and 0.35 μmol e−/g biochar), the equivalent current of direct interspecies electron transfer (DIET) flux for syntrophic methanogenesis of acetate and propionate obtained were 1.0 × 10−4 A and 0.9 × 10−4 A, which were 108 times than that of IHT. It should be noticed that the functional microorganisms like Methanosarcina which could participate DIET were only enriched on the surface of biochar, the dominant Methanothermobacter in suspended sludge probably indicate IHT was still the main pathway for syntrophic methanogenesis. Nevertheless, the DIET triggered by the redox-active moieties on the surface of biochar and the enhanced IHT by alleviating thermodynamic restrictions, promoted the syntrophic methanogenesis synergistically.

Field‐Aligned and Ionospheric Currents by AMPERE and SuperMAG During HSS/SIR‐Driven Storms

AbstractThis study considers 28 geomagnetic storms with Dst nT driven by high‐speed streams (HSSs) and associated stream interaction regions (SIRs) during 2010–2017. Their impact on ionospheric horizontal and field‐aligned currents (FACs) have been investigated using superposed epoch analysis of SuperMAG and AMPERE data, respectively. The zero epoch () was set to the onset of the storm main phase. Storms begin in the SIR with enhanced solar wind density and compressed southward oriented magnetic field. The integrated FAC and equivalent currents maximize 40 and 58 min after , respectively, followed by a small peak in the middle of the main phase ( + 4 hr), and a slightly larger peak just before the Dst minimum ( + 5.3 hr). The currents are strongly driven by the solar wind, and the correlation between the Akasofu and integrated FAC is 0.90. The number of substorm onsets maximizes near . The storms were also separated into two groups based on the solar wind dynamic pressure pdyn in the vicinity of the SIR. High pdyn storms reach solar wind velocity maxima earlier and have shorter lead times from the HSS arrival to storm onset compared with low pdyn events. The high pdyn events also have sudden storm commencements, stronger solar wind driving and ionospheric response at , and are primarily responsible for the first peak in the currents after . After days, the currents and number of substorm onsets become higher for low compared with high pdyn events, which may be related to higher solar wind speed.

Fast Power Density Assessment of 5G Mobile Handset Using Equivalent Currents Method

As the fifth-generation (5G) mobile communication is utilizing millimeter-wave (mmWave) frequency bands, electromagnetic field (EMF) exposure emitted from a 5G mmWave mobile handset should be evaluated and compliant with the relevant EMF exposure limits in terms of peak spatial-average incident power density (PD). In this work, a fast PD assessment method for a 5G mmWave mobile handset using the equivalent current (EQC) method is proposed. The EQC method utilizes the intermediate-field (IF) data collected by a spherical measurement system to reconstruct the EQCs over a reconstruction surface and then computes the PD in close proximity of the mobile handset with acceptable accuracy. The performance of the proposed method is evaluated using a mmWave mobile handset mock-up equipped with four quasi-Yagi antennas. The assessed PD results are compared with those computed using full-wave simulations and also those measured with a planar near-field (NF) scanning system. In addition, three influencing factors related to the accuracy of the EQC method, namely, the angular resolution, the phase error, and the handset position in the IF measurements, are also analyzed. The proposed method is a good candidate for fast PD assessment of EMF exposure compliance testing in the mmWave frequency range.

Internal Electric Field Reconstruction and SAR Estimation of In-Body Antenna Using Inverse Equivalent Current Method

In this article, we reconstruct the internal electric field due to a dipole antenna embedded in a dielectric phantom for developing a noninvasive specific absorption rate (SAR) measurement system. The reconstruction method is based on the surface equivalent theorem and boundary conditions, which relate the external field radiated from the embedded antenna to equivalent electromagnetic surface currents on the human body. The electric field data sampled at spatial points on a surface enclosing the phantom are used in the inverse calculation. All field integrals are discretized and numerically solved to obtain the electromagnetic currents on the phantom's surface. The internal electric field distribution and SAR value in a phantom can be calculated from the reconstructed surface currents if the electric properties of the phantom are known. The validity of the method was demonstrated numerically and experimentally using a dipole antenna embedded in the lossy rectangular phantom, which has a dielectric constant close to human skin tissue at 2.5 GHz. Comparison with forward numerical simulations has shown that the surface current and electric field distribution can be predicted with great precision. Carefully performing the experiments using a self-made phantom validated our numerical demonstration and provided satisfactory reconstruction results.

Physical optics framework for electromagnetic scattering from electrically large targets coated with a uniaxial electric anisotropic medium based on point-source excitation.

Aiming to determine the scattered estimation of complex and electrically large targets coated with the uniaxial electric anisotropic medium (UEAM) from a distributed excitation source, the demanding study is simplified by constructing the physical optics (PO) architecture which consists of three aspects, the discrete facet modeling, the tangent plane approximation, and the scattering of an infinite PEC plate coated with the UEAM based on point-source excitation, including the electric and magnetic dipole. We depict the outer surface of an electrically large scatterer as the constitution of countless tiny triangular facets. From the tangent plane approximation employed in the PO method, the scattered fields of any discretized facet induced by the equivalent electromagnetic currents (EECs) can be further evaluated as the surface fields of an infinite UEAM-coated PEC slab. Therefore, the rigorous solution of the dyadic Green's function (DGFs) for an infinite anisotropic-medium-coated PEC plate under point-source incidence is computed first. Moreover, characterizing the ray propagation process of the plane wave spectrum, the asymptotic technique of the saddle point is employed to obtain the scattered ray field in the spatial domain. Finally, the total scattered fields are obtained by the field superposition of the overall illuminated facets under point-source excitation. Compared with the reference solution, the proposed method is validated, and the simulation results of the representative shapes coated with the UEAM layer from a point source are presented.

Phaseless near‐field to far‐field transformation based on source current reconstruction and signal subspace optimization

In this article, an algorithm for the phaseless near-field (NF) to far-field (FF) transformation based on the source current reconstruction method (SRM) is proposed. The algorithm starts with decomposing the equivalent currents of the antenna under test (AUT) into a deterministic and ambiguous current. The deterministic portion of the current is determined from the phaseless signal subspace-based optimization method (SOM), while several iterative forward-backward propagations add the ambiguous portion. It is shown that with the SOM initialization, no further prior information about the antenna under test is needed and the iterative scheme can converge to the desired result within a few iterations. A simulation and a measurement example validate the proposed algorithm. All results show an accurate, fast, and stable phaseless field transformation is obtained.

Thermo-radiative energy conversion efficiency of a passive radiative fluid cooling system

In the passive radiative cooling process, a sky-facing surface emitting thermal radiation through the bandwidth coincident with the atmospheric window highly transparent to the radiation within 8–13 μm can preserve the temperature below ambient spontaneously. The cold surface can act as a fundamental building block for energy conversion, in which thermo-radiative energy conversion can be the simplest form and realized by a functionalized fluid-wall heat transfer interface. Energy conversion efficiency denotes the ratio of enthalpy converted by the working fluid to the cooling effect harvestable from the sky. In parallel with fluid cooling capacity, they are discussed by thermal and energy responses of a cooling system subjected to a perturbation in fluid flow, and demonstrated by measurement on a wafer-sized system acted by an equivalent heat current. According to interfacial heat transfer characteristics, cooling performance can be classified into inhibition, transition and saturation regimes, where the saturated performance is the most outstanding. However, fluid cooling and energy conversion capacities are always inversely correlated, where the reduction in fluid temperature decreases with increasing flow rate, but efficiency increases with increasing flow rate. Experimental results, in line with the theoretical prediction, show that 12.4 μL/s of water can be chilled by −4.1 °C at an overall efficiency of 14%, but 116 μL/s of water can be weakly chilled by −1.5 °C at an elevated efficiency of 49%. The dilemma in energy efficient collection of cooling fluid is an innate physical mechanism restricted by Newton's law of cooling and the 1st law of thermodynamics.

Capacity Bounds and Degrees of Freedom for MIMO Antennas Constrained by Q-Factor

The optimal spectral efficiency and number of independent channels for MIMO antennas in isotropic multipath channels are investigated when bandwidth requirements are placed on the antenna. By posing the problem as a convex optimization problem restricted by the port Q-factor a semi-analytical expression is formed for its solution. The antennas are simulated by method of moments and the solution is formulated both for structures fed by discrete ports, as well as for design regions characterized by an equivalent current. It is shown that the solution is solely dependent on the eigenvalues of the so-called energy modes of the antenna. The magnitude of these eigenvalues is analyzed for a linear dipole array as well as a plate with embedded antenna regions. The energy modes are also compared to the characteristic modes to validate characteristic modes as a design strategy for MIMO antennas. The antenna performance is illustrated through spectral efficiency over the Q-factor, a quantity that is connected to the capacity. It is proposed that the number of energy modes below a given Q-factor can be used to estimate the degrees of freedom for that Q-factor.

New analytical algorithm for calculating the end leakage magnetic field of a 300Mvar synchronous condenser under no‐load condition

Aiming at the complexity of end structures in the end region of large synchronous machines, it is difficult to obtain an analytical method for the end leakage magnetic field. In order to solve such a problem, a new analytical algorithm (NAA) considering the influence of the rotor end shaft and air gap is proposed. The mirror image of the rotor end current with the core end plane and the rotor shaft cylinder as mirror surfaces is studied. The air-gap effect is considered by the equivalent air-gap current, and the equivalent air-gap current equation of synchronous machines in the polar coordinate system is derived. Then, a 300Mvar synchronous condenser (SC) is proposed for the first time in China as an example; according to the Biot–Savart law and the superposition principle, the end leakage magnetic field of the SC under no-load condition is calculated, and the influence of different shaft structures on the end leakage magnetic field is analysed. Finally, the calculation results are compared with the 3-D finite element method, which verifies the accuracy of the NAA.

Design of Composite Microstrip-Monopole Antenna With 180$^\circ$ 1 dB Beamwidth Based on Complementary Sources Concept

A new perspective based on complementary sources radiation is presented for analyzing a widebeam composite microstrip-monopole antenna. The typical cavity model theory shows that the radiation patterns of the microstrip antenna could be calculated by using two parallel equivalent magnetic currents, and the E-plane beamwidth of the traditional microstrip antenna is mainly determined by the array factor. Loading the monopoles through the metal patch of the original microstrip antenna can construct complementary sources. Two monopoles are symmetrically loaded and two pairs of complementary sources are excited. Interestingly, the two pairs of complementary sources are aligned with in-phase magnetic current radiation sources and antiphase electronic current radiation sources, which indicates two heart-shaped radiation patterns pointing in opposite directions. The total far-zone radiated fields synthesized by the two heart-shaped radiation patterns can present wide E-plane beamwidth performance. An example antenna working at 4.4 GHz is designed for verification. With the introduction of a differential feeding scheme for a symmetrical radiation pattern, the E-plane radiation pattern can cover the upper half plane, i.e., 180°, with a fluctuation of less than 1 dB and an antenna gain of over 3 dBi.

Comparative Study of Preconditioners For The FFT-JVIE Solution of Highly Inhomogeneous Dielectric Objects

It was recently reported that the volume integral equation formulation based on equivalent volumetric currents (JVIE) can be a suitable choice to solve the dynamic electromagnetic scattering from highly inhomogeneous objects. This work presents a comparative study of some relatively cheap preconditioning strategies numerically in terms of the Generalized Minimum Residual (GMRES) iterative solver. The numerical experiments on a human head model show that different preconditioners behavior differently in improving the convergence.

Experimental Validation of a Microwave Imaging Method for Shallow Buried Target Detection by Under-Sampled Data and a Non-Cooperative Source.

In microwave imaging, it is often of interest to inspect electrically large spatial regions. In these cases, data must be collected over a great deal of measurement points which entails long measurement time and/or costly, and often unfeasible, measurement configurations. In order to counteract such drawbacks, we have recently introduced a microwave imaging algorithm that looks for the scattering targets in terms of equivalent surface currents supported over a given reference plane. While this method is suited to detect shallowly buried targets, it allows one to independently process all frequency data, and hence the source and the receivers do not need to be synchronized. Moreover, spatial data can be reduced to a large extent, without any aliasing artifacts, by properly combining single-frequency reconstructions. In this paper, we validate such an approach by experimental measurements. In particular, the experimental test site consists of a sand box in open air where metallic plate targets are shallowly buried a (few ) under the air/soil interface. The investigated region is illuminated by a fixed transmitting horn antenna, whereas the scattered field is collected over a planar measurement aperture at a fixed height from the air-sand interface. The transmitter and the receiver share only the working frequency information. Experimental results confirm the feasibility of the method.

Statistics on Omega Band Properties and Related Geomagnetic Variations

AbstractUsing the list of the omega structures based on the Magnetometers‐Ionospheric Radars‐All‐sky Cameras Large Experiment network (Partamies et al., 2017, https://doi.org/10.5194/angeo-35-1069-2017), we obtained a number of important statistical characteristics describing the surface magnetic field. Based on 438 events, typical magnetic variations associated with the passage of the single omega were obtained. The typical variation, obtained using superposed epoch analysis, is associated with a local bending of the westward electrojet and statistically confirms the distribution of equivalent ionospheric currents obtained in earlier observations of single omegas. It was found that during low and moderate geomagnetic activity, the appearance of the omega structures in the dark morning magnetic local time (MLT) sector results in two times higher than average dB/dt on the ground surface. Also, the velocity, direction of movement, and area of omega structures were calculated. It is shown that faster and bigger omegas produce larger time derivatives of the ground magnetic field. Furthermore, we demonstrate that in the 03–08 MLT sector, superposed magnetic variations for the arbitrary events of very high time derivatives |dB/dt| > 10 nT/s, reveal magnetic signatures similar to omegas. Our findings, together with the results described by Apatenkov et al. (2020, https://doi.org/10.1029/2019gl086677), emphasize the important role of omega structures in the formation of large geomagnetically induced currents.

Global Pc5 Pulsations From the Polar Cap to the Equator: Wave Characteristics, Phase Variations, Disturbance Current System, and Signal Transmission

AbstractWe present observations of global Pc5 pulsations by ∼180 ground magnetometers during the recovery phase of an intense geomagnetic storm. Measurements of magnetic fields along four latitudinal magnetometer chains and one longitudinal magnetometer chain are used to determine the wave characteristics of Pc5 pulsations. Many new features of Pc5 pulsations are identified from a single event for the first time. The Pc5 pulsations occur simultaneously at all latitudes and longitudes/local times, and the period of the Pc5 pulsations is about 10 min and does not depend on latitude and longitude. The latitudinal distributions of the northward (H) component and magnetic pressure of Pc5 perturbations are derived. The phase of the H component reverses across 50–70° magnetic latitude (MLat) but is nearly the same at middle and low latitudes. The phase of the H component at low latitudes does not vary much with longitude/local time. The phase of the D component magnetic field reverses near the equator in the latitudinal direction and also reverses around dawn, noon, dusk, and midnights in the longitudinal direction. The distribution and evolution of global ionospheric equivalent disturbance currents during Pc5 pulsations are derived. A coupled magnetospheric‐ionospheric current system is proposed to explain the observed characteristics of global Pc5 pulsations. It is suggested that the variations of the phase of Pc5 pulsations with latitude and local time are determined by the global distribution of the coupled magnetospheric‐ionospheric current system but not caused by propagation delay of the signals.

Design of a Leaky-Wave Antenna Featuring Beam Scanning From Backfire Utilizing Odd-Mode Spoof Surface Plasmon Polaritons

In this communication, a leaky-wave antenna (LWA) featuring beam scanning from backfire direction is investigated. The presented LWA is designed based on the odd-mode spoof surface plasmon polariton (SSPP) waveguide that consists of a row of complementary “cross-shaped” units. The odd-mode SSPP is excited by a convertor from the microstrip line to the slotline. As opposed to the even mode, the equivalent electric current of the odd-mode SSPP is perpendicularly distributed to the longitudinal direction, providing a complete backfire radiation component. Then a general method to design a sinusoidally modulated reactance surface (SMRS) LWA is introduced to efficiently generate backfire radiation at desired frequency and the depth of each SSPP unit is determined by calculation. By this way, the optimized working of the LWA will be drastically reduced. A prototype of the presented LWA is simulated, fabricated, and measured. Simulation and experimental results show that the main beam of the presented LWA scans from backfire at desired frequency of 20 GHz to the broadside direction at 27.5 GHz. And the antenna shows bidirectional radiation feature.

Busbar Differential Protection Using an Alternative Generalized Alpha Plane

This paper describes an alternative busbar differential protection function based on the generalized alpha plane. This approach faithfully maps several currents in two equivalent currents such that it preserves the original restraint and operation signals. The original formulation was applied to multi-terminal transmission lines protection but the number of terminals can be small if compared with the number of bays connected to busbars. For this reason, this first method is initially assessed in order to verify its suitability for busbar protection purposes. After that, an alternative algorithm to map the currents in the same plane is described and tested by using a double-bus-single-breaker 220 kV busbar configuration, modeled in ATPdraw. The simulations of internal and severe external faults, as well as evolving faults, are performed for a wide variety of scenarios including fault times, fault resistances and fault types. The results bring up a greater robustness and shorter response time if compared with original alpha plane approach, thus it represents an alternative as a busbar protection function which provides high reliability and it can be easily implemented in a commercial relay due to its mathematical simplicity.

MILP-Based Fault Diagnosis Model in Active Power Distribution Networks

With a rapid growth in the deployment of renewable and distributed energy resources (DERs) in active power distribution networks, especially the inverter-interfaced distributed generators (IIDGs), existing fault section estimation methods are facing additional challenges. This paper proposes an optimization model for fault diagnoses in active power distribution systems, which aims at simultaneous identifications of suspected fault line sections and potential false alarms sent by remote fault indicators (RFIs). First, mathematical expressions of expected and false alarms of oriented RFIs (ORFIs) and non-oriented RFIs (NRFIs) are formulated to construct a basic fault diagnosis model. Minimizing the number of false alarms is chosen as the objective function to find the most credible one from all possible fault hypotheses which represent different combinations of elements in the outage area. Next, considering IIDGs, a modified fault diagnosis model is established by eliminating misleading components from the objective function which are produced by incompetent RFIs and have failed to detect weak currents. The monitoring data provided by distribution level phasor measurement units (D-PMUs) for weak IIDG fault currents are leveraged to construct the equivalent RFI current, which is compared with the trigger threshold to find incompetent sensors. The proposed problem is formulated as a mixed-integer linear programming (MILP) model, which is solved by off-the-shelf commercial solvers. The effectiveness of the proposed fault diagnosis model is validated by test cases representing several DERs and false alarms applied to a utility feeder.

An Efficient Full-Wave Method for Analyzing the Radiation Pattern of an Antenna Enclosed by an Axisymmetric Radome

This article proposes an efficient full-wave method to analyze the radiation pattern of an antenna in the presence of a multilayer axisymmetric radome. In this method, first, the field distribution on the antenna aperture is replaced with the respective equivalent currents to compute the incident electromagnetic field on the inner surface of the radome. The radome is then modeled with a cascaded network of two-port devices and generalized transmission lines based on the theory of surface equivalence and the method of moments. The cascaded network is used to relate the tangential components of the electromagnetic field at the inner surface of the radome to their counterparts at the outer surface of the radome which, in turn, are used to obtain the respective equivalent currents. Finally, these currents are used to determine the radiation pattern of the antenna in the presence of the radome. The efficiency of the proposed method is demonstrated by comparing the simulation results of several case studies with those obtained by the rival theoretical models in the literature or computed by commercial numerical codes.