Surface Equivalence Principle Research Articles

Analysis of antenna arrays using equivalent sources for increase in computational efficiency for 5G and beyond

AbstractThe use of equivalent sources for the analysis of antenna arrays for high computational efficiency has been proposed. A single antenna element has been designed, and the fields have been saved on an enclosed geometry. The surface equivalence principle has been utilized to calculate the far‐field patterns from the fields saved on the enclosed geometry which has been termed as Huygens' box (HB). The antenna element has been used to design , , , and array and the far‐fields have been calculated. For linear arrays of HBs far‐field patterns and computation time have been compared with that of the actual antenna array. As the number of elements increases from 4 to 16, the computation time has been found to reduce from to . Further, the computation time has been found to reduce by and for and configurations, respectively. The method is suitable for analysis of complex geometry of antennas used in 5G technology and beyond.

An equivalent surface dipoles based electric field to magnetic field transformations for estimating radiated emissions

The new generation of communication devices operating in higher frequency bands is constantly pushing the complexity of field measurements for electromagnetic compliance and the design of field probes. These compliance are to be met for both electric and magnetic fields, of which if one set is available, the other can be estimated computationally using source reconstruction algorithms. The main objective of this paper is to refine the dipole-based source reconstruction algorithms using surface equivalence principle. Compared to earlier works, the algorithm is based on a novel way of placing a single dipole per point tangentially to a fictitious surface based on surface equivalence theorem instead of multiple orthogonal dipoles per point. The numerical results are compared with the state-of-art to demonstrate the effectiveness in obtaining accurate fields and locating the regions of the Device Under Test responsible for overshooting the interference limits.

Integral equation analysis of multiport H‐plane microwave circuits by using 2D rectangular cavity Green's functions accelerated by the Ewald Method

An integral equation technique for the analysis of multiport H-plane microwave circuits composed of an unlimited number of arbitrarily shaped metallic and/or dielectric elements is proposed. The structure under study is divided into different regions after the application of the surface equivalence principle. Following this approach, the access waveguide ports are modelled by means of parallel plate Green's functions, whereas the central region is characterised by 2D rectangular cavity Green's functions. The use of this kind of Green's functions represents a novelty for solving H-plane integral equation problems. For the first time, the Ewald method has been employed in order to accelerate the computation of the 2D rectangular cavity Green's functions and their derivatives, needed in the integral equation. In addition, convergence studies show the numerical convenience of using the Ewald method to achieve a fast and accurate evaluation of these Green's functions. Results show that the analysis can be very efficient if the structure is segmented in a proper way based on fitting the cavity resonator within the geometry of the structure under analysis. In fact, all the walls of the structure that are coincident with the auxiliary resonator need not to be discretised during the numerical solution. Finally, several simulation examples of practical inductive microwave circuits are presented and discussed, showing a good agreement and higher computational efficiency when compared to results provided by commercial full-wave software tools and measurements.

A Boundary Integral Equation Formalism for Modeling Multiple Scattering of Light from 3D Nanoparticles Incorporating Nonlocal Effects

AbstractA novel computational scheme that models the scattering of light at interfaces in a deep‐nanometric (deep‐nm) plasmonic system is presented. The nonclassical effects associated with the collective motion of free electrons in metals of the system are investigated by a nonlocal hydrodynamic (HD) model. Due to the HD model, three types of interfaces, that is, the dielectric–dielectric interface, the dielectric–metal interface, and the metal–metal interface, are distinguished. The scattering of light at these interfaces is described by Boundary Integral Equations (BIEs), which are constructed by using the surface equivalence principle, the concept of the Green' function and the interface conditions. The BIEs are numerically solved by the boundary element method (BEM) for 3D nanoparticles of arbitrary shapes. To validate, the computed results are first quantitatively contrasted with analytical solutions from the Mie theory for spherical core–shell structures, with good agreements being demonstrated in both the near field and the far field. Then, a qualitative study is performed for dimers consisting of spheres with various gap sizes for both the classical local response model and the nonlocal HD model. The observed trends agree well with the results reported in previous works.

An equivalent surface dipoles based source reconstruction for estimating radiated emissions numerically from shielded PCBs

This work proposes an improved dipole-based source reconstruction method for PCB inside shielding enclosures. This method applies the surface equivalence principle in conjunction with Babinet’s principle for replacing the PCB and the slots of the shielding enclosures with the equivalent surface dipoles. The tangential electric fields are measured on a spherical surface around the shielded PCB structure in the propagating near field region. The unknown dipole coefficients are obtained by solving the inverse problem iteratively and then used to estimate the radiated emissions. The advantage of the proposed method is that it does not require field measurements in the reactive near field region and identifies the areas of the PCBs responsible for radiated emissions. The numerical results provide similar error performance to the discussed state of art techniques. The effect of noise in the estimation is also presented.

Antenna Parameters for On-Body Communications With Wearable and Implantable Antennas

In this article, redefined antenna parameters regarding the additional effects occurring with on-body propagation are derived to enable a standardized characterization of on-body antennas. A model for the on-body propagation of arbitrary wearable and implantable antennas using Green's functions based on the Norton surface wave theory and the surface equivalence principle is presented, which subsequently is used as an on-body near-field-to-far-field transformation. The defined on-body far-field enables the redefinition of the antenna parameters (gain, effective area, and efficiency) for the on-body case. Based thereon, the antennas can be deembedded from the on-body channel and the on-body link between two antennas can be calculated by an adapted Friis transmission equation similar to free-space propagation. It is demonstrated by two examples, one of a hearing aid antenna and another of an antenna of an implantable pacemaker, that the on-body antenna parameters allow for an educated design of the antennas without the necessity of electromagnetic modeling of the entire system.

Scattering by a Chiral Cylinder of Arbitrary Cross Section Above a Dielectric Half-Space

A simple numerical solution for electromagnetic scattering from a 2-D homogeneous chiral cylinder of arbitrary cross section placed above a dielectric half-space (DHS) is presented. A modified surface equivalence principle is used to obtain coupled electric field integral equations. For feasible application of method of moments, a perturbation method is used where a strip of finite width approximates the surface of the infinite half-space. The perturbed currents on the interface are expressed as a difference of the currents with the cylinder present and the exact solution (cylinder removed). The excitation vector now contains the reflected field from the DHS in addition to the incident field. Transverse magnetic (TM) and transverse electric (TE) excitations are treated. Computed results include perturbed currents on the dielectric interface and the scattered fields. Excellent agreement is observed for special cases available in the literature.

Scattering From Chiral Cylinders of Arbitrary Cross-Sections Above a Ground Plane

The main purpose of this work is to solve the problem of electromagnetic scattering from a chiral cylinder of arbitrary cross-section above an infinite perfect electric conducting (PEC) plane. Using image theory, this problem is reduced to two chiral cylinders in free-space. Surface equivalence principle is used to obtain three different equivalent problems for this two-cylinder problem. Then, the method of moments is used to solve these equivalent problems numerically. It is known that the image of a chiral body through a ground plane is another chiral body with the same permittivity and permeability but opposite chirality. Using this property, the two-body problem in the moment method may be reduced to a one-body problem with a complicated moment matrix. Computed numerical results include scattered fields and equivalent surface currents on the cylinder.

A Single-Layer Dual-Mesh Boundary Element Method for Multiscale Electromagnetic Modeling of Penetrable Objects in Layered Media

A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM formulations either lead to a poorly conditioned system matrix for multiscale problems, or are computationally expensive for objects embedded in layered substrates. This article presents a new BEM formulation which leverages the surface equivalence principle and Buffa-Christiansen basis functions defined on a dual mesh, to obtain a well-conditioned system matrix suitable for multiscale EM modeling. Unlike existing methods involving dual meshes, the proposed formulation avoids the double-layer potential operator for the surrounding medium, which may be a stratified substrate requiring the use of an advanced Green's function. This feature greatly alleviates the computational expense associated with the use of Buffa-Christiansen functions. Numerical examples drawn from several applications, including remote sensing, chip-level EM analysis, and metasurface modeling, demonstrate speed-ups ranging from 3x to 7x compared to state-of-the-art formulations.

Controlling Electromagnetic Scattering of a Cylindrical Obstacle Using Concentric Array of Current Sources

In this article, a novel method is proposed to control the electromagnetic scattering due to an infinitely long cylinder, which is based on the concept of the concentric circular array. The method has its roots in the surface equivalence principle, according to which the scattering due to an object can alternatively be represented by putting induced current sources (electric or magnetic) on its surface and then assumed to radiate in an open medium (physical equivalent) or in the presence of the cylinder (induction equivalence). Using this, a cylindrical object is approximated by a circular array obtained by discretizing the induced current. The scattered field is then represented as field radiated by the circular array. Using this representation, it is now possible to tailor the scattering pattern of a cylinder by placing another circular array concentric to the original cylindrical object and controlling its excitation magnitude and phases. In this way, the proposed method also leads to a generalization of the active cloaking concept, in which the excitation amplitude of concentric circular array is negative of that induced on the original cylindrical obstacle’s surface. The method is applied both for plane wave and line-source scattering of infinitely long conducting as well as dielectric cylinders and verified by COMSOL simulations.

Illusion electromagnetics for free-standing objects using passive lossless metasurfaces

An electromagnetic illusion technique for free-standing objects for far-field observation using passive lossless metasurfaces is presented. Over a closed surface, the electric and magnetic surface currents needed for generating the scattered fields associated with a given physical scatterer are obtained using the surface equivalence principle. The closed surface defines an impenetrable metasurface characterized by surface impedance. A set of auxiliary evanescent surface waves are introduced and optimized over the entire surface to make the metasurface pointwise passive and lossless. Example 2D designs in TE polarization show that desired scattered fields are established immediately away from the illusion device surface. The illusion metasurfaces may be realized as tensor gradient metasurfaces.

A Surface Integral Equation Formulation for Efficient Simulation of Finite-Sized Multilayered Parallel-Plate Structure

The multilayered parallel-plate structure (MPPS) is a typical structure in microwave engineering. In numerical simulation, MPPS is usually modeled by an infinitely large planarly layered medium (PLM) to simplify the computation. For a realistic microwave circuit, however, the substrate is always finite in spatial extent, i.e., it is a finite-sized MPPS (FS-MPPS). To address this issue, a novel surface integral equation (SIE) formulation is proposed for the efficient simulation of FS-MPPS. In this article, the surface equivalence principle is first revisited. For the exterior and interior problems, different Green’s functions are utilized. In particular, the common homogeneous-medium Green’s function is used for the exterior homogeneous region, whereas the layered-medium Green’s function (LMGF) is applied for the interior multilayered structure. In this manner, FS-MPPS is no longer directly approximated by the infinite PLM model, but instead, it is modeled accurately by SIE whose integration kernel is derived from PLM. Finally, a PMCHWT SIE is established for the electromagnetic analysis of FS-MPPS. Due to the finite nature of the inner problem, the setting of PLM and LMGF is not unique. This nonuniqueness is studied in theory and verified by numerical simulation. It is revealed that such a nonuniqueness of the setting of the inner problem does not change the uniqueness of the final solution. To validate the proposed approach, a multidomain FS-MPPS and an FS-MPPS with embedded dielectric structures are investigated. Compared with the conventional brute-force SIE methods for FS-MPPS, where all the interfaces of the layered structure should be discretized and assigned with degrees of freedom (DOFs), the proposed method is more succinct and efficient.

Generalized Solver Hybridization Using Equivalence Principle Algorithm

The simulation of antennas often necessitates modeling the effect of nearby electrically large structures. Such structures are often unsuitable for modeling with the same technique as used on the antenna because of the prohibitive required unknown count. First-principles models of antennas (or other key features) must then be augmented with approximate models of the larger auxiliary structures, usually with high-frequency asymptotic models. The surface equivalence principle is applied to linear-media multiple scattering without regard to the formulations used for each contained domain. A Schur complement is then applied to convert the homogeneous medium equivalent problem into a inhomogeneous medium equivalent problem. The Schur complement form supports application of approximate models and makes the scattering physics plain. The results are provided for two cases modeled with the equivalence principle algorithm (EPA) hybridized with physical optics (PO) approximation.

On the analysis of capacitive rectangular waveguide discontinuities close to arbitrarily shaped conducting and dielectric posts

In this work, we propose an integral equation technique for the efficient analysis of capacitive step discontinuities in rectangular waveguides. The method allows for the inclusion of a number of arbitrarily shaped posts in the vicinity of the step discontinuity. The posts can be both metallic or composed of homogeneous dielectric materials. The integral equation formulation is based on the Surface Equivalence Principle, and uses the parallel plate Green’s functions that take into account for the boundary conditions imposed by the host waveguide. The formulation is written in the mixed spatial-spectral frequency domain, and takes advantage of the symmetry of the problem by reducing the original three dimensional (3D) problem to a so called 2.5D problem. The numerical technique has been validated with simulation examples, namely, two lowpass filters that use conducting and dielectric posts of different shapes as impedance inverters. The results provided by the method that we propose have been also compared to those obtained with a commercial full-wave software tool (ANSYS HFSS), showing in all cases a very good agreement with substantially higher computational efficiency.

A MoM solution for TM scattering by dielectric cylinders above an infinite flat surface

A simple solution method is presented for transverse magnetic plane wave scattering by a dielectric cylinder of arbitrary cross-section in front of an infinite flat dielectric surface. The interface between two semi-infinite, dissimilar half-spaces is considered by a perturbed equivalent magnetic current. Coupled integral equations are obtained from a special form of surface equivalence principles and are solved numerically by the Method of Moments. The scattered tangential electric field at interface is displayed and far-zone fields are compared to the results available in the literature.

Quasi-Static Surface-PEEC Modeling of Electromagnetic Problem With Finite Dielectrics

This paper presents a quasi-static surface-based partial element equivalent circuit (PEEC) model for electromagnetic problems consisting of coupled conductors and heterogeneous dielectrics of finite size. The PEEC model is based on the surface equivalent principle. Unlike the traditional surface-based PEEC models, in which the integral equations are set up by enforcing the field continuity in the true field region, the homogeneous integral equations in this model are obtained by enforcing the tangential null field condition in the null field regions. Simplified integral equations are obtained under the quasi-static assumption, in which the circuit elements carrying electric currents and magnetic charges on the dielectric surfaces are vanished. Consequently, the size of the subcircuit describing dielectrics is reduced significantly compared to the full-wave surface-PEEC (S-PEEC) model. Since the quasi-static S-PEEC model only contains frequency-independent circuit elements, it can be conveniently used for time-domain simulation. Three numerical examples are presented to validate the new PEEC model for typical embedded RF passive components, packaging and interconnection problems in both the frequency domain and the time domain. Excellent agreement is observed between the results of the proposed PEEC model, S-PEEC model, and those of commercial software within the quasi-static frequency range.

A Perturbation Method for Scattering by a Dielectric Cylinder Buried in a Half-Space

A simple method is presented for transverse magnetic plane-wave scattering by a dielectric cylinder of arbitrary cross section buried in a half-space. The interface between two semi-infinite dissimilar half-spaces is considered as an infinite aperture, which is represented by a perturbed equivalent magnetic current. Coupled integral equations for the aperture electric field (or equivalent magnetic current) and the equivalent currents on the buried cylinder are obtained from surface equivalence principles and are solved numerically by the method of moments. Data for the electric field at the interface and far field are presented for cases of interest and are compared to the results available in the literature.

Multiple-Traces Surface Integral Equations for Electromagnetic Scattering From Complex Microstrip Structures

In this communication, a new multiple-traces Poggio–Miller–Chang–Harrington–Wu–Tsai (MT-PMCHWT) equation is proposed to simulate the electromagnetic scattering from microstrip structures. Based on the surface equivalent principle, the original object can be decomposed into two independent domains, i.e., the exterior region (free space) and interior region (microstrip). Different from the traditional EFIE-PMCHWT method, in this new multiple-traces method, dielectric surface is discretized with two pairs of meshes, and Robin transmission conditions (TCs) are enforced on the interface between the exterior and interior regions to ensure the continuity of fields. In comparison with the traditional EFIE-PMCHWT, this new MT-PMCHWT has a better iteration convergence property. Additionally, a new multiple-traces electric field/combined field integral equation with better iteration convergence is also proposed. Because the continuity of fields is ensured by TCs, the exterior and interior regions can be discretized with nonconformal meshes, which improves the flexibility and efficiency of the proposed methods substantially.

Internally Combined Volume-Surface Integral Equation for EM Analysis of Inhomogeneous Negative Permittivity Plasma Scatterers

A well-conditioned internally combined volume-surface integral equation (ICVSIE) for analyzing electromagnetic scattering from perfect electrically conducting (PEC) surfaces coated with negative permittivity plasmas is presented. Existing integral equations pertinent to these problems oftentimes yield ill-conditioned systems of equations. The ill-conditioning stems from the presence of interfaces between a positive permittivity background medium and the negative permittivity plasma and/or is due to low-frequency breakdown. To tackle these issues, the proposed ICVSIE wraps the negative permittivity plasma into a Huygens surface and exploits surface equivalence principles to artificially change the sign of the permittivity of the medium in which equivalent volumetric polarization currents radiate. Next, it combines a Muller combined field integral equation on the Huygens surface with a volume-surface integral equation for the negative permittivity plasma that coats the PEC surface in a manner that circumvents low-frequency breakdown. The accuracy, efficiency, and stability of the proposed ICVSIE are demonstrated via its application to various canonical scatterers and a plasma-engulfed reentry vehicle.

Surface equivalence principle and Surface Integral Equation (SIE) revisited for bioelectromagnetics application

Surface equivalence principle and Surface Integral Equation (SIE) revisited for bioelectromagnetics application