Mixed Potential Integral Equation Research Articles

Surface Impedance Modeling of Plasmonic Circuits at Optical Communication Wavelengths

A novel surface impedance model is developed to analyze plasmonic circuits supporting long range surface plasmon polaritons (LR-SPP). The analysis is carried out in two steps. First, a higher order approximation of the surface impedance is obtained for the metal strip through a 2-D analysis of the waveguide cross section. Second, the developed surface impedance boundary condition is incorporated in the mixed potential integral equation formulation of the problem, and the method of moments is employed to find the unknown surface current distributions on the strips carrying LR-SPP. In other words, in this method, the volumetric currents flowing inside the metal are substituted by a surface current model flowing on an infinitely thin strip characterized by the developed surface impedance model. This procedure reduces the number of unknowns significantly, in this way increasing the speed of simulation. Validity and accuracy of the proposed model are demonstrated by analyzing three popular LR-SPP circuits.

Spherical Probe-Fed Antennas with Parasitic Elements

The theory and experiment of a probe-fed conformal antenna with a conducting parasitic element mounted on a spherical multilayer structure are presented in this article. Linear Rao–Wilton–Glisson triangular basis functions are applied in a mixed-potential integral equation formulation. Current distributions on coaxial probe and conformal radiating elements are computed by using the proper spatial domain electrical dyadic Green's function and its asymptotic approximation. A prototype of such an antenna is fabricated and tested. The effect of the parasitic element on the input impedance, gain, and radiation patterns of the antenna is investigated. It is shown that the antenna characteristics are improved significantly with the presence of the stack. Good agreement is achieved between the results obtained from the proposed methods and measurement results.

Quasi 3-D Mixed Potential Integral Equation Formulation for Periodic Structures

This paper introduces the use of the quasi 3-D mixed potential integral equation formulation for structures with a periodicity in two dimensions. The quasi 3-D formulation allows to use both horizontal and vertical conductors, and dielectric inclusions. The key innovation is the use of an effective algorithm to calculate Periodic Green's Functions (PGFs) for vertical currents in the planar multilayered background medium. This algorithm retains the same scheme as for a single source Green's Function (GF). In both cases, the GFs are calculated via an inverse Fourier transform of the GFs in the spectral domain, which are known in closed form. In order to remedy the poor convergence for small source—observation distances, an asymptotic extraction is used, yielding a very compact algorithm, and acceleration techniques are applied. Simple guidelines are proposed to construct asymptotes having the required leading terms and a good convergence. It is shown that many acceleration algorithms widely used in literature are actually able to perform well only in specific circumstances. As far as the authors can see, there is still no general and robust technique, yielding highly accurate results under all circumstances. Several examples illustrate the efficiency of the technique.

Accelerated Macro Basis Functions Analysis of Finite Printed Antenna Arrays Through 2D and 3D Multipole Expansions

An efficient technique is presented for the analysis of finite printed antenna arrays made of identical elements. It is based on a closed-form expression for the spatial-domain Green's function (GF) given as a finite sum of cylindrical waves (obtained through rational function fitting) plus one spherical wave. From there, a multipole expansion can be obtained for planar layered medium GFs. The macro basis function (MBF) technique is applied to the method of moments (MoM) solution of a mixed-potential integral equation, this reduces the size of the MoM impedance matrix and allows for a direct solution. However, the evaluation of the entries of this reduced matrix becomes the dominant contribution to the total computation time. The aforementioned multipole expansion is exploited to provide a fast construction of the reduced MoM matrix, whose elements are the reaction integrals between the MBFs considered to characterize the currents on the array element. The complexity of evaluating the interactions between MBFs is found to be dominated by the calculations related to the spherical wave term. Thus, taking into account the layered medium does not increase the order of the complexity with respect to a multipole-accelerated computation of reaction integrals in a homogeneous medium.

Full-Wave Analysis of Microstrip Antennas in Three-Layered Spherical Media

A model of three-layered spherical microstrip antenna has been analyzed based on Rao-Wilton-Glisson (RWG) triangular basis functions using mixed potential integral equation (MPIE). Firstly, the model of antenna and the dyadic Green’s function in spherical microstrip antennas are given at the beginning of this paper. Then, due to the infinite series convergence problem, asymptotic extraction approach is presented to accelerate the Green’s functions convergence speed when source and field points are located in the same layer and different layers. The convergence speed can be accelerated observably by using this method. Finally, in order to simplify impedance matrix elements calculation at the junction of the probe and patch, a novel division fashion of pair of triangles is adopted in this paper. The input impedance result obtained shows the validity and effectiveness of the analysis method comparing with published data.

A New Green's Function Formulation for Modeling Homogeneous Objects in Layered Medium

A new Green's function formulation is developed systematically for modeling general homogeneous (dielectric or magnetic) objects in a layered medium. The dyadic form of the Green's function is first derived based on the pilot vector potential approach. The matrix representation in the moment method implementation is then derived by applying integration by parts and vector identities. The line integral issue in the matrix representation is investigated, based on the continuity property of the propagation factor and the consistency of the primary term and the secondary term. The extinction theorem is then revisited in the inhomogeneous background and a surface integral equation for general homogeneous objects is set up. Different from the popular mixed potential integral equation formulation, this method avoids the artificial definition of scalar potential. The singularity of the matrix representation of the Green's function can be made as weak as possible. Several numerical results are demonstrated to validate the formulation developed in this paper. Finally, the duality principle of the layered medium Green's function is discussed in the appendix to make the formulation succinct.

MPIE/MoM Acceleration With a General-Purpose Graphics Processing Unit

In this paper, we describe an accelerated implementation of the Method of Moments (MoM). A framework is proposed, exploiting the graphics processing unit (GPU) computing power by means of the software platform compute unified device architecture (CUDA). The mixed-potential integral-equation formulation, applied to microstrip circuit modeling, is adopted, and both the impedance matrix computation and the linear system solution of the MoM are accelerated. The latter point has been handled by considering both a direct dense (LU-based) and an iterative sparse (bi-conjugate gradient stabilized) solver. The best suited method is selected automatically during a thresholding phase, which renders the impedance matrix as sparse as possible. The effectiveness of the GPU-enabled MoM has been extensively tested in the analysis of planar circuits and components. The results achieved confirm the validity, accuracy, and high performance of the proposed approach.

Effect of the wall structure on the level of the radiated electric field due to indoor PLC circuit

PurposeThe purpose of this paper is to present a frequency domain analysis of high frequency behaviour of an indoor Powerline communications (PLC) circuit in the presence of a plaster board/concrete wall structure. The main purpose of this analysis is to investigate the influence of the wall structure on the current distribution and the radiated electric field due to PLC signals in range from 3 MHz to 30 MHz.Design/methodology/approachThe mathematical model is based on the full‐wave theory formulated by the Mixed Potential Integral Equation (MPIE) for the electric field due to energized thin‐wire conductors in stratified media. The solution for the current and the electric field distribution is obtained by using the Method of Moments.FindingsNumerical results are obtained of the current distribution along the conductors of the PLC circuit and the radiated electric field in presence of a wall structure. Two cases are analyzed: when the circuitry is placed in the wall; and when the circuitry is placed outside the wall.Practical implicationsThe paper presents the mathematical model that may be applied for analysis of indoor PLC circuits placed in presence of wall structures.Originality/valueIn the paper, a full‐wave model of the PLC circuitry in presence of a wall structure is developed, on the basis of MPIE and the Method of Moments.

An Efficient 1-D Periodic Boundary Integral Equation Technique to Analyze Radiation onto Straight and Meandering Microstrip Lines

A modeling technique to analyze the radiation onto arbitrary 1-D periodic metallizations residing on a microstrip substrate is presented. In particular, straight and meandering lines are being studied. The method is based on a boundary integral equation, more specifically on a mixed potential integral equation (MPIE), that is solved by means of the method of moments. A plane wave excites the microstrip structure, and according to the Floquet–Bloch theorem, the analysis can be restricted to one single unit cell. Thereto, the MPIE must be constructed using the pertinent 1-D periodic layered medium Green’s functions. Here, these Green’s functions are obtained in closed form by invoking the perfectly matched layer paradigm. The proposed method is applied to assess the radiation onto 1) a semi-infinite plate, 2) a straight microstrip line, and 3) a serpentine delay line. These three types of examples clearly illustrate and validate the method. Also, its efficiency, compared to a previously developed fast microstrip analysis technique, is demonstrated.

An enhanced integral-equation formulation for accurate analysis of frequency-selective structures

In this work, a very efficient mixed-potential integral-equation formulation is implemented for the rigorous analysis of multilayered structures with arbitrarily shaped two-dimensional periodic metallic and/or dielectric inclusions. Original acceleration techniques have been developed for the computation of the components of the scalar and dyadic Green's functions, based on different types of asymptotic extractions according to the potential considered. The theoretical approach and its computational convenience have been validated through different full-wave analyses concerning both scattering problems and complex-mode dispersive behaviors in various frequency-selective structures for microwave applications.

Considerations on Double Exponential-Based Cubatures for the Computation of Weakly Singular Galerkin Inner Products

Highly accurate and efficient cubatures based on the double exponential quadrature rules are presented for the computation of weakly singular integrals arising in Galerkin mixed potential integral equation formulations. Due to their unique ability to handle non-smooth kernels, the proposed integration schemes can safely replace (in a “plug-n-play” sense) the traditional Gauss-Legendre rules in the existing singularity cancellation and singularity subtraction methods. Numerical examples using RWG basis functions confirm the excellent performance of the proposed method.

Low-Frequency Surface Integral Equation Solution by Multilevel Green's Function Interpolation With Fast Fourier Transform Acceleration

A fast low-frequency solver for surface integral equations is presented. Multilevel Lagrange interpolation of the pertinent homogenous space Green's functions is employed for the factorization of the integral operators. For high computational efficiency, the resulting multilevel convolution/translation operators are diagonalized by fast Fourier transform. A fast adaptive multilevel scheme of the interpolation procedure makes the approach also suitable for broadband applications. The method is investigated for the solution of electric field and combined field integral equations. For the electric field integral equation, the dyadic and mixed-potential integral equation formulations are considered and discussed. Furthermore, the impact of extrapolation errors on the approximation accuracy of the respective Green's functions is analyzed. In several numerical examples, excellent efficiency with respect to computation time and memory requirements as well as good accuracy of the obtained results is demonstrated.

ELECTROMAGNETIC CHARACTERISTICS OF CONFORMAL DIPOLE ANTENNAS OVER A PEC SPHERE

Rigorous mathematical Method of Moments (MoMs) for analyzing various radiating spherical structures is presented in this paper by using Dyadic Green's Functions (DGFs) in conjunction with Mixed Potential Integral Equation (MPIE) formulation. With the aid of linear Rao-Wilton-Glisson (RWG) triangular basis functions and by converting spherical DGFs to Cartesian DGFs, a conformal dipole antenna in free space and over a Perfect Electric Conductor (PEC) sphere is analyzed. The characteristics of such antennas are computed by applying multilayer spherical DGFs and asymptotic approximation methods. Mutual couplings between elements of a conformal dipole antenna array in free space and over a conducting sphere are also investigated. Good agreement between the computational results obtained by the proposed methods and those obtained from commercial simulator packages shows accuracy and high convergence speed of the presented methods.

Application of DCIM on Marine Controlled-Source Electromagnetic Survey

The discrete complex image method (DCIM) is used to calculate the mixed-potential electric field integral equation. The DCIM has been used broadly in high-frequency domain, and now is successfully introduced to the extremely low-frequency situation of marine controlled-source electromagnetic (MCSEM) survey. The integral path in high-frequency situation does not hold valid for extremely low-frequency situation. The reason can be ascribed to the change of wave number formulas. A new integral path suitable for the extremely low-frequency situation is proposed. The appropriate ranges of the parameters used in DCIM are given. The computation is stable at these considerably large ranges. The results of a five-layer model calculated with DCIM are compared with those with the filter method and the direct integral method. The computation time with DCIM is comparable to the time with filter method. The effects of water depth, upper-sediment thickness, and oil-layer thickness are studied with DCIM. The results show that electric field varies with the change of thickness. The effects accord to the physical meanings of MCSEM survey. It is safe to conclude that the DCIM with the new path is valid in MCSEM survey.

Fast broadband analysis of microstrip by interpolating both impedance and preconditioning matrices with MBPE

An interpolation scheme using model-based parameter estimation (MBPE) for fast analysis of the microstrip structures over a wideband is proposed.The microstrip structures are analyzed by the mixed potential integral equation with the generated dense impedance matrix partitioned and compressed hierarchically by the UV method. The linear systems are solved by the generalized minimal residual method with its convergence accelerated by the sparse approximate inversion (SAI) preconditioning technique. Over a wide frequency band, both the near field impedance matrix and the SAI preconditioning matrix are interpolated by MBPE. Numerical results show that the proposed method can reduce the computation time significantly. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26155

Performance Assessment of Bundled Carbon Nanotube for Antenna Applications at Terahertz Frequencies and Higher

The performance of bundled carbon nanotubes (BCNTs) as a conducting material for the fabrication of antennas in the terahertz frequency range and above is evaluated. The performance is compared against gold film, which is usually used for antenna fabrication. The macroscopic behavior of BCNTs is modeled by an anisotropic resistive sheet model which is extracted from the discrete circuit model of a single wall carbon nanotube (SWNT). Numerical simulations using the method of moments (MoM) and the mixed potential integral equation (MPIE) are performed to quantify radiation efficiencies of resonant strip antennas composed of BCNTs and thin gold films. For accurate high frequency simulations of antennas constructed from a thin gold layer, the Drude-Smith model is used to calculate the conductivity of gold. Simulations are carried out from 1 THz to 50 THz for conventional half-wave strip antennas. It is shown that the radiation efficiency of a BCNT antenna is consistently lower than the efficiency of a gold film antenna for BCNT equivalent density values up to 104 [CNTs/μm]. However, if equivalent density values above 104 [CNTs/μm] could ever be achieved, which are approximately 103 times higher than the currently realizable density (10 [CNTs/μm]), BCNTs would outperform thin gold film at frequencies above 1 THz.

A Grounded MoM-Based Spatial Green's Function Technique for the Analysis of Multilayered Circuits in Rectangular Shielded Enclosures

A continuous counterpart of the spatial images technique is proposed for the computation of the multilayered boxed Green's functions and their derivatives. The method employs a set of auxiliary linear distribution of sources to effectively impose the potential boundary conditions along the whole cavity contour. The imposition of these boundary conditions leads to a set of integral equations (IEs), on the unknown distributions of the auxiliary sources, which are solved by applying a method of moments approach. A convergence/efficiency study, related to the test and basis functions choice, is then presented and discussed. The technique is combined with the use of dynamic ground planes generating mirror basis functions, which completely remove any singular instability. Finally, the computed Green's functions are included into a mixed-potential IE formulation for the accurate and very fast analysis of practical multilayered shielded circuits. The proposed technique does not suffer from any convergence issue and it is extremely competitive in terms of accuracy and efficiency as compared to other methods known to the authors.

COMPUTATION OF PERIODIC GREEN'S FUNCTIONS IN LAYERED MEDIA USING COMPLEX IMAGES TECHNIQUE

In this paper, a new method based on the complex images technique has been presented to e-ciently compute the Green's functions required in a Mixed Potential Integral Equation (MPIE) analysis of a periodic structure located on a layered medium. This method leads to a closed-form representation of the Green's functions of these periodic structures given in terms of slowly convergent series valid for sub-wavelength as well as super-wavelength cell sizes for all source-point to fleld-point distances. Comparison between the results obtained by the proposed method and those obtained through other numerical methods verifles its accuracy. Fast convergence, simple flnal form and versatility of the proposed method are its main advantages which make it suitable for the analysis of the periodic structures using the integral equation techniques.

Adapting MoM With RWG Basis Functions to GPU Technology Using CUDA

In this letter, a CUDA-enabled graphics processing unit (GPU)-accelerated implementation of the method of moments (MoM) for solving three-dimensional conducting body-wire problems is presented. The solution is based on the mixed potential integral equation (MPIE) discretized using Rao-Wilton-Glisson (RWG) basis functions. The CUDA environment is employed to port a single-CPU sequential code to the parallel GPU platform, and some relevant issues are discussed. Numerical results are given for a helical antenna with a cylindrical cup reflector. The measured speedup of about eight times over the CPU implementation is demonstrated.

ANALYSIS ON SHIELDING PERFORMANCE OF METALLIC RECTANGULAR CASCADED ENCLOSURE WITH APERTURES

A full-wave approach is proposed to evaluate the shielding performance of metallic rectangular double-stage cascaded enclosures with apertures. The analysis has been carried out by means of the mode-matching technique and the mixed potential integral equation solved with the Method of Moments. The efiects of the dimension of enclosures, the orientation of apertures, the polarization direction of the incident wave, the aperture thickness and the high-order modes propagating in enclosures are taken into account. The accuracy of the proposed approach is validated by comparing with other methods and numerical simulation results can derive some conclusions: the shielding performance of cascaded enclosures is better than that of single-stage enclosures, the shielding efiectiveness can be improved with increasing the distance between stages in the range, and the shielding performance of the double-stage enclosure with parallel- pattern apertures in horizontal polarization case is better than that in vertical polarization case.