Method Of Moments In Spectral Domain Research Articles

Leveraging Symmetry in the Analysis of Mirror-Symmetric Multilayered Periodic Structures With Application to LP-to-CP Converter Design

This communication proves that the analysis of the scattering by a mirror-symmetric multilayered periodic structure can be replaced by the analysis of the scattering by two semi-structures with half the size in which the symmetry plane behaves either as a perfect magnetic conductor (PMC) or as a perfect electric conductor (PEC). The proof is based on the reflection properties of the electric and magnetic fields through PMCs and PECs, and it is valid for arbitrary oblique incidence. As an application of this concept, the spectral domain Method of Moments (SD-MoM) is reformulated to deal with MPSs limited by PMCs and PECs, and it is used in the design of a mirror-symmetric multilayered linear to circular polarization (LP-to-CP) converter. The results obtained with SD-MoM are validated by comparison with commercial software CST. Numerical simulations show that the CPU time required by both SD-MoM and CST in the analysis of half the LP-to-CP converter limited by PMC and PEC is between 30 and 42 per cent smaller than that required by the analysis of the complete LP-to-CP converter, which shows the numerical advantage gained in exploiting the symmetry when it is present.

Spectral MoM NUFFT-Based Formulation for the Efficient Analysis of High-Order Bandpass FSSs With Tightly Packed Nonresonant Elements in Skewed Grid

This communication presents a formulation of the spectral-domain Method of Moments (spectral MoM) for the analysis of periodic multilayered structures with a number of metallized interfaces alternating patches and apertures. Edge singularity entire-domain basis functions are used to model the electric currents on the patches and the tangential electric fields in the apertures. The formulation is especially suitable to characterize high-order bandpass frequency selective surfaces (FSSs) made up of nonresonant elements. Also in this communication, the nonuniform fast Fourier transform (NUFFT) is used in the spectral MoM to cover the case of unit cells in skewed grids, which enables the analysis of nonrectangular periodic lattices with tightly packed elements. Numerical examples of the design of third-order and fifth-order bandpass FSSs are presented. The FSSs are made up of hexagonal patches and apertures arranged in an equilateral triangular lattice. Results are cross-checked against commercial software CST Microwave Studio (CST MWS), and excellent agreement is found, our in-house software being more than one order of magnitude faster than CST MWS. This CPU time saving makes the proposed formulation very convenient for full-wave optimization and design.

NUFFT for the Efficient Spectral Domain MoM Analysis of a Wide Variety of Multilayered Periodic Structures

In this paper the Method of Moments (MoM) in the spectral domain is used for the analysis of multilayered structures containing periodic arrays of either patches or apertures. The patches and apertures may have many different geometries including complex surfaces limited by two parallel lines and two arbitrary curves, circular and elliptic rings, circular and elliptic arcs, and circular and elliptic sectors. Basis functions accounting for edge singularities are used in the approximation of the electric/magnetic current density on the patches/apertures, which enables a fast convergence of MoM with respect to the number of basis functions. Since the 2-D Fourier transforms of the basis functions cannot be obtained in closed-form, these Fourier transforms are efficiently computed by means of the nonuniform fast Fourier transform (NUFFT) algorithm. Results have been obtained for frequency-selective surfaces (FSSs), and for the elements used in the design of both reflectarray and metasurface antennas. The results obtained indicate that the software based on the NUFFT is only 15% slower than the standard spectral domain MoM software used for structures in which the 2-D Fourier transform of the basis functions is analytical, and between 50 and 80 times faster than CST.

Efficient Spectral Domain MoM for the Design of Circularly Polarized Reflectarray Antennas Made of Split Rings

The method of moments (MoM) in the spectral domain is used for the analysis of the scattering of a plane wave by a multilayered periodic structure containing conducting concentric split rings in the unit cell. Basis functions accounting for edge singularities are used in the approximation of the current density on the split rings, which makes it possible a fast convergence of MoM with respect to the number of basis functions. Since the 2-D Fourier transforms of the basis functions cannot be obtained in closed-form, judicious tricks (controlled truncation of infinite summations, interpolations, etc.) are used for the efficient numerical determination of these Fourier transforms. The implemented spectral domain MoM software has been used in the design of a circularly polarized reflectarray antenna based on split rings under the local periodicity condition. The antenna has been analyzed with our spectral domain MoM software, with CST and with HFSS, and good agreement has been found among all sets of results. Our software has proven to be around 27 times faster than CST and HFSS.

DESIGN OF COMPACT BANDPASS QUASI-ELLIPTIC MICROSTRIP FILTERS

This paper considers an algorithm for development of the sixth order compact microstrip bandpass filters with quasi-elliptic characteristics. The proposed technique is applied for synthesis of two filters for the L- and X-band. The recursive computational approach is employed to obtain the coupling matrix with simple topological implementation. Next, the full-wave transmission line analysis based on spectral-domain method of moments is applied for calculation of coupled microstrip resonator eigen frequencies. This approach is then used to compute magnitude and sign of the coupling coefficient for basic coupled resonator configurations. Finally, two quasi-elliptic filter topologies are synthesized and structure optimization in Ansys HFSS is performed. As a result, prototypes of the developed microstrip filters are manufactured and measured.

Optimized Periodic MoM for the Analysis and Design of Dual Polarization Multilayered Reflectarray Antennas Made of Dipoles

A hybrid version of the Method of Moments (MoM) is applied to the analysis of the scattering of plane waves by periodic multilayered structures containing dipoles at two metallization levels. The MoM matrix entries involving basis functions (BFs) at different metallization levels are computed in the spectral domain as double infinite summations with fast exponential convergence. The MoM matrix entries involving BFs at the same metallization level are computed in the spatial domain as double integrals, which require low-order quadrature rules. The integrands are cross correlations between BFs times multilayered periodic Green’s functions (MPGFs). The cross correlations between BFs are obtained in terms of elliptic integrals of first and second kind. Also, the MPGFs are accurately interpolated in 4-D in terms of both the spatial variables and the angles of incidence. The hybrid MoM proposed is used in the design of dual polarization reflectarray antennas under the local periodicity assumption. Thanks to the 4-D interpolation of the MPGFs, which minimizes the total number of MPGFs that have to be computed per reflectarray element, the proposed hybrid MoM is shown to be around 15 times faster than the standard spectral domain MoM in the design of the antennas.

SPECTRAL DOMAIN ANALYSIS OF GYROTROPIC ANISOTROPY CHIRAL EFFECT ON THE INPUT IMPEDANCE OF A PRINTED DIPOLE ANTENNA

A theoretical analysis of a printed dipole antenna on a gyrotropic-anisotropy chiral dielectric substrate is presented. The study is based on numerical techniques for the characterization of electromagnetic propagation in chiral media. The general complex wave equation and the dispersion relation for such a medium are derived in the spectral domain. The spectral Green's function of a grounded dielectric chiral slab is developed, and the spectral domain moment method impedance matrix elements are calculated. The effect of the chiral gyrotropy element on the input impedance of a dipole antenna printed on a grounded chiral substrate is analyzed using the Galerkin-based Method of Moments.

Efficient Full-Wave Analysis of Resonant Modes of Circular Microstrip Antenna Printed on Isotropic or Uniaxially Anisotropic Substrate

In this work, the influence of uniaxial anisotropy in the substrate on the radiation pattern of circular microstrip antenna is investigated theoretically. The analytical approach is based on the spectral-domain method of moments in conjunction with the stationary phase method. A new concise expression is derived for computing the radiation electric field. The validity of the solution is tested by comparing the computed results with the experimental data. Finally, numerical results of the variations of resonant frequency and radiation patterns of the structure of higher order mode, with respect to the anisotropy ratio of the substrate, for several values of substrate thickness and patch radius are also presented.

Effect of substrate dielectric inhomogeneity in the dispersion characteristics of a microstrip line

In this article, we apply the spectral domain method of moments to calculate the dispersion characteristics of a microstrip line, which is located on top of a grounded dielectric substrate. The dielectric substrate is a one-dimensional inhomogeneous material whose permittivity varies continuously in the direction normal to the ground plane. To make the spectral domain analysis applicable to a general inhomogeneous profile, we propose an accurate numerical algorithm to calculate the spectral domain transverse dyadic Green's function for an inhomogeneous substrate with an arbitrarily varying permittivity. The method is then used to obtain the dispersion curves for several inhomogeneous profiles and the results are compared with those of Ansoft HFSS simulator to verify the validity and accuracy of the proposed method. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1819–1822, 2014

The Generalized Direct Optimization Technique for Printed Reflectarrays

A generalized direct optimization technique (GDOT) for the design of printed reflectarrays using arbitrarily shaped elements with irregular orientation and position is presented. The GDOT is based on the spectral domain method of moments (SDMoM) assuming local periodicity (LP) and a minimax optimization algorithm. The accuracy of the LP-SDMoM for the design of reflectarrays with irregularly positioned and oriented array elements has been verified by comparisons with full wave method of moments. Three contoured beam reflectarrays, forming a high-gain beam on a European coverage area, have been designed: a broadband design, a circularly polarized design using the variable rotation technique, and a design with irregularly positioned array elements. The latter has been manufactured and measured at the DTU-ESA Spherical Near-Field Antenna Test Facility. An very good agreement between simulated and measured patterns have been obtained, showing accuracies that are comparable to those obtained for conventional shaped reflectors.

Resonance of High Tc Superconducting Microstrip Patch in a Substrate-Superstrate Configuration

The effect of a protecting dielectric superstrate on the resonance of a high Tc superconducting microstrip patch is investigated. The analysis approach is based on the spectral-domain method of moments in conjunction with the complex resistive boundary condition. The complex surface impedance of the superconducting thin film is determined using London’s equation and the two-fluid model of Gorter and Casimir. Numerical results show that the resonant frequency of the high Tc superconducting rectangular patch decreases monotonically with increasing superstrate thickness, the decrease being greater for high permittivity loading.

EFFICIENT MULTI-OBJECTIVE OPTIMIZATION OF FREQUENCY SELECTIVE RADOME WITH NONUNIFORM WALL THICKNESS

An e-cient optimization technique for frequency selective surface (FSS) radome with nonuniform wall thickness is proposed to improve the power transmission e-ciency and the boresight error (BSE) of FSS radome simultaneously. The high-frequency method based on the approximate locally planar technique is used to evaluate the transmission performance of FSS radome. An e-cient multi-dimensional adaptive sampling method combined with spectral domain method of moment (MoM) is employed to analyze transmission performance of FSS structure. The immune clone algorithm (ICA) is applied to the design of a FSS radome, in which the linear combination of the maximizing power transmission e-ciency and the minimizing BSE is adopted as the a-nity function, and the radome wall thickness is optimized. A design example for the three-dimensional tangent ogive radome with nonuniform thickness is given. The results show that the power transmission e-ciency is improved signiflcantly and the BSE of the optimal antenna-radome system is also reduced over the antenna scan volume.

Direct Optimization of Printed Reflectarrays for Contoured Beam Satellite Antenna Applications

An accurate and efficient direct optimization technique for the design of contoured beam reflectarrays is presented. It is based on the spectral domain method of moments assuming local periodicity and minimax optimization. Contrary to the conventional phase-only optimization techniques, the geometrical parameters of the array elements are directly optimized to fulfill the contoured beam requirements, thus maintaining a direct relation between optimization goals and optimization variables, and hence resulting in more optimal designs. Both co- and cross-polar radiation patterns of the reflectarray can be optimized for multiple frequencies, polarizations, and feed illuminations. Several contoured beam reflectarrays, that radiate a high-gain beam on a European coverage, have been designed and compared to similar designs obtained using the phase-only optimization technique. The comparisons show that the designs obtained using the proposed direct optimization technique are superior in performance, both for multi-frequency and dual-polarization designs. A reflectarray breadboard has been manufactured and measured at the DTU-ESA Spherical Near-Field Antenna Test Facility to validate the proposed technique. An excellent agreement of the simulated and measured patterns is obtained.

Accurate and Efficient Analysis of Printed Reflectarrays With Arbitrary Elements Using Higher-Order Hierarchical Legendre Basis Functions

It is demonstrated that nonsingular higher-order hierarchical Legendre basis functions are capable of accounting for the singularities of the electric currents at the edges of the reflectarray elements, thus yielding good convergence properties and very accurate results. In addition, the number of Floquet harmonics needed in the spectral domain method of moments is reduced by using higher-order hierarchical Legendre basis functions as compared to singular basis functions. At the same time, higher-order hierarchical Legendre basis functions can be applied to any arbitrarily shaped array elements, thus providing the flexibility required in the analysis of printed reflectarrays. A comparison to DTU-ESA Facility measurements of a reference offset reflectarray shows that higher-order hierarchical Legendre basis functions produce results of the same accuracy as those obtained using singular basis functions.

A MULTI-DIMENSIONAL ADAPTIVE SAMPLING METHOD FOR ANALYSIS AND DESIGN OF FREQUNECY SELECTIVE SURFACE WITH ARBITRARY ELEMENT

A fast and e-cient multi-dimensional adaptive sampling method (ASM) based on Stoer-Bulirsch (S-B) algorithm for frequency selective surface (FSS) analysis and design is presented in this paper. The multivariate rational function is established according to the functional relation of the scattering parameters with frequency and direction of incident wave, medium parameters and geometry dimensions of FSS structure, et al.. In order to evaluate the values of the multivariate rational function fully automatically without determining the coe-cients of the targeted rational interpolant, the one-dimensional S-B algorithm is expanded into multidimensional method. The sampling points in each dimension are chosen at the areas of maximum error in an adaptive way. The recursive interpolation results of one dimension are used as the initial values of next dimension in the recursive tabular until nth-dimensional recursive interpolation is accomplished. The initial values of recursive algorithm are calculated by spectral domain method of moments (MoM) at every sample point. The current distribution of FSS cell is predicted by Rao- Wilton-Glisson (RWG) subdomain basis functions which are applicable for arbitrarily shape elements. Four examples, including FSS with the eight-legged, cross and ring elements and FSS radome enclosed antennas, are considered to demonstrate the feasibility of applying the multi-dimensional ASM to analysis and optimal design of FSS. Numerical results show that the proposed method is superior in computation e-ciency compared to the direct MoM. Good agreement between the proposed technique and the direct MoM is observed.

The design of multi-layered gangbuster periodic array for wide-band filter application

The objective of this paper is to design a band-pass filter for wide-band application. Periodic array, frequency selective surfaces (FSS) with gangbuster elements is selected as optimization objective because of its good wide-band performance. The optimization algorithm, differential evolution strategy (DES) is employed to synthesis the configuration of FSS. The analysis of frequency response of FSS screen is solved by employing the spectral-domain method of moment (MoM) technique. The good stability of frequency response with respect to the incident angle is demonstrated.

An efficient analysis of frequency selective surface in spectral domain with RWG basis functions

AbstractIn this article, the spectral domain method of moment is utilized to analyze frequency selective surface with RWG basis functions for arbitrarily shaped metal geometry. The Fourier transform of the RWG basis function can be expressed in the analytical form and the fast convergence characteristic can reduce the computation time of impedance matrix. Some examples are calculated to demonstrate the efficiency of the proposed method. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2567–2570, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24674

Radiation of a rectangular microstrip patch antenna covered with a dielectric layer

The effect of a protecting dielectric superstrate on the radiation pattern of a rectangular microstrip patch antenna is investigated theoretically. The analysis approach is based on the spectral-domain method of moments in conjunction with the stationary phase method. A new concise expression is derived for computing the radiation electric field. The validity of the solution is tested by comparing the computed results with the experimental data. At higher superstrate thicknesses, numerical results indicate that the radiation pattern drastically changes into three lobes. The resonant frequency, on the other hand, increases with the increase of the thickness of the dielectric cover.

METHOD OF MOMENT ANALYSIS OF FINITE PHASED ARRAY OF APERTURE COUPLED CIRCULAR MICROSTRIP PATCH ANTENNAS

A full wave spectral domain method of moment along with reciprocity theorem analysis of finite phased array of aperture coupled circular microstrip patch antennas is presented. Both the electric surface currents on the patches and the equivalent magnetic current on the apertures are considered. Results of reflection coefficient magnitude, active input impedance, active element gain, efficiency and pattern are provided for different array size and element separations. By optimizing the parameters of the array, a better scan performance can be achieved. Furthermore, a comparison is made between array of rectangular and circular patches, with equal patch surface area, and it is shown that the array of circular patches provide a better scan performance than the array of rectangular patches.

A closed‐form solution to the asymptotic part of the MOM impedance matrix and the MOM excitation vector for printed structures on planar grounded dielectric slabs

AbstractIn the spectral domain method of moments (MoM) solution of printed structures on planar grounded dielectric slabs, the infinite double integrals which appear in the asymptotic parts of the MoM impedance matrix and the MoM excitation vector elements, have been previously transformed to one‐dimensional finite integrals, which have been numerically computed using the highly specialized “International Mathematics and Statistics Library” subroutines. In this paper, these one‐dimensional integrals are evaluated in closed‐form, resulting in an improved efficiency and accuracy for the rigorous investigation of printed antennas and complex millimeter and microwave integrated circuits. Numerical results in the form of mutual impedance between two expansion functions and input impedance of various microstrip antennas are presented to assess the accuracy of these closed‐form expressions. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 882–886, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22274