Moment Method Calculations Research Articles

Higher-order basis functions for MoM calculations

The extension of Rao, Wilton and Glisson basis functions on flat-faceted triangular elements to different element shapes, higher-order geometry and higher-order function support is outlined. A curvilinear coordinate formulation is used to obtain a family of finite elements for more accurate method of moments (MoM) computations. Results for the first two orders of geometry and function support in 1, 2 and 3 dimensions are presented. The basis functions are hierarchical, in that mixed orders of geometry and of function support can be used together in a single calculation to allow efficient local refinement. Practical issues of element assembly, treatment of singular and non-singular MoM integrals and of loop basis functions are addressed.

Conformational analysis of 2-substituted 1-nitro-and 1-bromo-1-nitroethenes

Conformational analysis of 2-trichloromethyl(ethoxycarbonyl)-1-nitro-and 2-trichloromethyl-(ethoxycarbonyl)-1-bromo-1-nitroethenes was performed using the dipole moment method, IR spectroscopy, and DFT quantum-chemical calculations (B3LYP/6-31G*). The nitro and ester (or trichloromethyl) groups in the molecules of these compounds were found to occupy trans positions with respect to the double C=C bond, i.e., the nitroalkenes have E, and their bromine-containing analogs, Z configuration; the compounds having an ethoxycarbonyl group are characterized by s-cis orientation of the C=C and C=O bonds.

A fast MoM calculation technique using sinusoidal basis and testing functions for a wire on a dielectric substrate and its application to meander loop and grid array antennas

The input impedance matrix element of the method of moments (MoM) for an arbitrarily shaped wire antenna printed on a dielectric material Z/sub m,n/ is formulated to be composed of three terms Z/sup /spl psi/s//sub m,n/, Z/sup /spl psi///sub m,n/, and /spl Delta/Z/sub m,n/ involving single-, double-, and triple-integral calculations, respectively. The MoM based on the Z/sub m,n/ formulated in this paper (new MoM) is applied to two antennas-a meander loop antenna and a grid array antenna-as well as a simple loop used as a reference antenna. The computation time to obtain the current distribution of each antenna by the new MoM technique is compared with the time required for the conventional MoM, which has an impedance matrix element composed of four terms, all involving triple-integral calculations. It is revealed that the new MoM drastically reduces the computation time: for example, by a factor of 937 for the grid array antenna. In addition, the radiation characteristics of these two antennas are discussed. It is found that a reduced-size meander loop (62% smaller than the simple loop reference) has a radiation pattern similar to the simple loop reference. It is also found that the grid array has an axial beam radiation pattern without side lobes in the principal planes.

Measurement of moments for centroid estimation in Shack–Hartmann wavefront sensor—a wavelet-based approach and comparison with other methods

A wavelet-based method of moment calculation with a set of basis functions is presented for centroid estimation in a Shack-Hartmann Wavefront Sensor. The method has been compared with other algorithms such as statistical averaging, FFT and least-squares method. A comparative analysis shows that wavelet method has a high accuracy and processing speed, and better suited for wavefront reconstruction applications. Further, the wavelet method presented here has a variable accuracy and resolution, and can be optimized for a particular application under consideration.

Correlation of Bragg scattering from the sea surface at different polarizations

The phase interference fading in Bragg backscattering from the sea surface at moderate incidence angles is considered using both moment method calculation of the scattering from measured water profiles and an implementation of the slightly rough, tilted facet model. The fading of the instantaneous scattering cross-section is shown to be independent of the instantaneous phase of the illuminating signal. The vertical and horizontal polarization fading responses are therefore strongly correlated when identical carrier frequencies and modulations are used at both polarizations since the electromagnetic energy is Bragg resonant with the same small-scale roughness in both cases, independent of whether the polarization channels are phase locked. Instantaneous horizontally polarized Bragg backscattering (HH) exceeding that at vertical polarization (VV) is extremely unlikely in this case. Use of an offset in the frequencies of monochromatic signals used at the two polarizations can lead to reduced correlation between the fading if the illumination footprint length is sufficiently large so that the frequency shift introduces a significant additional phase shift between the scattering from the leading and trailing edges of the footprint. The fading shows only a very weak correlation when this phase shift exceeds 400°. HH Bragg backscattering exceeding VV will be much more common under these specialized conditions.

A sharp threshold for a random constraint satisfaction problem

We consider random instances I of a constraint satisfaction problem generalizing k-SAT: given a set of ordered k-tuples over n literals, and a set of q “bad” clause assignments, find an assignment which does not set any of the k-tuples to a bad clause assignment. We consider the case where k= Ω( log n) , and study the probability of satisfiability for a random instance I formed by including every k-tuple of literals independently with probability p. Appropriate choice of the bad clause assignments results in random instances of k-SAT and not-all-equal k-SAT. A second moment method calculation yields the sharp threshold lim n→∞ Pr[I is satisfiable ]= 1 if p⩽(1−ε) ln 2/qn k−1, 0 if p⩾(1+ε) ln 2/qn k−1.

Fast CAD and Optimization of Waveguide Components and Aperture Antennas by Hybrid MM/FE/MoM/FD Methods—State-of-the-Art and Recent Advances

This paper presents an overview of the state-of-the-art of hybrid mode-matching (MM)/finite-element (FE)/method-of-moments (MoM)/finite-difference (FD) techniques applied for the rigorous, fast computer-aided design and optimization of waveguide components, combline filters, and coupled horns, as well as of slot arrays, and describes some recent advances. Related aspects involve the inclusion of coaxial and dielectric structures for related filters, the extension to multiports at cross-coupled filters, the rigorous consideration of outer and Inner mutual coupling effects at coupled horn and slot arrays, the application of the multilevel fast multipole algorithm for the more efficient MoM calculation part of horns and horn clusters, and the utilization of the MoM for the design of arbitrarily shaped three-dimensional waveguide elements. The described hybrid techniques combine advantageously the efficiency of the MM method with the flexibility of FE, MoM, and FD methods. Topical application examples demonstrate the versatility of the hybrid techniques; their accuracy is verified by available measurements.

Antennas for bolometric focal plane

The future Cosmic Microwave Background (CMB) experiments will require large focal planes with hundreds of bolometric receivers. For CMB detectors, the field of view should be restricted, as even with cryostat cooled liquid helium temperatures a significant deteriorating performance load will be present (Appl. Opt. 41 (2002) 6543). We present a planar antenna for millimeter band produced by lithographical methods only, which, without lens concentrator or a horn, has convenient beamwidth about F/3–F/4. The radiation and impedance characteristics of the antenna were obtained from a moment-method calculation. The measured beammap of the antenna prototype is presented in this paper.

Modes of the contrawound toroidal helix antenna

The contrawound toroidal helix antenna with constant current is examined; it has an omnidirectional pattern in the toroid plane. Radiation resistance is derived for the dipole mode, and results are validated by moment-method calculations. The radiation Qs of these antennas are greater than one million, making them unsuitable as dipole mode radiators. Ratios of loop-mode to dipole-mode radiation resistances range from several hundred to large values. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 365–368, 1999.

Moment method calculation of radiation from a cylindrical tube with an infinite flange

This work addresses the calculation of acoustic radiation from a cylindrical tube with an infinite flange, using the moment method. Expressions for the acoustic variables are presented in three separate regions: inside the tube, outside the tube, and on the boundary between them. Examination of the velocity field on this boundary shows that a singularity is present at the corner where the tube and flange meet. A set of basis functions is then developed, which can model this singularity efficiently, resulting in a solution that converges very rapidly. This is demonstrated by a comparison to a solution of the same problem, using the normal modes of the tube as basis functions. The present results are compared with those for the radiation from an unflanged tube, as given in the classic paper by Lewin and Schwinger.

Moment method calculation of the propagation constant for leaky-wave modes in slotted rectangular waveguide

A moment method analysis procedure is described to determine the aperture field distribution in a finite-length straight longitudinal slot cut in the broad wall of a rectangular waveguide. The waveguide is fed from one end with the dominant waveguide mode, while the other end of the waveguide is shorted, exactly at the far end of the slot. From the aperture distribution the far-field radiation pattern is then computed, and from the radiation pattern the attenuation and phase constants of the leaky-wave mode in the waveguide are determined. The method of determining the propagation constant from the radiation pattern is an often used experimental technique to determine leaky-wave propagation constants. Computed data is compared to measured data, and good correspondence observed. This propagation constant data can be used to design long meandering leaky-wave slot antennas.

Electromagnetic scattering from finite conductivity wind-roughened water surfaces

Numerical moment-method calculations of the electromagnetic backscattering from experimentally measured wind-roughened water surfaces that were previously made assuming perfectly conducting surfaces have been repeated taking into account the finite conductivity of sea water. The finite conductivity of the scattering medium was treated using impedance boundary conditions. Comparison with the earlier calculations shows that the backscattering drops slightly at horizontal polarization and much more dramatically at vertical polarization when the finite conductivity is considered. At small and moderate incidence angles, the magnitudes of the scattering drops are consistent with that predicted by the two-scale scattering model. The asymmetry in the upwind and downwind looking scattering that results from the non-uniform distribution of the Braggresonant electromagnetically small-scale waves across the larger scale waves is unaffected by the reduced conductivity at horizontal polarization and reduced very slightly at vertical polarization. The limitations of the two-scale model are essentially the same whether the surface is treatedwith perfect or sea-water conductivity.

A dual-polarized slot antenna for millimeter waves

We describe a new dual-polarized slot antenna to be used with quad-optical devices such as superconductor-insulator-superconductor (SIS) mixers at millimeter and submillimeter wavelengths. The radiation and impedance characteristics of the antenna were obtained from a moment-method calculation. The antenna has an excellent radiation pattern, a low impedance, wide bandwidth, and low cross polarization.

A model for discretization error in electromagnetic analysis of capacitors

The error due to discretization in a method-of-moments analysis of a parallel plate or metal-insulator-metal (MIM) capacitor is discussed. A technique related to Richardson extrapolation is used to develop a model for the error due to subsectional discretization. The results are for Galerkin's method using rooftop basis functions; however, the technique can be applied to any variational moment-method calculation. An expression is presented for the error in capacitance calculations, which is shown to hold for changes in geometry and dielectric constant. In addition, the expression for error is shown to be accurate for a wide range of meshing geometries. Surprisingly, the error model is not an upper bound, but rather is met nearly in equality for all geometries considered. Thus, the error may be simply subtracted from the calculated value for a more accurate result.

Interference microscopy of sub-λ structures: A rigorous computation method and measurements

The topometrical images of sub-wavelength structures as obtained in interferometrical microscopy with partially coherent illumination are computed and compared with measurements. The developed numerical model consists of: (i) a moment method calculation of the electromagnetic near-field of small (width < λ), inhomogeneous, 2D-structures embedded in a layer that is surrounded on each side by an infinite medium, and (ii) a simulation of the phase stepping method for partially coherent imaging.

Full-wave analysis of a disk-loaded spherical annular-ring microstrip antenna

In this article we analyze the effect of the disk loading on the characteristics of a spherical annular-ring microstrip antenna. The antenna is excited by a coaxial probe. The theoretical treatment is based on a full-wave analysis and a moment-method calculation. Numerical results of the resonant frequency, input impedance, voltage standing-wave ratio (VSWR), and radiation characteristics are presented. It is shown that the impedance bandwidth of the spherical annular-ring microstrip antenna can be broadened by adding a parasitic disk patch. Compared to the single annular-ring patch case, the spherical annular-ring microstrip antenna with a parasitic disk patch has larger minor lobes and larger cross-polarization radiation. © 1996 John Wiley & Sons, Inc.

Studies of slot-coupled double-sided perpendicular microstrip lines

The double-sided perpendicular microstrip lines coupled through an arbitrarily inclined narrow rectangular slot in the common ground plane are studied by applying the reciprocity theorem and by using the exact Green's functions for the structure in a moment-method calculation for the unknown slot electric fields. The S parameters of the slot-coupled perpendicular microstrip lines are formulated and calculated, and theoretical results are verified with measurements. The effects of the inclination angle and length of the coupling slot on the electromagnetic coupling between the slot-coupled perpendicular microstrip lines are also studied. © 1996 John Wiley & Sons, Inc.

Studies of slot‐coupled double‐sided perpendicular microstrip lines

The double-sided perpendicular microstrip lines coupled through an arbitrarily inclined narrow rectangular slot in the common ground plane are studied by applying the reciprocity theorem and by using the exact Green's functions for the structure in a moment-method calculation for the unknown slot electric fields. The S parameters of the slot-coupled perpendicular microstrip lines are formulated and calculated, and theoretical results are verified with measurements. The effects of the inclination angle and length of the coupling slot on the electromagnetic coupling between the slot-coupled perpendicular microstrip lines are also studied. © 1996 John Wiley & Sons, Inc.

Analysis of slot-coupled double-sided cylindrical microstrip lines

The problem of double-sided cylindrical microstrip lines coupled through a rectangular slot in the common cylindrical ground plane is studied using the reciprocity theorem and a moment-method calculation. Theoretical results of the S-parameters for the slot-coupled cylindrical microstrip lines are calculated and analyzed. Experiments are also conducted to verify the theoretical results.

Full-wave analysis of the effective relative permittivity of a coplanar waveguide printed inside a cylindrical substrate

The frequency-dependent dispersion characteristics of a coplanar wave-guide printed inside a cylindrical substrate are studied. A full-wave formulation incorporating the derived dyadic Green's function in a moment-method calculation is applied. The theoretical results are calculated and verified by the measurement, and the curvature effects on the dispersion characteristics of an inside cylindrical coplanar waveguide are discussed. © 1996 John Wiley & Sons, Inc.