Method Of Moments Formulation Research Articles

Scattering Characteristics of a Slot-Coupled T-Junction between Rectangular and Circular Waveguides

The scattering coefficients of a T-junction between rectangular and circular waveguides, coupled through a longitudinal slot in the narrow wall of the rectangular waveguide, are determined using moment method formulation, for excitation applied to the rectangular guide. The amplitude coefficients of the slot field distribution, computed in the process of determining the scattering coefficients, are used for the evaluation of the field distribution in the aperture plane of the coupling slot. The reflection and transmission coefficients, coupling as well as the equivalent network parameters are evaluated from the scattering coefficients, taking the effect of wall thickness into account. Comparison between the theoretical and experimental results on coupling and VSWR are presented.

Analysis of a transition between rectangular and circular waveguides

An analysis is presented of a transition between rectangular and circular waveguides coupled by a rectangular slot in a metallic wall of finite thickness in the common transverse cross section. Expressions for VSWR (voltage standing-wave ratio) and admittance are obtained using a moment-method formulation with entire basis and testing functions. Numerical data on the variation of input VSWR with frequency are obtained, and a comparison between the theoretical and experimental results is presented. The variations in the values of minimum VSWR with change in slot dimensions are also studied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Transient high-order ultrasonic scattering

To improve the reliability of diagnosis of tissue pathologies (e.g., cancers) based on ultrasonic imaging, quantitative images of physiological parameters such as speed of sound and/or absorption coefficient can in theory be obtained by inverse scattering procedures. Previous studies [Cavicchi et al., IEEE Trans. Ultrason. Ferroelec. Freq. Control UFFC-35, 22–33 (1988)] employed a moment-method matrix formulation under a monofrequency assumption. Periodicities of the field phasors caused a uniqueness problem in the inverse scattering solution for scatterers with phase shift magnitudes greater than π; in practical medical imaging, the phase shift would be hundreds of π. A reformulation of the method in the time domain appears more promising because the phase shifts are now merely time delays. The moment-method formulation is presented for forward scattering. A preliminary numerical study has verified the expansion using the moment-method equation and the internal field calculated by the inverse discrete Fourier transform of the well-known monofrequency solution solved at many frequencies. Future studies will address the more difficult problems of time-domain field inversion and inverse scattering.

Slotted waveguide directional coupler characteristics

A moment method (MoM) solution for slotted waveguide directional couplers which is sufficiently accurate for predicting the couplers' characteristics is demonstrated. The slot length in the waveguide directional couplers considered is about four wavelengths and the wall thickness is about 0.27 lambda . To simplify the numerical computation, the formulation assumes a uniform field across the slot aperture and utilizes Galerkin's method with the entire domain sinusoidal basis. A self-consistent method taking the finite wall thickness into account avoids an additional matrix equation, as in other MoM formulations. The final solution forms the basis for an efficient computer code applicable to dielectric-loaded slotted waveguide directional couplers. The uniform field assumption restricts the present solution to narrow slots. Numerical results verify, by comparisons with published analytical and experimental data, that this solution is valid for slot lengths as long as 4 lambda . A detailed discussion of the characteristics of narrow-wall and broad-wall slotted waveguide directional couplers is presented. >

Higher‐order time‐domain ultrasonic scattering

To improve the reliability of diagnosis of tissue pathologies (e.g., cancers) based on ultrasonic imaging, quantitative images of physiological parameters, such as speed of sound and/or absorption coefficient, can, in theory, be obtained by inverse scattering procedures. Previous studies [T. J. Cavicchi, S. A. Johnson, and W. D. O'Brien, Jr., IEEE Trans. UFFC‐35, 22–33 (1988)] employed a moment method matrix formulation under a monofrequency assumption. Periodicities of the field phasors caused a nonuniqueness problem in the inverse scattering solution for scatterers with phase shift magnitudes greater than π, in practical medical imaging, the phase shift would be hundreds of π. A reformulation of the method in the time domain appears more promising because the phase shifts are now merely time delays. The time‐domain moment method formulation is presented for forward scattering. A preliminary numerical study has been undertaken using the moment method equations and the internal field calculated by the inverse discrete Fourier transform of the well‐known monofrequency solution solved at many frequencies. Using the exact field within the integral produces a resulting good approximation of the exact field. Current studies are aimed at inversion for the forward‐scattered field; future work will address inverse scattering.

Efficient analysis of planar microstrip geometries using a closed-form asymptotic representation of the grounded dielectric slab Green's function

A newly developed closed-form asymptotic representation of the grounded dielectric slab Green's function is used in a moment-method formulation to calculate the propagation constant of an infinite microstrip transmission line and the input impedance of a finite-length, center-fed printed dipole. In these problems, source and field points are laterally rather than vertically separated with respect to the substrate. The conventional Sommerfeld integral and the plane wave spectral integral (PWS) representations of the microstrip Green's function converge very slowly in this case. However, the asymptotic closed-form representation of the Green's function does not have this limitation, and it remains accurate even for very small lateral separation between source and observation points. A modified form of the Sommerfeld integral representation is used only for observation points in the immediate vicinity of the source, while the asymptotic form is used elsewhere. Some numerical results based on this approach are presented and are shown to compare very well with previous results based on the corresponding exact-integral or PWS forms of the Green's function. >

Series expansions for the mutual coupling in microstrip patch arrays

A dominant-mode mutual coupling theory is developed for an array of microstrip patches. One of the key features of the formulation is that only values for isolated self- and mutual impedance are needed in the formulation, making the method suitable for either a cavity model or spectral-domain analysis, or compatible with experimental measurements. The formulation is equivalent with D.M. Pozar's (1982) moment-method formulation. A series expansion of the solution is derived, allowing for approximate formulas accurate to any specified order. These formulas do not require matrix inversion. Formulas up to third order require less computation time that the exact solution, for single elements of the impedance, admittance, and scattering matrices. These expansions are computationally efficient for large sparse arrays. >

Analysis of waveguides with metal inserts

A systematic analysis of waveguides with metal inserts is presented. The method is based on a field expansion in terms of the normal modes of the corresponding hollow waveguide without metal inserts. The analysis leads to two formulations: a matrix formulation and a moment-method formulation. The matrix formulation is suitable for structures with smooth metal inserts which are free from sharp edges, while the moment method is more suitable for metal sheets (e.g. strips and fins) or metal inserts with sharp edges (e.g. ridges). The validity of the method is tested by investigating some special cases in which the surface of the metal insert coincides with one of the coordinate surfaces, e.g. a bifurcation in circular or rectangular waveguides. The method is then applied to the analysis of striplines and ridge waveguides. It leads to a generalization of the widely used spectral-domain technique in that ridges, fins, and strips with finite thickness can now be analyzed likewise. Any existing routine for the analysis of planar structures which is based on the spectral-domain technique can then be slightly modified in order to take the metallization thickness into account.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Moment method formulation for asymmetrically excited conducting bodies of revolution

Expressions are given for certain terms required in the moment method formulation for a conducting body of revolution excited by asymmetrical slots in its surface. These appear to be unavailable elsewhere in the literature.

The Discrete Convolution Method for Electromagnetic Problems

ABSTRACT A discrete convolution method for electromagnetic problems is described. It is particularly well-suited to periodic structures such as linear and planar arrays, although some non-periodic structures may also be treated. The method may be applied to any structure for which a Moment Method formulation is available. The matrix equation becomes a discrete convolution equation which is treated by Discrete Fourier Transform methods using Fast Fourier Transform algorithms. An iterative procedure which converges rapidly is utilized. The number of complex multiplication and divisions is equal to kINlogN where N is the number of unknowns or expansion function, I is the number of iterations and k is a factor which depends on the type of problem treated. Typical results are presented for linear and planar arrays. Good agreement is obtained with direct methods such as Gaussian elimination.

Estimation of Complex Permittivities of Three-Dimensional Inhomogeneous Biological Bodies

Complex permittivities are estimated for a 36-cell model which represents the chest portion of the block model of man by using moment-method formulation of the electric field integral equation. The errors in the calculated complex permittivities are lower with saline/water the surrounding medium, as compared to air, presumably on account of better matching of energy to the biological body. It has been shown that the rest of the human body has little effect on the estimation of complex permittivities because of the near-field natore of the illuminating sonrces. small number of buried cells can be handled for solving the inverse problem, but the problem becomes ill-posed and unsolvable for a larger number of buried cells.

Assessment of MOM Techniques for Shipboard Applications

This paper is intended to help the EMC Engineer to decide whether a particular problem can be solved by the Method of Moments (MOM) given the constraints of his computer facility. The paper is divided into four main sections. The first is the MOM formulation, the second deals with specific formulations that have been successfully applied, the third gives guidelines on how to estimate the computer power needed to solve a specific problem, and the fourth is an annotated bibliography for those who want more detail in the different aspects of MOM. An example of how to use the information developed in the paper is given at the end. Although this paper was generated initially to solve shipboard problems, it can apply to many large problems.