Showing papers in "Electromagnetics in 1981"

Evaluation of sommerfeld integrals for lossy half-space problems

Abstract: This paper reviews some of the recent techniques investigated by the authors for numerical, asymptotic and approximate evaluations of the Somraerfeld integrals. Only the summaries of the final formulations are given and their numerical characteristics are illustrated using representative numerical data. Due to space limitations, the discussion in this paper is limited to the cases where both the source and the observation points are above the lossy half-space.

Computer modeling of antennas near the ground

Abstract: An accurate and efficient numerical method based on the rigorous Sommer-feld theory is described for modeling antennas near an interface such as the ground. The Sommerfeld integrals are evaluated by numerical integration along contours in the complex plane and two-dimensional interpolation is used subsequently to obtain the many Sommerfeld integral values needed for the moment-method solution of an integral equation. These methods permit modeling an antenna within 10-6 wavelengths of the ground for about two to four times the computation time for the same antenna in free space. Results showing currents and radiation patterns are included.

Effective methods for solving integral and integro-differential equations

Abstract: Effective numerical methods for solving simple integral and integro-differential equations with logarithmically singular kernels are presented tutorially in this paper. Fundamental features and interrelationships of the methods are discussed. Procedures for applying the techniques to practical equations of electromagnetics are suggested.

On the convergence and numerical sensitivity of the sem pole-series in early-time scattering response

Abstract: The most general form of the Singularity Expansion Method (SEM) representation of the transient scattering response of a finite extent object allows considerable freedom of choice as to the time at which one begins to include the sum of residue contributions into the transient response--i.e., the “turn-on” time. The issue of the chosen form of the coupling coefficient used in computing these residue constituents relates intimately with the choice of turn-on time. The practical range of choices for turn-on time is considerably more restricted than the theoretical one. In this paper limitations on turn-on time are established in terms of the maximum geometric extent of the object and of the geometric extent of the object projected in the direction of propagation of the incident wave. These limitations are dictated in order to insure the convergence of the SEM residue series, and are, in general, different for the Class 1 and for the Class 2 coupling coefficient. It is further argued that the conver...

Electromagnetic wave propagation along horizontal wire systems in or near a layered earth

Abstract: A review of the theory of electromagnetic wave propagation along a system of horizontal wires in a layered medium is given. Numerical results for the propagation constants of a variety of specific structures are presented and examined as functions of wire and medium parameters. The full modal description of such structures is discussed, and its relation to excitation by specific sources is examined. Finally, a brief assessment of currently outstanding problems in this area is given.

Embedded insulated antennas for communication and heating

Abstract: The properties of insulated antennas that make them useful for subsurface communication or heating are discussed. Several antennas and associated feed lines suitable for use in bore holes or for in...

The singularity expansion method: background and developments

Abstract: The singularity expansion method (SEM) arose from the observation that the transient response of complex electromagnetic scatterers appeared to be dominated by a small number of damped sinusoids. In the complex frequency plane, these damped sinusoids are poles of the Laplace-transformed response. The question is then one of characterizing the object response (time and frequency domains) in terms of all the singularities (poles, branch cuts, entire functions) in the complex frequency plane (hence singularity expansion method). Building on the older concept of natural frequencies, formulae were developed for the pole terms from an integral-equation formulation of the scattering process. The resulting factoring of the pole terms has important application consequences. Later developments include the eigenmode expansion method (EEM) which diagonalizes the integral-equation kernels and which can be used as an intermediate step in ordering the SEM terms. Additional concepts which have appeared include e...

Evidence that bears on the left half plane asymptotic behavior of the sem expansion of surface currents

Abstract: The issues which have persisted in connection with the so-called “entire function contribution” and in connection with alternative coupling coefficient form interrelate closely with the larges asymptotic behavior in the left half plane in SEM representations. To date, no generally applicable rigorous information has been gleaned about this asymptotic behavior. On the other hand, the specific scattering geometries of the sphere and the wire loop yield analytic solutions which can be analyzed asymptotically. Further information can be discerned on a numerical basis or through a procedure based on the discretization of an integral equation. All of this evidence form a mutually-consistent picture of the asymptotic behavior in question. The principal conclusion which results is that the observed behavior taken with the Mittag-Leffler-type expansion theory for complex functions leads to SEM representations which are free from entire function constituents.

Electromagnetic scattering by two bodies of revolution

Abstract: A systematic procedure is presented for computing the electromagnetic scattering by two arbitrarily oriented bodies of revolution when the size of the objects are in the resonance region. The analysis uses a System Transfer Operator (T-matrix) approach and iteratively solves for the scattering of the two-body configuration. A modified unimoment technique is employed to generate the system transfer matrix of each body of revolution. Results are presented and compared to measured data to demonstrate the versatility and accuracy of the analysis. Applications of the two-body analysis stem from extending it to N-bodies. Some potential applications are discussed along with the major problems that need to be addressed.

Computation of fresnel and fraunhofer fields of planar apertures and reflector antennas by the jacobi-bessel series-a review

Abstract: This paper reviews the basic analytical and numerical characteristics of the Jacobi-Bessel series applied to the determination of the Fresnel and Fraunhofer fields radiated by planar apertures and reflector antennas. Only the final formulations are presented here and the reader is referred to the published papers by the authors for specific details. Many useful representative numerical results are generated to demonstrate the applicability of the technique.

Microstrip dipoles on cylindrical structures

Abstract: The fundamental solution for printed circuit antennas on cylindrical substrates is presented in this paper. Exact expressions are obtained for the electromagnetic field both inside the substrate as well as the surrounding free space produced by an arbitrarily oriented printed circuit dipole. Asymptotic results are derived for a cylindrical thin substrate whose diameter is large compared to wavelength.

Multipole expansion technique for electromagnetic scattering by buried objects

Abstract: A conceptually simple technique is introduced to solve the electromagnetic scattering by buried objects. The technique applies the multipole expansions in two-medium half spaces accompanied with their generalized Sommerfeld integrals to represent the scattering waves. Since the modal fields of the expansions all satisfy the boundary conditions on the planar air-earth interface, the scattering problem is reduced to solving the expansion coefficients by matching the boundary conditions on a sphere. Hence the method is very similar to that of the scattering in an infinite space using the method of separation of variables. Scattering results of buried conducting and dielectric spheres are presented. Some polarization anomalies of the scattered electric field components are observed on the earth surface. The technique can be directly applied to solve the scattering by buried non-spherical objects when the finite element method is used to treat the scatterer boundaries and inhomogenuities.

Large frequency asymptotic properties of resolvent kernels

Abstract: A conjecture on the large complex frequency asymptotic behaviour of the resolvent kernel of the electric field integral equation operator is presented. The conjecture is based on a detailed examination of the corresponding large frequency behaviour of a matrix approximant to the operator. From this analysis it is concluded that the resolvent decays exponentially on a sequence of concentric circular contours of increasing radius threading between poles in the left half plane. The decay rate is proportional to the distance between observation and source points.

On the use of singularity expansion method for analysis of antennas in conducting media

Abstract: The application of the singularity expansion method (SEM) to the analysis of antennas and electromagnetic scatterers has usually been applied to simple, isolated bodies in free space or to simple bodies near a perfectly conducting ground plane. Theoretical studies of SEM have been applied to these relatively simple geometries to yield significant insight into the radiation and scattering process. In analytically investigating the behavior or antennas in a lossy medium, it is known that in addition to simple pole singularities, there is a branch cut linking two branch points in the complex frequency representation of the antenna response. While significant information regarding the nature of the branch cut and its effect on the antenna response can be obtained by purely analytical methods, a numerical study of this antenna can provide useful results. This paper provides an analysis of the behavior of a linear antenna in a conducting region. Special attention is paid to the importance of the branch...

A method of computing the capacitance of flat discs of arbitrary shape

Abstract: A method of moments procedure is presented for solving the integral equation satisfied by the electrostatic charge distribution over arbitrary planar domains. This procedure is based on a representation of such domains as a collection of quadrilateral subdomains, using the Gordon-Hall and Zienkiewicz-Phillips subdivision techniques. All integrals are effectively evaluated over triangles, and rely on an expression for the potential at a point due to a constant charge distribution over a triangular domain. As an illustration, the computational procedure is applied to a variety of discs. The computed results are in excellent agreement with the exact values for the circle and the ellipse, and are compared with known numerical values for certain other configurations.

Computer graphics applications in electromagnetic computer modeling

Abstract: The use of computer graphics as an integral part of the solution process in electromagnetic computer modeling is as yet relatively undeveloped. In this paper we consider now and in what ways computer graphics might be employee in EM modeling. First, we summarize plotting quantities, variables, and formats that can be used. Then, we provide a selection of representative examples to illustrate various graphics applications. It is our nope to stimulate increased attention to an area that we believe can contribute significantly to the more effective use of computer modeling.

Surface fields and radiation patterns of a vertical electric dipole over a radial-wire ground system

Abstract: SUMMARY EM propagation over and radiation from radially varying ground systems are numerically modeled using the compensation theorem integral formulation. The source is taken to be a vertical electric dipole (VED) situated either on or above an azimuthally symmetric plane ground system having an assumed surface impedance profile which can vary arbitrarily in the radial direction. Because the formulation is based on the surface impedance concept, it can be applied to a variety of ground system configurations having a radius greater then about one wavelength. Particular attention is given to conventional HF radial-wire systems laid on both well and poorly conducting earth. For simple radial-wire ground systems, the radiation patterns were found to be independent of increasing radial length if the magnitude of the composite surface impedance is within 90percnt of the surface impedance of the underlying ground. It is also found that the radially varying feature tends to suppress high-angle lobes which are ot...

Finite element calculation of microwave absorption by the cranial structure

Abstract: Using an axisymmetric inhomogeneous lossy dielectric model of the human cranial structure, calculations yielding interior absorbed power density spatial distributions and whole-body cross sections are presented. These computations are performed by way of a finite element implementation of the coupled azimuthal potential formulation. Results are considered for two angles of plane wave incidence, with two orthogonal polarizations, at the frequencies of 1 GHz and 3 GHz. Comparisons are made with a simpler multi-layered spherical model. Attention is given to the sensitivity of “hot spot” intensities to incident field orientations and model parameter uncertainties.

Radar echo analysis by the singularity expansion method

Abstract: Pulse mode radar operation is analyzed under the assumption that the scattering object Γ lies in the far field of both the transmitter and the receiver. It is shown that, in this approximation, the radar signal is a plane wave s(x · θ0 − t, θ0) near Γ, where θ0 is a unit vector directed from the transmitter toward Γ, and similarly the echo is a plane wave e(x θ − t, θ, θ0) near the receiver, where θ is a unit vector directed from Γ toward the receiver. Moreover, it is shown that where ŝ(ω,θ0) is the Fourier transform of s(τ,θ0) and T(ωθ,ωθ0) is the scattering amplitude in the direction θ due to the scattering by Γ of a CW mode plane wave with frequency ω and propagation direction θ0. Finally the singularity expansion method is used to show that

Major results and unresolved issues in singularity expansion method

Abstract: The Singularity Expansion Method (SEM) was derived as a means of interpreting/estimating responses measured during electromagnetic testing of aerospace systems. These responses appeared to consist of a superposition of exponentially damped sinusoidal oscillations. It was shown that the electromagnetic response of a finite-sized, perfectly conducting object to a delta-function incident plane wave is a meromorphic function of the complex frequency. The physical interpretation, computational advantages and fundamental problems associated with using the poles (natural frequencies) of the meromorphic function to construct the transient responses of objects are reviewed. Areas of future investigations, both for the purpose of improving the mathematical foundations and the computational tools are discussed.

Scalar singularity expansion method and lax-phillips theory

Abstract: A scalar theory of SEM based on the eigenmode expansion method (EEM) is related to the Lax-Phillips theory of scattering. The Lax-Phillips scattering theory contains results which can be immediately applied to SEM. A byproduct of developing this relationship is a formal proof that SEM poles are simple. A demonstration of scalar EEM/SEM is presented for scattering by a hard prolate spheroid which includes the sphere as a limiting case. The EEM spheroid solution is shown to have direct bearing on issues of recent concern regarding the validity of certain EEM expansions. The SEM sphere results are shown to contain all of the features of the electromagnetic SEM sphere scattering solution.

Numerical calculation and tables of weinstein's diffraction functions

Abstract: Using the terminology of the Wiener-Hopf technique, the Weinstein's diffraction function is defined as the “plus” part G+ (s,p) of the Green's function This function plays an important role in the solutions of parallel–plate diffracti on problems, roughly equivalent to the Fresnel function in the half-plane diffraction problem. A table of G+(s,p) is given in Weinstein's book, The Theory of Diffraction and the Factorization Method (Golen Press, 1969), and a more extensive five-figure table was later published in Russian by E. I. Nefedov. Both tables are calculated from an approximate version of G+(s,p). In the present paper, we provide a s e t of numerical tables for exact Weinstein's diffraction functions, together with a summary of relevant formulas and a discussion of numerical computations. This paper studies the numerical calculation of a special function G+(s,p), which arises in the Wiener-Hopf solution of problems involving parallel plates . Our work is motivated by two factors. First, abri...

On some mathematical aspects of sem, eem and scattering

Abstract: The relationship between the integral equations usually used in SEM and the scattering matrix is examined. Alternate integral equations which exhibit only the poles of the S matrix are given. Examples are used for illustration for a solvable case.The analytic Fredholm theorem in Banach spaces is discussed and its advantages for numerical calculations emphasized.The relationship between EEM, SEM and the theory of nonselfadjoint operators is briefly discussed.

Coupled mode analysis for ground wave propagation overinhomogeneous paths

Abstract: We analyze a two dimensional cylindrical model of the earth which Is characterized by a surface admittance with any specified azimuthal dependence. The atmospheric refractive index is assumed to be laterally uniform but It may be any continuous function of the radial coordinate. We show that the coupled mode formalism developed for this problem is consistent with previous approaches for sectionally homogeneous paths based on mode matching.

Analytical and experimental studies of a jacketed segmented shielded buried cable for use in an elf transmitting antenna system

Abstract: One type of cable being considered for direct buried use in the SEAFARER ELF transmitting system has a tubular metallic shield covered with an insulating jacket which surrounds the insulated main current carrying conductor. An analytical model is developed to predict the induced currents and potentials and impedance loading effects of such a cable shield segmented by circumferential gaps. We first set up the EM field equations and solve the boundary value problem to obtain two modes of propagation on such a cable buried at great depth. The shield segments may be grounded at either end or both. By applying terminal conditions at the source end and load end of a segment, the current and potential distributions and impedance seen by the source are calculated. With this type of shielded cable, gaps in the shield are needed only at intervals of several miles to limit the incremental resistance added by the shield to less than a percent. Comparisons are shown between the theoretical calculations and ex...