• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.17 no.8 s.111
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• pp.788-794
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• 2006

In this paper, a Sommerfeld integral for an impedance half-plane is considered, which is one of classical problems in electromagnetic theory. First, the integral is evaluated into two series representations which are expressed in terms of exponential integral and Lommel function, respectively. Then based on the Lommel function expansion, an exact, closed-form expression of the integral is formulated, written in terms of incomplete Weber integrals. Additionally, based on the exponential integral expansion, an approximate expression of the integral is obtained. Validity of all formulations derived in this paper is demonstrated through comparisons with a numerical integration of the integral for various situations.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.28 no.2
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• pp.147-154
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• 2017

The impedance approximation has been widely used to model an earth surface such as ocean surface. In calculation of the dyadic Green's function for the impedance half plane, Sommerfeld integral and its partial derivatives are required. It is known that two far-field approximation of the Sommerfeld integral can be represented in terms of Legendre or Laguerre polynomials. Hence, a criterion is required to choose one of two far-field approximations for a given application, which can be expressed in a complex plane of the surface impedance. Also, we approximate the required partial derivatives of Sommerfeld integral and numerically verify the accuracy of the approximation.

• Journal of the Korean Society for Nondestructive Testing
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• v.20 no.2
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• pp.91-101
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• 2000

Modeling of radiation beam from ultrasonic transducers has been investigated extensively, since it is one of the most important, fundamental issues that have great influence on the accuracy of an ultrasonic measurement model. Here, three popular radiation models, namely the Rayleigh-Sommerfeld integral model, the boundary diffraction wave model and the edge element model, are discussed briefly, and the radiation beam fields from ultrasonic transducers with planar, circular and rectangular cross-sections are calculated using these three models. Then, the accuracy and the time-efficiency of these methods are compared based on the calculation results.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2007.10a
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• pp.219-222
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• 2007

The paper deals with the rigorous analysis of three layered media structures. The dyadic Green's function for three layer medium is derived. The Green's functions belonging to the kernel of the integral equation are expressed as Sommerfeld integrals, in which surface wave effects are automatically included. We propose this integral representation as the most appropriate in the spatial domain analysis of slive structure. Also, we used extraction method for the convergence of this integral function. Finally, some numerical results are presented. These computed value show good agreement with proposed this method.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• 2003.11a
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• pp.64-68
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• 2003

For the purpose of the efficient derivation of the closed-form Green's functions by which MoM matrix elements can be analytically evaluated, the optimum approximation path which is deformed from the Sommerfeld integration path on the complex $k_{\rho}$-plane is proposed based upon the steepest descent method and three level approximation procedure.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.8
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• pp.1059-1068
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• 1993

We will put the emphasis on the analysis of arbitrarily shaped microstrip antennas. The most general and rigorous treatment of microstrip antennas is given by the electric field integral equation(EFIE), usally formulated in the spectral domain. In this paper, we use a modification of EFIE, called the mixed potential integral equation(MPIE) , and we solve it in the space domain. This technique uses Green's functions associated with the scalar and vector potential which are calculated by using stratified media theory and are expressed as Sommerfeld integrals. The integral equation is solved by a moment's method using rooftop subsectional basis function. Thus, microstrip patches of any shape can be analysed at any frequency and for any substrate. Numerical results for a rectangular patch and for a L-shaped patch are given and compared with measured values.

• The Journal of the Acoustical Society of Korea
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• v.17 no.3E
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• pp.27-34
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• 1998

The validity of the image model is investigated both analytically and experimentally in a half space with an infinite single reflecting surface present. This paper exploits the Sommerfeld integral that represents the exact solution for the reflected field in the half space. The solution is shown to be obtained by direct numerical integration which yields more accurate and stable results. The predicted results from the image model are compared to those from the direct numerical integration of the Sommerfeld integral. It is also experimentally demonstrated that the image model gives acceptably accurate results. It is of significance that this paper reveals analytical and experimental validation of using the image model except near-grazing incidence.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.39 no.7
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• pp.38-45
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• 2002

This paper derives the electric field integral equation to calculate scattering from arbitrary large target above and radiating of an electric line source within a lossy ground. Sommerfeld’s type integral requires a lot of time to calculate and has some difficulties and limitations for an analysis region. But SDP (steepest descent path) integration gives fast calculation of the integral, and the result shows that SDP integration has the validity for all over the analysis region with fast evaluation. Moment method with SDP integration is used to calculate the scattering of an arbitrary large conducting target and the results are compared with that of the numerical integration with Gaussian quadrature rule and GPOF (generalized pencil of function) method.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.05a
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• pp.677-680
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• 2008

The paper deals with the analysis of radiation characteristics of antenna in the multi-layered media structures. The dyadic Green's function for three layer medium is complex because the Green's functions belonging to the kernel of the integral equation are expressed as Sommerfeld integrals, in which surface wave effects are automatically included. When certain condition are met, the integral can be evaluated approximated by the method of Saddle-point integration. In this study, we propose a method to calculate a radiation pattern for several antennas by using the method of Saddle-point integration. Numerical results show how the radiation characteristics are affected by parameter of dielectric media.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.12
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• pp.25-35
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• 1995

An analysis method of electromagnetic coupling through an arbitrarily shaped aperture on the upper wall of parallel-plate waveguide, when excited by an electromagnetic plane wave from outside, is considered. The mixed-potential integral equation, in which Green's functions are expressed in a computationally efficient closed form by using the Prony's method and the Sommerfeld identity, is formulated. Expanding the unknown equivalent magnetic surface current in terms of two-dimensional rooftop-type basis functions and choosing razor testing, the integral equation is reduced to a linear algebraic equation, which is solved. The results are compared with the previous results. Fairly good agreements between them are observed.