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Journal ArticleDOI

New closed-form Green's functions for microstrip structures - theory and results

07 Aug 2002-IEEE Transactions on Microwave Theory and Techniques (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 50, Iss: 6, pp 1556-1560
TL;DR: In this paper, the generalized pencil of function method was used to evaluate the Green's functions of single-layer and multilayer structures, and closed-form expressions for the method-of-moments matrix coefficients were obtained.
Abstract: This paper presents an efficient technique to evaluate the Green's functions of single-layer and multilayer structures. Using the generalized pencil of function method, a Green's function in the spectral domain is accurately approximated by a short series of exponentials, which represent images in spatial domain. New compact closed-form spatial-domain Green's functions are found from these images using several semi-infinite integrals of Bessel functions. With the numerical integration of the Sommerfeld integrals avoided, this method has the advantages of speed and simplicity over numerical techniques, and it leads to closed-form expressions for the method-of-moments matrix coefficients. Numerical examples are given and compared with those from numerical integration.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a special subtraction procedure is applied to each term of the Sommerfeld integrands to make them rapidly decreasing functions of krho, and the contributions of the subtracted terms are calculated analytically.
Abstract: This paper presents an efficient method to evaluate the two- and three-dimensional multilayered medium Green's functions for general electric and magnetic sources. Without finding any surface poles or steepest descent path, a special subtraction procedure is applied to each term of the Sommerfeld integrands to make them rapidly decreasing functions of krho. The contributions of the subtracted terms are calculated analytically. The remaining integrals are computed adaptively by using Gaussian quadratures. The accuracy of the method has been confirmed by comparison with many examples in literature, and the high efficiency has been verified

132 citations


Cites methods from "New closed-form Green's functions f..."

  • ...Extensive research has been done to accelerate this process through methods such as the fast Hankel transform (FHT) approach [12], [13], the window function approach [14], the steepest descent path (SDP) approach [2], and the discrete complex image method (DCIM) [15]–[29]....

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  • ...More recently, Eselle and Ge [29] proposed a new closed-form formulation based on a class of semi-infinite integrals of Bessel functions and applied the generalized pencil of function (GPOF) method to approximate the remaining integrand with another set of complex images (having only dependence), making the method valid for any kind of source-field point combination....

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Journal ArticleDOI
TL;DR: In this paper, an extension of the two-level discrete complex image method is proposed to eliminate any concerns on and shortcomings of the approximations of the spatial-domain Green's functions in closed form in planar multilayered media.
Abstract: An important extension of the two-level discrete complex image method is proposed to eliminate any concerns on and shortcomings of the approximations of the spatial-domain Green's functions in closed form in planar multilayered media. The proposed approach has been devised to account for the possible wave constituents of a dipole in layered media, such as spherical, cylindrical, and lateral waves, with the aim of obtaining accurate closed-form approximations of Green's functions over all distances from the source. This goal has been achieved by judiciously introducing an additional level into the two-level approach to pick up the contributions of lateral waves in the spatial domain. As a result, three different three-level algorithms have been proposed, investigated, and shown that they work properly over all ranges of distances from the source. In addition to the accuracy of the results at all distances, these approaches also proved to be robust and computationally efficient as compared to the previous algorithms, which can be attributed to the fact that the sampling of the spectral-domain Green's functions in the proposed approaches gives proper emphasis to the associated singularities of the wave types in the spectral domain. However, the judicious choices of the sampling paths may not be enough to get accurate results from the approximations unless the approximating functions in the spectral domain can provide similar wave natures in the spatial domain. To address this issue, the proposed algorithms employ two different approximations; the rational function fitting methods to capture the cylindrical waves (surface waves), and exponential fitting methods to capture both spherical and lateral waves. It is shown and numerically verified that a linear combination of exponential functions in the spectral domain represent the lateral waves at the interface of the involved layers.

124 citations

Journal ArticleDOI
TL;DR: A new direct DCIM without any quasi-static and surface-wave extraction is introduced and a novel path to include more variation before the MPM is introduced to avoid large variations of the spectral kernel.
Abstract: Sommerfeld integration is introduced to calculate the spatial-domain Green's functions (GF) for the method of moments in multilayered media. To avoid time-consuming numerical integration, the discrete complex image method (DCIM) was introduced by approximating the spectral-domain GF by a sum of exponentials. However, traditional DCIM is not accurate in the far- and/or near-field region. Quasi-static and surface-wave terms need to be extracted before the approximation and it is complicated to extract the surface-wave terms. In this paper, some features of the matrix pencil method (MPM) are clarified. A new direct DCIM without any quasi-static and surface-wave extraction is introduced. Instead of avoiding large variations of the spectral kernel, we introduce a novel path to include more variation before we apply the MPM. The spatial-domain GF obtained by the new DCIM is accurate both in the near- and far-field regions. The CPU time used to perform the new DCIM is less than 1 s for computing the fields with a horizontal source-field separation from 1.6/spl times/10/sup -4//spl lambda/ to 16/spl lambda/. The new DCIM can be even accurate up to 160/spl lambda/ provided the variation of the spectral kernel is large enough and we have accounted for a sufficient number of complex images.

108 citations


Cites background from "New closed-form Green's functions f..."

  • ...The DCIM in the -plane ( is the radial wavenumber) is introduced in [8], but or cannot be extracted from the spectral-domain GF to simplify the computation....

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Journal ArticleDOI
TL;DR: In this article, the spectral-domain Green's functions are approximated by an asymptotic term plus a ratio of two polynomials, the coefficients of these two coefficients being determined via the method of total least squares.
Abstract: A new technique is presented for the numerical derivation of closed-form expressions of spatial-domain Green's functions for multilayered media. In the new technique, the spectral-domain Green's functions are approximated by an asymptotic term plus a ratio of two polynomials, the coefficients of these two polynomials being determined via the method of total least squares. The approximation makes it possible to obtain closed-form expressions of the spatial-domain Green's functions consisting of a term containing the near-field singularities plus a finite sum of Hankel functions. A judicious choice of the coefficients of the spectral-domain polynomials prevents the Hankel functions from introducing nonphysical singularities as the horizontal separation between source and field points goes to zero. The new numerical technique requires very few computational resources, and it has the merit of providing single closed-form approximations for the Green's functions that are accurate both in the near and far fields. A very good agreement has been found when comparing the results obtained with the new technique with those obtained via a numerically intensive computation of Sommerfeld integrals

66 citations

Journal ArticleDOI
TL;DR: A new and better technique is proposed to obtain accurate results for the computation of the Green's function for a layered media in the spatial domain using the matrix pencil method.
Abstract: The oscillating infinite domain Sommerfeld integrals (SI) are difficult to integrate using a numerical procedure when dealing with structures in a layered media, even though several researchers have attempted to do that. Generally, integration along the real axis is used to compute the SI. However, significant computational effort is required to integrate the oscillating and slowly decaying function along the tail. Extrapolation methods are generally applied to accelerate the rate of convergence of these integrals. However, there are difficulties with the extrapolation methods, such as locations for the breakpoints. In this paper, we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the SI. In this paper, we fit the tail by a sum of finite (usually 10 to 20) complex exponentials using the matrix pencil method (MPM). The integral of the tail of the SI is then simply calculated by summing some complex numbers. No numerical integration is needed in this process, as the integrals can be done analytically. Good accuracy is achieved with a small number of evaluations for the integral kernel (60 points for the MPM as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods) along the tails of the SI. Simulation results show that to obtain the similar accuracy in the evaluation of the SI, the MPM is approximately 10 times faster than the traditional extrapolation methods. Moreover, since the MPM is robust to the effects of noise, this method is more stable, especially for large values of the horizontal distances. The method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the Green's function for a layered media in the spatial domain.

45 citations


Cites background or methods from "New closed-form Green's functions f..."

  • ...The study of DCIM also requires rigorous results from other methods as a verification of the performance....

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  • ...One of these ideas is to avoid the numerical integrations by approximating the integrands or a part of the integrand with some simple functions....

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  • ...Among the many methods of approximating a function by a sum of complex exponentials, we choose the matrix pencil method (MPM) since it is robust to noise and computationally efficient [13]....

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  • ...Finally some conclusions are drawn in Section V....

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References
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Book
28 Jun 1990
TL;DR: Inverse scattering problems in planar and spherically layered media have been studied in this article, where Dyadic Green's functions have been applied to the mode matching method to solve the problem.
Abstract: Preface. Acknowledgements. 1: Preliminary background. 2: Planarly layered media. 3: Cylindrically and spherically layered media. 4: Transients. 5: Variational methods. 6: Mode matching method. 7: Dyadic Green's functions. 8: Integral equations. 9: Inverse scattering problems. Appendixes A, B, C, & D. Index

3,872 citations


"New closed-form Green's functions f..." refers background in this paper

  • ...for a horizontal source have been discussed in [9], [10], and [11], and one may represent it as...

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Journal ArticleDOI
TL;DR: In this paper, a compact representation of the electric and magnetic-type dyadic Green's functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification is given.
Abstract: A compact representation is given of the electric- and magnetic-type dyadic Green's functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification. Furthermore, mixed-potential integral equations are derived within the framework of this transmission-line formalism for arbitrarily shaped, conducting or penetrable objects embedded in the multilayered medium. The development emphasizes laterally unbounded environments, but an extension to the case of a medium enclosed by a rectangular shield is also included.

774 citations


"New closed-form Green's functions f..." refers background in this paper

  • ...for a horizontal source have been discussed in [9], [10], and [ 11 ], and one may represent it as...

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Journal ArticleDOI
TL;DR: In this paper, an accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed.
Abstract: An accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed. The key step in this procedure is a formulation of the so-called mixed-potential electric field integral equation (MPIE) that is amenable to an existing advanced solution technique developed for objects in free space and that employs the method of moments in conjunction with a triangular-patch model of the arbitrary surface. Hence, the goal is to immediately increase analysis capabilities in electromagnetics, yet remain compatible with the large existing base of knowledge concerning the solution of surface integral equations. Three alternative forms of the MPIE in plane-stratified media are developed, and their properties are discussed. One of the developed MPIEs is used to analyze scatterers and antennas of arbitrary shape that penetrate the interface between contiguous dielectric half-spaces. >

773 citations


"New closed-form Green's functions f..." refers background in this paper

  • ...for a horizontal source have been discussed in [9], [10], and [11], and one may represent it as...

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Journal ArticleDOI
TL;DR: In this article, a generalized pencil-of-function (GPOF) method is developed for extracting the poles of an electromagnetic system from its transient response, which needs the solution of a generalized eigenvalue problem to find the poles.
Abstract: A generalized pencil-of-function (GPOF) method is developed for extracting the poles of an electromagnetic system from its transient response. The GPOF method needs the solution of a generalized eigenvalue problem to find the poles. Subspace decomposition is also used to optimize the performance of the GPOF method. The GPOF method has advantages over the Prony method in both computation and noise sensitivity, and approaches the Cramer-Rao bound when the signal-to-noise ratio (SNR) is above threshold. An application of the GPOF method to a thin-wire target is presented. >

693 citations


"New closed-form Green's functions f..." refers methods in this paper

  • ...method was improved by Aksun [6], who uses a two-level method and the generalized pencil of function (GPOF) method [7] to approximate the spectral domain without extracting the quasi-static and surface-wave contributions....

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  • ...This method’s accuracy depends on the accuracy of the approximation by the series of exponentials, and the GPOF method [7] was found to be very accurate for this purpose....

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  • ...For the approximation, the GPOF method [7] is a good choice because we do not need to consider the quasi-static images and surface-wave poles (SWPs) when performing the approximation of the spectral-domain Green’s functions....

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Journal ArticleDOI
TL;DR: In this paper, a closed-form spatial Green's function for the open microstrip structure, especially with a thick substrate, is represented in the time-consuming Sommerfield integrals.
Abstract: The spatial Green's function for the open microstrip structure, especially with a thick substrate, is generally represented in the time-consuming Sommerfield integrals. Through the Sommerfield identity, a closed-form spatial Green's function of a few terms is found from the quasi-dynamic images, the complex images, and the surface waves. With the numerical integration of the Sommerfeld integrals thus avoided, this closed-form Green's function is computationally very efficient. Numerical examples show that the closed-form Green's function gives less than 1% error for all substrates and source-to-field distances. >

684 citations


"New closed-form Green's functions f..." refers methods in this paper

  • ...based on the Sommerfeld identity, called the discrete image method, has been developed [4], [5]....

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  • ...It should be noted that the complex images in our method are distributed on the complex-plane, while the images obtained in the previous method [5], [6] are on the complex -plane....

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  • ...This method first extracts all the quasi-static and surface-wave contributions from the spectral-domain Green’s function, and then approximates the remainder by a series of exponentials using the Prony’s method [5]....

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  • ...Details of this method can be found in [5]....

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  • ...In one of the previous complex image methods, all the quasistatic images [5] and SWPs [2], [5] were extracted from the spectral-domain Green’s function and then the remainder was approximated by a series of complex exponentials using the Prony’s method [5]....

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