Rafael R. Boix

Application of Total Least Squares to the Derivation of Closed-Form Green's Functions for Planar Layered Media

A new technique is presented for the numerical derivation of closed-form expressions of spatial-domain Greens functions for multilayered media. In the new technique, the spectral-domain Greens 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 Greens 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 Greens 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

Full-wave analysis of circular microstrip resonators in multilayered media containing uniaxial anisotropic dielectrics, magnetized ferrites, and chiral materials

In this paper, Galerkins method in the Hankel transform domain is applied to the determination of the resonant frequencies, quality factors, and radiation patterns of circular microstrip patch resonators. The metallic patches are assumed to be embedded in a multilayered substrate, which may contain uniaxial anisotropic dielectrics, magnetized ferrites, and/or chiral materials. The numerical results obtained show that important errors can be made in the computation of the resonant frequencies of the resonators when substrate dielectric anisotropy, substrate magnetic anisotropy and/or substrate chirality are ignored. Also, it is shown that the resonant frequencies of circular microstrip resonators on magnetized ferrites can be tuned over a wide frequency range by varying the applied bias magnetic field. Finally, the computed results show that the resonance and radiation properties of a circular microstrip patch on a chiral material is very similar to those of a circular patch of the same size printed on a nonchiral material of lower permittivity.

On the fast approximation of Green's functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Greens function of a mixed-potential integral-equation formulation is examined and is found to be limited to low values of /spl kappa//sub o//spl rho/ (in this context /spl kappa//sub 0//spl rho/ = 2/spl pi//spl rho///spl lambda//sub 0/, where /spl rho/ is the distance between the source and the field points of the Greens function and /spl lambda//sub 0/ is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large /spl kappa//sub 0//spl rho/ is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Greens functions. In this paper, the method developed for the computation of the Greens function is used for planar structures containing both lossless and lossy media.

Closed-Form Expressions of Multilayered Planar Green's Functions That Account for the Continuous Spectrum in the Far Field

The rational function fitting method has been found useful in the derivation of closed-form expressions of spatial-domain Greens functions for multilayered media. However, former implementations of the rational function fitting method lead to Greens functions expressions that are not accurate in the far field when this far field is dominated by the continuous spectrum instead of being dominated by surface waves (as it happens, for instance, in the case of lossy multilayered media). In this paper, the authors introduce a novel implementation of the rational function fitting method, which leads to Greens functions expressions that are accurate in the far field when this is dominated either by the continuous spectrum or by surface waves. In the new approach, the far-field contribution of the continuous spectrum to the Greens functions is numerically fitted in terms of functions with closed-form Hankel transforms, and this far-field contribution is explicitly added to the total least squares approximations of the Greens functions. The numerical results obtained for the Greens functions with the new approach have been compared with numerical results obtained via direct numerical integration of Sommerfeld integrals, and excellent agreement has been found despite the contribution - continuous spectrum or surface waves - dominating the far field.

Fast full-wave analysis of multistrip transmission lines based on MPIE and complex image theory

The mixed-potential electric-field integral equation is used in conjunction with the Galerkins method and complex image theory for analyzing a transmission line with multiple strips embedded in different layers of a multilayered uniaxially anisotropic dielectric substrate. The two-dimensional Greens functions for the scalar and vector potentials are analytically obtained in the space domain due to the approximation of its spectral-domain version with complex images, thus avoiding lengthy numerical evaluations. Double integrals involved in the computation of Galerkins matrix entries are quasi-analytically carried out for the chosen basis functions, which are well suited to the problem.

Reflectarray Antennas for Dual Polarization and Broadband Telecom Satellite Applications

A reflectarray antenna with improved performance is proposed to operate in dual-polarization and transmit-receive frequencies in Ku-band for broadcast satellite applications. The reflectarray element contains two orthogonal sets of four coplanar parallel dipoles printed on two surfaces, each set combining lateral and broadside coupling. A 40-cm prototype has been designed, manufactured, and tested. The lengths of the coupled dipoles in the reflectarray cells have been optimized to produce a collimated beam in dual polarization in the transmit and receive bands. The measured radiation patterns confirm the high performance of the antenna in terms of bandwidth (27%), low losses, and low levels of cross polarization. Some preliminary simulations at 11.95 GHz for a 1.2-m antenna with South American coverage are presented to show the potential of the proposed antenna for spaceborne antennas in Ku-band.

Analysis of a microstrip crossover embedded in a multilayered anisotropic and lossy media

The equivalent circuit and the scattering parameters of the orthogonal microstrip crossover discontinuity are determined by assuming that the conducting strips are embedded in a multilayered substrate which may contain both anisotropic dielectrics and materials with a nonnegligible conductivity. The equivalent circuit of the crossover is obtained in terms of the complex excess charge densities on the strips. These excess charge densities are computed by means of the Galerkin method in the spectral domain. Comparison is carried out with previously existing results for microstrip crossovers on lossless isotropic substrates and original results are presented for crossovers on anisotropic and lossy substrates. >

Static analysis of microstrip discontinuities using the excess charge density in the spectral domain

Galerkins method in the spectral domain is applied to solve for the excess charge density existing on the strips of open-end and symmetric gap discontinuities in multilayered anisotropic substrates. The excess charge density is used to determine the capacitance components of the equivalent circuits, of these discontinuities. Numerical results are provided and a comparison with previous results is carried out. >

Resonant modes of circular microstrip patches over ground planes with circular apertures in multilayered substrates containing anisotropic and ferrite materials

In this paper, the authors analyze how the resonant modes of circular microstrip patch resonators are affected by the presence of circular apertures in the ground plane located under the patches. A rigorous full-wave analysis in the Hankel transform domain (HTD) is carried out in order to obtain the resonant frequencies, quality factors, and radiation patterns of the circular microstrip patch resonators over ground planes with circular apertures. With the use of suitable Greens functions in the HTD, the analysis is performed for the case where the circular patches, as well as the ground planes containing the apertures are embedded in a multilayered substrate consisting of isotropic dielectrics, uniaxial anisotropic dielectrics, and/or magnetized ferrites. The numerical results obtained are compared with experimental results, and good agreement is found. The results show that the circular apertures significantly affect the resonant frequencies of circular microstrip patches.

Efficient numerical computation of the spectral transverse dyadic Green's function in stratified anisotropic media

Several new ideas are provided for computing the spectral transverse dyadic Greens function (STDGF) of a stratified anisotropic medium in an accurate and efficient way. A modified version of the equivalent boundary method is developed which makes it possible to compute the asymptotic values of the aforementioned STDGF without employing exponential terms. This new technique for the computation of the STDGF of a stratified anisotropic medium has more numerical stability than the other techniques proposed so far, in which the use of exponential terms for the computation of the STDGF in all the range of variation of the spectral variables unavoidably leads to numerical problems for high values of the spectral variables. Also in this paper, it is shown how a two-step interpolation approach can be used for obtaining simple closed-form expressions of the STDGF of a stratified anisotropic medium in wide ranges of the spectral variables. It is expected that the use of this interpolation approach will introduce im...