Spectral Domain Green's Functions Research Articles

Closed-form Green's functions for general sources and stratified media

The closed-form Green's functions of the vector and scalar potentials in the spatial domain are presented for the sources of horizontal electric, magnetic, and vertical electric, magnetic dipoles embedded in general, multilayer, planar media. First, the spectral domain Green's functions in an arbitrary layer are derived analytically from the Green's functions in the source layer by using a recursive algorithm. Then, the spatial domain Green's functions are obtained by adding the contributions of the direct terms, surface waves, and complex images approximated by the Generalized Pencil of Functions Method (GPOF). In the derivations, the main emphasis is to put these closed-form representations in a suitable form for the solution of the mixed potential integral equation (MPIE) by the method of moments in a general three-dimensional geometry. The contributions of this paper are: 1) providing the complete set of closed-form Green's functions in spectral and spatial domains for general stratified media; 2) using the GPOF method, which is more robust and less noise sensitive, in the derivation of the closed-form spatial domain Green's functions; and 3) casting the closed-form Green's functions in a form to provide efficient applications of the method of moments.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of coplanar waveguide-fed microstrip antennas

A moment method analysis of a microstrip antenna fed by an open-end coplanar waveguide is presented. The surface electric current on the microstrip antenna is represented by the entire domain basis functions, while the surface magnetic currents in the open-end slot and in the slots of the coplanar waveguide near the open end are expanded by the subsectional roof-top basis functions. Some practical numerical aspects are carefully discussed, and a numerical device is introduced to reduce the computation time for the integrals involving roof-top basis functions and the spectral-domain Green's function. The solution accuracy is thus improved. Computed results for the reflection coefficients and input impedances are given and compared with measured values. Good agreement between theory and experiment is obtained. >

A general expression of dyadic Green's functions in radially multilayered chiral media

A general expression of spectral-domain dyadic Green's function (DGF) is presented for defining the electromagnetic radiation fields in spherically arbitrary multilayered and chiral media. Without any loss of the generality, each of the radial multilayers could be the chiral layer with different permittivity, permeability, and chirality admittance, while both distribution and location of current sources are assumed to be arbitrary. The DGF is composed of the unbounded DGF and the scattering DGF, based on the method of scattering superposition. The scattering DGF in each layer is constructed in terms of the modified and normalized spherical vector wave functions. The coefficients of the scattering DGFs are derived and expressed in terms of the equivalent reflection and transmission coefficients, by applying boundary conditions satisfied by the coefficient matrices. >

Scattering from perfectly conducting and resistive strips on a grounded dielectric slab

The scattering properties of perfectly conducting and resistive strips are predicted for strips which are located on a dielectric slab backed by a perfectly conducting ground plane. The spectral domain Green's function is used to relate the currents and fields on the strip, and the resulting integral equation is solved using the method of moments. Both TE and TM strips are examined using piecewise linear and pulse subdomain basis functions, respectively, to model the current on the strip. Calculated results are compared with results measured at the NASA Langley Research Center. >

Spectral dyadic Green's function formulation for uniaxial bianisotropic superstrate-substrate structure

In this paper, spectral-domain dyadic Green's functions for the time harmonic electric current source embedded in a two-layer grounded uniaxial bianisotropic media are obtained using Fourier tranform. It is shown that in the uniaxial bianisotropic medium, total spectral electromagnetic field can also be separated into the superposition of transverse electric (TE) and transverse magnetic (TM) wave. Because of the generality of constitutive relations our results include the special cases of achiral, uniaxial, reciprocal and nonreciprocal biisotropic media.

Scalar space-time waves in their spectral-domain first- and second-order Thiele approximations

For the simple case of the scalar wave motion generated by a point source in an unbounded homogeneous medium, it is investigated what the consequences of the first- and second-order Thiele approximations in the spectral domain are in the space-time domain. To this end, the corresponding spectral domain Green's function is transformed back to the space-time domain with the aid of the modified Cagniard method. The exact solution to the problem is a spherical wave with the same wave shape as the source signature and a single wave front. The first-order Thiele, or parabolic, approximation has a wave front in the shape of a double oblate spheroid, combined with a head-wave like precursor having a cylindrical wave front. The second-order Thiele approximation contains two wave fronts, one associated with a fast body wave and the other with a slow body wave, in combination with a head-wave-like precursor, the latter again having a cylindrical wave front. From the results, it can be concluded in which regions below or above the source the approximations have sufficient accuracy for application in inversion and “true amplitude” depth migration procedures in geophysical prospecting.

Derivation of closed-form Green's functions for a general microstrip geometry

The derivation of the closed-form spatial domain Green's functions for the vector and scalar potentials is presented for a microstrip geometry with a substrate and a superstrate, whose thicknesses can be arbitrary. The spatial domain Green's functions for printed circuits are typically expressed as Sommerfeld integrals, which are inverse Hankel transforms of the corresponding spectral domain Green's functions and are time-consuming to evaluate. Closed-form representations of these Green's functions in the spatial domains can only be obtained if the integrands are approximated by a linear combination of functions that are analytically integrable. This is accomplished here by approximating the spectral domain Green's functions in terms of complex exponentials by using the least square Prony's method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computation of mutual coupling between slot-coupled microstrip patches in a finite array

An analytical method is presented for the evaluation of mutual coupling between slot-coupled microstrip patches in a finite array. The approach is a combination of the equivalence principle and the reciprocity theorem and uses the spectral domain Green's functions for a dielectric slab in a moment method solution for the unknown patch and slot current distribution. The excitation mechanism of the patches is taken into account by introducing an N-port equivalent network, and the impedance matrix of an array of N-element slot-coupled patches is evaluated directly from its network voltage and current matrices of order N/sup 2/. As examples, the mutual impedances and scattering coefficients for two-, four-, and eight-element arrays are evaluated. Results are compared with measured data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A generalized CAD model for printed antennas and arrays with arbitrary multilayer geometries

A general full-wave solution to arbitrary multilayer geometries of printed antennas and arrays coupled to multiple printed feed lines has been developed. It uses spectral-domain Green's functions for multilayer substrates to account for the substrate layering of the printed antenna, and a newly developed generalized multiport reciprocity analysis to treat the coupling of the transmission feed lines to the antenna elements. The analysis is completely rigorous, including all surface wave or other non-radiating modal effects. The solution has been developed for both isolated elements as well as infinite arrays. The theoretical formulation of the generalized multiport reciprocity analysis is described in details and results for several practical examples are presented to demonstrate the accuracy and versatility of the analysis used. Considering the rigor and versatility of the analysis, it should find useful for full-wave simulation and computer aided design of a variety of multilayered printed phased-array configurations.

Critical distance for grating lobe series

Estimating a transition or critical distance above a planar periodic array of point sources radiating into an unbounded medium is considered. It is shown that as an observation point approaches a periodic planar phased array of point sources, the corresponding spectral-domain Green's function, or grating lobe series, converges much more slowly than an equivalent mixed-domain representation exhibiting Gaussian convergence. For a given argument of the Green's function, the critical transition distance above the array for which both representations take the same time to compute can be estimated numerically. Since phased array antenna structures with cavity- or waveguide-type backings often have dimensions that fall well below the critical distance, investigations of such structures would seem to benefit significantly from formulations incorporating such hybrid Green's functions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Far field analysis of spherical-circular microstrip antennas by electric surface current models

The far field radiation patterns of a circular disk microstrip antenna mounted on a sphere are studied theoretically. The radiator is replaced by an assumed surface current distribution. The effects of the dielectric layer and the metallic sphere are rigorously taken into account by the spectral domain Green's function formulation. In the spectral domain represented by the vector Legendre series, the Green's function matrix is diagonal. The results are verified by comparison with results obtained from the cavity model theory. The cavity model agrees asymptotically with the present method for the case of a thin dielectric substrate.

Analysis and design of series-fed arrays of printed-dipoles proximity-coupled to a perpendicular microstripline

An analysis of a printed dipole element and a generalized configuration of a series-fed array of such elements, electromagnetically coupled to a covered microstripline running perpendicularly under it in a substrate-superstrate configuration, is presented. The solution is based on the principle of reciprocity and is formulated using a rigorous method of moments and full-wave spectral-domain Green's functions for multilayer dielectric substrates. The dipole excitation is characterized by an equivalent impedance, and can be controlled by suitably selecting the offset of the dipole from the feed line. Mutual coupling between dipoles is included. Using the results of the element analysis, a series-fed array prototype has been successfully designed, built, and tested in a standing-wave configuration; the design details are described, and measured performances are evaluated using the results of the array analysis. Mutual coupling effects are found to be not detrimental for this configuration, but can be severe for other nonstanding-wave configurations. >

A Generalized Spectral-Domain Green's Function for Multilayer Dielectric Substrates with Application to Multilayer Transmission Lines

A generalized full-wave Green's function completely defining the field inside a multilayer dielectric structure due to a current element arbitrarily placed between any two layers is derived in two-dimensional spectral-domain form. It is derived by solving a "standard" form containing the current element with two substrates on either side of it, and using an iterative algorithm to take care of additional layers. Another iterative algorithm is then used to find the field in any layer in terms of the field expressions in the two layers of the "standard" form. The locations of the poles of the Green's function are predicted, and an asymptotic form is derived along with the asymptotic limit, by use of which the multilayer Green's function can be used in numerical methods as efficiently as the single-layer grounded-dielectric-substrate Green's function. This Green's function is then applied to a few multilayer transmission lines for which data are not found in the literature to date.

MIC Overlay Coupler Design Using Spectral Domain Techniques

A quasi-TEM analysis of dielectric overlay microstrip is described for an overlay extending several conductor Iinewidths beyond the coupled lines. This method permits the analysis of numerous variations of overlay coupler geometries. The relevant spectral domain Green's function is given and used to generate a set of design curves when the overlay is identical in thickness and dielectric constant to the main substrate. A trial 8.34-dB coupler was built. Significant improvement in isolation was noted with the overlay when compared to the equivalently designed uncompensated coupler. The measured values of isolation agree very well with predicted values.