Rigorous analysis of shielded cylindrical dielectric resonators bydyadic Green's functions

This paper presents a rigorous approach for the calculation of resonant frequencies of a metallic cavity loaded by a dielectric resonator. Tangential fields at the air-dielectric interface are derived from dyadic Green's functions and boundary conditions are applied. Dyadic Green's identity and the boundary element method are used to solve the numerical problem. In order to validate the method, resonant frequencies are calculated for a cylindrical cavity loaded with a dielectric cylinder and compared with available results in the literature. Then resonance is studied for dielectric cylinder in a rectangular cavity. In the case of multiple dielectric resonators in the cavity, the coupling coefficient is computed with an original method based on the use of symmetries     

Numerically efficient analysis of planar microstrip configurationsusing closed-form Green's functions

An efficient technique for the analysis of a general class of microstrip structures with a substrate and a superstrate is investigated in this paper using newly-derived closed-form spatial domain Green's functions employed in conjunction with the Method of Moments (MoM). The computed current distributions on the microstrip structure are used to determine the scattering parameters of microstrip discontinuities and the input impedances of microstrip patch antennas. It is shown that the use of the closed-form Green's functions in the context of the MoM provides a computational advantage in terms of the CPU time by almost two orders of magnitude over the conventional spectral domain approach employing the transformed version of the Green's functions     

Green's functions analysis of planar circuits in a two-layergrounded medium

A moment method analysis of planar circuits in a layered medium is developed. The Green's functions of a two-layer grounded medium are used in order to take into account the effect of the surface wave, coupling, and radiation. Interpolation techniques are used to increase computational efficiency. The embedded conductors are modeled with triangular patches. Results for several configurations, including direct and proximity coupled radiators, are in good agreement with measurements and other calculations     

On the electromagnetic dyadic Green's functions for planar multi-layered anistropic uniaxial material media

A complete, plane-wave spectral, vector-wave function expansion of the electromagnetic, electric, and magnetic, dyadic Green's function for electric, as well as magnetic, point currents for a planar, anisotropic uniaxial multi-layered medium is presented. It is given in terms ofz-propagating, source-free vector-wave functions, where ? is normal to the interfaces, and it is developed via a utilization of the Lorentz reciprocity theorem. The electromagnetic dyadic Green's function for periodic electric as well as magnetic point current sources is also presented. Some salient features of the Green's dyadics, along with a physical interpretation are also described.     

A new technique for the derivation of closed-form electromagnetic Green's functions for unbounded planar layered media

A closed-form electromagnetic Green's function for unbounded, planar, layered media is derived in terms of a finite sum of Hankel functions. The derivation is based on the direct inverse Hankel transform of a pole-residue representation of the spectral-domain form of the Green's function. Such a pole-residue form is obtained through the solution of the spectral-domain form of the governing Green's function equation numerically, through a finite-difference approximation, rather than analytically. The proposed methodology can handle any number of layers, including the general case where the planar media exhibit arbitrary variation in their electrical properties in the vertical direction. The numerical implementation of the proposed methodology is straightforward and robust, and does not require any preprocessing of the spectrum of the Green's function for the extraction of surface-wave poles or its quasi-static part. The number of terms in the derived closed-form expression is chosen adaptively with the distance between source and observation point as parameter. The development of the closed-form Green's function is presented for both vertical and horizontal dipoles. Its accuracy is verified through a series of numerical examples and comparisons with results from other established methods.     

Strongly convergent Green's function expansions for rectangularlyshielded microstrip lines

The exact analytical treatment of the quasi-TEM mode in various cross-sectional configurations of microstrip lines may be used on Carleman-type singular integral equations (SIEs). Their kernel is a Laplacian Green's function G with source point limited on the interface separating the dielectric media. Strongly convergent expansion for G, particularly suited for the subsequent solution of the SIE and for exact field-point evaluations in rectangularly shielded microstrip configurations, are developed. Extraction of the singular logarithmic term leads to rapidly converging series expansions for the nonsingular part. The convergence of certain of these series is further improved when the field point lies also on the interface or when the source point approaches the shielding boundaries     

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

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integral-equation formulation is examined and is found to be limited to low values of κ_oρ (in this context κ₀ρ = 2πρ/λ₀, where ρ is the distance between the source and the field points of the Green's function and λ₀ 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 κ₀ρ 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 Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media     

Scalarization of dyadic spectral Green's functions and networkformalism for three-dimensional full-wave analysis of planar lines andantennas

A novel and systematic method is presented for the complete determination of dyadic spectral Green's functions directly from Maxwell's equations. With the use of generalized scalarizations developed in this paper, four general and concise expressions for the spectral Green's functions for one-dimensionally inhomogeneous multilayer structures, excited by three-dimensional electric and magnetic current sources, are given in terms of modal amplitudes together with appropriate explicit singular terms at the source region. It is shown that Maxwell's equations in spectral-domain can be reduced, by using dyadic spectral eigenfunctions, to two sets of z-dependent inhomogeneous transmission-line equations for the modal amplitudes. One set of the transmission-line equations are due to the transverse current sources and the other set due to the vertical current sources. Utilizing these equations, network schematizations of the excitation, transmission and reflection processes of three-dimensional electromagnetic waves in one-dimensionally inhomogeneous multilayer structures are achieved in a full-wave manner. The determination of the spectral Green's functions becomes so simple that it is accomplished by the investigation of voltages and currents on the derived equivalent circuits. Examples of singleand multilayer structures are used to validate the general expressions and the equivalent circuits     

Spectral dyadic Green's function formulation for planar integratedstructures

The problem of the complete determination of the dyadic spectral Green's function for an integrated planar structure with a grounded dielectric slab has been considered and solved in a rigorous way by using the spectral theory of the electromagnetic field. The reciprocity theorem and the geometrical symmetry of the structure have demonstrated the different roles played by the independent terms of the spectral Green's function in the evaluation of the electromagnetic characteristics of the grounded slab excited with a general source. Furthermore, an equivalent circuit representation of the structure, allowing a noteworthy simplification in the determination of the total power, has been obtained. These equivalent circuits and the derived spectral Green's function presented here can be used to analyze and design microstrip antennas of arbitrary shape with a general type of loading, such as matched or unmatched loads, parasitic, and shorting pins     

Rigorous analysis of planar MIS transmission lines

The realisation of distributed microwave integrated circuits can be expected by using very low phase velocity propagation modes on MIS and Schottky planar transmission lines. Up to now, the frequency behaviour of such lines has been obtained by using analytical models. We present a rigorous analysis of a MIS microstrip line, the validity of which is testified by comparison to experimental values.     

Closed-form Green's functions for cylindrically stratified media

A numerically efficient technique is developed to obtain the spatial-domain closed-form Green's functions of the electric and magnetic fields due to z- and φ-oriented electric and magnetic sources embedded in an arbitrary layer of a cylindrical stratified medium. First, the electric- and magnetic-field components representing the coupled TM and TE modes are derived in the spectral domain for an arbitrary observation layer. The spectral-domain Green's functions are then obtained and approximated in terms of complex exponentials in two consecutive steps by using the generalized pencil of function method. For the Green's functions approximated in the first step, the large argument behavior of the zeroth-order Hankel functions is used for the transformation into the spatial domain with the use of the Sommerfeld identity. In the second step, the remaining part of the Green's functions are approximated on two complementary parts of a proposed deformed path and transformed into the spatial domain, analytically. The results obtained in the two consecutive steps are combined to yield the spatial-domain Green's functions in closed forms     

Dyadic Green's functions for a coaxial line

The eigenfunction expansions of the dyadic Green's functions for a coaxial line have been derived based on the method ofbarbar{G}_{m}, whereby the irrotational vector wave functionbar{L}is not needed. A dyadic boundary condition for the discontinuity of the tangential component ofbarbar{G}_{m}has been used to facilitate the derivation of the expression for the electric dyadic Green's function.     

Static Green's functions with conformal mapping and MATLAB

In this paper, conformal mapping was combined with Matlab. An application of the theory was showed in examples showing its ability to provide analytical expressions for two-dimensional Green's functions associated with Poisson's equation, i.e., electrostatic potentials created by infinite line sources parallel to metallic infinite cylinders of the various shapes. The solution is naturally expressed in the transformed domain, but usually a direct expression in the original (x,y) coordinates is easily obtained. In most cases, the proposed solutions are an order of magnitude simpler than those obtained by other approaches.     

Time-dependent dyadic Green's functions for rectangular andcircular waveguides

Closed-form expressions for the time-dependent dyadic Green's functions of electric and magnetic types for rectangular and circular waveguides are derived from the dyadic Maxwell equations in the time domain. These functions can be used to obtain the time-dependent electric and magnetic fields propagating in those guides due to any arbitrary time-dependent current distribution inside the guide. Stationary vector wave functions are introduced that separate the space-dependent parts from the time-dependent parts of the Green's functions. Comparison of the results for the rectangular and circular guides reveals that the time-dependent parts are identical. Thus the results can be easily extended to some other cylindrical pipes such as elliptical waveguides and also to coaxial cables     

Thermal analysis of layered electronic circuits with Green's functions

This paper presents a method for thermal simulation of electronic circuits using an analytical solution of the three-dimensional heat equation resulting from an appropriate circuit thermal model. The temperature fields in multilayered structures are computed analytically employing the Green's functions solution method. The entire solution methodology is illustrated in detail on the particular examples of electronic circuits containing multiple heat sources. Compared to the previous papers published by the authors, the method has been extended by including the possibility of simulating imperfect layer contacts. The simulation results are validated with infra-red measurements and results obtained using other methods. Additionally, the discussion of simulation errors caused mainly by different non-linear phenomena is included.     

On the dyadic Green's functions for Beltrami fields

A simple derivation of the Green's functions for Beltrami fields is presented for use with time-harmonic electromagnetism in homogeneous biisotropic media.     

Two-dimensional Green's functions for a rotationally invariantanisotropic medium

A coordinate transformation is introduced to map the anisotropic region into a fictitious isotropic region of finite angular extent where the field equations can be easily solved. This results in an infinite series representation which is not convenient for numerical calculations. An alternative representation is found by introduction of an apparently new integral form for the product of two-cylinder functions. The new representation provides physical insight as to the nature of the solution and is attractive from the computational standpoint. The results are analyzed, and a new corner-reflector-type effect is found for certain kinds of materials, which is in agreement with independent calculations. The analysis is of special importance for the derivation of a mathematical statement of a Huygen's principle for this type of material     

Derivation of closed-form Green's functions for a generalmicrostrip 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     

Dyadic Green's function for a multilayered planar medium-a dyadic eigenfunction approach

A new formulation of the dyadic Green's function for a planarly layered medium is presented, based on dyadic eigenfunctions of the Green's function operator. The general development of the dyadic Green's function is shown, resulting in a three-dimensional purely spectral representation. The spectral form is converted to a Hankel-function form using standard techniques, analogous to the sum-of-residues plus branch-cut representation often obtained from the Sommerfeld Green's function. Advantages and disadvantages of both the eigenfunction and Hankel function forms are outlined, and compared to other Green's function representations. Examples of the Green's dyadic for free space and for a grounded dielectric slab environment are provided, and the role of the continuous and discrete spectrum is discussed.     

Dyadic Green's functions for the perfectly conducting parabolic cylinder

Solutions of the scalar wave equation for parabolic cylinder coordinate system are discussed here. Dyadic Green's functions of the magnetic type for free space and for a perfectly conducting parabolic cylinder are developed. These functions are of fundamental importance for the solution of electromagnetic problems developed in the parabolic cylinder coordinate system, particularly those in the presence of perfectly conducting parabolic cylinders such as that of a parabolic cylinder reflector.