Analysis of microstrip patch antennas with tuning stubs using the closed-form Green's function

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>

A numerically efficient technique for the analysis of slot-line geometries in multilayer media is presented using closed-form Green's functions in the spatial domain employed in conjunction with the Method of Moments (MoM). The computed equivalent magnetic current distribution on the slot is used to determine the power radiated by the slot and the input impedance. In power calculations, the spatial domain Green's functions are approximated as a power series of radial distance, and the integrals involving the Green's functions are carried out analytically saving considerable amount of computation time.

We present compact and efficient closed form expressions for the mixed potential Green's functions in multilayered media with general electric and magnetic sources. By generalizing the Sommerfeld identity we can express also the first and second order Sommerfeld integrals in closed form and the spatial domain Green's functions can be obtained in closed form without numerical differentiation. The presented formulation leads to a very efficient method since in each layer the GPOF approximations are needed only for three (source layer) or four (other layers) spectral domain Green's functions. The applied mixed potential integral equations, identical with the Michalski-Zheng (1990) C-formulation (MZC), are solved by the method of moments (Galerkin's method) with the Rao-Wilton-Glisson (RWG) basis functions. The developed method has been applied for the analysis of complicated 3D microstrip structures and scattering by various 3D objects.

A numerically efficient technique for the analysis and design of MMIC circuits is introduced and applied to some realistic problems. The formulation is based on the method of moments (MoM) in the spatial domain, and utilizes closed-form Green's functions. Incorporating the closed-form Green's functions into the MoM has resulted in an efficient and accurate CAD algorithm. This is because use of the closed-form Green's functions not only eliminates the calculation of the spatial-domain Green's functions, but also makes it possible to evaluate the MoM matrix elements analytically We have demonstrated the application of this method here for some stripline and microstrip geometries, and compared the results with those obtained from commercial EM software, em (Sonnet Software, Inc.) © 1997 John Wiley & Sons, Inc. Int J Microwave Millimeter-Wave CAE 7: 344–358, 1997

Double-sided open periodic structures are analyzed using inhomogeneous plane wave scattering.The leaky and surface wave modes of several unit cells of different structures are computed using the poles of generalized reflection and transmission coefficients of inhomogeneous plane waves in the spectral domain.It is shown that the reflection and transmission coefficients of the zeroth order Floquet mode contain the poles of the Green's function of the complex stratified periodic structure.The properties of evanescent mode amplification as well as super resolution near field imaging in a wire medium are addressed.A balanced leaky wave antenna unit cell with double-sided radiation feature is introduced and it is shown that, in contrast to grounded structures, total absorption in lossless nonchiral double-sided open unit cells is not feasible as long as the behavior of the unit cell is well described by its fundamental mode.

Closed-form Green?s function representations for cylindrically stratified media, which can be used in conjunction with a Method of Moments, are developed. The closed-form expressions are valid for all possible source and field points including the axial line (ρ = ρ' and θ= θ'), which has not been available before. In the course of obtaining these expressions, the spectral domain Green's function components are calculated efficiently and transformed to the spatial domain using the discrete complex image method with the help of the generalized pencil of function method. Numerical results are presented in the form of a mutual coupling between two current modes and the input impedance of various rectangular microstrip antennas on dielectric coated circular cylinders.

An efficient and rigorous numerical method, based on the spatial-domain method of moments (MoM) in conjunction with the closed-form Green's functions, is devised for the analysis of multiple vertical conductors in printed circuits. As this combination has already proven to be very efficient for the analysis of printed structures with horizontal and vertical conductors, it is extended to efficiently handle multiple vertical conductors. Some circuits with multiple vertical strips are analyzed using the proposed method, and results are compared either to those presented in the literature or to those obtained from the commercial software em by SONNET Software, North Syracuse, NY. Computational efficiency of the algorithm is assessed in terms of CPU time, and it is observed that the computational cost of the proposed algorithm is an order of magnitude less than that of the straightforward implementation of the underlaying method of the algorithm-the spatial-domain MOM using closed-form Green's functions

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. >

Microstrip patch antenna analysis on a finite size model of the dielectric substrate is proposed and investigated using the method of moments. The surface-patch dipole modes are used to model the arbitrarily shaped microstrip patch while the volume polarisation current theorem with rectangular volume cells is used to model the dielectric. Galerkin's solution is applied except at the edges of the patch. Various copper patches have been tested experimentally. The results of the measurement are in good agreement with the computations.

Green's functions are obtained in exact closed-forms for the elastic fields in bi-material elastic solids with slipping interface and differing transversely isotropic properties induced by concentrated point and ring force vectors. For the concentrated point force vector, the Green functions are expressed in terms of elementary harmonic functions. For the concentrated ring force vector, the Green functions are expressed in terms of the complete elliptic integral. Numerical results are presented to illustrate the effect of anisotropic bi-material properties on the transmission of normal contact stress and the discontinuity of lateral displacements at the slipping interface. The closed-form Green's functions are systematically presented in matrix forms which can be easily implemented in numerical schemes such as boundary element methods to solve elastic problems in computational mechanics.

In this paper, a new representation for the space domain Green's function of general multilayer media is presented. This approach is based on an efficient plane wave expansion of the source incident field. Using the transmission line model for the multilayer medium, the effect of the layered medium on the incident plane waves is determined by a transmission coefficient, and the amplitude and phase of each plane wave at the field point are obtained. The total field is evaluated by summing the resultant plane waves at the field point. The main advantage of the proposed method is that the spatial domain Green's function of multilayer media can be obtained easily as a summation of simple exponential functions, without the need for Sommerfeld integration or complex image approximation. The plane wave approximation is independent of the parameters of the medium and is valid over a wide frequency range. Furthermore, the exponential form of the plane wave solution makes it possible to compute the method of moments matrix elements analytically for most important types of basis functions in multilayer problems.

A moment method based on triangular (RWG) basis functions and new closed-form Green's functions is presented for the analysis of microstrip structures of arbitrary shapes. It combines the flexibility of the triangular basis functions with the efficiency of the closed-form Green's functions. The new method is applied to obtain the scattering coefficients of a two-gap microstrip filter and it is found to be accurate and efficient.

Indoor communication systems operating at millimeter wave frequencies are getting increasing attention due to their ability of having wider bandwidth and as a result conveying information at higher bit rates. At these systems, the capacity of channel is very important especially where there is no line of sight due to an obstacle. Here we examine the use of a multiple-input multiple-output (MIMO) system in a 2D room with an obstacle at 60 GHz. We estimate the channel by using the closed-form Green's function of the room and show the ability of MIMO to increase the available capacity of the system in the room chiefly behind the obstacle.

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.

This paper comes with a new study on the conception of a CPW-Fed multi bands planar antenna. The design takes into account that this structure can be integrated with circuits behind, that why the Fed is a CPW one. The antenna validated is suitable for GSM, DCS and ISM band. The entire area of the antenna is 36×72.5 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and it is printed on an FR4 substrate. The printed U-shaped antenna is formed from two horizontal arms of different lengths and an L-shaped shorted strip which is connected between the vertical arm and the ground plane. The antenna is designed, optimized, and miniaturized by using ADS "Advanced Design System" and the results are compared with CST Microwave Studio.