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.

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

A survey is given of the so-called spectral-domain approach, an analytical and numerical technique particularly suited for the solution of boundary-value problems in microwave and millimeter-wave integrated circuits, The mathematical formulation of the analytical part of that approach is described in a generalized notation for two- and three-dimensional strip and slot-type fields. In a similar way, the numerical part of the technique is treated, keeping always in touch with the mathematical and physical background, as well as with the respective microwave applications. A discussion of different specific aspects of the approach is presented and outlines the peculiarities of shielded-, covered-, and open-type problems, followed by a brief review of the progress achieved in the last decade (1975-1984). we survey closes with considerations on numerical efficiency, demonstrating that spectral-domain computations can by speeded up remarkably by analytical preprocessing. The presented materal is based on ten years of active involvement by the author in the field and reveals a variety of contributions by West German researchers previously not known to the intenational microwave community.

The Spectral-Domain Approach for Microwave Integrated Circuits

A solution to the problem of plane wave scattering by a rectangular microstrip patch on a grounded dielectric substrate is presented. The model does not include the microstrip feed, and thus does not include the so-called "antenna mode" component of the scattering. The solution begins by formulating an electric field integral equation for the surface current density on the microstrip patch. The integral equation is solved using the method of moments. Computed data for the patch radar cross section (RCS) is found to be in close agreement with measurements over a broad frequency range. The microstrip RCS versus frequency consists of a number of large peaks which are identified as impedance or pattern factor resonance peaks.

Scattering from a microstrip patch

Simple approximate formulas for the input resistance, bandwidth, and radiation efficiency of a resonant rectangular microstrip patch are derived. These formulas become increasingly accurate as the substrate thickness decreases. Because the formulas are derived from approximations of a rigorous Sommerfeld solution, they provide insight into the effect of the substrate parameters on the patch properties, in addition to providing approximate design equations. >

Simple approximate formulas for input resistance, bandwidth, and efficiency of a resonant rectangular patch

Using Richmond's reaction integral equation, an expression is derived for the input impedance of microstrip patch antennas excited by either a microstrip line or a coaxial probe. The effects of the finite substrate thickness, a dielectric protective cover, and associated surface waves are properly included by the use of the exact dyadic Green's function. Using the present formulation the input impedance of a rectangular microstrip antenna is determined and compared with experimental and earlier calculated results.

Input impedance of microstrip antennas

The problem of a microstrip antenna covered by a dielectric is formulated in terms of coupled integro-differential equations with the current distribution on the microstrip patch as an unknown variable. Galerkin's method is used to solve for the unknown patch current. Using the present formulation the resonant frequency and bandwidth of a rectangular microstrip antenna are determined and compared with experimental results.

M. Deshpande

Papers

Integral equation formulation of microstrip antennas