Spectral domain analysis of large (M)MIC‐structures using novel quadrature methods

Abstract

SUMMARYThe spectral domain approach for the solution of integral equations is especially attractive for planar circuits and antennas in multilayered environments characterized by analytically derived Green's functions. However, for circuits with large lateral dimensions the spectral integrands are strongly oscillatory and accurate evaluation of the integrals is extremely difficult and often time-consuming. In this paper, we propose higher-order Legendre quadrature rules optimized for the integration of the oscillating integrands using the Filon principle. The Legendre-Filon quadrature weights are computed for the specific oscillations by solving a small linear system of equations. The method is applied within a spectral domain solution approach evaluating the spectral integrals in cartesian wavenumbers and using asymptotic extraction techniques as well as complex integration path deformation for improved convergence. Since the asymptotic extraction causes a singularity in the origin of the wavenumber domain that is not annihilated by cartesian wavenumber integration, a special procedure for the treatment of this singularity is also introduced. The overall method needs very few sampling points for the numerical evaluation of the spectral integrals but is still applicable to very large structures as compared to the wavelength.

Modal Analysis of Microstrip Antenna on Fiber Reinforced Anisotropic Substrates

“…Integral equation techniques were applied to analyze a microstrip antenna on anisotropic substrate [13]. Solutions by dyadic Green's function on ferrites [14] and by Lagendre quadrature on microwave integrated circuit (MIC) structures [15] were reported. A quasi-static circuit model [16], a full-wave method-of-moments [17], and the transverse resonance technique [18] have been presented to model microstrip antenna on anisotropic substrates.…”

The effect of dielectric overlay on microstrip antenna embedded in composite laminated substrates

“…Because of the complexity involved, the antenna performance is often determined by FEMs or integral equations based on numerical techniques . Analytical solutions, if available, would be desirable to conduct parametric study of the substrate's variable affecting the antenna performance.…”

A fast space-spectral domain solver for quasi-3D structures with arbitrary vertical conductors in multilayered media

“…After sampling the Cartesian wavenumber plane, all Green's functions are computed and stored at the selected sampling points. After this, the whole quasi-3D structure can be analyzed by enhanced spectral domain techniques in the same way and the same high performance as structures with only planar components [6]. In contrast to [5], the analytical space domain integrations are now formulated in such a way, that the vertical currents can cross an arbitrary number of dielectric layers with an arbitrary vertical discretization.…”