Fullwave analysis of planar microwave circuits by integral equation methods and bilinear transformations

A novel algorithm based on generalized transmission line equations (GTL) and on the method of lines (MoL) for the analysis of planar waveguide circuits with anisotropic layers is proposed and substantiated. The algorithm uses discretization lines in the propagation direction of the waves. As in the case of multiconductor transmission lines two modal matrices are determined. Impedance/admittance transformation equations are determined on the basis of the GTL equations. Using these equations numerically stable and accurate impedance transformations and field calculations can be performed.

The work presented here introduces lumped elements to an iterative method based on the wave concept combined with the two-dimentional fast Fourrier transformation algorithm known as fast modal transformation (FMT). We extend this method to the analysis of microwave-distributed circuits containing passive or active, linear or nonlinear lumped elements which are characterized by their surface impedance as defined in this article. Simulation results of varactor-tuned filter and phase-shifter circuit examples are compared with the measurement results. Good agreement between simulated and experimental results validates the use of the iterative method for the analysis of planar circuits, including lumped elements. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 269–275, 2003.

We present a new formulation of the integral equation (IE) method for models with variable background conductivity. This method overcomes the standard limitation of the conventional IE method related to the use of a horizontally layered background only. The new IE method still employs the Green's functions for a horizontally layered 1‐D model. However, the new method allows us to use an inhomogeneous background with the IE method. The method was carefully tested for modeling the electromagnetic (EM) field for complex structures with known variable background conductivity. It can find wide application in modeling EM data for multiple geological models with some common geoelectrical features. As an example, we consider marine controlled source EM (MCSEM) application for simulating EM response of a petroleum reservoir in the presence of a salt dome structure.

This paper compares the accuracy of the integral equation method and the multiple scales method in solving the amplitude equation of multi degree of freedom nonlinear vibration systems. We consider three examples: a two-degree-of-freedom stainless-steel beam system controlled by a saturation controller, a three-degree-of-freedom rotating compressor blade model and a four-degree-of-freedom horizontally supported Jeffcott-rotor system controlled by a PPF controller. The amplitude equations are obtained by applying the integral equation method and the method of multiple scales. The stability analysis is achieved based on the Floquet theory together with Routh–Hurwitz criterion. Furthermore, we modified the iterative procedure of the integral equation method to make the analytic approximate solution more accurate. Finally, the analyses show that in most cases, the analytical solutions obtained by the integral equation method are more excellent agreement with the numerical solutions than the most commonly used method of multiple scales. Therefore, the integral equation method is worth popularizing to obtain the approximate analytical solutions of the multi-degree-of-freedom nonlinear vibration system.

The integral equation method has been proven to be an efficient tool to model three‐dimensional electromagnetic problems. Owing to the full linear system to be solved, the method has been considered effective only in the case of models consisting of a strongly limited number of cells. However, recent advances in matrix storage and multiplication issues facilitate the modeling of horizontally large structures. Iterative methods are the most feasible techniques for obtaining accurate solutions for such problems. In this paper we demonstrate that the convergence of iterative methods can be improved significantly, if the original integral equation is replaced by an equation based on the modified Green's operator with the norm less or equal to one. That is why we call this technique the Contraction Integral Equation (CIE) method. We demonstrate that application of the modified Green's operator can be treated as a preconditioning of the original problem. We have performed a comparative study of the convergence of different iterative solvers applied to the original and contraction integral equations. The results show that the most effective solvers are the BIGGSTAB, QMRCGSTAB, and CGMRES algorithms, equipped with preconditioning based on the CIE method.

Dispersive shallow water waves over a porous sea bed

A new fullwave global analysis of complex inhomogeneous microwave structures including passive or active, linear or nonlinear lumped elements is presented. For a given structure, only one electromagnetic simulation of the distributed part, by a three-dimensional (3-D) finite element method using edge elements, is needed corresponding to the insertion of variable lumped elements placed at the same position. Simulation results of various test cases, containing either resistor, diode, or active component, are compared with those provided by a commercial circuit analysis software or with measurements results. Our validated electromagnetic simulator is then used for analyzing a planar balanced mixer operating in the millimetric range.

An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners.

An efficient method to improve the integral equations method is presented in this article. A delta gap source generator and the fundamental mode sampling technique are employed. By employing this modified method, observation of the SWR and the creation of a large matrix in the conventional method employing a delta gap source generator are not necessary. Also, the modeling complexity and the time-consuming computation of the conventional method, which employs the semiinfinite traveling-wave mode, are avoided. In this article we use the coplanar waveguide short-end discontinuity as an example to describe this method in the spectral domain. Moreover, numerical results are compared with our experimental data and they show good agreement. ©1996 John Wiley & Sons, Inc.

An attempt is made to enhance the effectiveness of the method of moments in solving planar microwave circuits problems. The proposed dynamic model is a modified version of that presented by H.Y. Yang and N.G. Alexopolous (1988). The novelty of this approach consists of introducing a technique of fundamental mode sampling which substantially reduces the complexity of the analysis and the computation time involved in the characterization of all practical discontinuities. The numerical results are in good agreement with experimental data. >

An integral equation method is developed for the computer modeling of the magnetic fields produced by color television deflection yokes. Saddle or toroidal yokes with either radial or nonradial winding distributions can be analyzed using this new technique. The integral equation method is shown to yield magnetic field calculations that are at least as accurate as those produced by conventional finite-difference analysis. In most cases computer algorithms using the integral equation approach have been found to be more computationally efficient than existing finite-difference programs.

New boundary integral equation method which was previously proposed have been examined in detail and extended to the computer‐aided design (CAD) of asymmetrical dielectric slab waveguide bends. Many numerical results of symmetric waveguide discontinuities and asymmetric waveguide bends confirm the validity of the new method. They show that all numerical results satisfy the energy conservation law within an accuracy of 1% and indicate that the new integral equation method is very suitable for the basic theory or a solver of CAD software for various open dielectric waveguide circuits.

In order to effectively solve the problem of the accuracy of the magnetic field measurement of submarine upper vault sensor, an integral equation method based on the magnetic field detection method of submarine upper vault was proposed. By analyzing the simulation data of the dome magnetic sensor, the analysis solution and the integral equation solution of the ellipsoid shell of the ship model are compared, so as to verify the accuracy of the integral equation method and provide a reference for the magnetic field measurement accuracy of the submarine upper part.

In this study, we analyzed dielectric shimming by formulating it as an electromagnetic scattering problem using integral equations. Three-dimensional simulations of the radiofrequency field in two configurations using different materials were analyzed in terms of induced currents and secondary fields. A two-dimensional integral equation method with different backgrounds was used to identify the underlying physical mechanisms. This framework was then used to develop an inversion method for the design of dielectric pads. The effects of a dielectric pad can be attributed to the interference of a secondary field that is produced by the currents induced in the dielectric pad, radiating in an inhomogeneous background. The integral equation method with inhomogeneous background reduces the complexity of the forward and inverse problem significantly and can be used to optimize the permittivity distribution for a desired B1+ field. Agreement with experimental B1+ maps was obtained in a cylindrical phantom, demonstrating the validity of the method. The integral equation method with inhomogeneous background yields an efficient numerical framework for the analysis and inverse design of dielectric shimming materials.