Complete network characterisation of stratified planar circuits using the method of moments technique: an integrated approach to lumped and wave ports

This study gives a full treatment of the network characterisation of multi-port planar circuits embedded in shielded stratified media with an integrated approach to lumped ports and wave ports. The details of the mathematical formulation for the retrieval of scattering parameters are given in three cases: networks possessing only lumped ports, networks possessing only wave ports and networks with a combination of both types. A detailed description of the computer algorithm is presented to help the reader easily reproduce our results. The implementation of combined ports in the framework of planar multi-layered structures is particularly useful in analysing systems that have waveguide connections and planar circuitries in their structure, such as cavity-backed antennas and their associated feeding systems, dielectric resonator antennas or compound microwave filters. In such structures one can divide the system into the waveguide structure and the planar circuitries and analyse each part separately with an appropriate and efficient numerical technique. Network characterisations will be consequently communicated at the port interfaces. This strategy enhances the total performance of the computational scheme to a great extent, while not affecting the accuracy of the full-wave analysis.

3D analysis and optimization of microwave circuits by the method of moments

Francisco Jesus Nunez

The design and minaturization of microwave circuits involves the analysis and optimization of a large varity of structures, which, in general, are based on arbritrary objects embedded in also arbritary media. The most common situation is found when optimizing terminal antennas, whose main constraint is the antenna's volume, which must be fitted into a specified space, which in general is the phone or laptop case. This kind of antennas can also include stratified media, oblique metallizations, dielectric objects, waveguide components, in their definition making their analysis more difficult from the numeric point of view. The complete treatment of this kind of problems has been performed traditionally using Finite Differences or Finite Elements software, while it is more rare to find Method of Moments implementations for the solution of this kind of general problems. The Method of Moments has a certain number of advantages as the inclusion of radiation conditions or stratified media in the Green's function of the problem. Due to this it is possible to mesh only the surfaces or boundary conditions that are not included in the Green's function definition, obtaining, for instance, a more natural radiation boundary condition compared to other fullwave methods. The other big concern is the optimization of this kind of structures. In general the structures we are dealing with in this work can have very irregular shapes, in order to fit within the required volume constraints. The traditional optimizations techniques based on the gradient or conjugated gradient are not efficient when optimizing functions containning multiple minima and a large search space, which is the case in the optimization of terminal antennas. When miniaturizing terminal antennas or just a simple microstrip filter, the number of unknowns can be very large, and the different optimization variables can vary within wide limits in the search space. In this situation the Genetic Algorithms are ideal for seeking the global optimum solution of our problem. This work covers the analysis and optimization of microwave circuits, including antennas and filters in microstrip and waveguide technologies, paying more attention to the implementation of the Method of Moments (MoM) in conjugation with the Mixed Potential Integral Equation (MPIE) and Electric/Magnetic Field Integral Equation (EFIE/MFIE). The work has been split into 3 main goals: The analysis of 3 dimensional structures in stratified media, including arbritary shaped dielectric bodies using the Method of Moments, (MPIE,EFIE,MFIE). The analysis of shielded environments and more precisely the analysis of retangular waveguide cavities with the Method of Moments. The implementation of several optimization techniques, emcompassed in the frame of genetic algorithms, for the design and miniaturization of terminal antennas and microstrip filters. Some relevant examples linked to the efficiency and accuracy of the different methods and techiques explained in this work are included in each chapter, yielding to practical results suitable to be used in real life design problems. The main contributions of this work can be summarized as follows: In Chapter 2 we have developed the interpolation of 3D Green's function to the general solution of dielectric objects embedded in multilayered media. The interpolation method itself is preceeded by a spectral extraction of the quasi-static terms. This technique, very often applied in complex images techniques, has been applied to our specific Green's function problem yielding very good results in terms of accuracy and Green's function computation time. Another contribution, also emcompassed in Chapter 2, is the integration of the static part of the field dyadic G̿EM, performed by splitting the field dyadic into TM and TE components, allowing then an analytical integration of the dyadic terms in stratified media. In the frame of shielded environments in Chapter 3, the most important contribution is the extension of Ewald's acceleration technique to full electric and magnetic problems, allowing the acceleration of the field dyadic G̿EM and thus permit the extension of the MoM to the simulation of arbritary metallic shapes coupled to apertures through Ewald's approach. In Chapter 4 the most important contribution is the implementation of a Bayesian optimiser based on the estimation of probability made by dependencies trees. The dependency tree based method found in [1] and later in [2] has been adapted to the terminal antenna miniaturization yielding to excellent results in optimisation time and quality of the solution provided by the optimiser. Our implementation of the dependency tree method was found to be better than the traditional method used in this kind of problems. Chapter 4 contains also an implementation of the growing cells method presented in [3] for the specific problem of optimising pseudo periodic structures, like microwave filters, yielding to a powerful interpolating method which accelerates the optimisation process of microwaves devices whose fitness response is very time consuming.

EPFL2006

Numerical analysis of axisymmetric flows and methods for fluid-structure interaction arising in blood flow simulation

Simone Deparis

In this thesis we propose and analyze the numerical methods for the approximation of axisymmetric flows as well as algorithms suitable for the solution of fluid-structure interaction problems. Our investigation is aimed at, but are not restricted to, the simulation of the blood flow dynamics. The first part of this work deals with an axisymmetric fluid model based on three-dimensional incompressible Stokes or Navier–Stokes equations which are solved on a two-dimensional half-section of the domain under consideration. In particular we show optimal a priori error estimates for P1isoP2/P1 axisymmetric finite elements for the steady Stokes equations under the assumption that the domain and the data are axisymmetric and that the data have no angular component. Our analysis is carried out in the framework of weighted Sobolev spaces and takes advantage of a suitably defined Cl´ement type projection operator. We then introduce an axisymmetric formulation of the Navier–Stokes equations in moving domains and, starting from existing results in three-dimensions, we set up an Arbitrary Lagrangian–Eulerian (ALE) formulation and prove some stability results. In the second part, we deal with algorithms for the solution of fluid-structure interaction problems. We introduce the problem in a generic form where the fluid is described by means of incompressible Navier–Stokes equations and the structure by a viscoelastic model. We account for large deformations of the structure and we show how existing algorithms may be improved to reduce the computational time. In particular we show how to use transpiration boundary conditions to approximate the fluid-structure problem in a fixed point strategy. Moreover, in a quasi-Newton strategy we reduce the cost by replacing the Jacobian with inexact Jacobians stemming from reduced physical models for the problem at hand. To speed up the convergence of the Newton algorithm, we also define a dynamic preconditioner and an acceleration scheme which have been successfully tested in haemodynamics simulations in two and three dimensions.

EPFL2004

Electromagnetic Modelling of Planar Circuits Embedded in Laterally Shielded Multilayered Media

Laleh Golestanirad

Multilayered media with printed circuits embedded between their dielectric layers are one of the most successful technologies for manufacturing planar structures with a very promising performance-to-price ratio. These planar structures include many different geometries ranging from cavity-backed microstrip antennas through Frequency Selective Surfaces (FSS) and photonic band-gap structures, to shielded printed circuits and ultra-wide-band slot-line microwave filters. The electromagnetic characteristics of such structures can be modeled with a wide range of numerical techniques. In recent years we have witnessed a remarkable progress in developing numerical solvers specialized in analyzing specific electromagnetic problems including the Integral Equation technique (IE) solved by the Method of Moments (MoM) which has proven to be very robust and efficient in the framework of partially open or shielded planar structures. As a part of this study an efficient CAD tool was developed based on the IE formulation and implemented in the context of the MoM technique. It includes a rigorous mathematical formulation of the electromagnetic problem which automatically incorporates the effects of the metallic shield (cavity) and the multilayered substrate which supports different layers of metallization (interfaces). A comprehensive study has been carried out to point out the convergence of the proposed algorithm along with a detailed validation, verification and benchmarking plan. The tool is developed in such a way that is capable of working with a hybrid mesh (combination of both rectangular and triangular cells) which gives it a great flexibility in analyzing any arbitrarily-shaped embedded circuitry. To enhance the overall performance of the algorithm, symmetry options have been formulated and implemented. These additional features have shown to dramatically reduce the computational and temporal requirements and thus expand the range of microwave devices which can be efficiently analyzed by the software, such as filters based on waveguide structures and FSSs. Other enhancement techniques have been envisaged based on selective MoM matrix member calculation which successfully reduce the number of unknowns in large microstrip layouts while maintaining an acceptable accuracy. Mathematical formulations are developed to provide the capability of handling lumped ports (representing coaxial-line feeds) and waveguide excitations. The implementation of combined ports in the framework of planar multilayered structures is shown to be practically useful in analyzing systems that have both waveguide connections and planar circuitries in their structure as it enables the application of highly specialized algorithms in the analysis of each part of the system and subsequent communication of the network characterizations at the ports' interfaces. This approach has considerably enhanced the overall performance of the analysis tool by reducing the computation time and memory requirements to a great extent.

EPFL2011