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There is often a need to interpolate data that is obtained through experiment or computational analysis, because the data is difficult or expensive to obtain. An example is the scattering parameters of microwave devices, obtained through computationally intensive finite element (FE) analysis. Cauchy interpolation is an established solution to this problem. In this thesis it is extended to interpolate data over a multi-parameter space, when the data available includes not just the function to be interpolated, but also its derivatives with respect to each parameter. The finite element method (FEM) provides such derivatives. The new algorithm is applied to a simple RLC circuit test case, and to real data from a 3D FE analysis of a rectangular waveguide component, in a 4-parameter space. Results show the effectiveness of the approach taken.

by Cheng Yat Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 1-6 (2nd gp.)). / Abstracts in English and Chinese. / Acknowledgements / Abstract: / A CD containing the Simulator and Results / List of Figures / List of Tables / Chapter 1. --- Introduction / Introduction --- p.1 / Chapter 2 --- Background Theory / Chapter 2.1 --- Empirical Design Formulas for Some Passive Microwave structures --- p.2 / Chapter 2.2.1 --- Short Dipole and Monopole --- p.4 / Chapter 2.2.2 --- Slot Antenna --- p.6 / Chapter 2.2.3 --- Stripline --- p.8 / Chapter 2.2.4 --- Microstrip --- p.10 / Chapter 2.2 --- Edge Based Finite Element Method and the Generalized Variational Principle --- p.12 / Chapter 2.2.1 --- Vector Finite Element Method for Electromagnetics --- p.14 / Chapter 2.2.1.1 --- Variational Formulation --- p.14 / Chapter 2.2.1.2 --- Advantages in Total Field Formulation --- p.16 / Chapter 2.2.2 --- Formulation by Method of Weighted Residual the Galerkin's Approach --- p.17 / Chapter 2.2.3 --- "the Vector Bases for BRICK, PRISM, TETRA" --- p.21 / Chapter 2.2.3.1 --- BRICK --- p.23 / Chapter 2.2.3.2 --- PRISM --- p.26 / Chapter 2.2.4 --- "Domain Discretization: Mesh Generation Scheme for 3D, 2D, ID Geometrical Entities in the Cartesian Domain" --- p.29 / Chapter 2.3 --- Construction of the Functional with Total Field Formulation --- p.31 / Chapter 2.3.1 --- Vector Wave Equation in the Cartesian Domain --- p.32 / Chapter 2.3.2 --- Boundary Conditions in the Cartesian Domain --- p.33 / Chapter 2.3.2.1 --- Perfect Magnetic Wall (Neumann's Boundary Condition) --- p.34 / Chapter 2.3.2.2 --- Perfect Electric Wall (Dirichlet Boundary Condition) --- p.34 / Chapter 2.3.2.3 --- Anisotropic Perfectly Matched Layer (APML) --- p.35 / Chapter 2.3.2.4 --- 2nd Order Absorbing Boundary Conditions --- p.39 / Chapter 2.3.2.5 --- Plane Wave Incidence (Uinc) --- p.40 / Chapter 2.3.2.6 --- Magnetic Aperture (M) --- p.42 / Chapter 2.3.2.7 --- Passive Lumped Load (ZL1D ) --- p.42 / Chapter 2.3.2.8 --- Current Feed (J) --- p.42 / Chapter 2.3.2.9 --- Voltage Feed (impressed E-field) --- p.43 / Chapter 2.3.2.10 --- Resistive Sheet ( =lst order ABC = standard IBC ) --- p.44 / Chapter 2.4 --- Visualization and Post-Processing of the Solution Field --- p.45 / Chapter 2.4.1 --- Field Pattern Plot --- p.45 / Chapter 2.4.2 --- Impedance at Input Port --- p.45 / Chapter 2.4.3 --- Y-parameter Extraction. --- p.46 / Chapter 3. --- Simulation Results and Discussion; / Chapter 3.1 --- Radiating Structures --- p.48 / Chapter 3.1.1 --- Short Dipole and Monopole --- p.48 / Chapter 3.1.1.1 --- Short Dipole --- p.48 / Chapter 3.1.1.2 --- Equivalent Monopole --- p.50 / Chapter 3.1.2 --- Slot Antenna --- p.52 / Chapter 3.1.2.1 --- Slot Antenna excited by the equivalent magnetic aperture --- p.52 / Chapter 3.1.2.3 --- Slot Antenna Excited by Unit Current Feed with Plane Wave Incidence ( Uinc) --- p.54 / Chapter 3.2 --- Striplines --- p.57 / Chapter 3.2.1 --- A Straight 50Ω Stripline --- p.57 / Chapter 3.2.1.1 --- Optimizing the Thickness and Number of Layer of PML --- p.58 / Chapter 3.2.1.2 --- Different Combination of BRICK and PRISM Mesh --- p.60 / Chapter 3.2.2 --- A Cross Junction --- p.63 / Chapter 3.2.3 --- A Squared 90° Corner --- p.69 / Chapter 3.2.4 --- A Champfered 90° Corner --- p.73 / Chapter 3.2.5 --- A Pair of Slot-Coupled Stripline Each Terminated with Open Circuit at Slot + λ/2 --- p.75 / Chapter 3.2.6 --- A Pair of Slot-Coupled Stripline Each Terminated with Short Circuit at Slot + λ/4 --- p.78 / Chapter 3.2.7 --- A Pair of Slot-Coupled Striplines Each Terminated with Short Circuit at Slot + λ/4 and Shorted through the Slot --- p.80 / Chapter 3.2.8 --- A Pair of Slot-Coupled Striplines Each Terminated with Short Circuit at Slot + λ/4 and has 50Ω Load through the Slot --- p.83 / Chapter 3.3 --- Calculating the Input Impedance ( Vport / Iport ) / Chapter 3.3.1 --- A Pair of Slot-Coupled Stripline Each Terminated with Short Circuit at Slot + λ/4 --- p.85 / Chapter 4 --- Conclusion / Chapter 4.1 --- Conclusion --- p.88 / Chapter 4.2 --- Minor Problems Encountered --- p.89 / Chapter 4.2 --- To Probe Further --- p.90 / Chapter Appendex: --- Implementation of the Edge-Based Finite Element Method / Chapter A.1 --- Mesh Generation Scheme --- p.92 / Chapter A.1.1 --- "Global Node, Edge and Primitive Assignment" --- p.93 / Chapter A.1.2 --- Property Assignment Local to Every Basis and Primitive --- p.94 / Chapter A.2 --- Assembly the Global System of Equations from the Element Stamps of all Primitives wrt. Global Edge Numbering --- p.95 / Chapter A.2.1 --- Setting up the Volumetric Integral for the Vector Wave Equation --- p.95 / Chapter A.2.1.1 --- Volume Integration of Constant Tangential Brick Elements --- p.96 / Chapter A.2.1.2 --- Volume Integration of Constant Tangential Pyramidal Elements --- p.98 / Chapter A.2.2 --- Incorporation of Boundary Conditions --- p.100 / Chapter A.2.2.1 --- Surface Integration of Constant Tangential Brick Elements --- p.100 / Chapter A.2.2.2 --- Surface Integration of Constant Tangential Pyramidal Elements --- p.105 / Chapter A.3 --- Solution to the Final System --- p.110 / Chapter A.3.1 --- Solving a System of Linear Equations by Diagonalization & Blockwise Partitioning --- p.111 / Chapter A.3.2 --- Direct Solution Method for Complex-valued System --- p.114 / Chapter A.4 --- Visualization and Post-Processing of the Solution Field --- p.115 / Chapter A.4.1 --- Field Pattern Visualization --- p.115 / Chapter A.4.2 --- Input Impedance Definition ( Vport /Iport). --- p.115 / Chapter A.4.3 --- Y-parameter Extraction. --- p.115 / Chapter A.4.3.1 --- Surface Integration of Brick Elements --- p.115 / Chapter A.4.3.2 --- Surface Integration of Pyramidal Elements --- p.117 / Chapter A.5 --- Simulation Setup with BRICK+PRISM+higher order TETRA --- p.119 / References / Books: / Journals and Papers: / for Hierarchal Edge Bases and FEM Formulations: / for ABC and PML: / for Mesh Generation: / for Free FEM Source Code Matrix Solver: / Miscellaneous:

First-pass success is important for cost-effective Monolithic Microwave and Millimeter-wave Integrated Circuits (MMMICs) since additional iterations to the MMMIC design are costly and take months to complete. In order to meet these goals, new levels of capabilities in the design, test and comprehensive simulations are required. The MMMICs employ microstrip line as a component connecting transmission medium as well as a distributed matching element. In a circuit layout, any deviation from straight transmission lines causes the introduction of discontinuity parasitics which must also be modeled as accurately as possible in order to predict the circuit performance. These discontinuities should either be taken into account or compensated for at the final stage of the design. A comparative study of different circuit simulators is undertaken to characterize microstrip discontinuities. Several microstrip discontinuities, such as bends, steps, and tees are examined and optimum compensated models are determined. / Master of Science