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Title: Study of unconditionally stable time-domain methods with unsplit-field perfectly matched layer absorbing boundary condition and fast computation method for electrostatic parameter extraction of radio frequency integrated circuit
Other Titles: Dui wu chang fen lie de wan quan pi pei ceng xi shou bian jie tiao jian xia wu tiao jian wen ding shi yu fang fa yi ji she pin ji ti dian lu zhong dian jing tai can shu ti qu kuai su yan suan fa zhi yan jiu
Authors: Leung, Yiu-fung (梁耀峰)
Department: Dept. of Electronic Engineering
Degree: Doctor of Philosophy
Issue Date: 2007
Publisher: City University of Hong Kong
Subjects: Electromagnetic fields -- Mathematics
Radio frequency integrated circuits
Time-domain analysis
Notes: 1 v. (various pagings) : ill. ; 30 cm.
CityU Call Number: QC665.E4 L486 2007
Includes bibliographical references.
Thesis (Ph.D.)--City University of Hong Kong, 2007
Type: Thesis
Abstract: This dissertation work will be presented in seven chapters. The first chapter is an overall introduction to the work I had done during my whole PhD candidature. The other four of them are mainly related to fast computational methods analysis for solving Maxwell’s equation without Courant-Friedrich-Levy (CFL) limitation while providing high performance absorbing boundary condition – Unsplit-field Perfectly Matched layer (UPML) to prevent unnecessary reflection from the domain of concern. The remaining two chapters are about a new fast computation algorithm: Equivalent Charge Formulation Multi-Level Green’s Function Interpolation (ECF-MLGFIM) and the analysis on Fractal Structure Capacitors by using this new method. Chapter 2 - A hybrid method using the Finite-Difference Time-Domain (FDTD) (second-order accurate in time and fourth-order in space) and Pseudo-Spectral Time-Domain (PSTD) method is presented. The dispersion relation, stability criterion, and the performance of the UPML of this new method are given. Chapter 3 - An UPML medium is introduced for higher-order Alternating Direction Implicit (ADI) formulation of the FDTD Method. Results for second-order and fourth-order simulation are used to illustrate the effectiveness of the media constructed using the proposed approach as absorbers for numerical grid truncation. Chapter 4 - An UPML medium is introduced to a recently developed unconditionally stable scheme which mainly applies the weighted Laguerre polynomials and the Galerkin’s temporal testing procedure to eliminate the time step limitation occurred in conventional FDTD method. By applying the proposed formulation, no field splitting is required for putting the UPML in the scheme and thus the unconditionally stable nature of the scheme is maintained. Results for 1D simulation is used to illustrate the performance of UPML. Chapter 5 - The analysis for using the scheme by Crank-Nicolson Peaceman-Rachford (CNPR) to solve the two-dimensional Maxwell’s Equations will be performed. It is found that the CNPR scheme is unconditionally stable and can be solved simply by Thomas Algorithm. The dispersion relation of CNPR is nearly the same with the Crank-Nicolson (CN) scheme. Moreover, it is found that when the number of grids per wavelength is larger than three, the dispersion relation of the FDTD will have a better performance than CNPR and the CN schemes. Mathematical derivation on stability condition and dispersion relation will also be given in this chapter. Chapter 6 - It is known that Equivalent Charge Formulation (ECF) is a surface oriented formulation. It separates geometry into conductor surfaces and dielectric interface surfaces. However, in Multi-Level Green’s Function Interpolation Method (MLGFIM), like many other fast matrix computational methods, it is a geometry oriented method which divides the structures under investigation into cube or sub-matrices, i.e., a cube or sub-matrices may contain conductor, dielectric or combination of them. A new algorithm, ECF-MLGFIM is proposed in this chapter to solve this intrinsic problem and make the computation of ECF matrix in a very efficient way. Numerical results are provided to show the accuracy and efficiency of this new method. Chapter 7 – With the efficient algorithm ECF-MLGFIM developed in Chapter 6, eight fractal capacitor structures will be investigated in this chapter. First, the capacitance boost factor versus the minimum metal width and the metal thickness will be investigated. Then, the capacitance comparison for various fractal capacitors under the same effective area will be examined. Finally, the fractal capacitor capacitance at various dielectric constant will also be studied. A conclusion of the thesis is given in Chapter 8.
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