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©Copyright 2015 Shaowu Huang ©Copyright 2015 Shaowu Huang Broadband Green’s Function and Applications to Fast Electromagnetic Analysis of High-Speed Interconnects Shaowu Huang A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2015 Reading Committee: Leung Tsang, Chair Henning Braunisch Kung-Hau Ding Yasuo Kuga Program Authorized to Offer Degree: Electrical Engineering University of Washington Abstract Broadband Green’s Function and Applications to Fast Electromagnetic Analysis of High-Speed Interconnects Shaowu Huang Chair of the Supervisory Committee Professor Leung Tsang Department of Electrical Engineering This dissertation is focused on research and development of an innovative Broadband Green’s Function method and the applications to fast electromagnetic modeling and simulations of high-speed interconnects. Innovative solutions based on proposed broadband Green’s function method are presented and demonstrated to solve the challenging problems in signal integrity, power integrity, and electromagnetic compatibility and interference for computer system designs. The main contents of this dissertation are twofold: to overcome the fundamental restrictions in the conventional Green’s function methods through introducing the broadband Green’s function method, to explore the applications of the broadband Green’s function to modeling of high-speed interconnects in modern electronic devices and systems. In the first project, the method of broadband Green’s function with low wavenumber extraction (BBGFL) is proposed for arbitrary shaped waveguide. The methodologies of BBGFL are derived for both Neumann and Dirichlet boundary conditions. In the second project, we combine the BBGFL with method of moment (MoM) for fast full wave modeling and simulations of scattering in arbitrary shaped waveguides. The method is applied to solve the problem of vias inside PCB power/ground plane waveguide. In the third project, a number of applications are investigated, including modeling of vias in arbitrary shaped power/ground planes, modeling of emissions from printed circuit boards, modeling of stripline connecting transition vias in power/ground planes, modeling of arbitrary shaped waveguide structures in microwave components. The proposed methods are compared to in-house method of moment program and commercial HFSS tool. Simulation results of various problems are illustrated. The present methods are verified by comparing the resonant frequencies, Green’s functions, S-parameters, surface fields, and/or radiated emission for different problems. BBGFL has good agreement with MoM and/or HFSS on the numerical results. The computational efficiency is checked by comparing the CPU time. BBGFL is about two or three orders faster than MoM and HFSS for most cases in modeling of high-speed interconnects. TABLE OF CONTENTS Chapter 1 Introduction .................................................................................................... 1 1.1 Research Background.......................................................................................... 1 1.2 Research Methodology ....................................................................................... 2 1.3 Organization of the Dissertation ......................................................................... 4 Chapter 2 Broadband Green's Function with Low Wavenumber Extraction Method for Arbitrary Shaped Waveguides: TE case and Application to Modelling of Vias in Finite Power/Ground Plane .......................................................................................................... 9 2.1 Summery ............................................................................................................. 9 2.2 Introduction ........................................................................................................ 9 2.3 Methodology ..................................................................................................... 12 Broadband Bounded Green’s Function with Low Frequency Extractions for Neumann Case .................................................................................................... 12 2.3.1.1 Broadband Green’s Function and with Low Wavenumber Extraction. ..............................................................................., , , , ....... 13 2.3.1.2 Calculation of Modal Solution and Resonant , , Wavenumber ................................................................................................... 15 2.3.1.3 Normalization of Modes for Neumann Case ........................................ 18 2.3.1.4 Broadband Green’s Function for L-shaped Waveguide and Low Wavenumber Extraction ....................................................................................... 21 2.3.1.5 Summary Procedure for Computing ................................ 22 , , Application of Broadband Green’s Function of Arbitrary Waveguide to Foldy Lax Multiple Scattering Equation for Scattering by Vertical Vias .................... 24 Small Patch Green’s Function for TE Case ................................................ 29 2.3.3.1 Small Patch Integrated Green’s Function for TE Case .......................... 30 2.3.3.2 Derivative of Small Patch Integrated Green’s Function for TE Case ..... 31 2.4 Numerical Results ............................................................................................. 35 i Computation of Green’s Functions for Neumann Case ............................ 35 2.4.1.1 Resonant Wavenumber Comparison .................................................... 35 2.4.1.2 Modal Solution Comparison ................................................................. 37 2.4.1.3 Comparison of Green’s Function .................................................... 39 2.4.1.4 Comparison of CPU Times ..................................................................... 41 Application of BBGFL to the Simulation of Vias in Arbitrarily Shaped PCB Power/Ground Plane Pair ......................................................................................... 43 2.4.2.1 Modeling of Two Signal Vias in a Rectangular Power/Ground Plane Pair with Small Cut Out ................................................................................................ 43 2.4.2.2 Modeling of Two Signal Vias in A Rectangular Power/Ground Plane Pair with Large Cut Out ................................................................................................ 46 2.4.2.3 Modeling of Two Signal Vias and Two Shorting Vias in a Rectangular Power/Power (or Ground/Ground) Plane Pair with Large Cut Out ...................... 49 2.4.2.4 Modeling of 8 Vias: Four Signal Vias and Four Shorting Vias in a Rectangular Power/Power (or Ground/Ground) Plane Pair with Large Cut Out .. 52 2.4.2.5 Comparison of CPU Time for Vias Simulations ..................................... 55 2.5 Conclusion ......................................................................................................... 56 Chapter 3 Fast Electromagnetic Analysis of Emissions from Printed Circuit Board Using Broadband Green’s Function ............................................................................................ 57 3.1 Summary ........................................................................................................... 57 3.2 Introduction ...................................................................................................... 57 3.3 Methodology ..................................................................................................... 60 Broadband Green’s Function with Low Wavenumber Extraction for Calculation of Fields on Boundary Walls of Power/Ground Plane ........................... 61 Calculation of Radiated Emissions From Power/Ground Plane with Green’s Functions .................................................................................................... 64 3.4 Simulation ......................................................................................................... 67 Case A: 0.5 by 0.5 Square-inch Rectangular Power/Ground Plane Pair with 0.125 by 0.35 Square-inch Cut-out ................................................................... 68 Case B: 1.5 by 1.5 Square-inch Rectangular Power/Ground Plane Pair with 0.125 by 0.35 Square-inch Cut-out ................................................................... 72 ii Case C: 5 by 5 Square-inch Rectangular Power/Ground Plane Pair with 0.125 by 0.35 Square-inch Cut-out ........................................................................... 75 Case D: 5 by 5 Square-inch Rectangular Power/Ground Plane Pair with 1.25 by 3.5 Square-inch Cut-out ............................................................................... 78 Case E: 0.5 by 0.5 Square-inch Rectangular Power/Ground Plane Pair with 0.1 by 0.1 Square-inch Cut-out ......................................................................... 81 Case F: 1 by 1 Square-inch Rectangular Power/Ground Plane Pair with 0.125 by 0.35 Square-inch Cut-out ........................................................................... 85 Comparison of CPU Time for Vias Simulations ......................................... 88 3.5 Conclusion ......................................................................................................... 90 Chapter 4 Combining Broadband Green's Function with Low Wavenumber Extraction and Method of Moment for Fast Broadband Simulations of Scattering in Arbitrary Shaped Waveguides .........................................................................................................
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