Simulation Technology For Multi-Conductor Transmission Line Based On FEM

In high-speed large-scale integrated circuits and high-frequency long-distance communication lines,multi-conductor transmission lines(MTL)are often used as interconnects to achieve signal and energy transmission.Therefore,it is necessary to extract its terminal network parameters to evaluate its signal integrity and electromagnetic compatibility performance.The finite element method is an accurate,flexible,efficient and expandable numerical method that can obtain the electric and magnetic field values at various locations inside the transmission line structure through full-wave simulation based on this method.However,traditional finite element methods cannot directly obtain the scattering parameters of corresponding conductors from numerous coupled modes.The transfinite element method is a numerical method for dealing with truncated boundaries.It expands the mode function at the port,which can not only handle truncated ports but also calculate multi-mode problems.Therefore,this thesis systematically discusses MTL theory and applies the transfinite element method based on finite element method to solve MTL.The calculation formula of each terminal network parameter is given,which effectively solves the problem of MTL parameter calculation.Based on this,a terminal simulation tool based on finite element method for MTL full-wave analysis is developed.Specifically,after expounding the basic theory of the finite element method,this thesis verifies the feasibility of the finite element method by solving the waveguide discontinuity problem on an H-T junction example.Then,this thesis discusses the transfinite element method,which uses the truncated surface mode function expansion to approximate the truncated port electric field on the weak form of the Helmholtz equation.The same model is calculated and compared,proving that the transfinite element method has higher solving efficiency and less memory consumption in the simulation of this kind of problem.Then,this thesis applies the transfinite element method to the solution of MTL,and extracts the terminal network parameters by solving the voltage and current matrix of the transmission line.This thesis also discusses some parameter calculation problems of MTL in some special cases,and gives corresponding solutions.Finally,some commonly used MTL devices in engineering are calculated and compared with the results of HFSS software,which shows that the calculation method expounded in this thesis can perform the simulation analysis of MTL.The main work and innovation points of this thesis are as follows:1.The finite element method of electromagnetic field is systematically studied,the basic theory of finite element is mastered,and the discontinuous waveguide is analyzed by finite element method based on the weak form of Helmholtz equation.2.The process of dealing with truncated boundary by transfinite element method is studied,and the transfinite element analysis methods for discontinuous waveguide and high-order mode waveguide are discussed.3.The MTL theory is systematically discussed,and the transfinite element method is introduced into the solution of MTL,and the calculation method of terminal network parameters is derived,which is one of the main innovations of this thesis.4.The methods of extracting terminal network parameters in special cases such as differential pairs and multi-reference conductors in MTL are studied,which is also one of the innovations of this thesis.5.Based on the previous work,a terminal simulation tool is developed and integrated into EMLAB software.Through the calculation and comparison of several examples,the accuracy of the calculation method and simulation tool developed in this thesis are verified.