FINITE ELEMENT ANALYSIS OF EMI IN A MULTI-CONDUCTOR CONNECTOR A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Mohammed Zafaruddin May, 2013 FINITE ELEMENT ANALYSIS OF EMI IN A MULTI-CONDUCTOR CONNECTOR Mohammed Zafaruddin Thesis Approved: Accepted: _______________________________ _______________________________ Advisor Department Chair Dr. Nathan Ida Dr. Jose Alexis De Abreu Garcia _______________________________ _______________________________ Committee Member Dean of the College Dr. George C. Giakos Dr. George K. Haritos _______________________________ _______________________________ Committee Member Dean of the Graduate School Dr. Hamid Bahrami Dr. George R. Newkome _______________________________ Date ii ABSTRACT This thesis discusses the numerical analysis of electrical multi-conductor connectors intended for operation at high frequencies. The analysis is based on a Finite Element Tool and looks at the effect of conductors on each other with a view to design for electromagnetic compatibility of connectors. When there is an electrically excited conductor in a medium, it acts as an antenna at high frequencies and radiates electromagnetic power. If there are any conductors in its vicinity they too act as antennas and receive a part of the EM power. Electromagnetic Interference (EMI) from nearby excited conductors causes induced currents, according to Faraday‘s law, which is considered as noise for other conductors. This noise is affected by factors such as distance between the conductors, strength and frequency of currents, permittivity, permeability and conductivity of the medium between the conductors. To reduce the effects of EMI in a shielded multi-conductor connector, values of induced currents at various distances between the conductors have been calculated and analyzed. The currents have been calculated at high excitation frequencies varying from 0.2GHz to 1GHz and distances between the conductors varying from 0.2 mm to 0.8mm. iii ACKNOWLEDGEMENTS I would like to take this opportunity to express my sincere gratitude to my advisor, Dr. Nathan Ida, for providing an opportunity to work under him, his guidance, encouragement and support during my graduate studies. His sound technical knowledge, managerial skills, confidence in me have been a source of inspiration. I thank Dr. Ida for providing me with the software Ansoft HFSS. I would like to thank Dr. Steve Bardi from Ansoft Corporation for helping me understand technical aspects of the software tool and his support. I would like to thank Drs. Hamid Bahrami and George Giakos for their insight and valuable ideas into the research. I would also like to thank Dr. John Heminger who taught the course Advanced Numerical Analysis which helped me understand the numerical and computational aspects of Finite Element Analysis in an effective way. His course work, exams and projects were very relevant, organized. I would like to offer special thanks to the chair, Dr. De Abreu Garcia for supporting me financially by assigning a Graduate Assistantship throughout my Masters. I acknowledge Ms. Tammy A Stitz for the help with my documentation and access to library resources. Finally, I would like to thank my family and friends for their unconditional help and encouragement all the time. iv TABLE OF CONTENTS Page LIST OF TABLES ........................................................................................................... viii LIST OF FIGURES ........................................................................................................... xi CHAPTER I. INTRODUCTION .................................................................................................. 1 1.1 Electrical Connector.................................................................................................. 1 1.2 Finite Element Analysis ............................................................................................ 2 1.3 Problem Description ................................................................................................. 3 II. ELECTROMAGNETIC INTERFERENCE IN CABLES AND CONNECTORS .......................................................................................4 2.1 Introduction ............................................................................................................... 4 2.2 Accidental Antennas ................................................................................................. 5 2.3 Electromagnetic Compatibility for Cables................................................................ 9 2.4 Electromagnetic Compatibility for Connectors ...................................................... 12 2.5 Shielding ................................................................................................................. 14 III. FINITE ELEMENT METHOD AND ANALYSIS ...............................................17 3.1 Finite Element Method ........................................................................................... 17 3.1.1 Finite Element Formulations ............................................................................ 17 3.1.2 The Variational Method ................................................................................... 23 v 3.1.3 Variational Finite Element Method .................................................................. 26 3.2 Computational Aspects in Finite Element Analysis ............................................... 29 3.3 Matrix Storage Schemes ......................................................................................... 30 3.3.1 Compact Storage Method ................................................................................. 34 3.4 Matrix Computation ................................................................................................ 35 3.4.1 Application of Boundary Conditions ............................................................... 35 3.4.2 Direct Methods ................................................................................................. 36 3.4.3 Iterative Methods .............................................................................................. 42 3.5 Eigenvalues and Eigenvectors in Computational Electromgnetics ........................ 47 3.6 Finite Element Based Electromagnetic Computation Software.............................. 49 3.6.1 Pre-Processor .................................................................................................... 50 3.6.2 Processor .......................................................................................................... 55 3.6.3 Post-Processor .................................................................................................. 55 IV. ANALYSIS AND RESULTS ................................................................................58 4.1 Introduction ............................................................................................................. 58 4.2 Description .............................................................................................................. 58 4.3 Dimensions ............................................................................................................. 60 4.4 Properties ................................................................................................................ 60 4.5 Case 1: Two Conductors connector ........................................................................ 60 4.5.1 Excitation .......................................................................................................... 61 4.5.2 Mesh ................................................................................................................. 61 4.5.3 Electric and Magnetic Field Plots .................................................................... 64 vi 4.5.4 Induced Currents .............................................................................................. 68 4.6 Case 2: Three Conductors connector ...................................................................... 70 4.6.1 Excitation .......................................................................................................... 71 4.6.2 Mesh ................................................................................................................. 71 4.6.3 Electric and Magnetic Field Plots .................................................................... 72 4.6.4 Induced Currents .............................................................................................. 85 4.7 Summary ................................................................................................................. 91 V. CONCLUSIONS AND FUTURE WORK ............................................................92 5.1 Conclusions ............................................................................................................. 92 5.2 Future Work ............................................................................................................ 92 BIBLIOGRAPHY ..............................................................................................................94 APPENDICES ...................................................................................................................97 APPENDIX A. LIST OF ABBREVIATIONS ..................................................................98 APPENDIX B. TABLES OF INDUCED CURRENTS FOR TWO CONDUCTOR CONNECTOR .................................................................100