Shielded-Twisted-Pair Cable Model for Chafe Fault Detection Via Time-Domain Reflectometry
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NASA/TM–2012–216001 Shielded-twisted-pair cable model for chafe fault detection via time-domain reflectometry Stefan R. Schuet Ames Research Center Moffett Field, California Do˘gan A. Timu¸cin Ames Research Center Moffett Field, California Kevin R. Wheeler Ames Research Center Moffett Field, California March 2012 NASA STI Program . in Profile Since its founding, NASA has been • CONFERENCE PUBLICATION. dedicated to the advancement of Collected papers from scientific and aeronautics and space science. The technical conferences, symposia, NASA scientific and technical seminars, or other meetings information (STI) program plays a key sponsored or co-sponsored by NASA. part in helping NASA maintain this • important role. SPECIAL PUBLICATION. Scientific, technical, or historical The NASA STI Program operates information from NASA programs, under the auspices of the Agency Chief projects, and missions, often Information Officer. 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NASA STI Help Desk Scientific and technical findings that NASA Center for AeroSpace are preliminary or of specialized Information interest, e.g., quick release reports, 7115 Standard Drive working papers, and bibliographies Hanover, MD 21076–1320 that contain minimal annotation. Does not contain extensive analysis. • CONTRACTOR REPORT. Scientific and technical findings by NASA-sponsored contractors and grantees. NASA/TM–2012–216001 Shielded-twisted-pair cable model for chafe fault detection via time-domain reflectometry Stefan R. Schuet Ames Research Center Moffett Field, California Do˘gan A. Timu¸cin Ames Research Center Moffett Field, California Kevin R. Wheeler Ames Research Center Moffett Field, California National Aeronautics and Space Administration Ames Research Center Moffett Field, California 94035-1000 March 2012 Acknowledgments This work was funded by NASA’s Aeronautics Research Mission Directorate under the Vehicle Systems Safety Technologies Project of the Aviation Safety Program. The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constitute an offical endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics and Space Administration. Available from: NASA Center for AeroSpace Information 7115 Standard Drive Hanover, MD 21076-1320 443-757-5802 Contents List of Tables 3 List of Figures 4 List of Symbols 5 Executive Summary 8 1 Introduction 9 1.1 Problemstatement .................................. ........ 9 1.2 Literaturesurvey.................................. ......... 10 1.3 Reportoverview .................................... ....... 11 2 Theory 13 2.1 Basicmodelformulation ............................... ........ 13 2.1.1 Cable specification . .... 13 2.1.2 Maxwellequations .................................. .... 14 2.1.3 Field solutions . .. 16 2.1.4 Eigenvalue equation . .... 16 2.2 Uniformcable....................................... ...... 17 2.2.1 Eigenvalues....................................... ... 17 2.2.2 Modefields ........................................ .. 17 2.2.3 Choice of rc .......................................... 20 2.2.4 Exactpotentials ................................... .... 22 2.3 Equivalent circuit model . ........ 23 2.3.1 Basic variables . ... 23 2.3.2 Transmission-line equations . ...... 24 2.3.3 Calculation of C ....................................... 26 2.3.4 Calculation of Z ....................................... 28 2.3.5 Generalsolution ................................... .... 32 2.4 Twistedcable....................................... ...... 36 2.4.1 Eigenvalues....................................... ... 36 2.4.2 Modefields ........................................ .. 36 3 Simulation 38 3.1 Overview .......................................... ..... 38 3.2 Geometricfidelity.................................... ....... 38 3.3 Mesh............................................. ..... 39 3.4 2Danalysis ......................................... ..... 40 3.5 3Danalysis ......................................... ..... 40 3.6 Chafefaults....................................... ....... 43 1 4 Experiment 46 4.1 Overview .......................................... ..... 46 4.2 Systemmodel...................................... ....... 46 4.2.1 Common-modecablemodel . .. .. .. .. .. .. .. .. .. .. .. .. ..... 46 4.2.2 A simple chafe fault model . .... 47 4.2.3 System S-parameters..................................... 48 4.3 Bayesianparameterinference . ........... 49 4.4 Experimentalresults ................................ ......... 51 4.4.1 Nominal cable examples . .... 51 4.4.2 Faulty cable example . .... 57 5 Conclusion 60 5.1 Summaryofmainresults ............................... ....... 60 5.2 Areasoffutureresearch .. .. .. .. .. .. .. .. .. .. .. .. ........... 61 5.3 Acknowledgments................................... ........ 61 5.4 Contactinformation ................................. ........ 61 Bibliography 62 2 List of Tables 2.1 Shielded-pair cable parameters . .......... 14 2.2 Comparison of sup cable capacitance values obtained with different models . 28 3.1 Capacitancesfrom2Danalysis . ......... 40 3.2 Eigenvalues from 3D analysis . ........ 41 3.3 stp cable eigenvalues from 3D analysis for theoretical model . ........... 41 3.4 Capacitanceswithfaultsfortheevenmode . ............ 44 4.1 Parameterpriorinformation. .......... 51 4.2 Parameterestimatesforexample1 . ........... 52 4.3 Parameterestimatesforexample2 . ........... 54 3 List of Figures 2.1 Shielded-pair waveguide cross-section . ............. 13 2.2 A pair of helically wound current-carrying filaments inside a cylindrical shield . 15 2.3 Cut-off frequencies of the even and the odd waveguide modes of sup cable........... 18 2.4 Potential distributions for the even and the odd modes of sup cable .............. 19 2.5 Surface charge distributions for the even and the odd modes of sup cable ........... 19 2.6 Electric-field distributions for the even and the odd modes of sup cable ............ 21 2.7 Optimal filament positions for the even and the odd modes of sup cable............ 22 2.8 Variation of the approximate potential on the periphery of conductor 1 for the even and the odd modes of sup cable ....................................... 22 2.9 Comparison of the approximate analytical and the exact numerical solutions for the even and the odd mode potentials of sup cable................................ 23 2.10 Magnitudes and phases of the surface impedances of a round wire and a cylindrical tube in a coaxialarrangement .................................. ....... 30 2.11 Real and imaginary parts of the even- and the odd-mode eigenvalues for lossy sup cable . 33 2.12 Phase velocities and attenuation lengths of the even and the odd modes for lossy sup cable . 33 2.13 Magnitudes and phases of the even- and the odd-mode characteristic impedances for lossy sup cable ............................................... 34 2.14 A transmission-line circuit featuring stp cable .......................... 34 3.1 Cross-sections of simulated cable geometries . .............. 38 3.2 Meshes for stp cableandholefault................................. 39 3.3 Simulated electric-field distributions for the even mode . .............. 40 3.4 Simulated eigenmode fields . ....... 42 3.5 Electric field penetration into metals . .......... 42 3.6 Attenuation per meter in theoretical stp cable .......................... 43 3.7 Profile of transverse Ex field..................................... 44 3.8 Profile of transverse Ey field..................................... 45 3.9 Electric-field distribution for faulty cable . ............ 45 3.10 Axial electric field in the hole . ........ 45 4.1 Model of chafe fault on a shielded cable . .......... 47 4.2 vna hardwaremodel...................................... ... 49 4.3 S-parameter block diagram of the measurement setup . ............ 49 4.4 Example 1: Samples from the marginal posterior distribution . .............. 53 4.5 Example 1: Comparison between the measured and modeled