TRANSACTIONS OF THE ILLUMINATING ENGINEERING SOCIETY
CONTENTS 1 INTRODUCTION EXAMPLES OF MULTICONDUCTOR TRANSMISSION-LINE STRUCTURES PROPERTIES OF THE TEM MODE OF PROPAGATION THE TRANSMISSION-LINE EQUATIONS: A PREVIEW UNIQUE DE?NITION OF VOLTAGE AND CURRENT FOR THE TEM MODE OF PROPAGATION DE?NING THE PER-UNIT-LENGTH PARAMETERS OBTAINING THE TRANSMISSION-LINE EQUATIONS FROM THE TRANSVERSE ELECTROMAGNETIC FIELD EQUATIONS PROPERTIES OF THE PER-UNIT-LENGTH PARAMETERS CLASSI?CATION OF TRANSMISSION LINES UNIFORM VERSUS NONUNIFORM LINES HOMOGENEOUS VERSUS INHOMOGENEOUS SURROUNDING MEDIA LOSSLESS VERSUS LOSSY LINES RESTRICTIONS ON THE APPLICABILITY OF THE TRANSMISSION-LINE EQUATION FORMULATION HIGHER ORDER MODES 1 5 1 1 THE IN?NITE, PARALLEL-PLATE TRANSMISSION LINE 1 5 1 2 THE COAXIAL TRANSMISSION LINE 1 5 1 3 TWO-WIRE LINES TRANSMISSION-LINE CURRENTS VERSUS ANTENNA CURRENTS THE TIME DOMAIN VERSUS THE FREQUENCY DOMAIN THE FOURIER SERIES AND TRANSFORM SPECTRA AND BANDWIDTH OF DIGITAL WAVEFORMS COMPUTING THE TIME-DOMAIN RESPONSE OF TRANSMISSION LINES HAVING LINEAR TERMINATIONS USING FOURIER METHODS AND SUPERPOSITION PROBLEMS REFERENCES 2 THE TRANSMISSION-LINE EQUATIONS FOR TWO-CONDUCTOR LINES DERIVATION OF THE TRANSMISSION-LINE EQUATIONS FROM THE INTEGRAL FORM OF MAXWELL’S EQUATIONS DERIVATION OF THE TRANSMISSION-LINE EQUATIONS FROM THE PER-UNIT-LENGTH EQUIVALENT CIRCUIT INCORPORATING FREQUENCY-DEPENDENT LOSSES PROPERTIES OF THE FREQUENCY-DOMAIN PER-UNIT-LENGTH IMPEDANCE ˆZ(?) AND ADMITTANCE ˆY(?) 3 THE TRANSMISSION-LINE EQUATIONS FOR MULTICONDUCTOR LINES DERIVATION OF THE MULTICONDUCTOR TRANSMISSION-LINE EQUATIONS FROM THE INTEGRAL FORM OF MAXWELL’S EQUATIONS DERIVATION OF THE MULTICONDUCTOR TRANSMISSION-LINE EQUATIONS FROM THE PER-UNIT-LENGTH EQUIVALENT CIRCUIT SUMMARY OF THE MTL EQUATIONS PROPERTIES OF THE PER-UNIT-LENGTH PARAMETER MATRICES L, C, G 4 THE PER-UNIT-LENGTH PARAMETERS FOR TWO-CONDUCTOR LINES DE?NITIONS OF THE PER-UNIT-LENGTH PARAMETERS L, C, AND G LINES HAVING CONDUCTORS OF CIRCULAR, CYLINDRICAL CROSS SECTION (WIRES) FUNDAMENTAL SUBPROBLEMS FOR WIRES 4 2 1 1 THE METHOD OF IMAGES PER-UNIT-LENGTH INDUCTANCE AND CAPACITANCE FOR WIRE-TYPE LINES PER-UNIT-LENGTH CONDUCTANCE AND RESISTANCE FOR WIRE-TYPE LINES LINES HAVING CONDUCTORS OF RECTANGULAR CROSS SECTION (PCB LANDS) PER-UNIT-LENGTH INDUCTANCE AND CAPACITANCE FOR PCB-TYPE LINES PER-UNIT-LENGTH CONDUCTANCE AND RESISTANCE FOR PCB-TYPE LINES 5 THE PER-UNIT-LENGTH PARAMETERS FOR MULTICONDUCTOR LINES DE?NITIONS OF THE PER-UNIT-LENGTH PARAMETER MATRICES L, C, AND G THE GENERALIZED CAPACITANCE MATRIX C MULTICONDUCTOR LINES HAVING CONDUCTORS OF CIRCULAR, CYLINDRICAL CROSS SECTION (WIRES) WIDE-SEPARATION APPROXIMATIONS FOR WIRES IN HOMOGENEOUS MEDIA 5 2 1 1 N + 1 WIRES 5 2 1 2 N WIRES ABOVE AN IN?NITE, PERFECTLY CONDUCTING PLANE 5 2 1 3 N WIRES WITHIN A PERFECTLY CONDUCTING CYLINDRICAL SHIELD NUMERICAL METHODS FOR THE GENERAL CASE 5 2 2 1 APPLICATIONS TO INHOMOGENEOUS DIELECTRIC MEDIA COMPUTED RESULTS: RIBBON CABLES MULTICONDUCTOR LINES HAVING CONDUCTORS OF RECTANGULAR CROSS SECTION METHOD OF MOMENTS (MOM) TECHNIQUES 5 3 1 1 APPLICATIONS TO PRINTED CIRCUIT BOARDS 5 3 1 2 APPLICATIONS TO COUPLED MICROSTRIP LINES 5 3 1 3 APPLICATIONS TO COUPLED STRIPLINES FINITE DIFFERENCE TECHNIQUES FINITE-ELEMENT TECHNIQUES 6 FREQUENCY-DOMAIN ANALYSIS OF TWO-CONDUCTOR LINES THE TRANSMISSION-LINE EQUATIONS IN THE FREQUENCY DOMAIN THE GENERAL SOLUTION FOR LOSSLESS LINES THE RE?ECTION COEF?CIENT AND INPUT IMPEDANCE SOLUTIONS FOR THE TERMINAL VOLTAGES AND CURRENTS THE SPICE (PSPICE) SOLUTION FOR LOSSLESS LINES VOLTAGE AND CURRENT AS A FUNCTION OF POSITION ON THE LINE MATCHING AND VSWR POWER FLOW ON A LOSSLESS LINE THE GENERAL SOLUTION FOR LOSSY LINES THE LOW-LOSS APPROXIMATION LUMPED-CIRCUIT APPROXIMATE MODELS OF THE LINE ALTERNATIVE TWO-PORT REPRESENTATIONS OF THE LINE THE CHAIN PARAMETERS APPROXIMATING ABRUPTLY NONUNIFORM LINES WITH THE CHAIN-PARAMETER MATRIX THE Z AND Y PARAMETERS 7 FREQUENCY-DOMAIN ANALYSIS OF MULTICONDUCTOR LINES THE MTL TRANSMISSION-LINE EQUATIONS IN THE FREQUENCY DOMAIN THE GENERAL SOLUTION FOR AN (N + 1)-CONDUCTOR LINE DECOUPLING THE MTL EQUATIONS BY SIMILARITY TRANSFORMATIONS SOLUTION FOR LINE CATEGORIES 7 2 2 1 PERFECT CONDUCTORS IN LOSSY, HOMOGENEOUS MEDIA 7 2 2 2 LOSSY CONDUCTORS IN LOSSY, HOMOGENEOUS MEDIA 7 2 2 3 PERFECT CONDUCTORS IN LOSSLESS, INHOMOGENEOUS MEDIA 7 2 2 4 THE GENERAL CASE: LOSSY CONDUCTORS IN LOSSY, INHOMOGENEOUS MEDIA 7 2 2 5 CYCLIC-SYMMETRIC STRUCTURES INCORPORATING THE TERMINAL CONDITIONS THE GENERALIZED THEVENIN EQUIVALENT THE GENERALIZED NORTON EQUIVALENT MIXED REPRESENTATIONS LUMPED-CIRCUIT APPROXIMATE CHARACTERIZATIONS ALTERNATIVE 2N-PORT CHARACTERIZATIONS ANALOGY OF THE FREQUENCY-DOMAIN MTL EQUATIONS TO STATE-VARIABLE EQUATIONS CHARACTERIZING THE LINE AS A 2N-PORT WITH THE CHAIN-PARAMETER MATRIX PROPERTIES OF THE CHAIN-PARAMETER MATRIX APPROXIMATING NONUNIFORM LINES WITH THE CHAIN-PARAMETER MATRIX THE IMPEDANCE AND ADMITTANCE PARAMETER MATRIX CHARACTERIZATIONS POWER FLOW AND THE RE?ECTION COEF?CIENT MATRIX COMPUTED AND EXPERIMENTAL RESULTS RIBBON CABLES PRINTED CIRCUIT BOARDS 8 TIME-DOMAIN ANALYSIS OF TWO-CONDUCTOR LINES THE SOLUTION FOR LOSSLESS LINES WAVE TRACING AND THE RE?ECTION COEF?CIENTS SERIES SOLUTIONS AND THE DIFFERENCE OPERATOR THE METHOD OF CHARACTERISTICS AND A TWO-PORT MODEL OF THE LINE THE LAPLACE TRANSFORM SOLUTION 8 1 5 1 LINES WITH CAPACITIVE AND INDUCTIVE LOADS 8 1 6 1 WHEN IS THE LINE ELECTRICALLY SHORT IN THE TIME DOMAIN? THE TIME-DOMAIN TO FREQUENCY-DOMAIN (TDFD) TRANSFORMATION METHOD THE FINITE-DIFFERENCE, TIME-DOMAIN (FDTD) METHOD 8 1 8 1 THE MAGIC TIME STEP MATCHING FOR SIGNAL INTEGRITY 8 1 9 1 WHEN IS MATCHING REQUIRED? 8 1 9 2 EFFECTS OF LINE DISCONTINUITIES INCORPORATION OF LOSSES REPRESENTING FREQUENCY-DEPENDENT LOSSES 8 2 1 1 REPRESENTING LOSSES IN THE MEDIUM 8 2 1 2 REPRESENTING LOSSES IN THE CONDUCTORS AND SKIN EFFECT 8 2 1 3 CONVOLUTION WITH FREQUENCY-DEPENDENT LOSSES 8 2 3 1 INCLUDING FREQUENCY-INDEPENDENT LOSSES 8 2 3 2 INCLUDING FREQUENCY-DEPENDENT LOSSES 8 2 3 3 PRONY’S METHOD FOR REPRESENTING A FUNCTION 8 2 3 4 RECURSIVE CONVOLUTION 8 2 3 5 AN EXAMPLE: A HIGH-LOSS LINE 8 2 3 6 A CORRECTION FOR THE FDTD ERRORS THE USE OF MACROMODELS IN MODELING THE LINE REPRESENTING FREQUENCY-DEPENDENT FUNCTIONS IN THE TIME DOMAIN USING PADE METHODS 9 TIME-DOMAIN ANALYSIS OF MULTICONDUCTOR LINES THE RECURSIVE SOLUTION FOR MTLS DECOUPLING THE MTL EQUATIONS 9 1 2 1 LOSSLESS LINES IN HOMOGENEOUS MEDIA 9 1 2 2 LOSSLESS LINES IN INHOMOGENEOUS MEDIA 9 1 2 3 INCORPORATING THE TERMINAL CONDITIONS VIA THE SPICE PROGRAM 9 1 5 1 INCLUDING DYNAMIC AND/OR NONLINEAR TERMINATIONS IN THE FDTD ANALYSIS THE TIME-DOMAIN TO FREQUENCY-DOMAIN (TDFD) METHOD REPRESENTATION OF THE LOSSY MTL WITH THE GENERALIZED METHOD OF CHARACTERISTICS MODEL ORDER REDUCTION (MOR) METHODS 9 2 5 1 PADE APPROXIMATION OF THE MATRIX EXPONENTIAL 9 2 5 2 ASYMPTOTIC WAVEFORM EVALUATION (AWE) 9 2 5 3 COMPLEX FREQUENCY HOPPING (CFH) 9 2 5 4 VECTOR FITTING 10 LITERAL (SYMBOLIC) SOLUTIONS FOR THREE-CONDUCTOR LINES 10 1 THE LITERAL FREQUENCY-DOMAIN SOLUTION FOR A HOMOGENEOUS MEDIUM 10 1 1 INDUCTIVE AND CAPACITIVE COUPLING 10 1 2 COMMON-IMPEDANCE COUPLING 10 2 THE LITERAL TIME-DOMAIN SOLUTION FOR A HOMOGENEOUS MEDIUM 10 2 1 EXPLICIT SOLUTION 10 2 2 WEAKLY COUPLED LINES 10 2 3 INDUCTIVE AND CAPACITIVE COUPLING 10 2 4 COMMON-IMPEDANCE COUPLING 10 3 COMPUTED AND EXPERIMENTAL RESULTS 10 3 1 A THREE-WIRE RIBBON CABLE 10 3 2 A THREE-CONDUCTOR PRINTED CIRCUIT BOARD 11 INCIDENT FIELD EXCITATION OF TWO-CONDUCTOR LINES 11 1 DERIVATION OF THE TRANSMISSION-LINE EQUATIONS FOR INCIDENT FIELD EXCITATION 11 1 1 EQUIVALENCE OF SOURCE REPRESENTATIONS 11 2 THE FREQUENCY-DOMAIN SOLUTION 11 2 1 SOLUTION OF THE TRANSMISSION-LINE EQUATIONS 11 2 2 SIMPLI?ED FORMS OF THE EXCITATIONS 11 2 3 INCORPORATING THE LINE TERMINATIONS 11 2 4 UNIFORM PLANE-WAVE EXCITATION OF THE LINE 11 2 4 1 SPECIAL CASES 11 2 4 2 ONE CONDUCTOR ABOVE A GROUND PLANE 11 2 5 COMPARISON WITH PREDICTIONS OF METHOD OF MOMENTS CODES 11 3 THE TIME-DOMAIN SOLUTION 11 3 1 THE LAPLACE TRANSFORM SOLUTION 11 3 2 UNIFORM PLANE-WAVE EXCITATION OF THE LINE 11 3 3 A SPICE EQUIVALENT CIRCUIT 11 3 4 THE TIME-DOMAIN TO FREQUENCY-DOMAIN (TDFD) TRANSFORMATION 11 3 5 THE FINITE-DIFFERENCE, TIME-DOMAIN (FDTD) SOLUTION METHOD 11 3 6 COMPUTED RESULTS 12 INCIDENT FIELD EXCITATION OF MULTICONDUCTOR LINES 12 1 DERIVATION OF THE MTL EQUATIONS FOR INCIDENT FIELD EXCITATION 12 1 1 EQUIVALENCE OF SOURCE REPRESENTATIONS 12 2 FREQUENCY-DOMAIN SOLUTIONS 12 2 1 SOLUTION OF THE MTL EQUATIONS 12 2 2 SIMPLI?ED FORMS OF THE EXCITATIONS 12 2 3 INCORPORATING THE LINE TERMINATIONS 12 2 3 1 LOSSLESS LINES IN HOMOGENEOUS MEDIA 12 2 4 LUMPED-CIRCUIT APPROXIMATE CHARACTERIZATIONS 12 2 5 UNIFORM PLANE-WAVE EXCITATION OF THE LINE 12 3 THE TIME-DOMAIN SOLUTION 12 3 1 DECOUPLING THE MTL EQUATIONS 12 3 2 A SPICE EQUIVALENT CIRCUIT 12 3 3 LUMPED-CIRCUIT APPROXIMATE CHARACTERIZATIONS 12 3 4 THE TIME-DOMAIN TO FREQUENCY-DOMAIN (TDFD) TRANSFORMATION 12 3 5 THE FINITE-DIFFERENCE, TIME-DOMAIN (FDTD) SOLUTION METHOD 12 4 COMPUTED RESULTS 13 TRANSMISSION-LINE NETWORKS 13 1 REPRESENTATION OF LOSSLESS LINES WITH THE SPICE MODEL 13 2 REPRESENTATION WITH LUMPED-CIRCUIT APPROXIMATE MODELS 13 3 REPRESENTATION VIA THE ADMITTANCE OR IMPEDANCE 2N-PORT PARAMETERS 13 4 REPRESENTATION WITH THE BLT EQUATIONS 13 5 DIRECT TIME-DOMAIN SOLUTIONS IN TERMS OF TRAVELING WAVES 13 6 A SUMMARY OF METHODS FOR ANALYZING MULTICONDUCTOR TRANSMISSION LINES