### Table of Contents

Chapter | Section | Title | Page |
---|---|---|---|

1 | The Transmision Line Equations | 1 | |

1.1 | The Transmission Line: A Definition | 1 | |

1.2 | The Transmission Line Equations From Maxwell's Equations | 2 | |

1.3 | The Transmission Line Equations From Kirchhoff's Equations | 6 | |

1.4 | Low Pass Filters And Simulated Transmission Lines | 9 | |

1.5 | The Wave Equation | 10 | |

1.6 | Lossy Media | 12 | |

1.7 | Suggested Further Reading | 14 | |

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2 | Time Domain Solutions To The Transmission Line Equations | 15 | |

2.1 | Travelling Waves On A Lossless Line | 15 | |

2.2 | The Finite Length Lossless Line | 17 | |

2.3 | Laplace Transform Solutions For The Lossless Line | 22 | |

2.4 | Transmission Coefficients | 26 | |

2.5 | Gas Discharges And Lighting Devices | 30 | |

2.6 | Time Domain Reflectometry | 27 | |

2.7 | Suggested Further Reading | 32 | |

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3 | The Alternating Current Steady State | 33 | |

3.1 | General Solutions | 33 | |

3.2 | The Finite Line And Its Two-Port Network Parameters | 36 | |

3.3 | Standing Waves, VSWR And The Smith Chart | 38 | |

3.4 | Suggested Further Reading | 45 | |

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4 | Scattering Parameters | 46 | |

4.1 | The Scattering Matrix | 47 | |

4.2 | Basic Properties of S Parameters | 51 | |

4.3 | Examples of Two-Port Networks Characterized By S Parameters | 51 | |

4.4 | The Network Analyzer Measurement System | 57 | |

4.5 | Reflectometer Network Measurements | 62 | |

4.6 | Suggested Further Reading | 64 | |

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5 | Some Non-TEM Transmission Lines | 65 | |

5.1 | The Quasi-Static Microstrip Line | 66 | |

5.2 | The Frequency-Dependent Microstrip Line | 69 | |

5.3 | The Microstrip Slow Wave Mode | 74 | |

5.4 | The Parallel Stripline About A Sheet Of Dielectric | 75 | |

5.5 | Slotline | 76 | |

5.6 | Helical Line | 79 | |

5.7 | Suggested Further Reading | 80 | |

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6 | Introduction To Conformal Transformations | 82 | |

6.1 | Conformal Transformations | 82 | |

6.2 | Example: The Coaxial Cable | 88 | |

6.3 | Example: The Parallel Wire Line | 89 | |

6.4 | Example: Two Thin Strips In The Same Plane | 92 | |

6.5 | Stripline | 93 | |

6.6 | Suggested Further Reading | 95 | |

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7 | The Skin Effect And Losses In Transmission Lines | 97 | |

7.1 | The Skin Effect Equation | 98 | |

7.2 | The Incremental Inductance Calculation | 105 | |

7.3 | Suggested Further Reading | 107 | |

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8 | Coupled Transmission Lines | 109 | |

8.1 | The Four-Port Impedance Matrix For a Coupled Pair Of
Identical Lines | 109 | |

8.2 | Example: The Bi-Directional Coupler | 114 | |

8.3 | Example: Coupled Transmission Line Filters | 117 | |

8.4 | Miscellaneous Coupled Line Structures | 124 | |

8.5 | Asymmetric Coupled Lines | 126 | |

8.6 | Suggested Further Reading | 135 | |

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9 | Discrete Variable Solutions Of Laplace's Equation | 137 | |

9.1 | Transmission Line Parameters From Laplace's Equation | 138 | |

9.2 | The Discrete Form Of Laplace's Equation | 140 | |

9.3 | The Total Energy Capacitance Calculation | 143 | |

9.4 | A Simple Relaxation Program | 144 | |

9.5 | Overrelaxation And Predictor Equations | 147 | |

9.6 | The Relaxation Equation For Non-Uniform Dielectrics | 152 | |

9.7 | Example: The Boxed Microstrip Line | 156 | |

9.8 | Example: Coupled Lines | 159 | |

9.9 | Example: The Total Charge Capacitance | 162 | |

9.10 | Probabilistic Potential Theory | 165 | |

9.11 | Suggested Further Reading | 169 | |

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10 | Determination Of Transmission Line Parameters | 170 | |

10.1 | Poisson's Equation And A Green's Function Solution | 171 | |

10.2 | An Analytic Laplace's Equation Solution For Stripline | 179 | |

10.3 | Transmission Line Discontinuities And The Capacitance Matrix | 184 | |

10.4 | Suggested Further Reading | 197 | |

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11 | Transmission Lines As Impedance Matching Networks | 199 | |

11.1 | Impedance Matching With Quarter-Wave Sections Of Line | 200 | |

11.2 | Tapered Transmission Lines | 203 | |

11.3 | Transmission Line Transformers | 208 | |

11.4 | Unbalanced Circuits, Grounding And Balun Transformers | 215 | |

11.5 | Suggested Further Reading | 221 | |

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12 | Potpourri: Several Uses Of Transmission Lines As
Circuit Elements | 223 | |

12.1 | Impedance Approximations For Low-Loss Lines | 223 | |

12.2 | DC Blocks, DC Returns and Bias T's | 227 | |

12.3 | Attenuator Circuits | 231 | |

12.4 | Suggested Further Reading | 234 | |

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Index | 235 |