## Fundamentals of Electromagnetics 2: Quasistatics and WavesThis book is the second of two volumes which have been created to provide an understanding of the basic principles and applications of electromagnetic fields for electrical engineering students. Fundamentals of Electromagnetics Vol 2: Quasistatics and Waves examines how the low-frequency models of lumped elements are modified to include parasitic elements. For even higher frequencies, wave behavior in space and on transmission lines is explained. Finally, the textbook concludes with details of transmission line properties and applications. Upon completion of this book and its companion Fundamentals of Electromagnetics Vol 1: Internal Behavior of Lumped Elements, with a focus on the DC and low-frequency behavior of electromagnetic fields within lumped elements, students will have gained the necessary knowledge to progress to advanced studies of electromagnetics. |

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### Contents

1 | |

5 | |

8 | |

10 | |

CAPACITORS | 12 |

552 First Order Term | 13 |

553 Second Order Term | 14 |

554 Higher Order Terms | 20 |

77 TRANSIENT WAVES ON LINES | 98 |

78 MORE ABOUT TRANSIENT WAVES | 102 |

79 BOUNCE DIAGRAMS | 107 |

710 REACTIVE LOAD TRANSIENTS | 111 |

711 STEADYSTATE WAVES | 114 |

712 STEADYSTATE VOLTAGES AND CURRENTS | 125 |

The Smith Chart | 131 |

82 THE SMITH CHART | 135 |

INDUCTORS | 23 |

562 First Order Term | 24 |

563 Second Order Term | 25 |

564 Higher Order Terms | 27 |

57 RESISTIVE TERMINATIONS | 28 |

571 Zero Order Term | 29 |

572 First Order Term | 30 |

Electromagnetic Waves | 33 |

62 TEM WAVES AND IMPEDANCE | 39 |

63 SOURCES OF TEM WAVES | 41 |

64 WAVES IN ARBITRARY DIRECTIONS | 42 |

65 WAVES IN LOSSY MATERIAL | 45 |

66 GOOD CONDUCTORS AND SKIN DEPTH | 49 |

67 SKIN EFFECT IN CIRCUITS | 51 |

68 POWER FLOW AND POYNTINGS VECTOR | 59 |

69 WAVES INCIDENT ON BOUNDARIES | 67 |

610 STANDING WAVES | 76 |

Transmission Lines | 79 |

72 TEM WAVES ON TRANSMISSION LINES | 81 |

73 VOLTAGE AND CURRENT WAVES | 83 |

74 TELEGRAPHERS EQUATIONS AND DISTRIBUTED ELEMENT CIRCUIT MODELS | 86 |

75 LOUSY TRANSMISSION LINES | 90 |

76 REFLECTED WAVES | 95 |

83 IMPEDANCE TRANSFORMATIONS WITH SMITH CHARTS | 141 |

84 LOSSY TRANSMISSION LINES | 143 |

85 SLOTTEDLINE MEASUREMENTS | 146 |

Transmission Line Circuits | 151 |

93 QUARTERWAVE TRANSFORMER | 152 |

94 QUARTERWAVE TRANSFORMERS AND A SINGLE REACTIVE ELEMENT | 155 |

95 SINGLE SUSCEPTANCE TUNERS | 158 |

96 GENERAL MATCHING PRINCIPLES | 161 |

98 ATTENUATORS | 163 |

99 DISTORTIONLESS LINES | 164 |

910 DIRECTIONAL COUPLERS | 166 |

Vector Identities | 169 |

Coordinate Systems and Transformations | 171 |

CARTESIAN RECTANGULAR COORDINATES | 172 |

SPHERICAL COORDINATES | 173 |

Vector Calculus | 175 |

INTERGRAL OPERATIONS | 176 |

INTEGRAL EVALUATION | 177 |

Material Properties | 179 |

PERMITTIVITY | 181 |

PERMEABILITY | 182 |

Author Biography | 185 |

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### Common terms and phrases

admittance Ampere's law amplitude attenuation behavior boundary calculated capacitive capacitor characteristic impedance circuit model complex component conductor current density current flow cylindrical dielectric distance electric and magnetic electric field electrodes equations Example expressed Faraday's law ﬁeld field intensity FIGURE ﬂow frequency incident and reflected incident voltage incident wave induced voltage inductance inductor input impedance integral line length load impedance lossless lossy lumped elements magnetic energy magnetic field magnetic flux material Maxwell's equations minima negative order electric Order Term phase phasor phasor form plane wave positively propagating Poynting's vector propagation constant quarter-wave transformer reactance reflected voltage reflected wave reflection coefficient region represents resistance resistor rotation second order short circuit shown in Fig signal skin depth Smith chart surface time-varying transmission line transmitted wave tuner voltage and current voltage drop VSWR circle wave impedance wave propagating wavelength wire z-direction zero order