Note for Electromagnetic Field - EMF By JNTU Heroes

Topics ( 6 )

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Lecture Notes on Electromagnetic Field

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Contents Contents 1 1 Fundamental concepts 3 1.1 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Phasors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Constitutive relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Waves in homogeneous media 14 2.1 Plane waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Cylindrical waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Spherical waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Waves in non homogeneous media . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Propagation in good conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Radiation in free space 28 3.1 Green’s functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 Elementary dipoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 Radiation of generic sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4 Antennas 4.1 49 Antenna parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1.1 Input impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.1.2 Radiation pattern, Directivity and Gain . . . . . . . . . . . . . . . . . . . . 51 4.1.3 Effective area, effective height . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.2 Friis transmission formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.3 Examples of simple antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3.1 Wire antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.3.2 Aperture antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 1

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CONTENTS 5 Waveguides 76 5.1 Waveguide modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2 Equivalent transmission lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.3 Rectangular waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.3.1 Design of a single mode rectangular waveguide . . . . . . . . . . . . . . . . 92 5.3.2 Tunneling effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.3 Irises and waveguide discontinuities . . . . . . . . . . . . . . . . . . . . . . . 100 A Mathematical Basics 1 A.1 Coordinate systems and algebra of vector fields . . . . . . . . . . . . . . . . . . . . 1 A.2 Calculus of vector fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 A.3 Multidimensional Dirac delta functions . . . . . . . . . . . . . . . . . . . . . . . . . 17 B Solved Exercises 20 B.1 Polarization and Phasors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 B.2 Plane Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 B.3 Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 B.4 Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Bibliography 45 2

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Chapter 1 Fundamental concepts 1.1 Maxwell’s Equations All electromagnetic phenomena of interest in this course can be modeled by means of Maxwell’s equations  ∂    ∇ × E(r,t) = − B(r,t) − M(r,t) ∂t (1.1)  ∂   ∇ × H(r,t) = D(r,t) + J (r,t) ∂t Let us review the meaning of the symbols and the relevant measurement units. E(r,t) electric field V/m H(r,t) magnetic field A/m D(r,t) electric induction C/m2 B(r,t) magnetic induction Wb/m2 J (r,t) electric current density (source) A/m2 M(r,t) magnetic current density (source) [V/m2 ] Customarily, only electric currents are introduced; it is in particular stated that magnetic charges and currents do not exist. However, it will be seen in later chapters, that the introduction of fictitious magnetic currents has some advantages: • The radiation of some antennas, such as loops or horns, is easily obtained • Maxwell’s equations are more symmetric 3