×
There is no substitute for HARD WORK.
--Your friends at LectureNotes
Close

Note for Electromagnetic Field And Waves - EMFW By JNTU Heroes

  • Electromagnetic Field And Waves - EMFW
  • Note
  • Jawaharlal Nehru Technological University Anantapur (JNTU) College of Engineering (CEP), Pulivendula, Pulivendula, Andhra Pradesh, India - JNTUACEP
  • 7 Topics
  • 788 Views
  • 20 Offline Downloads
  • Uploaded 1 year ago
0 User(s)
Download PDFOrder Printed Copy

Share it with your friends

Leave your Comments

Text from page-2

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 smartworlD.asia 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 2

Text from page-3

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 smartworlD.asia Bibliography 2 3 45

Text from page-4

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. smartworlD.asia 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 4

Text from page-5

4 • (surface) magnetic currents are necessary for the formulation of the equivalence theorem, a fundamental tool for the rigorous modelling of antennas In circuit theory, one has two types of ideal generators, i.e. current and voltage ones: likewise, in electromagnetism one introduces two types of sources. Concerning the symmetry of Maxwell’s equations, we cite the principle of duality: performing the exchanges E ↔H B ↔ −D J ↔ −M Maxwell’s equations transform into each others. Experiments show that the electric charge is a conserved quantity. This implies that electric current density and electric charge (volume density are related by a continuity equation ∇ · J (r,t) + ∂ρ(r,t) =0 ∂t (1.2) By analogy, we assume that also magnetic charges are conserved, so that a similar continuity equation must be satisfied: ∂ρm (r,t) =0 (1.3) ∇ · M(r,t) + ∂t It can be proved that eqs.(1.1), (1.2) (1.3) imply the well known divergence equations smartworlD.asia ∇ · B(r,t) = ρm (r,t) ∇ · D(r,t) = ρ(r,t) (1.4) Some authors prefer to assume eqs.(1.1), 1.4) as fundamental equations and obtain the conservation of charge (1.2) (1.3) as a consequence. Maxwell’s equations can be written in differential form as above, so that they are assumed to hold in every point of a domain, or in integral form, so that they refer to a finite volume. The integral form can be obtained by integrating eq.(1.1) over an open surface Σo with boundary Γ and applying Stokes theorem: Z Z I d B·ν ˆ dΣo − M·ν ˆ dΣo E · τˆ ds = − dt Σo Σo Γ (1.5) Z Z I d D·ν ˆ dΣo + J ·ν ˆ dΣo H · τˆ ds = dt Σo Σo Γ In words, the first equation says that the line integral of the electric field, i.e. the sum of all voltage drops along a closed loop, equals the time rate of change of the magnetic induction flux plus the total magnetic current. The second equation says that the line integral of the magnetic field along a closed loop equals the time rate of change of the electric induction flux plus the total electric current. Then we integrate eq.(1.4) over a volume V with surface Σ and apply the divergence theorem: I Z B·ν ˆ dΣ = Σ I ρm dV Z D·ν ˆ dΣ = V Σ 5 ρ dV V (1.6)

Lecture Notes