ELECTROMAGNETIC WAVES AND RADIATING SYSTEMS

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CONTENTS

1. FUNDAMENTALS OF ELECTROMAGNETIC EN-GINEERING

1.01 Circuits and fields. 1.02 Vector analysis. 1.03 Physical interpretation of gradient, divergence and curl. 1.04 Vector relations in other co-ordinate systems. 1.05 Units and dimensions. 1.06 Order of magnitude of the units.

2. ELECTROSTATICS.

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2.01 Introduction. 2.02 Fundamental relations of the electro-static field. 2.03 Gauss's law. 2.04 Electric field due to several charges. 2.05 The potential function. 2.06 Field due to a con-tinuous distribution of charge. 2.07 Equipotential surfaces. 2.08 Divergence theorem. 2.09 Poisson's equation and Laplace's equa-tion. 2.10 Capacitance. 2.11 Energy stored in an electric field. 2.12 Conditions at a boundary between dielectrics. 2.13 Cylin-drical and spherical harmonics.

3. THE STEADY MAGNETIC FIELD.

3.01 Theories of the magnetic field. 3.02 Magnetic flux 4. 3.03 Magnetic flux density B. 3.04 Magnetic intensity H and magneto-motive force 5. 3.05 Permeability µ. 3.06 Energy stored in the magnetic field. 3.07 Ampere's law for a current element. 3.08 Magnetic vector potential. 3.09 Magnetic vector potential of a current element. 3.10 Analogies between electric and magnetic fields.

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4. MAXWELL'S EQUATIONS.

94

4.01 Ampere's work law in the differential vector form. 4.02 Er-ror in simple statement of Ampere's law for time-varying fields. 4.03 The generalized magnetomotive force equation. 4.04 Fara-day's law and Maxwell's second equation. 4.05 The field equa-tions in vector form. 4.06 Conditions at a boundary surface,

5. ELECTROMAGNETIC WAVES.

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Part 1 Electromagnetic Waves in a Homogeneous Medium

5.01 Solution for free-space conditions. 5.02 Uniform plane-wave propagation. 5.03 Sinusoidal time variations. 5.04 Uniform plane waves. 5.05 The wave equations for a conducting medium. 5.06 Conductors and dielectrics.

Part II Reflection and Refraction of Plane Waves

5.07 Reflection by a perfect conductor-normal incidence. 5.08 Reflection by a perfect dielectric-normal incidence. 5.09 Reflection by a perfect insulator-oblique incidence. 5.10 Direction cosines. 5.11 Reflection by a perfect conductor-oblique incidence. 5.12 The transmission line analogy. 5.13 Surface impedance.

6. POYNTING VECTOR AND THE FLOW OF POWER.

160

6.01 Poynting's theorem. 6.02 Note on the interpretation of EXH. 6.03 Instantaneous, average, and complex Poynting vector. 6.04 Power loss in a plane conductor.

7. GUIDED WAVES.

7.01 Waves between parallel planes. 7.02 Transverse electric

175

waves. 7.03 Transverse magnetic waves. 7.04 Characteristics of TE and TM waves. 7.05 Transverse electromagnetic waves. 7.06 Velocities of propagation. 7.07 Attenuation in parallel plane guides. 7.08 Wave impedances. 7.09 Electric field and current flow within the conductor.

8. TRANSMISSION LINES

211

8.01 Introduction. 8.02 Circuit representation of the parallel-plane transmission line. 8.03 Parallel-plane transmission lines with loss. 8.04 Coaxial and parallel-wire lines. 8.05 E and H about long parallel eylindrical conductors. 8.06 Transmission line theory. 8.07 Low-loss radio frequency and UHF transmission lines. 8.08 UHF lines as circuit elements. 8.09 Impedance matching by means of stub lines. 8.10 Graphical representation of transmission-line phenomena.

9. WAVE GUIDES.

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9.01 Rectangular guides. 9.02 Transverse magnetic waves in rectangular guides. 9.03 Transverse electric waves in rectangular guides. 9.04 The TEM wave in cylindrical guides. 9.05 Bessel functions. 9.06 Solution of the field equations in cylindrical co-ordinates, 9.07 TM and TE waves in circular guides. 9.08 Wave impedances and characteristic impedances. 9.09 Transmission line analogy for waves in cylindrical guides. 9.10 Attenuation factor and Q wave guides.

10. RADIATION.

294

10.01 Vector potential in the electromagnetic field. 10.02 The alternating current element (or oscillating electric dipole). 10.03 Power radiated by a current element. 10.04 Application to short antennas. 10.05 Assumed current distribution. 10.06 Radiation from a quarter-wave monopole or half-wave dipole. 10.07 Sine in-tegral and cosine integral. 10.08 Electromagnetic field close to an antenna. 10.09 Network and antenna theorems.

11. IMPEDANCE.

Part I - Induced-Emf Method of Computing Impedances

342

11.01 Radiation resistance by the induced-emf method. 11.02 Radiation resistance referred to the base, 11.03 Mutual impedance between antennas. 11.04 Computation of mutual imped-ance. 11.05 Reactance of an antenna. 11.06 Note on the induced-emf method. 11.07 Equivalence of the induced-emf and Poynting vector methods. 11.08 Uniform cylindrical waves and the in-finitely long wire.

Part II Circuit Relations and Field Theory

11.09 Circuit relations and Maxwell's equations in the integral form. 11.10 Derivation of circuit relations from field theory.

12. DIRECTIONAL CHARACTERISTICS OF ANTEN-NAS

391

12.01 Introduction. 12.02 Directional properties of dipole anten-nas. 12.03 Traveling-wave antennas and effect of the point of feed on standing-wave antennas. 12.04 Two-element array. 12.05 Horizontal patterns of broadcast antennas. 12.06 Linear arrays. 12.07 Multiplication of patterns. 12.08 Effect of the earth on vertical patterns. 12.09 Binomial array. 12.10 Antenna gain. 12.11 Effective area of an antenna, 12.12 Elliptical polarization. 12.13 Antenna gain from pattern measurements. 12.14 The mathematics of linear arrays. 12.15 Antenna synthesis. 12.16 The Tchebyscheff distribution. 12.17 Supergain arrays.

13. IMPEDANCE CHARACTERISTICS OF ANTEN-NAS.

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13.01 Lumped-constant representation of antenna input imped-ance. 13.02 The antenna as an opened-out transmission line, 13.03 Wide-band impedance matching. 13.04 The cylindrical antenna problem. 13.05 Spherical waves. 13.06 Spherical waves and the biconical antenna. 13.07 Equivalent transmission-line and termi-nal impedance. 13.08 Impedance of cylindrical antennas.

14. ANTENNA PRACTICE AND DESIGN .

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14.01 Low-frequency practice-electrically short antennas. 14.02 Broadcast antennas. 14.03 High-frequency (short-wave) anten-nas. 14.04 Very high-frequency antennas. 14.05 Receiving antennas.

15. SECONDARY SOURCES AND APERTURE AN-TENNAS..

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15.01 Magnetic currents. 15.02 The induction and equivalence theorems. 15.03 Field of a secondary or Huygen's source. 15.04 Radiation from the open end of a coaxial line. 15.05 Radiation through an aperture in an absorbing screen. 15.06 Fraunhofer and Fresnel diffraction. 15.07 Radiation from electromagnetic horns. 15.08 The infinitely long narrow slit. 15.09 Babinet's principle. 15.10 Slot antennas. 15.11 The slotted-cylinder antenna. 15.12 Dipole and slot arrays around cylinders
16. GROUND WAVE PROPAGATION.

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16.01 Reflection at the surface of a finitely conducting plane earth. 16.02 Space wave and surface wave. 16.03 The surface wave. 16.04 Elevated dipole antennas above a plane earth. 16.05 Wave tilt of the surface wave. 16.06 Spherical earth propagation. 16.07 Tropospheric refraction and reflection.

17. SKY WAVE PROPAGATION

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17.01 Introduction. 17.02 The ionosphere. 17.03 Effective e and of an ionized layer. 17.04 Reflection and refraction of waves. by the ionosphere. 17.05 Regular and irregular variations of the ionosphere. 17.06 Attenuation factor for ionospheric propagation. 17.07 Effect of the earth's magnetic field. 17.08. Transmission-line representation of the ionosphere. 17.09 Sky wave transmission calculations.

APPENDICES

689

I. Velocities of Propagation, 689

II. Bessel Functions, 693

LIST OF SYMBOLS

698

INDEX.

701

CONVERSION OF UNITS.

. Inside back cover

Prácticamente todos los ingenieros de comunicaciones y electrónicos necesitan conocimientos sobre la radiación y la propagación electromagnética. Este libro está diseñado para proporcionar un curso en este campo para ingenieros eléctricos y físicos. Es una consecuencia de los cursos impartidos por el autor en la Universidad Estatal de Ohio y en la Universidad de Illinois. El nivel de la primera parte del libro es adecuado para estudiantes de último año y estudiantes de posgrado principiantes; los capítulos posteriores son principalmente para estudiantes de posgrado más avanzados. Aunque hay suficiente material para un curso de dos semestres, muchos instructores pueden preferir seleccionar solo ciertos capítulos para cubrirlos en un curso de un semestre o un trimestre. La división del material entre los capítulos se ha realizado teniendo en cuenta este hecho

En un texto de este alcance es necesario recurrir a los escritos de muchos especialistas. Agradezco al profesor Erik Hallén el uso de sus curvas de impedancia de antena en el capítulo 13. Para los capítulos sobre propagación, se ha utilizado material de los artículos de K. A. Norton y C. R. Burrows. Los escritos de S. A. Schelkunoff ya son clásicos y son en gran medida responsables de muchos conceptos de ingeniería, como la impedancia de onda y las corrientes magnéticas, ahora de uso general. Se encontrarán referencias a sus artículos y libros a lo largo del texto

Es un placer agradecer la ayuda brindada por los asociados del autor en la Universidad de Illinois y otros lugares. W. G. Albright, R. S. Elliott, P. K. Hudson, Ray DuHamel, Edgar Hayden, John Myers, Douglas Royal, John Bell y muchos otros donaron generosamente su tiempo para revisar el manuscrito y leer las pruebas. Las conversaciones con George Sinclair siempre fueron útiles. Estoy especialmente en deuda con J. A. Barkson, quien leyó gran parte del manuscrito y ofreció muchas sugerencias, y con Nicholas Yaru, quien dibujó los originales para las ilustraciones.

Hace varios años tuve el privilegio de tomar un curso de posgrado en radiación del profesor W. L. Everitt de la Universidad Estatal de Ohio. El conjunto original de notas, "Radiación y sistemas radiantes", utilizado para ese curso, ha formado el núcleo sobre el cual se ha desarrollado este libro. Espero que parte de la filosofía de la ingeniería que fue una parte tan importante de ese curso inicial se haya trasladado a este trabajo