The mathematical radio Inside the magic of AM, FM, and single-sideband

Paul J. Nahin

Book - 2024

"A trade book on the mathematics of radio"--

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Subjects
Published
Princeton, New Jersey : Princeton University Press [2024]
Language
English
Main Author
Paul J. Nahin (author)
Other Authors
Andrew J. Simoson (writer of foreword)
Item Description
Includes bibliographical references and index
Physical Description
lxii, 311 pages : illustrations ; 25 cm
ISBN
9780691235318
  • Foreword
  • Preface
  • 1. Radio Mathematics, Oscillators, and Transmitters
  • 1.1. Kirchhoff's Laws and FitzGerald's Oscillating Circuit
  • 1.2. Laplace Transforms, AC Impedance, and Transfer Functions
  • 1.3. Van der Pol's Negative Resistance Oscillator Equation
  • 1.4. Filters and the Wiener-Paley Theorem
  • 1.5. An Electronic Phase-Shift Oscillator
  • 1.6. Fourier Series and Transforms, and Signal Spectrums
  • 1.7. Impulses in Time and Frequency
  • Challenge Problems
  • 2. More Radio Mathematics: Circuits That Multiply
  • 2.1. Spectrum Shifting at the Transmitter
  • 2.2. Large-Carrier AM
  • 2.3. Convolution, and Multiplying by Squaring and Filtering
  • 2.4. Fleming's Vacuum Tube Diode and the Detection of Radio-Frequency Waves
  • 2.5. Multiplying by Sampling and Filtering
  • 2.6. AM Envelope Detection, Tuning, and Impedance Matching
  • Challenge Problems
  • 3. The AM Radio Receiver
  • 3.1. Prelude to the Superheterodyne
  • 3.2. The Superheterodyne
  • 3.3.. Fancy Heterodyning
  • Challenge Problems
  • 4. SSB Radio
  • 4.1. The Origin of SSB and Carson's SSB Transmitter
  • 4.2. Hilbert Transforms and Hartley's SSB Transmitter
  • 4.3. The Mathematics of the Hilbert Transformer
  • 4.4. The Physics of the Hilbert Transformer
  • 4.5. Receiving an SSB Signal
  • 4.6. Weaver's SSB Transmitter
  • Challenge Problems
  • 5. FM Radio
  • 5.1. Why FM?
  • 5.2. Instantaneous Frequency
  • 5.3. FM Sidebands
  • 5.4. The FM Receiver
  • 5.5. Bilotti's Phase Quadrature Detector
  • Challenge Problems
  • 6. American AM Broadcast Radio: A Historical Postscript
  • A Final Author's Note to the Reader
  • Appendix-Maxwell's Theory, the Poynting Vector, and a Simple Radio Transmitting Antenna Solutions, Partial Answers, and More Hints to Most of the End-of-Chapter Challenge Problems
  • Acknowledgments
  • Illustration Credits
  • Index
Review by Choice Review

Nahin's latest book supplies thorough mathematics backing for a century's worth of AM, FM, and single-sideband radios. Coverage begins with the mathematical underpinnings of oscillators and circuits. Trigonometric relationships, calculus, and differential equations model aspects are crucial to transmitting and receiving signals. Nahin (emer., electrical engineering, Univ. of New Hampshire) also includes historical notes about the challenges that arose as radio capabilities were created or improved. He frequently refers to G. H. Hardy's persistent position that only pure mathematics is worth considering and counterattacks with statements about the intuitive inventiveness inherent in the applied mathematics behind radio capabilities. As a bonus, each chapter ends with a series of challenge problems, with hints or solutions in the back of the book. Mathematicians, especially educators who want to demonstrate the power and usefulness of their discipline, will find much to enjoy here. Electronics and radio experts may be intrigued by what lies behind the engineering aspects of their knowledge. This is not the type of book that lends itself to curling up in a comfortable chair for a few hours of mindless reading, but its challenges are worthwhile. Summing Up: Recommended. Advanced undergraduates through faculty; professionals. --Ned W. Schillow, emeritus, Lehigh Carbon Community College

Copyright American Library Association, used with permission.