General Questions of the Theory of Impedance Vibrators in the Spatial-Frequency Representation

  • Mikhail V. Nesterenko
  • Victor A. Katrich
  • Yuriy M. Penkin
  • Victor M. Dakhov
  • Sergey L. Berdnik
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 95)


In this chapter, the main equations of macroscopic electrodynamics, the theory of thin impedance vibrators and the approximate analytical methods of their solution, and expressions for the tensor Green’s functions of various spatial regions are briefly presented. The materials presented here will be used throughout the book, allowing readers to use the book without any additional references.


Integral Equation Integrodifferential Equation Approximate Analytical Method Small Parameter Method Sommerfeld Radiation Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Khizhnyak, N.A.: Integral Equations of Macroscopical Electrodynamics. Naukova dumka, Kiev (1986) (in Russian).Google Scholar
  2. 2.
    Nesterenko, M.V., Katrich, V.A., Penkin, Yu.M., Berdnik, S.L.: Analytical and Hybrid Methods in the Theory of Slot-Hole Coupling of Electrodynamic Volumes. Springer, New York (2008).Google Scholar
  3. 3.
    Leontovich, M.A.: On Approximate Boundary Conditions for the Electromagnetic Field on Surfaces of Good Conductive Bodies. Investigations of Radiowave Propagation. Printing House of the Academy of Sciences of the USSR, Moscow-Leningrad (1948) (in Russian).Google Scholar
  4. 4.
    Levin, H., Schwinger, J.: On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen. Commun. Pure Appl. Math. 3, 355–391 (1950).CrossRefGoogle Scholar
  5. 5.
    Collin, R.E.: Field Theory of Guided Waves. McGraw-Hill, New York (1960).Google Scholar
  6. 6.
    Morse, P.M., Feshbach, H.: Methods of Theoretical Physics. McGraw-Hill, New York (1953).MATHGoogle Scholar
  7. 7.
    Tai, C.T.: Dyadic Green’s Function in Electromagnetic Theory. Intex Educational Publishers, Scranton (1971).Google Scholar
  8. 8.
    Tikhonov, A.N., Samarsky, A.A.: Equations of Mathematical Physics. Nauka, Moscow (1977) (in Russian).Google Scholar
  9. 9.
    Van Bladel, J.: Some remarks on Green’s dyadic for infinite space. IEEE Trans. Antennas Propag. AP-9, 563–566 (1961).Google Scholar
  10. 10.
    Felsen, L.B., Marcuvitz, N.: Radiation and Scattering of Waves. Prentice-Hall, Inc., Englewood Cliffs, NJ, (1973).Google Scholar
  11. 11.
    King, R.W.P.: The Theory of Linear Antennas. Harvard University Press, Cambridge, MA (1956).MATHGoogle Scholar
  12. 12.
    King, R.W.P., Aronson, E.A., Harrison, C.W.: Determination of the admittance and effective length of cylindrical antennas. Radio Sci. 1, 835–850 (1966).Google Scholar
  13. 13.
    Pocklington, H.C.: Electrical oscillations in wires. Proc. Camb. Philol Soc. 9, pt VII, 324–332 (1897).Google Scholar
  14. 14.
    Brillouin, L.: The antenna problem. Quart. Appl. Math. 1, 201–214 (1943).MathSciNetMATHGoogle Scholar
  15. 15.
    Mei, K.K.: On the integral equation of thin wire antennas. IEEE Trans. Antennas Propag. AP-13, 374–378 (1965).CrossRefGoogle Scholar
  16. 16.
    Mittra, R. (ed.): Computer Techniques for Electromagnetics. Pergamon, New York (1973).Google Scholar
  17. 17.
    Nesterenko, M.V.: Analytical methods in the theory of thin impedance vibrators. Prog. Electromagn. Res. B 21, 299–328 (2010).Google Scholar
  18. 18.
    Hallen, E.: Theoretical investigations into the transmitting and receiving qualities of antennas. Nova Acta Reg. Soc. Sci. Ups. Ser. IV 11, 1–44 (1938).Google Scholar
  19. 19.
    Leontovich, M., Levin, M.: On the theory of oscillations excitation in antennas’ vibrators. J. Tech. Phys. 14, 481–506 (1944) (in Russian).Google Scholar
  20. 20.
    Vineshtein, L.A.: Current waves in a thin cylindrical conductor. J. Tech. Phys. 29, 65–91 (1959) (in Russian).Google Scholar
  21. 21.
    Bogoliubov, N.N., Mitropolsky, Y.A.: Asymptotic Methods in the Theory of Nonlinear Oscillations. Internat. Monog. Adv. Math. Physics, Gordon and Breach, New York (1961).Google Scholar
  22. 22.
    Philatov, A.N.: Asymptotic Methods in the Theory of Differential and Integrodifferential Equations. PHAN, Tashkent (1974) (in Russian).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Mikhail V. Nesterenko
    • 1
  • Victor A. Katrich
    • 1
  • Yuriy M. Penkin
    • 2
  • Victor M. Dakhov
    • 1
  • Sergey L. Berdnik
    • 1
  1. 1.Dept. RadiophysicsV.N. Karazin Kharkov National UniversityKharkovUkraine
  2. 2.Dept. Information TechnologyNational Pharmaceutical UniversityKharkovUkraine

Personalised recommendations