Applied Scientific Research, Section A

, Volume 3, Issue 1, pp 51–68 | Cite as

On the calculation of some definite integrals in antenna theory

  • H. Lottrup Knudsen


The mutual radiation resistance of two identical linear antennae is usually calculated by using the e.m.f. method. However, in a recent paper it has been demonstrated by the author that sometimes a simple expression for the mutual radiation resistance of two antennae, derived on the basis of the Poynting vector method, may be used with advantage. In most cases, however, the results obtained by using this modified Poynting vector method contain integrals which are difficult to express by known functions. By equating the expression for the mutual radiation resistance derived on the basis of the Poynting vector method with that obtained by the e.m.f. method we may therefore obtain a useful mathematical formula expressing a definite integral by known functions. This heuristic procedure for generating formulae for some definite integrals has been used in several simple cases of pairs of antennae. Only an outline of the rather bulky calculations has been given here, details being reserved for separate papers on some new antenna formulae. Although the paper is mainly concerned with demonstrating the above mentioned method for generating integral formulae, the compilation of formulae for mutual radiation resistance of antennae, mostly not published before, should be of interest for those working in antenna theory.


Radiation Integral Formula Simple Expression Radiation Resistance Separate Paper 
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  1. 1).
    Knudsen, H. L., Mutual radiation resistance of antennas and antenna arrays; Wireless Engr, to be published.Google Scholar
  2. 2).
    King, R., Electromagnetic engineering; vol. 1, Fundamentals; New York and London 1945; p. 303.Google Scholar
  3. 3).
    Schelkunoff, S. A., Proc. Inst. Radio Engrs27 (1939) 660.Google Scholar
  4. 4).
    Burgess, R. E., Wireless Engr21 (1944) 154.Google Scholar
  5. 5).
    Brillouin, L., Ann. Radioelectricité3 (1922) 147.Google Scholar
  6. 6).
    Kliatzkin, Telegrafia i telefonia bez provodov40 (1927) 33.Google Scholar
  7. 7).
    Pistolkors, A. A., Proc. Inst. Radio Engrs17 (1929) 562.Google Scholar
  8. 8).
    Hertz, H., Wied. Ann.36 (1888) 1.Google Scholar
  9. 9).
    Foster, R. M., Bell Syst. Tech. J.5 (1926) 292.Google Scholar
  10. 10).
    Bontsch-Bruewitsch, M. A., Ann. Phys., Vierte Folge81 (1926) 425.Google Scholar
  11. 11).
    Kraus, J. D., Antennas; New York, Toronto, and London 1950; p. 141.Google Scholar
  12. 12).
    Jahnke, E. and F. Emde, Funktionentafeln, Dritte Auflage; Leipzig und Berlin 1938; p. 149.Google Scholar
  13. 13).
    Bechmann, R., Hochfrequenztechn. u. Elektroakustik36 (1930) 182, 201.Google Scholar
  14. 14).
    Bechmann, R., Proc. Inst. Radio Engrs19 (1931) 1471.Google Scholar
  15. 15).
    Carter, P. S., Proc. Inst. Radio Engrs20 (1932) 1004.Google Scholar
  16. 16).
    Cox, C. R., Proc. Inst. Radio Engrs35 (1947) 1367.Google Scholar
  17. 17).
    Barzilai, G., Wireless Engr25 (1948) 343.Google Scholar
  18. 18).
    Starnecki, B. and E. Fitch, Wireless Engr25 (1948) 385.Google Scholar
  19. 19).
    Tai, C. T., Proc. Inst. Radio Engrs36 (1948) 487.Google Scholar
  20. 20).
    Watson, G. N., A treatise on the theory of Bessel functions; second edition; Cambridge 1944; p. 378.Google Scholar
  21. 21).
    Harrison, C. W., Proc. Inst. Radio Engrs33 (1945) 398.Google Scholar
  22. 22).
    Kraus, J. D., loc. cit. p. 132.Google Scholar
  23. 23).
    Tables of generalized sine- and cosine-integrals; Cambridge 1949.Google Scholar
  24. 24).
    Watson, G. N., loc. cit. p. 373.Google Scholar

Copyright information

© Martinus Nijhoff 1954

Authors and Affiliations

  • H. Lottrup Knudsen
    • 1
  1. 1.The Royal Technical University of DenmarkCopenhagen

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