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The distribution of current on a cylindrical antenna

Published online by Cambridge University Press:  24 October 2008

C. C. Harvey
C. C. Harvey
Affiliation:
St Catharine's College, Cambridge††
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Abstract

The iterative solution of Hallen's integral equation for the current distribution on a lossless dipole transmitting antenna is studied from first principles, and a general solution in terms of an expansion function is derived. In this new solution even the zero-order approximation gives a reasonable representation of both the quadrature and the in-phase current distributions. The choice of an expansion function is discussed. At each stage the approximations which must be made in order to obtain earlier iterative solutions are clearly described. Three low order solutions are derived in detail: the zero-order solution using both a constant expansion parameter and a simple expansion function, and the rst-order solution using a constant expansion parameter. The results are compared and special attention is paid to the very short antenna, although the results are good for lengths up to and including the half-wave dipole. The results are presented in such a way that the first-order admittance of any given antenna may be readily calculated.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 2 , September 1971 , pp. 351 - 381
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Balmain, K. O.The impedance of a short dipole in a magnetoplasma. IEEE Trans. Antennas and Propagation 12 (1964), 605.CrossRefGoogle Scholar
(2)Bouwkamp, C. J.Hallé's theory for a straight perfectly conducting wire used as a transmitting or receiving aerial. Physica 9 (1942), 609.CrossRefGoogle Scholar
(3)Deschamps, G. A.The impedance of an antenna in a conducting medium. I.R.E. Trans., AP 10 (1962), 648.Google Scholar
(4)Duncan, R. H. and Hinchey, F. A.Cylindrical antenna theory. J. Res. Nat. Bur. Standards Sect. D 64 (1960), 569.Google Scholar
(5)Hallén, E.Theoretical investigations into the transmitting and receiving qualities of antennae. Nova. Acta Soc. Sci. Upsal. 11 (1938), 1.Google Scholar
(6)Hugill, J.The measurement of random radio frequency fields by the use of short electric and magnetic dipoles. Planet. Space Sci. 8 (1961), 68.CrossRefGoogle Scholar
(7)King, R. P. W.The theory of linear antennas (Harvard University Press, 1956).CrossRefGoogle Scholar
(8)King, R. P. W., Aronson, E. A. and Harrison, C. W.Determination of the admittance and effective length of cylindrical antennas. Radio Sci. 1 (1966), 835.CrossRefGoogle Scholar
(9)King, R. P. W. and Blake, F. G.The self-impedance of a symmetrical antenna. Proc. I.R.E. 30 (1942), 335.CrossRefGoogle Scholar
(10)King, R. P. W., Harrison, C. W. and Denton, D. H.The electrically short antenna as a probe for measuring free electron densities and collision frequencies in an ionised region. J. Res. Nat. Bur. Standards Sect. D 65 (1961), 371.Google Scholar
(11)King, R. P. W. and Middleton, D.The cylindrical antenna: current and impedance. Quart. Appl. Math. 3 (1946), 302.CrossRefGoogle Scholar
(12)King, R. P. W. and Middleton, D.Correction and supplement to our paper ‘The cylindrical antenna: current and impedance’. Quart. Appl. Math. 4 (1946), 199.CrossRefGoogle Scholar
(13)Kogelnik, H.On electromagnetic radiation in magnetoionic media. J. Res. Nat. Bur. Standards Sect. D 64 (1960), 515.Google Scholar
(14)Mei, K. K.On the integral equations of thin wire antennas. IEEE Trans. Antennas and Propagation 13 (1965), 374.CrossRefGoogle Scholar
(15)Schelkunoff, S. A. and Fruis, H. T.Antennas: theory and practice (John Wiley and Sons, New York, 1952).Google Scholar
(16)Vainshtein, L. A.Waves of current in a thin cylindrical conductor. Soviet Physics Tech. Phys. 4 (1959), 601.Google Scholar
(17)Weil, H. and Walsh, D.Radiation resistance of an electric dipole in a magnetoionic medium. IEEE Trans. Antennas and Propagation 12 (1964), 297.CrossRefGoogle Scholar
(18)Wu, T. T.Theory of the dipole antenna and the two-wire transmission line. J. Mathematical Phys. 2 (1961), 550.CrossRefGoogle Scholar
(19)Wu, T. T. and King, R. W. P.Driving point and input admittance of linear antennas. J. Appl. Phys. 30 (1959), 74.CrossRefGoogle Scholar