By Y.T. Lo, S.W Lee

Lo Y., Lee S. Antenna guide (Van Nostrand Reinhold, 1993, 2)(ISBN 0442015933)

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0 J Fig. 13. Aperture efficiencies of compound symmetrical distributions in a circular aperture. } J \ ) E(r,O) = 62jEoe-jkr [C(U) - jS(U)][C(U') - jS(U')] i (90) where C(u) and S(u) are the Fresnel integrals defined by (72), u = alvz;:I, and u' = bIV2rA.. The power radiated is Pr = '/2 Yo Eo2ab and the axial near-field gain can be written as (91) where (92) is the near-field gain reduction factor for a one-dimensional uniform distribution. This factor is plotted in Fig. 14. For a uniform and cosinusoidal distribution linearly polarized in the aperture of Fig.

D. R. Rhodes, Synthesis of Planar Antenna Sources, Oxford: Oxford University Press, 1974, pp. 9-42. E. V. , England: Peter Peregrinus, 1981, pp. 7-17. W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, New York: John Wiley & Sons, 1981, pp. 375-384. C. A. Balanis, Antenna Theory: Analysis and Design, New York: Harper and Row, 1982, pp. 446-456. S. , 1946, pp. 159-168. T. T. Taylor, "Design of line-source antennas for narrow beamwidth and low side lobe levels," IRE Trans. , vol. AP-3, pp.

Hence D«(J, f/J) = k2Zol1inl21hl2 8nPr = ~Zolhl2 4nTJRin (20) on account of (16) and (17). Eliminatil)g Rin/Zo between (15) and (20), we obtain aR A? = 4n TJQpD «(J,f/J) (21) where P = Ih. Eil2 Ihl21Eil2 (22) is designated as the polarization-matching factor, and its value lies between zero and unity. Equation 21 is the most general formula to characterize the receiving capability of an antenna [2]. To compute the value of p, it is convenient to introduce the complex polarization ratios for hand Ei defined by (23) E~ -, = E'4> Then , se'u (24) Antenna Theory 1 + 2st cos( a + fJ) + s2t2 P= (1 + s2)(1 + t 2) (25) The maximum value of p, equal to unity, occurs when s = t and a = -fJ, and corresponds to two identical elliptically polarized states with opposite sense of rotation.