Aperture antennas and diffraction theory by E.V. Jull

By E.V. Jull

Substitute tools of aperture antenna research are defined during this book.

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05 r/2a2/X Fig. 2 for a rectangular aperture with uniform and cosinusoidal distributions simplify considerably on the beam axis where kx = k2 = 0. In eqn. 7, u2 = —ux = a/\/2r\ and, since C{— u) = — C(u) and S(— u) = —S(u), eqn. 19) For a uniformly illuminated rectangular aperture D2(0) is given by eqn. 19 with v = b/\/2r\ replacing u. The on-axis near field of the aperture of Fig. 1 is, from eqns. 21) Gn = -^-RE(u)RE(v) where with u = a/y/lrX and C(w) and S(u) defined by eqn. 8. The gain reduction factor RE(u) for a uniform line source was first tabulated by Polk (1956).

4 Displaced aperture distributions Assuming eqn. 12, let Ex (x) = E(x — x0), which implies a lateral shift x0 of the distribution in the aperture plane. 17) Fourier transform representation of aperture patterns 25 The effect on the radiation pattern is a linear phase change of k\XQ radians. Usually in measuring a pattern field strength magnitude is observed and there is no apparent change in the pattern at a range r > x0. Hence in far-field antenna pattern measurements there is no need for the centre of rotation to coincide with the centre of the aperture under test.

30) where An are tabulated functions (Jahnke and Emde, 1945, p. 180). Normalised patterns for n = 0,1 and 2 are shown in Fig. 9. 31) 30 Fourier transform representation of aperture patterns Dividing by /", the pattern resulting from the distribution where the operator Dn = dn/dkin. 32) a_ X 2 (a) Fig. 10 -4T7W-27T, • I • \ i \ i / i i / i \ i ZZ /i 2^^4TT J/ ^ (b) a Rectilinear aperture distribution b Its radiation pattern As an example, the radiation pattern of the rectilinear distribution ^(JC) = 2x1a can be obtained by differentiation of the pattern of the uniform distribution.

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