A theoretical and experimental investigation of the radiation behaviour of conical corrugated horns is described. The horn-aperture field is determined using spherical-mode analysis, and the radiation pattern is obtained by two methods, one of which employs a Kirchhoff-Huygen integration over a constant-phase surface at the mouth of the horn, and the other of which employs an expansion of the aperture field in terms of TE and TM spherical modes of freespace. Excellent agreement is obtained between the two methods and with experimental results. A theoretical investigation is reported of the use of lenses to correct the phase of a conical corrugated horn. Finally, the performance of paraboloid antennas using corrugated horns as feeds is briefly discussed.
List of principal symbolsF r (Q') = real and imaginary part of pattern function i fy(fi) = balanced hybrid-mode aperture-field function -p ? ( c o s 0) dP™(cos 6) sin0 + dd /JT(0) = spherical-mode field function G>(0,0') = function defined in eqn. 37 Y = normalised wave admittance = -j'Y g m (B) = mA 6) dPy(cos 6) r . H ^--[in places, the d sin a dv superscript m is omitted from g m (6) for clarity] = spherical Hankel function of the 2nd kind and of order v = A' dd [m places, the superscript m is omitted from/i" 1^) for clarity] h (x) = ^' ( x ) J m (x) = Bessel function of the 1st kind and order m k = free-space wavenumber m = azimuthal wavenumber n = order of spherical mode P™(cos 6) = associated Legendre function of the first kind and of order v rtQ) = P?(cos 0) Q^(cos 6) = associated Legendre function of the 2nd kind and of order v R, R o , R' = radial spherical co-ordinate, radius of horn at aperture and radial distance to far-field point, respectively r x j 2 = radii defining slot (see Fig. la) XQ = fCl\Q Y = wave admittance of slot at 6 = 0, y 0 y 0 = free-space wave admittance a = { v (y + i)}i/2 a' = {«(/! + I)} 1 ' 2 v = separation constant obtained from eqn. 12 ,6',d { ,9 2 = polar spherical co-ordinate of point in aperture of horn, in space, at boundary of corrugations and at base of corrugations, respectively cf>, (f>' = azimuthal spherical co-ordinate of point in aperture of horn and at radiation-field point, respectively -B A = normalised hybrid factor = j'y 0 -r] 0 = free-space wave impedance co = angular frequency 1 IntroductionThe cylindrical-mode analysis of corrugated-waveguide feeds presented in Pt. I 1 may be applied to corrugated conical horns (Fig. la) only if the horn flare angle and length are sufficiently small for phase variation across the aperture plane to be negligible. This consideration usually restricts the results to horns with flare semiangles not exceeding about 5°i f accurate radiation patterns are required.* In this paper, we apply spherical-mode analysis to the conical corrugated horn. Results have been obtained which are in good agreement with measurements for flare semiangles in the range 9-70°. For angles smaller than about 5°, computational inaccuracies may occur, and, since the cylindrical-mode analysis is then valid, c...
