Low Cross-polar Dielectric Loaded Corrugated Horn For Broadband Applications

Introduction

Research has been done on a new type of horn comprising a corrugated feed loaded with a dielectric cone. This has the potential for broadband operation.

A need developed beginning thirty years ago for a horn radiator exhibiting very low cross-polarisation. The corrugated horn satisfied the need enabling orthogonal polarisations to be separated at levels down to -4OdB over bandwidths of 10- 15% [Clarricoats, P.J.B. and Olver, A.D. Corrugated horns for microwave antennas IEE Press, Electromagnetic Wave Series vol. 18 1984]. Larger bandwidths were achievable if a less favourable level of cross-polarisation could be tolerated. At very low microwave frequencies, below about 3GHz, the horn becomes massive while at very high frequencies above 100GHz there are significant manufacturing problems because of the small size of the corrugations. Because of these difficulties Peter Clarricoats and David Olver proposed an alternative structure [Clarricoats, P.J.B., Olver, A.D. and Rizk, M.S.A.S. A dielectric loaded comical feed with low crosspolar radiation Proceedings 1983 URSI Electromagnetic Symposium] comprising a horn partially filled with a dielectric cone. This yielded a slightly inferior cross-polar performance but provided operation over a much wider bandwidth. The present research is aimed at combining the best properties of both structures, the new device comprises a dielectric loaded corrugated horn. At the lowest frequency it behaves as a corrugated horn while at the upper frequency, where the corrugations are half wave length deep, it behaves as a dielectric loaded smooth wall horn.

Theoretical Analysis

The dielectric loaded corrugated horn possesses many parameters and an optimum design requires an adequate theoretical analysis. Two approaches have been used: the surface impedance method and the modal matching method. Both methods have been used successfully in prior studies of the corrugated and dielectric loaded horns so considerable confidence resides in the successful outcome of the present theoretical investigation. In both cases the objective is to determine the electric field in the aperture of the horn so that the E-field method can be used to derive the radiation pattern and, in particular, the maximum level of cross-polarisation. To obtain the field it is necessary first to obtain the propagation coefficient and the transverse wave-numbers.

Surface Impedance Method

Two approximations are employed in the determination of the aperture electric field by means of the surface impedance method. First, the structure is assumed to be cylindrical. A correction is applied to the aperture fields to account for the small phase change over the aperture arising from the shallow flare-angle of the horn. Second, the corrugated wall is represented by means of a continuous surface admittance appropriate to a TM1 mode in a short-circuited coaxial waveguide corresponding to the corrugation. The TE1 mode is assumed not to propagate in the corrugation and the azimuthal electric field component is made zero at the inner wall of the corrugated waveguide. As in the corrugated horn, only the HEII mode is assumed to be propagating, a condition which is realised in practice by appropriate design of the transition between the input waveguide and the horn. Note that in all three structures, modes are hybrid if the azimuthal variation is other than zero. Fields with unity azimuthal variation are the norm in all antenna horns, other. than those used for special applications such as tracking feeds. Matching the tangential fields across the boundaries leads to six equations in six unknowns. When this determinant is equated to zero, the characteristic equation yields the HE11 mode propagation coefficient.

Dispersion curves showing the normalised propagation coefficient as a function of normalised frequency k were generated for the first two modes of each of the cylindrical structures corresponding to the three types of horn. Once the propagation coefficient is known it is a straightforward matter to determine the fields in the aperture and radiation pattern using the E-field Fourier Transform method. The co-polar and cross-polar radiation patterns of the dielectric loaded corrugated horn compared to the dielectric horn and corrugated horn are shown in the figure. The maximum cross-polar radiated field for a dielectric loaded corrugated horn at three values of normalised rod radius is shown right. The choice of permittivity was based on that corresponding to an available sample used in early work at QMC on dielguides in the 1970's and dielectric loaded horns in the 1980's. The dielectric loaded corrugated horn behaves in a manner similar to the empty corrugated horn at lower frequencies but has a superior cross polarisation at higher frequencies. At a frequency of 18.75 GHz where the corrugation depth is half wavelength the dielectric loaded horn and dielectric loaded corrugated horn have the same level of maximum cross-polarisation around -45 dB.

To observe these results in practice it would be necessary to achieve a number of conditions:

1. Near perfect launch of the HE11 mode in the throat region of the horn
   
2. Control of the corrugation depth along the horn so as to suppress higher-order modes
   
3. Homogeneity of the low permittivity dielectric

Modal Matching Method

The principle of the modal matching method applied to conical horns has been described in Chapters 4 and 10 of Olver, A.D., Clarricoats, P.J.B., Kishk, AA. And Shafaz, L. Microwave horns and feeds IEE Press, Electromagnetic Wave Series Vol. 39 1994. In the method the continuous horn wall and the dielectric cone are both represented by means of a'series of cylindrical steps. If furthermore the wall is also corrugated initially then the same concept applies except that the discontiiiuities when we move from the top to the bottom of the corrugations are much larger than when a smooth wall horn is stepped. It is essential to appreciate that while canonical solutions exist for a conical horn expressed in terms of spherical TE and TM modes no such representation exists for either a dielectric cone or a cone within a horn. By representing the dielectric-loaded horn through a series of cylindrical steps we reduce the problem to one where canonical solutions in terms of hybrid HE and EH modes exist. Provided the steps are small enough and a sufficient number of modes are included then in principle a highly accurate description of the field along the horn can be obtained. For the dielectric loaded corrugated horn the problem is greatly complicated by the need to solve the characteristic equation for a dielectric rod in a circular waveguide for a very large number of modes. When the horn is empty the modes are TE and TM and the solutions are simply roots of Bessel functions of the first kind or their derivatives. When a dielectric rod is present the modes are hybrid. The program for the new structure has been developed and partially tested and the investigation continues.

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