A geometrical optics procedure for designing electrically optimized classical offset dual reflector antennas with circular apertures is presented. Equations are derived that allow the size and spacing of the main and subreflectors of the antenna system, along with the feed horn subintended angle, to be used as input variables of the design procedure. The procedure, together with these equations, yields an optimized design, starting from general system requirements. The procedure is demonstrated by designing both an offset Cassegrain and an offset Gregorian antenna, and is validated by analyzing their radiation patterns using physical optics surface current integration on both the main and subreflectors. >

A design procedure for classical offset dual reflector antennas with circular apertures

In the complex source point technique, an omnidirectional source diffraction solution becomes that for a directive beam when the coordinates of the source position are given appropriate complex values. This is applied to include feed directivity in reflector edge diffraction. Solutions and numerical examples for planar strip and parabolic cylinder reflectors are given, including an offset parabolic reflector. The main beams of parabolic reflectors are calculated by aperture integration and the edge diffracted fields by uniform diffraction theory. In both cases, a complex source point feed in the near or far field of the reflector may be used in the pattern calculation, with improvements in accuracy in the lateral and spillover pattern lobes. >

Beam diffraction by planar and parabolic reflectors

The far field of a two-dimensional beam resulting from an electric line source at a complex position is described, its half-power beamwidth determined, and its validity as an antenna beam indicated. Farfield diffraction by a half-plane is then determined from an exact uniform solution for an isotropic line source by making the source position complex. The same basic solution and technique are used for beam diffraction by a wide slit, with first-order interaction between the slit edges included. Numerical results for normal incidence illustrate the evolution of the diffraction patterns from those for an omnidirectional source to those for a highly directive beam. Results for plane wave incidence by a slit also come out of this solution. The remarkable simplicity and convenience of this method relative to alternative asymptotic procedures is discussed.

Two-dimensional beam diffraction by a half-plane and wide slit

Dual mode horns employed commonly as feeds for parabolic reflector antennas generate a radiation pattern that can be well-approximated by a Gaussian beam. To determine the far field of the antenna, it has been customary to perform integrations either of the physical optics currents on the reflector surfaces or of the ray optically determined field in the antenna aperture. These time-consuming integrations may be avoided if the Gaussian beam is tracked directly from the feed horn via subreflectors, if any, to the main reflector and then to the far zone. The tracking of such fields may be accomplished either by the complex-source point method or, in principle, by evanescent wave tracking. The former utilizes a complex coordinate space while the latter tracks fields entirely in the physical (real) coordinate space. For a parabolic antenna with an offset beam feed centered at the focus, both methods are examined here and an assessment is made of how the one can best complement the other. Numerical comparisons with results deduced elsewhere by a semi-heuristic procedure, and with experimental data, reveal the accuracy and versatility of the complex ray procedure.

Asymptotic analysis of parabolic reflector antennas

The "extinction theorem" is used to prove that the fields of reflector antennas determined by integration of the current on the illuminated surface of the reflector are identical to the fields determined by aperture field integration with the Kottler-Franz formulas over any surface S_{a} that caps the reflector As a corollary to this equivalence theorem, the fields predicted by integration of the physical optics (PO) surface currents and the Kottler-Franz integration of the geometrical optics (GO) aperture fields on S_{a} agree to within the locally plane-wave approximation inherent in PO and GO Moreover, within the region of accuracy of the fields predicted by PO current or GO aperture field integration, the far fields predicted by the Kottler-Franz aperture integration are closely approximated by the far fields obtained from aperture integration of the tangential electric or magnetic field alone In particular, discrepancies in symmetry between the far fields of offset reflector antennas obtained from PO current and GO aperture field integrations disappear when the aperture of integration is chosen to cap (or nearly cap) the reflector

Equivalence of surface current and aperture field integrations for reflector antennas

The paper presents various methods for the calculation of the field reflected from a subreflector in a dual reflector antenna system. It is demonstrated that the physical-optics (PO) solution agrees well with the geometrical theory of diffraction (GTD) for the copolar component. Significant discrepancies may appear for the crosspolar component, and it is necessary to introduce additional fringe currents in the PO solution. If the subreflector is located in the near field of the feed, special precautions must be taken. One can either subdivide the feed aperture into a number of smaller subapertures for each of which standard GTD can be applied or an alternative and more efficient method is to use complex ray analysis (CRA), where the directive feed is represented by a point source located in the complex co-ordinate space. Both methods are compared with PO solutions taking the near-field effects into account. The theoretical results are verified experimentally for a near-field illuminated offset hyperboloidal subreflector.

N.C. Albertsen

Papers

Analysis of subreflectors for dual reflector antennas