Although used for some decades, the offset-parabolicreflector antenna's electrical properties and performance were not accurately modeled and optimized until the 1960's. This paper reviews, in a tutorial fashion, the state of the art of this important antenna for readers who are not necessarily experts in antenna theory and technology. After a discussion of fundamentals, the performances of both single- and double-reflector configurations are treated and compared, and practical primary feeds are described. Comments are given on the present status of analysis and design and on problems to be solved.

Offset-parabolic-reflector antennas: A review

An analysis is presented of a thin cylindrical-rectangular microstrip patch antenna. After obtaining the electric field under the curved patch and the resonant frequencies using the cavity model, the far-field is found by considering the equivalent magnetic current radiating in the presence of a cylindrical surface. The input impedance and the total Q-factor are then calculated. Numerical and graphical results are presented to illustrate the effect of curvature on the characteristics of the TM/sub 10/ and TM/sub 01/ modes. >

Analysis of the cylindrical-rectangular patch antenna

General coordinate transformations which are commonly encountered in many antenna applications are presented. Neither the feed coordinates nor the far-field pattern coordinates in general coincide with the antenna coordinates. Transformations discussed allow one to relate the spherical and Cartesian components of one system to the spherical and Cartesian compoents of the other system. In particular, attempts are made to use unified notations to assist the reader in a straightforward application of the transformations.

Useful coordinate transformations for antenna applications

The theory, techniques, details of the important equations, and description of two computer programs are presented for calculating efficiently the mutual coupling at a single frequency between any two antennas arbitrarily oriented and separated in free space. Both programs emphasize efficiency and generality, and require, basically, the complex electric far field of each antenna, and the Eulerian angles designating the relative orientation of each antenna. Multiple reflections between the antennas are neglected but no other restrictive assumptions are involved. If an electric field component is desired instead of coupling, the receiving antenna is replaced by a virtual antenna with uniform far field. The first computer program computes coupling (or fields) versus transverse displacement of the antennas in a plane normal to their axis of separation. An efficient fast Fourier transform (FFT) program was made possible by "collapsing" the far-field input data and showing that inmost cases the spectrum integration need cover only the solid angle mutually subtended by the smallest spheres circumscribing the antennas. Limiting the integration to this solid angle artifically band limits the coupling function, thereby allowing much larger integration increments and reducing run times and storage requirements to a feasible amount for electrically large antennas. The second program is based on a spherical wave representation of the coupling function and rapidly computes coupling (or fields) versus separation distance between the antennas. The spherical wave representation emerged naturally from an intriguing characteristic proven for the mutual coupling function; it, like each rectangular component of electric and magnetic field in free space, satisfies the homogeneous wave equation.

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Efficient computation of antenna coupling and fields within the near-field region

Both geometrical optics (GO)/aperture-field and physical-optics (PO) methods are used extensively in the diffraction analysis of offset parabolic and dual reflectors. An analytical/numerical comparative study is performed to demonstrate the limitations of the GO/aperture-field method for accurately predicting the sidelobe and null positions and levels. In particular, it is shown that for offset parabolic reflectors and for feeds located at the focal point, the predicted far-field patterns (amplitude) by the GO/aperture-field method will always be symmetric even in the offset plane. This, of course, is inaccurate fur the general case and it is shown that the physical-optics method can result in asymmetric patterns for cases in which the feed is located at the focal point. Representative numerical data are presented and a comparison is made with available measured data.

A comparison between GO/aperture-field and physical-optics methods of offset reflectors

The development and application of a numerical technique for the rapid calculation of the far-field radiation patterns of a reflector antenna from either a measured or computed feed pattern are reported. The reflector is defined by the intersection of a cone with any surface of revolution or an offset sector of any surface of revolution. The feed is assumed to be linearly polarized and can have an arbitrary location. Both the copolarized and the cross polarized reflector radiation patterns are computed. Calculations using the technique compare closely with measured radiation patterns of a waveguide-fed offset parabolic reflector. The unique features of this technique are the freedom from restrictive feed assumptions and the numerical methods used in preparing the aperture plane electric field data for integration.

Analysis of the radiation patterns of reflector antennas

Microstrip antennas may be mounted on spherical surfaces on some vehicles of practical interest such as missiles and satellites. One possible application, for example, might be to build phased array microstrip radiators on a spherical surface to give wide angle scan capability much like that of a Luneberg lens antenna. The cavity model method is used to obtain the electric field at the edge of the radiating patch. Then, the radiation field may be evaluated from the edge field for a given excitation current. A spherical-rectangular microstrip structure is studied. The study is based on the assumption that the thickness of the dielectric layer is much smaller than the radius of the ground sphere. Then, the radiation frequency for single mode radiation is defined and the radiation patterns for typical spherical-rectangular microstrip antennas are presented.

Radiation pattern computations for cylindrical-rectangular microstrip antennas

One dimensional integral formulas are derived for mutual impedance of arbitrary size, coplanar, parallel, and perpendicular surface monopoles. The integrals in formulas are expressed as exponential integrals where possible. The mutual impedance expression for parallel monopoles is a summation of exponential integrals and one-dimensional integrals. For perpendicular monopoles, the mutual impedance is in closed form, containing exponential integrals only. The final expressions are in a form suitable for numerical computation. Since the expressions contain at most one-dimensional integrals, they can be utilized to reduce the matrix filling time in the moment method formulations, especially when inhomogeneous sectioning is preferred. Additionally, they can be used in rectangular surface patch modeling of conducting surfaces with edges which are at an angle to the surface patches, providing the angle is small. To this end, the expressions were utilized in the moment method analysis of linearly tapered slot antennas. Very good accuracy was obtained with a reduction in computer time. >

Mutual impedance of parallel and perpendicular coplanar surface monopoles

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k -space) formulation is presented with an emphasis on application to periodic surfaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

The application of contraction theory to an iterative formulation of electromagnetic scattering

The results of a theoretical and experimental investigation are presented for a dual mode horn fed offset parabola for feed displacements of \pm7 wavelengths about the focus in a direction along the offset axis. Beamwidths, sidelobe levels, relative gain, and crosspolarization patterns exhibit approximately equal E and H plane beamwidths as the feed is moved, along with wide angle sidelobes outside the main ridged beam that are similar in level to those of the same antenna with the feed on focus. The cross-polarization pattern levels diminish as the feed is moved off focus. The ridged main patterns have a shape similar to that of a corrugated horn with the same quadratic phase error. Therefore for some applications, it should be possible to use a defocused offset parabolic reflector rather than a corrugated horn, thereby effecting a sizeable decrease in antenna volume.

J. Kauffman

Papers

Analysis of the radiation patterns of reflector antennas

Radiation pattern computations for cylindrical-rectangular microstrip antennas

Mutual impedance of parallel and perpendicular coplanar surface monopoles

The application of contraction theory to an iterative formulation of electromagnetic scattering

Off focus characteristics of the offset fed parabola