The so-called equivalent parabola technique has been used extensively in the design of Cassegrainian systems. Hannan substantiated the validity of the technique by showing the excellent agreement between his measured data on a Cassegrainian system and the calculated results obtained using the equivalent parabola technique. However, his demonstration was restricted to an on-axis feed Cassegrainian. This paper derives an analytical expression involving only a 2-dimensional vector integral for the secondary vector field from the Cassegrain system with an offset feed by integrating over the surface currents on both the main dish and subdish with the \phi integrations performed in closed form, and proceeds to compare its results with those obtained from the equivalent parabola technique, for different f/D of the main dish, eccentricities of the subdish, illumination patterns, and lateral displacements of the primary radiator. The agreement in general is good for Cassegrainians with an on-axis feed. For Cassegrainians with an offset feed, the error in using the equivalent parabola technique remains negligible for a beam scan of as much as four beamwidths.

On the equivalent parabola technique to predict the performance characteristics of a Cassegrainian system with an offset feed

A method is presented for the computation of the far field radiation patterns of paraboloid reflector antennas by using a modified stationary phase approximation to eliminate one integration. This method is applicable to open cassegrain, offset paraboloid and horn reflector antennas. For symmetrical paraboloid antennas the modified approximation reduces to the exact expression obtained by direct integration. The errors introduced by the stationary phase and modified stationary phase approximations are investigated. Specifically the far field of an open cassegrain with a 128 wavelength aperture diameter is computed by the approximate method up to 20 degrees off-axis. The difference between these radiation patterns and those computed by double integration, is less than a few tenths of a dB up to 1.0 degree, and less than a few hundredths of a dB at larger angles off-axis. In order to estimate the computational advantage of this approximation, the number of points required for integration of an oscillatory function by Simpson's rule is also examined and it is determined that at least 6 points per cycle are necessary to obtain 4 decimal accuracy. For fewer points the error is appreciable.

A stationary phase method for the computation of the far field of open cassegrain antennas

An efficient numerical algorithm for physical optics (PO) analysis of reflectors is presented. Cylindrical symmetry of the reflector is not essential but is assumed for purposes of illustration, and this leads to the use of Fourier representation in the azimuthal variable. The algorithm is based on quadratic approximation of the phase and polynomial approximation of the remaining portion of the integrand. The necessary integrals are generated recursively and they involve the Fresnel integral. Additional efficiency is achieved by means of an interpolation scheme. Therein one interpolates all but the rapidly varying edge diffraction contribution to the integral and then adds the explicitly calculated edge contribution at each far-field point. A few illustrative examples are included.

Correction to "A new integration algorithm and its application to the analysis of symmetrical Cassegrain microwave antennas"

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https://pure.tue.nl/ws/files/4306129/7007985.pdf

On conical horn antennas

A short review on the modern design techniques of Cassegrainian antennas having high efficiency is presented Attention is focussed on the following techniques: (a) Cassegrainian antenna with far-field feed, (b) Casegrainian antenna with near-field feed, (c) geometrical optics technique for shaping subreflector and reflector, (d) diffraction method for shaping subreflector and reflector, (e) use of dielectric guiding structure (dielguide)Relative merits and demerits of the techniques are discussed Design procedure and formulae illustrating the techniques are given

Modern Design Techniques of Cassegrainian Antennas

A method of analyzing, in detail, the performance of symmetrical Cassegrain antennas has been developed that uses a digital computer efficiently. For a specified antenna geometry and feed excitation, the program will compute and graphically display the amplitude and phase illumination of the subreflector, main reflector, and far-field pattern. These results may be used to optimize antenna performance by changing parameters and observing the effect. Analysis of a Cassegrain antenna with a near-field conical horn feed is discussed as an application of the method. Because the radiation characteristics of the horn are determined by the horn flare angle rather than the horn aperture, broadband performance is obtained. It was indeed found that a 50 per cent bandwidth is achieved with a dual mode TE 11 –TM 11 mode feed, provided the proper phase relationship between the modes can be maintained over the band. For dual mode excitation an aperture efficiency of 70% and a noise temperature due to the power loss at the sub and main reflectors of less than 6.5$dGK was obtained. For a single mode feed (TE 11 ), there was a degradation in the E-plane side lobe levels and a corresponding 10$dGK increase in noise temperature. Excitation in the TM 01 mode was also examined for angle-error sensing purposes. Also, the antenna can be used with reasonable efficiency well below the design frequency in which case it functions as a far-field fed Cassegrain antenna.

http://ieeexplore.ieee.org/iel7/6731005/6779217/06779220.pdf

H. Zucker

Papers

Computer-aided analysis of cassegrain antennas