UTD analysis of a shaped subreflector in a dual offset-reflectorantenna system

The geometrical theory of diffraction (GTD) is known as an efficient high-frequency method for the analysis of electrically large objects such as a reflector antenna. However it is difficult to obtain geometrical parameters in order to apply GTD to an arbitrary shaped reflector, especially a subreflector. The geometrical parameters of an arbitrary shaped subreflector for the uniform theory of diffraction (UTD) analysis are derived based on differential geometry. The radiation patterns of various subreflector types, including hyperboloidal and a shaped subreflector, are evaluated by UTD. The computed result for the hyperboloidal reflector agrees well with that obtained by uniform asymptotic theory (UAT)     

GTD analysis of the radiation patterns of a shaped subreflector

A technique of analyzing the principal plane radiation patterns of a subreflector shaped using the method enunciated by Collins [1] has been presented. The analysis is based on the uniform geometrical theory of diffraction (UGTD) [2], and a simplified procedure has been adopted in the determination of the principal plane radii of curvature of the subreflector. The numerical results obtained based on UGTD correlate well with those obtained using the method of physical optics (PO).     

Subreflector extension for improved efficiencies in Cassegrain antennas--GTD/PO analysis

Both offset and symmetric Cassegrain reflector antennas are used in satellite and ground communication systems. It is known that the subreflector diffraction can degrade the performance of these reflectors. A geometrical theory of diffraction/physical optics (GTD/PO) analysis technique is used to investigate the improving effects of the extended subreflector, beyond its optical rim, on the reflector efficiency and farfield patterns. Representative numerical results are shown for an offset Cassegrain reflector antenna with different feed illumination tapers and subreflector extensions. It is observed that for subreflector extensions as small as1 lambdanoticeable improvements in the overall efficiencies can be expected. Useful design data are generated for the efficiency curves and far-field patterns.     

GTD analysis of a hyperboloidal subreflector with conical flange attachment

A geometrical theory of diffraction (GTD) analysis of the principal plane far-field radiation patterns of a hyperboloidal subreflector with a conical flange attachment (HWF) fed by a primary feed located at its focus is presented. While using the uniform geometrical theory of diffraction (UGTD) for evaluating the nonaxial fields, the method of equivalent currents is used in the axial region. In this paper, both the diffraction by the wedge formed between the hyperboloid and the conical flange and the diffraction by the edge of the flange are considered. While considering the diffraction by the edge due to the diffracted ray from the wedge in theH-plane, the slope diffraction technique has been used. The computed diffracted farfields of a typical HWF illuminated by a high performance primary feed shows good agreement with the available measured data and with the results based on the method of physical optics (PO). The sharp cutoff and the low spillover characteristics of the HWF are highlighted by comparing its radiation pattern with that of a hyperboloid without a flange. Further, the effects of the different parameters of the HWF on its radiation pattern are also studied and plotted, so that these results can be utilized in the design of the HWF for a specific requirement.     

A correction to the available formula for the GTD near-field patterns of conical horns

An error in the geometrical theory of diffraction (GTD) near-field analysis of a conical horn published earlier is pointed out. This error is corrected, and the correct expression for the near-field patterns for the conical horn is presented. Computations based on the corrected formulas correlate better with results based on measurement as well as aperture integration technique [4].     

An offset-fed reflector antenna with an axially symmetric main reflector

A design method for an offset-fed, dual reflector antenna (Cassegrain type or Gregorian type) system with an axisymmetric main reflector is presented. Geometrical optics (GO) and the geometrical theory of diffraction (GTD) are used to find the surface-current density on the main reflector. A modified Jacobi-Bessel series (JBS) method is used to find the far-field pattern for the physical optics (PO) integral. In the defocused mode of operation, a new technique is developed to find the reflection point on the subreflector corresponding to the defocused feed and a general field point on the main reflector. Two sample systems are designed.     

GTD analysis of the radiation patterns of conical horns

The far-field radiation patterns of conical horns of arbitrary flare angles excited in theTE_{11}mode are obtained employing the geometric theory of diffraction (GTD) based on the theory of Kouyoumjian and Pathak [3] and the slope diffraction technique [4]. The analysis presented enables one to predict accurately radiation patterns over the main beam, near and far sidelobes, and the becklobe of the horn. Validity of the analysis is established by satisfactory agreement between the calculated and measured patterns of an experimental conical horn. The radiation patterns of wide-flare corrugated conical horns excited in theHE_{11}mode of operation have also been calculated over the main beam, which contains most of the radiated energy (up to -40 dB with respect to boresight field), employing slope diffraction technique, and a good agreement is noticed between the calculated and measured radiation patterns.     

Analysis of near-field Cassegrain reflector: plane wave versuselement-by-element approach

A near-field Cassegrain reflector (NFCR) is an effective way to magnify a small phased array into a much larger aperture antenna for limited scan applications. Traditionally the pattern wave approach, i.e. the field from the feed array incident on the subreflector is approximated by a truncated collimated beam with planar phase and tapered amplitude distribution. This approach simplifies the computation tremendously, but fails to provide design information about the most critical component of the whole antenna system, namely, the feed array. With the help of today's computers, it is now feasible to calculate the pattern of a NFCR by a more exact element-by-element approach. Each element in the feed array is considered individually and the diffraction pattern from the subreflector is calculated by the geometrical theory of diffraction (GTD). The field contributions from all elements are superimposed at the curved main reflector surface, and a physical optics integration is performed to obtain the secondary pattern     

Application of the geometrical theory of diffraction to Cassegrain subreflectors with laterally defocused feeds

The geometrical theory of diffraction (GTD) as formulated by R. G. Kouyoumjian has been applied to predict the radiation characteristics of hyperboloidal subreflectors with laterally defocused feeds. In caustic or multicaustic directions the scattered fields are determined using an equivalent ring current placed along the edge of the subreflector. The theoretical results are compared to measured amplitude and phase data. In order to improve the agreement, the blocking effects of the feed horn have been accounted for using the geometrical theory of diffraction. The calculated subreflector fields have been used to illuminate a paraboloid from which the scattered field is determined by physical optics. The results are compared to those obtained using a laterally defocused equivalent paraboloid.     

The effects of subreflector diffraction on the aperture efficiency of a conventional Cassegrain antenna--An analytical approach

An asymptotic theory is presented with which the reduction in aperture efficiency caused by diffraction from a subreflector edge can be calculated for any dual-reflector system. The theory is applied to conventional Cassegrain antennas, for which approximate analytical effieiency formulas are derived. These formulas show that subreflector diffraction may represent a significant efficiency loss even for subreflector diameters as large as 20 wavelengths. The formulas are used to obtain an optimum subreflector size which represents the best trade-off between losses due to subreflector diffraction and geometrical shadowing.     

Scattering from a circular disk: a comparative study of PTD and GTDtechniques

Two groups of techniques, PTD (physical theory of diffraction) and GTD (geometric theory of diffraction), are studied by analyzing the scattering from a conducting circular disk. The authors include comparisons of calculations based on several different asymptotic high-frequency theories with the method of moments (MoM) as a baseline. The latter is treated as numerically exact. Features of particular interest include the performance at the reflection boundaries, boresight caustics, and far-angle sidelobes. The bistatic radar cross sections (RCSs) calculated by these techniques are examined. Although only far-field radiation is considered, these methods can also be used for near-field calculations     

Dihedral corner reflector backscatter using higher order reflections and diffractions

The uniform theory of diffraction (UTD) plus an imposed edge diffraction extension is used to predict the backscatter cross sections of dihedral corner reflectors which have right, obtuse, and acute included angles. UTD allows individual backscattering mechanisms of the dihedral corner reflectors to be identified and provides good agreement with experimental cross section measurements in the azimuthal plane. Multiply reflected and diffracted fields of up to third order are included in the analysis for both horizontal and vertical polarizations. The coefficients of the uniform theory of diffraction revert to Keller's original geometrical theory of diffraction (GTD) in far-field cross section analyses, but finite cross sections can be obtained everywhere by considering mutual cancellation of diffractions from parallel edges. Analytic calculations are performed using UTD coefficients; hence accuracy required in angular measurements is more critical as the distance increases. In particular, the common "far-field" approximation that all rays to the observation point are parallel is too gross of an approximation for the angular parameters in the UTD coefficients in the far field.     

A new method of analysis of the near and far fields of paraboloidal reflectors

An analytical technique for predicting accurately the near (electric and magnetic) fields as well as the far fields of a reflector antenna with a pencil beam is presented. The technique proposed involves the near-field geometrical theory of diffraction (GTD) analysis of reflector antennas developed earlier and spherical vector mode functions. The proposed technique does not place any restriction on the range of polar angles or radial distances of the observation point. It is demonstrated that the technique proposed can predict the fields radiated by the reflector with greater accuracy by comparing the calculated results with the available measured results. A few important applications of the analysis proposed are also highlighted.     

Slope diffraction and its application to horns

The first order geometrical theory of diffraction (GTD) predicts vanishing fields along the surface of a conducting wedge for the incident electric field polarized parallel to the diffracting edge. The slope diffraction coefficient is a valid correction term for incidence angles removed from the shadow boundary. A new slope diffraction function for the half plane is presented along with applications. This new form of slope diffraction coefficient for the half plane is valid through the shadow region. Reciprocity is invoked to find the far-fields for a source on the surface of the conducting wedge. In addition to applying the two-dimensional slope diffraction analysis to practical problems, the equivalent current concepts have been extended to include equivalent slope currents for the analysis of either finite or curved edges. This new form of the slope diffraction function has been successfully used to provide anH-plane horn pattern analysis that is considerably less tedious than previously possible with GTD. Both pure GTD solutions and hybrid solutions using conventional aperture integration for the main beam region and GTD for the far-out side and back lobes are compared with experimental results.     

A study of three techniques used in the diffraction analysis ofshaped dual-reflector antennas

An examination is presented of three techniques used for the efficient computation of fields diffracted by a subreflector that has been shaped by geometrical optics synthesis. It is found that these techniques, which are based on the geometrical theory of diffraction (GTD), produce errors in the computed fields that are specific to shaped reflectors. These errors are examined for a reflector system shaped to produce maximum gain from a tapered feed illumination. The discrepancies are directly related to the caustic being located near an observation point of the GTD calculations. The errors found are localized, and they increase in magnitude as the caustic approaches the main reflector. In a general offset geometry, the location of the caustic may be located arbitrarily close to the main reflector given a prescribed output aperture distribution. For the specific case considered here-the common situation of shaping to produce maximum gain-the caustic is located near the edge of the main reflector and on the reflection shadow boundary. A local correction is derived which creates a uniform solution through the caustic and across the reflection shadow boundary. Away from this point the calculation recedes to the standard GTD solution     

Near-field pattern analysis of airborne antennas

Results of a newly formulated analysis for computing patterns of an aperture or monopole antenna mounted on the fuselage of an aircraft are presented. Approximate models of the aircraft structure are employed in conjunction with the geometrical theory of diffraction (GTD) to obtain the computed fields. A major feature of the analysis is that it can accommodate receiver range specifications varying from as close as a wavelength to the aircraft surface to the true far field. This feature is especially useful in that computed on-aircraft pattern performance can be compared with measurements taken at any convenient range, including the near field. Further, after such crucial checks between computations and measurements have been made, the numerical solution can be employed to predict accurately the far-field performance of the on-aircraft antenna system. The accuracy of the numerical solutions obtainable with the analysis is demonstrated by comparison with model measurements.     

Diffraction by a thick perfectly conducting half-plane

The angular spectrum method involves the integral representation of the scattered field in terms of the angular spectra of the pertinent surface currents. Here the angular spectrum method in conjunction with the scattering matrix formulation is used for the diffraction analysis of a thick perfectly conducting half-plane considering both polarizations of incidence. Of particular interest is the scattering behavior by edges of thicknesses less than a wavelength where a geometrical theory of diffraction (GTD) solution is generally not applicable. Several backscatter and bistatic patterns are then presented in this range of thicknesses, and for the backscatter case some are also compared with measured data. It is found that a combination of the angular spectrum method and GTD can be employed for the efficient analysis of an edge of arbitrary thickness.     

Complete radiation pattern of a focus-fed offset paraboloidal reflector

Complete radiation pattern of a focus-fed offset paraboloid is presented. Forward radiation is computed by physical optics, and wide-angle radiation is calculated by using the geometrical theory of diffraction (GTD). The presented formulation is also capable of calculating the patterns of symmetric paraboloids. Effects of the offset angle and the feed pattern asymmetry on the cross-polar isolation are presented.     

The finite ground plane effect on the microstrip antenna radiation patterns

The uniform geometrical theory of diffraction (GTD) is employed for calculating the edge diffracted fields from the finite ground plane of a microstrip antenna. The source field from the radiating patch is calculated by two different methods: the slot theory and the modal expansion theory. Many numerical and measured results are presented to demonstrate the accuracy of the calculations and the finite ground plane edge effect.     

The SNFGTD method and its accuracy

The spherical near-field geometrical theory of diffraction (SNFGTD) method is an extended aperture method by which the near field from an antenna is computed on a spherical surface enclosing the antenna using the geometrical theory of diffraction. The far field is subsequently found by means of a spherical near-field to far-field transformation based on a spherical wave expansion of the near field. Due to the properties of the SNF-transformation, the total far field may be obtained as a sum of transformed contributions which facilitates analysis of collimated beams. It is demonstrated that the method possesses some advantages Over traditional methods of pattern prediction, but also that the accuracy of the method is determined by the quasioptical methods used to calculate the near field.