Shuxin Zhang

Sensitivity Analysis of Reflector Antennas and Its Application on Shaped Geo-Truss Unfurlable Antennas

This paper presents the sensitivity of far-field radiation performance with respect to reflector surface nodal displacements. The reflector surface is divided into a series of triangular elements and in any deformation state the surface can be determined by the element nodal displacements. The radiation integrals over each small element are summed to obtain the whole electromagnetic performance. With the aid of shape functions in triangular elements, the integration points inside each element are expressed as functions of element nodal displacements. Then the partial derivatives of electric far field and directivity with respect to each nodal displacement are derived. The sensitivity contour plots of maximum directivity with respect to surface nodal displacements for axis-symmetrical and offset parabolic reflectors are numerical simulated. The sensitivity is applied to a shaped geo-truss unfurlable antenna with accepted results.

An Approximation of Pattern Analysis for Distorted Reflector Antennas Using Structural-Electromagnetic Coupling Model

Based on the concept of structural-electromagnetic field coupling, an approximation method is developed to analyze the radiation pattern for distorted reflectors. In this method, the integration point deformation is obtained by a local interpolation scheme which utilizes the same shape functions as that in the structural analysis for the radiation calculation. The phase error caused by the distortion is added to the far field integral which is computed on the structural element. Similar to the assembly of element stiffness matrices in Finite Element Method (FEM), the far field electrical vector is derived as a function of structural nodal displacements in a matrix form by collecting the integrals on structural elements. Simulation is performed with good results. The method can benefit the computation for a given reflector in the integrated structural-electromagnetic optimization design procedure.

A Pattern Approximation Method for Distorted Reflector Antennas Using Piecewise Linear Fitting of the Exponential Error Term

Integrated structural-electromagnetic (EM) optimization design is of great importance in the area of antenna design. The quick and exact calculation of patterns for distorted reflectors is an important research topic. In this communication, based on the previous works, a novel pattern approximation method using piecewise linear fitting is presented. The exponential error term in the physical optics (PO) formulation is first approximated by a series of straight lines through the piecewise linear fitting by least-square algorithm. Then, the radiation integral on each structural element is expressed as the summation of the ideal term and perturbation term, which are both weighted by the combinations of coefficients of the corresponding straight lines. Finally, the far field is derived as a simple linear function of structural nodal displacements in a matrix form by assembling the radiation integrals on all the structural elements. Simulation results show that the proposed method (PM) could save the storage space because there is no second-order term of the nodal displacements, facilitate rapid calculation by recalling the prestored data, and has high calculation accuracy even for large size of surface-error profiles.

Integrated Structural Electromagnetic Analysis of Mesh Reflectors with Structural Random Dimensional Errors

A new procedure for the integrated structural electromagnetic analysis of cable mesh reflectors with structural random dimensional errors is presented. The procedure combines the integrated structural electromagnetic analysis with reliability analysis and aims to investigate the effects of structural random dimensional errors on the antenna far-field directivity pattern. Both the antenna far-field directivity pattern and structural member dimensions are taken as random variables in this procedure. The computational expressions of the mean value and variance of the far-field directivity are developed by means of the random factor method and the random variable’s functional moment method. The influences of structural random dimensional errors on the randomness of radiation directivity pattern are inspected via an offset cable mesh reflector.

A Novel Contoured Beam Synthesis Method for AstroMesh Reflectors Based on Integrated Electromagnetic-Structural Design

The self-equilibrium characteristic of the tensioned AstroMesh reflector antennas leads to the result that the concave–convex reflector surface for contoured beams cannot be realized by AstroMesh reflector antennas. To realize the contoured beam synthesis for AstroMesh reflector antennas, a novel contoured beam synthesis technology based on integrated electromagnetic-structural design is presented, and the corresponding optimization model is established. In the model, with all the force densities being constrained to be positive, force densities of the AstroMesh reflector antennas are designed to realize the desired far-field pattern. Moreover, the tension uniformity of the AstroMesh reflector antenna is additionally chosen as an objective function to ensure that the shaped AstroMesh reflectors have excellent engineering practicability with good tension uniformity. Finally, a shaped AstroMesh reflector antenna is designed to produce a contoured beam covering the continental United States (CONUS), which verified the effectiveness of the proposed method.

An Approximation Mathematical Formula of Pattern Analysis for Distorted Reflector Antennas considering Surface Normal Vector Variation

An approximation mathematical formula to compute the distorted radiation pattern for reflector antennas is presented. In this approximation formula, besides the phase error caused by the structural deformation being added in the far field integral, the surface normal vector variation is also taken into consideration. The formula is derived by expanding the surface normal vector into a first-order Taylor series and the phase error into a second-order Taylor series. By assembling the integrals including the contributions of both surface normal vector variation and phase error, the far field electrical vector expressed as a function of structural nodal displacements is further obtained in a matrix form. Simulation results of a distorted reflector show the application of this formula.

Shape Control of Cable-Network Antennas Considering the RF Performance

Manufacturing errors can result in variation of the cable tensions and degradation of the RF performance of cable-network antennas. To compensate the effects of the manufacturing errors, a novel shape control procedure, which takes the RF performance into consideration, is presented. Both the boundary cables and the tension ties are selected as adjustable cables. Sensitivity analysis is adopted to evaluate the influence of the unstrained cable lengths on the RF performance and cable tensions. The antenna performance is finally expressed as the incremental form of the adjustable cable lengths on the basis of the sensitivity analysis. A mathematical model of the shape control procedure is established and solved using optimization strategy. The proposed shape control method is applied to a 10-m diameter cable-network antenna. Numerical results show that the directivity of the antenna is more sensitive to the boundary cable lengths, while the tension in a cable is much more sensitive to the length changes of itself, the cables connected to it, and the boundary cables. Comparisons of the directivities and tensions before and after shape control demonstrate the feasibility of the proposed shape control method and recommend the antenna RF performance as the shape control objective.