Daniel R. Prado

Complex Reflection Coefficient Synthesis Applied to Dual-Polarized Reflectarrays With Cross-Polar Requirements

An extended formulation of the intersection approach (IA) algorithm is presented to synthesize matrices of complex reflection coefficients for dual-polarized reflectarrays. The synthesis of complex reflection coefficients allows to impose copolar as well as cross-polar specifications, since these coefficients fully characterize the behavior of the unit cell. The implementation of the algorithm is based on the use of the fast Fourier transform (FFT) in both the forward and backward projectors of the IA, allowing for a highly efficient and fast synthesis process of dual-polarized reflectarrays. Although arbitrary restrictions can be enforced in the reflection coefficients, they might not be feasible for passive antennas. Hence, the unit cell is analyzed as a lossless and lossy passive two-port network and the restriction equations are derived for both cases involving amplitudes and phases of the reflection coefficients. The lossless constraints proved to be too restrictive so lossy restrictions should be applied to achieve feasible reflection coefficients for passive array design. Test cases are provided, which confirm that the algorithm is able to synthesize with success radiation patterns with copolar and cross-polar requirements with restrictions applied to the reflection coefficients.

Implementation of transformed lenses in bed of nails reducing refractive index maximum value and sub-unity regions

Transformation optics with quasi-conformal mapping is applied to design a Generalized Maxwell Fish-eye Lens (GMFEL) which can be used as a power splitter. The flattened focal line obtained as a result of the transformation allows the lens to adapt to planar antenna feeding systems. Moreover, sub-unity refraction index regions are reduced because of the space compression effect of the transformation, reducing the negative impact of removing those regions when implementing the lens. A technique to reduce the maximum value of the refractive index is presented to compensate for its increase because of the transformation. Finally, the lens is implemented with the bed of nails technology, employing a commercial dielectric slab to improve the range of the effective refractive index. The lens was simulated with a 3D full-wave simulator to validate the design, obtaining an original and feasible power splitter based on a dielectric lens.

Design, Manufacture, and Measurement of a Low-Cost Reflectarray for Global Earth Coverage

In this work, a low-cost reflectarray with isoflux pattern for global Earth coverage is designed, manufactured, and measured at 30 GHz. The isoflux template is mathematically derived for a generic satellite and then particularized for a geostationary orbit. In order to reduce costs, the synthesis and design processes have to be accordingly adapted. First, the most simple unit cell is selected, consisting of a single layer of rectangular patches backed by a ground plane. This cell is not able to provide a 360 ° phase range, and thus the synthesis algorithm has to be modified to include a phase constraint to match the range provided by the element, ensuring at the same time a smooth variation of the elements in order to obtain a reliable design. This is further ensured by limiting the patch size to a given range during the design process. Finally, the reflectarray is manufactured and measured, showing good agreement with the simulations.

An Efficient Calculation of the Far Field Radiated by Non-Uniformly Sampled Planar Fields Complying Nyquist Theorem

An efficient and accurate method to calculate the far field radiated by non-uniformly sampled planar apertures using the non-uniform fast Fourier transform (NUFFT) is shown. The sampled fields in the planar aperture have to comply the Nyquist theorem. The method takes into account the amplitude of the unit cell radiation pattern, which allows to compute more accurately the copolar and crosspolar components of the far field. Due to the generality of the NUFFT, it also allows to overcome some limitations of the FFT when computing the radiated fields of reflectarrays with periodicity larger than half a wavelength. Because the NUFFT is precision-dependent, a discussion of how its accuracy can affect the computed radiated fields is carried out. Numerical examples are provided to show the accuracy and performance of the NUFFT with regard to the FFT and direct evaluation of the fields. Finally, a study of computing times comparing the FFT, NUFFT and direct evaluation is presented.

Improved Reflectarray Phase-Only Synthesis Using the Generalized Intersection Approach with Dielectric Frame and First Principle of Equivalence

An improved reflectarray Phase-Only Synthesis technique which employs the generalized Intersection Approach (IA) algorithm is fully described. It is formulated with the First Principle of Equivalence and takes into account a dielectric frame which is usually present to screw the reflectarray breadboard to the supporting structure. The effects of the First Principle of Equivalence versus the Second Principle in the computation of the radiation patterns, as well as the dielectric frame, are assessed and taken into account in an efficient implementation of the generalized IA in order to obtain more accurate results. Different strategies to speed up the synthesis process are presented and to improve convergence. The technique is demonstrated through two examples for space and terrestrial applications: an isoflux pattern for global Earth coverage from a satellite and a Local Multipoint Distribution Service pattern for central stations of cellular systems, both with a working frequency of 25.5 GHz. In addition, experimental results validate the approach described in this work with a prototype with an isoflux pattern working at 30 GHz.

Efficient Crosspolar Optimization of Shaped-Beam Dual-Polarized Reflectarrays Using Full-Wave Analysis for the Antenna Element Characterization

A method for the optimization of the crosspolar component of dual-polarized reflectarrays using full-wave analysis at the element level is described and demonstrated. The reflectarray full-wave analysis is based on local periodicity (LP) and integrated within the optimization process in order to accurately characterize the crosspolar far field. The proposed method is based on the generalized Intersection Approach framework using the Levenberg–Marquardt Algorithm as backward projector, and the employed full-wave analysis is based on the Method of Moments assuming Local Periodicity (MoM-LP). Several strategies to accelerate the computations are exploited, such as the parallelization of all the algorithm building blocks. To minimize the impact of MoM-LP in the optimization process, a strategy to reduce the number of MoM-LP calls is described, further accelerating the algorithm. Moreover, the convergence is improved by working with the squared field amplitude, alleviating the trap problem of local optimizers. This method allows to optimize the crosspolar component in the whole visible region or only in the coverage zone to facilitate the convergence, reducing computing time and memory usage. Two test cases are provided to validate the technique, one with an isoflux pattern for global Earth coverage and another with European coverage for direct broadcast satellite application.

Evaluation of the quiet zone generated by a reflectarray antenna

In this work, the quiet zone achieved by a reflectarray antenna is evaluated. The study is focused on obtaining the near field generated by the reflectarray and the evaluation of the quiet zone in terms of the design parameters of the reflectarray antenna is presented. Then, the most critical parameters in the design of the quiet zone are identified. Finally, the quiet zone generated by the reflectarray is compared with that obtained by a classic parabolic reflector.

Fast and Accurate Modeling of Dual-Polarized Reflectarray Unit Cells Using Support Vector Machines

This paper describes the characterization of reflectarray unit cells using support vector machines (SVMs) to obtain fast and accurately the full matrix of reflection coefficients, which is used for an analysis of dual-polarized reflectarrays, demonstrating the performance of the model. First, a surrogate model of the reflectarray unit cell is obtained using SVMs. To this end, a set of random samples of the reflection coefficient matrix with a full-wave method of moments based on local periodicity (MoM-LP) is used to train the SVMs. To efficiently obtain the surrogate model, a novel strategy to accelerate the training process is presented, remarkably reducing computing time. Next, the model is tested against a different set of samples, obtaining an excellent agreement between the SVM model and MoM-LP simulations for all reflection coefficients, including the cross-coefficients. The surrogate model is then used for an efficient analysis of three reflectarrays with pencil beam for point-to-point communications, isoflux pattern for global Earth coverage, and a shaped beam for local multipoint distribution service application, showing excellent agreement in both copolar and crosspolar patterns between the SVM and MoM-LP simulations. Finally, the analysis is accelerated by a factor larger than three orders of magnitude using SVMs instead of MoM-LP.

Efficient computation of the reflectarray far fields in adaptive grids for speed improvement

A technique for the efficient computation of the radiation patterns of reflectarray antennas in an adaptive grid for speed improvement is presented. It relies on the use of the Non-Uniform Fast Fourier Transform (NUFFT) to efficiently compute the spectrum functions. This new application of the NUFFT improves computing times and memory usage, with regard to the use of the FFT, for very directive reflectarrays in which a high resolution in the UV grid is needed to correctly characterize the main beam and adjacent secondary lobes.

Application of the NUFFT to the analysis and synthesis of aperiodic arrays

This paper presents a novel formulation to efficiently analyze aperiodic arrays using the NUFFT and considering the amplitude of the unit cell radiation pattern. This formulation is extended to consider a smooth-varying incident field within each unit cell. Finally, it is employed in the optimization of an aperiodic array, obtaining excellent results.