Predicting Tolerance Effects on The Radiation Pattern of Reflectarray Antennas Through Interval Analysis

The thesis focuses on predicting tolerance effects on the radiation pattern of reflectarray antennas through Interval Analysis. In fact, the uncertainty on the actual size of all parameters under fabrication tolerates such as element dimensions and dielectric properties, are modeled with interval values. Afterwards, the rules of Interval Arithmetic are exploited to compute the bounds of deviation in the resonance frequency of each element, the phase response of the element and the radiated power pattern. Due to the redundancy problems of using Interval Cartesian (IA−CS) for complex structure, the interval bounds are overestimated and the reasons are the Dependency and Wrapping effects of using interval analysis for complex structures. Different techniques are proposed and assessed in order to eliminate the dependency effect such as reformulating the interval function and the Enumerative interval analysis. Moreover, the Minkowski sum approach is used to eliminate the wrapping effect. In numerical validation, a set of representative results, show the power bounds computations with Interval Cartesian method (IA − CS), a modified Interval Cartesian method (IA − CS*), Interval Enumerative method (IA − ENUM) and Interval Enumerative Minkowski method ( IA − ENUM − MS) and a comparative study is reported in order to assess the effectiveness of the proposed approach (IA − ENUM − MS) with respect to the other methods. Furthermore, different tolerances in patch width,length, substrate thickness and dielectric permittivity are considered which shows that the higher uncertainty produces the larger deviation of the pattern bounds and the larger deviation include the smaller deviation and the nominal one. To validate the inclusion properties of the interval bounds, the results are compared with Monte Carlo simulation results. Then, a numerical study is devoted to analyse the dependency of the degradation of the pattern features to steering angle and the bandwidth. Finally, the effect of feed displacement errors on the power pattern of reflecttarray antennas is considered with Interval Enumerative Minkowski method. The maximal deviations from the nominal power pattern (error free) and its features are analysed for several reflectarray structures with different focal-length-to-diameter ratios to prove the effectiveness of the proposed method.