Tolerance analysis of the reflectarray antenna through Minkowski-based interval analysis

Having a robust architecture against tolerances is one of the most important aspects in high frequency antenna design. In this paper, the effect of the fabrication errors on the power pattern of reflectarray antenna is investigated. The uncertainty on the actual size of the patch width is modeled as an interval value. The rules of Interval Analysis (IA) and Interval Arithmetic are then exploited to compute the bounds of the deviation of the resonance frequency, the reflection phase of each element, and the resulting radiated power pattern. The Minkowski Sum (MS) is used to combine the interval phasors in the complex domain in order to avoid the bounds over-estimation affecting the standard/Cartesian Interval Analysis (IA-CS). We show that the IA-MS can produce narrower, but still inclusive bounds, as compared to the IA-CS. To guarantee the validity of the model and reliability of the obtained bounds, a Monte Carlo test has been carried out.