Statistical Analysis of Electromagnetic Structures and Antennas Using the Polynomial Chaos Expansion Method

Electromagnetic (EM) structures such as antennas, resonators, are widely used in EM communication systems. It is not uncommon to find that the performance characteristics of these structures are not as expected because of the uncertainties introduced during the manufacturing process. These uncertainties may arise, for instance, from variations of the dimensions of the device or its material properties, e.g., permittivity and permeability. A statistical tool based on the use of the Polynomial Chaos Expansion (PCE) technique is proposed in this work. The results of investigation of two EM structures, namely an E-shaped patch antenna and a split-ring resonator (SRR), are presented as examples. The results confirm that the variability of the design parameters must be taken into account while designing such structures. A sensitivity analysis is also performed in order to determine the most influential parameters that affect the performance of the studied structures. The Sobol indices, whose definitions are provided in this work, are used for this purpose.