Second-order sensitivity analysis of electromagnetic performance with respect to surface nodal displacements for reflector antennas and its benefits in integrated structural–electromagnetic optimisation

Integrated structural–electromagnetic optimisation design is an interesting area in the field of antenna design. Due to the urgent requirements on second-order sensitivity analysis to benefit the integrated iterative procedure, based on the authors’ previous work, an analytic second-order partial derivative formula of electromagnetic performance – directivity with respect to surface nodal displacements for reflector antennas is deduced. In this formula, the electromagnetic performance is obtained by superposition of radiation integrals on each small triangular element. Then, a perturbation of surface nodal displacement is introduced to re-express the distorted radiation integral. By partially differentiating the distorted phase error in radiation integral with respect to nodal perturbation over the corresponding triangular element twice, the second-order partial derivative is derived. Two reflectors – an axis-symmetrical one and an offset one, are illustrated in simulation to show the second-order partial derivatives in contour plots. A comparative simulation is performed to illustrate its benefits in integrated structural–electromagnetic optimisation.