An Approximation of Pattern Analysis for Distorted Reflector Antennas Using Structural-Electromagnetic Coupling Model

An Approximation Mathematical Formula of Pattern Analysis for Distorted Reflector Antennas considering Surface Normal Vector Variation

“…The main difference between this formula and the one in [17] lies in the normal vector variation. The approximated formula in [17] just takes the phase error caused by surface nodal displacements into account, while it fails to consider the surface normal vector variation.…”

“…The proposed method benefits the repeated calculations with allowable computation accuracy. Furthermore, referencing to the three-term Taylor series of phase error in [16], a matrix form 2 International Journal of Antennas and Propagation formula between the surface nodal displacements obtained by structural finite element method (FEM) and far field electrical vector was derived in [17]. The far field pattern can be directly and easily calculated by substituting the surface nodal displacements into the matrix form, which benefits the iterative pattern analysis procedure of antenna design.…”

“…In the previous study, the surface normal variation is neglected, which is based on the fact that, for small-amplitude, smoothly varying errors, the surface normal vector will not deviate substantially from the surface of an undistorted reflector [16]. The questions appear as what percentage of the surface normal variation contributes in the far field integral for distorted reflectors so as to be neglected, and what is the final expression for the matrix form in [17] when considering both the surface normal variation and phase error. The aim of this study, which is a continuation of the work in [17], is to further develop the matrix form formula considering both the phase error and the surface normal vector variation caused by surface nodal displacements.…”

“…In this study, the reflector surface is divided into many small elements as in structural FEM analysis, and the far field pattern is obtained by superposition of each element's far field contribution. The surface normal vector variation caused by surface nodal displacement is expanded into a firstorder Taylor series during the implementation, and the shape functions in [17] are also employed to express the integration point displacements as functions of nodal displacements. Both the phase error and the surface normal variation are included in these integrals, and the matrix form in [17] by assembling the integrals on elements is thus extended.…”

“…The approximated formula in [17] just takes the phase error caused by surface nodal displacements into account, while it fails to consider the surface normal vector variation. The derived formula in this study will take both the phase error and normal vector variation into account theoretically, which can be considered as an extended formula for the one in [17].…”