Gradient-based shape optimisation of conformal array antennas

Journal article, 2010

We present and test a gradient-based shape optimisation method for the minimisation of the active reflection coefficient for conformal array antennas. The goal function is an average of the active reflection coefficient with respect to all antenna elements, a prespecified frequency interval, and a set of excitation modes. The sensitivity of the goal function with respect to changes of the antenna's shape is based on the continuum form of Maxwell's equations, which provides good flexibility for the choice of field solver. The sensitivity is formulated in terms of the field solution of the original antenna problem and a similar adjoint field problem, which gives the sensitivity for an arbitrary number of design parameters given the solution of Maxwell's equations. We test the optimisation method in two dimensions for array antennas that conform to a circular cylinder, where both uniform arrays and arrays that occupy a part of the cylinder's circumference are considered. For some cases, we find that it is feasible to reduce the active reflection coefficient for arrays that partially cover the circumference of the cylinder by means of end elements that differ from the bulk elements of the array. In general, substantial reductions in the active reflection coefficient can be achieved by relatively small shape changes of the antenna elements. For the test cases considered in this article, the optimisation method typically converges to an optimised design within 5-15 iterations.