Full-polarisation three-dimensional pattern synthesis for conformal conical arrays with dynamic range ratio constraint by using the initialisations based on equivalence theorem

To design three-dimensional (3D) conformal conical arrays with desired 3D co-polarisation and crosspolarisation radiation patterns, a pattern synthesis method based on equivalent principle and trust region method is presented. Dynamic range ratio (DRR) of element excitations is taken into consideration. An analytical function is utilised to constrain DRR and avoid discontinuity of objective function. Owing to the optimisation is based on very good initial currents distribution, the optimisation procedure is very fast. The analytical gradient and Hessian matrix expressions of the objective function are derived. This also improves the optimisation efficiency compared with using the finite difference methods to solve gradient and Hessian matrix. To demonstrate the effectiveness of this proposed method, a conformal conical array with 454 elements has been designed. The amplitude and phase excitations were optimised by using the proposed method.