角锥天线设计的非线性方程求解

Pyramidal Horn Design by Nonlinear Equations Solving

角锥喇叭天线设计被等同于求解一组非线性方程,方程组的约束条件是两个主波束宽度和增益指标,解向量是决定喇叭形状的一组独立尺寸。求解采用全局收敛准则的Newton-Raphson迭代法。将指标扩展到一个连续变域后,解向量的矢端将描绘出三维空间曲面,曲面的边界恰对应指标的容许界限。作出该收敛域的几组二维投影图,看出角锥天线特性和算法收敛特征之间的诸多关联。解向量的存在和唯一性得到回答。几种特殊情况下的指标界限被列于文中。设计并加工测量一个S波段角锥天线,证实方法在应用层面的效果。

Iteration for nonlinear sets of equations is applied to pyramidal horn design.The restrictions are established by forcing the beamwidthes and the gain expressions to satisfy simultaneously the corresponding indices while the solution vector,each dimension of which represents an independent geometrical parameter of the horn,is found by Newton-Raphson iteration with an entire-domain convergence strategy.By extending the indices to a continumm,the solution vector is found to limn continuous sheets in 3D space,...