频变交叉耦合滤波器的矩阵优化综合方法

Matrix optimization synthesis method for the cross-coupled filter with frequency dependent couplings

为了解决传统交叉耦合滤波器模型中的非频变耦合系数无法准确表征宽带条件下耦合结构的频率特性问题,提出了一种含有频变耦合系数的N+2型交叉耦合滤波器矩阵优化综合方法。首先通过矩阵的缩放和相似变换过程,将指定拓扑的N+2型频变耦合矩阵变换为非频变耦合矩阵;然后以N+2型全规范耦合矩阵的特征值为趋近目标构造目标函数;最后通过梯度优化算法进行搜索,即可获得指定拓扑的N+2型频变耦合矩阵。不同拓扑结构的优化综合实例表明,该方法可以高效地解决复杂频变交叉耦合滤波器的综合问题。

The traditional coupling coefficients in the cross-coupled filter model do not accurately characterize the frequency characteristics of the coupled structure under the broadband condition. To solve this problem, a matrix optimization synthesis method for the N+2 cross-coupled filter with frequency dependent coupling coefficients is proposed. First, the N+2 frequency dependent coupling matrix of a given topology is transformed into a frequency independent coupling matrix by matrix scaling and similarity transformation. Then, the objective function is constructed by approaching the eigenvalues of the N+2 canonical coupling matrix. Finally, the N+2 frequency dependent coupling matrix with a specified topology can be obtained by the gradient optimization algorithm. Numerical synthetical results of different topologies prove that the proposed method can efficiently solve the synthesis problem of filters with complex frequency dependent couplings.