一种新的自适应宽带扫频方法及其在分层微带结构全波分析中的应用

An adaptive wideband frequency-sweeping algorithm and its application to full-wave analysis of multilayered structures

本文基于分层媒质空域并矢Green函数的精确、快速计算,结合混合位积分方程的矩量法模型,建立了一种自适应的分层微带无源电路宽带扫频算法.该算法以目标频段内Chebyshev多项式零点为频率样点建立插值机制,其插值矩阵的相对误差通过矩阵Frobenius范数给予定义,并由此作为自适应机制的判敛依据.实验表明,以频率区间内的Chebyshev多项式零点作插值节点,相比于等间距样点,拥有更低和更平稳的误差表现.该方法在无需任何先验条件的情况下,通过自适应反馈系统可以精确、快速地求得宽带微波无源电路的全波分析结果.根据大量统计数据,本文还定量地给出了该算法在数值精度和计算效率之间的权衡关系.

In this paper, with the fast and accurate evaluation of multilayered Green＇s functions, we propose an adaptive algorithm of wideband frequency sweeping for microwave passive circuits, which is based on the mixed potential integral equation（MPIE）. The proposed method selects Chebyshev zeros from the frequency band as sampling points to perform interpolation. The relative error of the interpolated matrix can be calculated using the Frobenius norm, which can also be used as a criterion for convergence in the adaptive mechanism. A numerical example demonstrates that sampling Chebyshev zeros provides a much lower and more consistent error rate.Furthermore, the full-wave analysis of a microwave wideband passive circuit can be efficiently obtained using this algorithm without any a priori conditions. The trade-off between numerical accuracy and computational efficiency of this algorithm is obtained through numerous statistical experiments and discussed quantitatively.