Pole–Zero Dynamics of High-Order Ring Resonator Filters
Pole–Zero Dynamics of High-Order Ring Resonator Filters
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DOI：
10.1109/jlt.2007.895551
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发表时间：
2007-06
影响因子：
4.7
通讯作者：
S. Darmawan;Y. Landobasa;M. Chin
中科院分区：
文献类型：
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作者：
S. Darmawan;Y. Landobasa;M. Chin
我们提出了一种基于传递矩阵方法的极零分析，用于I型和II型环形谐振器滤波器，由相互耦合和侧耦合的RR组成。极零图决定了滤波器的光谱特性，主要由谐振器之间的耦合系数决定。极点-零点动力学（或根轨迹）显示了当我们改变耦合系数时极点和零点如何在复频率平面上移动。我们证明了两种类型的滤波器的极零动力学是互补的，此外，极零图与存在损耗或增益时的临界耦合和振荡条件有关。我们还展示了基于主动可调谐mach - zehnder型耦合器的这些滤波器的极点零分析，其中表明极点零对应于设计宽间距的极点零对，而所需的带宽决定了耦合系数的具体值。
We present a pole-zero analysis, based on the transfer matrix method, for ring resonator (RR)-based filters of Type I and Type II, consisting of mutually coupled and side-coupled RRs. The pole-zero plot determines the filter spectral characteristics and is determined primarily by the coupling coefficient between the resonators. The pole-zero dynamics (or root locus) shows how the poles and zeros move in the complex frequency plane as we vary the coupling coefficient. We show that the pole-zero dynamics for the two types of filter are complementary and, furthermore, that the pole-zero plots are related to the conditions of critical coupling and oscillation in the presence of loss or gain. We also show a pole-zero analysis for the apodization of these filters based on an actively tunable Mach-Zehnder-type coupler, where it is shown that apodization corresponds to designing pole-zero pairs with wide separations, whereas the required bandwidth determines the specific values of the coupling coefficient.