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将串联结构的环型谐振滤波器类比为四端口网络,利用传输矩阵法推导出通路和下话路传输函数的通用公式。对表征串联双环谐振滤波器响应的特性参量:幅度平坦性、通带带宽、相位群时延进行了数值计算和优化设计。结果表明:尽管损耗将引起滤波响应幅度的轻微降低,但在目前改善了的制作工艺下,损耗对器件的影响可以忽略;滤波器的传输特性主要由环与环间耦合系数决定,通过优化使其从中间到两侧对称增加,可以在实现滤波响应最大平坦性的同时,改善通带带宽和过渡带的滚降特性。与单环结构相比,不仅幅度特性得到了明显的改善,而且消除了二阶群时延色散效应。
The ring resonant filter with series structure is analogized as a four-port network, and the general formula of the transmission function of the path and the next path is deduced by using the transfer matrix method. The characterization of the characteristic parameters of the series double loop resonant filter: amplitude flatness, passband bandwidth and phase group delay are numerically calculated and optimized. The results show that although the loss will cause a slight decrease of the amplitude of the filter response, the influence of the loss on the device can be ignored under the current improved fabrication process. The transmission characteristic of the filter is mainly determined by the coupling coefficient between the ring and the ring. Its symmetrical increase from the middle to both sides can improve the passband bandwidth and the roll-off characteristic of the transition band while realizing the maximum flatness of the filtering response. Compared with the single-ring structure, not only the amplitude characteristics have been significantly improved, but also eliminate the second-order group delay dispersion effect.