Explicit solution is derived for the exact synthesis of cross-coupled quadruplet filters with a real-frequency zero pair. Through a comparison of two-port S-parameters of the low-pass prototype circuit with the canonical generalized Chebyshev insertion loss function, a univariate quadratic function is formulated, and all element values of the circuit are explicitly expressed in terms of the designated zero and in-band ripple levels. The analytical expression of the sidelobe attenuation level is also obtained in terms of the zero, and vice versa. Results are checked against those from the existing literature.

中文翻译：

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具有实频零对的交叉耦合四元组滤波器精确合成的显式解决方案

为具有实频零对的交叉耦合四元组滤波器的精确合成推导出显式解。通过将低通原型电路的两端口 S 参数与规范的广义切比雪夫插入损耗函数进行比较，公式化了单变量二次函数，并且电路的所有元素值都明确表示为指定的零和带内纹波电平。旁瓣衰减电平的解析表达式也可以根据零获得，反之亦然。结果与现有文献中的结果进行核对。