It is shown that a well-designed lumped $LC$ loop network with a phase inverter can exhibit perfect reflectionless filtering response at its all four ports. The network is composed of two pairs of symmetrical $LC$ ladder circuits, in which one pair is obtained from lowpass transformation at a prescribed frequency based on a special lowpass prototype, and the other pair is from highpass transformation based on the same prototype at the same frequency. The input power, at any port, is divided into the two adjacent ports in the frequency domain through different paths of the loop. Each path between any two ports nearby can be treated as a mono-functional filter, whereas the adjacent two paths work as two filters with complementary responses. The overall circuit performs as a generalized diplexer without a specified “common” or “separation/combination” port. By using a numerical equation solver, the element values of the reflectionless lowpass/highpass prototype filter of order one, three, five, and seven are given. Then, the values of order nine, eleven, thirteen, and fifteen are obtained by using the optimization method. Other filtering functions such as bandpass/bandstop or dual-band can be easily implemented with the proposed prototype by using the standard frequency transformation method. For verification, two sample filters are fabricated and measured. The experimental data agree well with the predictions.

中文翻译：

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四端口对称无反射集总滤波器/双工器：原型和设计表

结果表明，一个精心设计的集总 $ LC $ 带有反相器的环路网络在其所有四个端口上都能表现出完美的无反射滤波响应。网络由两对对称组成 $ LC $ 梯形电路，其中一对是基于特殊的低通原型从指定频率的低通变换获得的，另一对则是基于相同原型在相同频率的高通变换的。通过环路的不同路径，任何端口的输入功率在频域中被分为两个相邻的端口。可以将附近任意两个端口之间的每条路径视为一个单功能滤波器，而相邻的两个路径可以用作具有互补响应的两个滤波器。整个电路用作通用双工器，没有指定的“公共”或“分离/组合”端口。通过使用数值方程求解器，给出了1、3、5和7阶无反射低通/高通原型滤波器的元素值。然后，阶数为9、11，通过使用优化方法获得13和15。通过使用标准的频率转换方法，可以通过提出的原型轻松实现其他滤波功能，例如带通/带阻或双频带。为了验证，制造并测量了两个样品过滤器。实验数据与预测结果吻合良好。