In this paper, we propose an optimization-driven framework for the design of wideband multi-section branch-lines that exhibit varying branch impedances. Even-odd mode analysis is performed utilizing transmission lines theory to derive the expressions of the S-parameters. Then, an error function is developed to control the electrical characteristics of the branch-lines considering predefined physical constraints including impedance matching and machining tolerance. By modifying the error function, cascaded branch-lines can operate as crossovers or couplers. To validate the proposed concept, wideband crossover and coupler prototypes are designed, simulated and measured. Simulations and measurements agree well and show improved fractional bandwidths. Moreover, odd harmonics are suppressed in the proposed designs due to enforcing the desired electrical characteristics over a given frequency band.

在本文中，我们提出了一种优化驱动的框架，用于设计具有变化的分支阻抗的宽带多节分支线。利用传输线理论进行奇偶模分析，得出S的表达式参数。然后，考虑预定义的物理约束（包括阻抗匹配和加工公差），开发一个误差函数来控制支线的电气特性。通过修改误差函数，级联的分支线可以用作分频器或耦合器。为了验证所提出的概念，设计，仿真和测量了宽带分频器和耦合器原型。仿真和测量结果吻合良好，并显示出改进的分数带宽。此外，由于在给定的频带上加强了所需的电气特性，因此在拟议的设计中抑制了奇次谐波。