In this article, we provide exact closed-form expressions for three trap exchanges that are useful in transforming LC ladder networks. Trap exchanges are equivalency transforms that provide designers with alternate ladder realizations without requiring network re-synthesis. The novel solution methods employing Norton transformers and in one case a Colin equivalency are fully explained and developed. Alternate methods are also suggested. We note the given expressions fill a longstanding gap in the otherwise rich network transformation literature. The features and place of transformations in filter design is recounted along with the history of trap exchange literature. A simulation example of the most difficult case is provided as an affirmation of the expressions. The exchanges reported here were selected for their usefulness in manipulating minimum inductor band-pass filters, thus brief notes regarding the class and application are also provided. We note that future investigators may increase the catalog of trap exchanges by using the given methods as templates. Finally, we note that trap exchange capability is appropriate for incorporation into advanced filter design software.

中文翻译：

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LC 梯形网络的无合成陷阱交换


在本文中，我们为三个陷阱交换提供了精确的封闭式表达式，这对于转换 LC 梯形网络非常有用。陷阱交换是等价变换，为设计人员提供替代的梯形实现，而不需要重新综合网络。充分解释和发展了采用诺顿变压器和在一种情况下科林等价的新颖解决方法。还建议使用替代方法。我们注意到给定的表达式填补了丰富的网络转换文献中长期存在的空白。过滤器设计中转变的特征和位置与陷阱交换文献的历史一起被叙述。提供了最困难情况的模拟示例作为对表达式的肯定。选择此处报告的交流是因为它们在操作最小电感器带通滤波器方面非常有用，因此还提供了有关该类别和应用的简要说明。我们注意到，未来的研究人员可能会使用给定的方法作为模板来增加陷阱交换的目录。最后，我们注意到陷阱交换功能适合合并到先进的滤波器设计软件中。