Synthesis-Free Trap Exchanges for LC Ladder Networks

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.