Authors' reply

Abstract

This is a reply to comments from Hu etal. regarding, of which there are three concerns. The first concern in the comments is a one-to-one mapping relationship between coupling paths in a transversal array network topology and coupling elements in a physical filter structure. In conclusion, it is not necessary to determine the order of parallel paths corresponding to physical structures, as shown. This is because resonators in parallel paths of a transversal array network topology represent eigenmode resonances appearing in coupled resonators. This physical understanding has already been presented in using an example of a direct-coupled waveguide filter. The viewpoint of the order in parallel paths may come from a conventional design method of direct-coupled resonator filters, where the one-to-one mapping relationships can be easily found because the filters are composed of physically separated resonators. On the other hand, multiple resonances of a multi-mode resonator cannot be divided into physical coupling elements. In such cases, the transversal array network topology is a powerful tool for multi-mode filter designs. Therefore, three multi-mode filters have been demonstrated as examples of applications of our proposed parameter-extraction technique. The second concern in the comments of Hu et al. is the treatment of stray couplings in the transversal array coupling network. The stray couplings such as undesired cross couplings need to be evaluated in conventional filter designs based on direct-coupled resonator filter synthesis theory in order to obtain a desired frequency response. In the transversal resonator array network, as pointed out in, such stray couplings are included into parallel paths of resonators. We think that this is one of the advantages of the transversal resonator array network since coupled-resonator filters may be designed without any decomposition of main and stray couplings. In the initial design step of a filter, a well-known design approach of coupled-resonator filters is useful for intuitive designs, but stray couplings are not taken into account in this design step. In the final design step, the introduction of a transversal coupling network may help the fine adjustments of structural parameters, because all couplings are considered in terms of eigenmodes. To verify this idea, further studies will be needed. A similar design methodology has already been provided. The third concern in the comments of Hu etal. is a reference-phase equation.