The N+2 order coupling matrix synthesis can start from the transversal coupling matrix for the lossless case [6] and lossy case [7], which can be obtained directly from the poles and residues of.
A novel coupling matrix synthesis method for dual‐band bandpass filter is presented in this article. The output admittance poles and zeros of the single‐band filter prototype are firstly obtained and then transformed into dual‐band prototype.

Then the coupling matrix with predefined topology is optimized according to these poles and zeroes directly. This method can be achieved with no need to construct the characteristic function of dual‐band filter and reconfigure the coupling matrix. Symmetric and asymmetric dual‐band bandpass filter coupling matrix synthesis has been carried out to illustrate and validate this method. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:603–606, 2016.
SynMatrix360 is the world's first cloud based tool for microwave filter design. The first version named as 'Gravity' mainly includes filter synthesis, Peak power handling analysis, computer aided tuning and convenient tools such as Monte-Carlo analysis and coupling matrix optimization. The software provides a fast and accurate overview of filter performances versus filter input parameters, such as the filter order, return loss, and positions of transmission zeros, to facilitate and standardize engineering and development work. In order to offer the maximum design flexibility and convenience, SynMatrix360 allow user to define the arbitrary topology with numbers of real, imaginary and complex transmission zeros of the physical filter by simply defining the topology matrix. It can support more than 10 types of popular and practical topologies covering from academic research to industrial applications such as: Cascaded Trisection (CT), Cascaded Quadruplet (CQ), Cascade Quartets, Folded Configuration, Cul-de-sac Configuration, Arrow Configuration, Box Section, Hybrid Configuration etc.