Can anyone explain how we can analytically solve the coupling matrix. Any good calculating tools for solving the coupling matrix, specifically useful for microwave Filters? Realize the coupling matrix using computer software or empirical methods. More video tutorials on filter synthesis. A demonstration of advanced filter synthesis concepts that can be applied to your future designs to meet the demand for stringent requirements. Couplings Designer makes it easy.

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This app can be used for synthesis of generalized Chebyshev bandpass filter. It has fully graphical user interface for user-friendly operation. The user can choose from a variety of optimizer and also choose coupling value boundaries for customized filter synthesis. This app generates the required coupling matrix for the user supplied specifications and coupling topology. It also shows a comparison between the S-parameters generated from specification and those from the optimized coupling matrix which match well. Also group delay of the synthesized filter can be observed.
How to use?
1. Install the app in MATLAB.
2. Graphically create the topology matrix (where node 1 represents Source and the last node represents Load and rest of the nodes are considered as resonators with resonator numbers 1 less than those in the graph e.g. node 3 is resonator 2 etc.). Close the graph window (this is must for further execution of the program to go on). Draw edges between nodes (source, resonators or load) according to the desired topology. Please note, For coupling matrix containing non-zero diagonal elements (Mii ~=0) the corresponding i th node should have self loop on the graph. Please select Draw Edge option and click on any vertex for the same.
3. The coupling matrix synthesis code is written for generalized Chebyshev bandpass filter synthesis. Run the main file. The actual coupling topology will pop up. Input all the required data. Choose the optimizer and chose gradient option yes/no. Set possible upper and lower bound on coupling value for optimization. Input span of frequencies after it is prompted.

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4. The optimized coupling matrix can be seen from the figure. The coupling matrix is also saved in variable 'M' in workspace. The responses of filtering function, the synthesized filter and group delay are also plotted.

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Reference:
S. Amari, U. Rosenberg and J. Bornemann, 'Adaptive synthesis and design of resonator filters with source/load-multiresonator coupling,' in IEEE Transactions on Microwave Theory and Techniques, vol. 50, no. 8, pp. 1969-1978, Aug 2002.
doi: 10.1109/TMTT.2002.801348