This paper proposes a methodology for numerically synthesizing element values of coupled resonator filters. These element values are compatible in retrieving coupling matrix of a cross-coupled quadruplet structure (also known as the folded structure). Differed from direct synthesis by matrix rotation, numerical solution has been adopted here to its equivalent coupling model. For varied specified return loss, numerical solutions of these element values have been derived and their accuracy is verified with their analytical counterparts to be extended for stringent design requirement. In addition, multiple sets of data are tabulated and categorized for efficient filter synthesis design under different specified pass-band return loss. In the end, an example quadruplet filter is designed, fabricated and measured for validation of the presented synthesis design methodology.
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