Direct design method for wideband quadruplet and higher-order bandpass filters with a pair of transmission zeros based on explicit design formulas

This paper presents a direct design approach and explicit design formulas for a wideband quadruplet bandpass filter with a pair of transmission zeros. A filter can be designed based on a filter schematic composed of only transmission lines and a short-circuited coupled-line section. The electrical length of all lines including the coupled-line section is 90 degrees ${}<^>{\circ}$. The impedances of all lines can be calculated by explicit design formulas given in terms of the normalised coupling values in a coupling matrix of a quadruplet filter, which differentiates this work from existing design approaches. A fourth-order filter example is illustrated for demonstrating the practicality of using the presented structure and design formulas. This paper also discusses the expansion of the presented direct design approach for higher-order filter designs.