Synthesis of filters with stub-loaded multiple-mode resonators

Exact synthesis of compact and wide-band filters with stub-loaded multiple-mode resonators is investigated in this letter. The multi-mode behavior and characteristics of the proposed filter structure are studied by conventional natural modes analysis. To develop the complete synthesis procedure, a bandpass prototype in the $S$-plane is used for good spurious suppression and size reduction. Approximation of the driving point impedance then proceeds, with the help of transformed variable. Network elements are then extracted by using Richards' theorem. The method is demonstrated by a design example of a third-order bandpass filter. Although six elements are used in this design, the total length is only one third of the wavelength at its center frequency. The experiment results justify the proposed procedure.