Determining resonant frequencies of single dual-mode resonator and its application

Determining resonant frequency was proposed for the bandpass filter using single dual-mode resonator. Because a coupling coefficient implied the information which is the position of poles for the bandpass filter, the resonant frequencies (ƒ
e
, ƒ
m
) were obtained through the equivalent circuit analysis and the simple calculation. Furthermore, the frequencies were determined to even- and odd-mode resonant frequency proper for the position of the transmission zero (at a lower or upper stopband). To verify the theory, the filter example was demonstrated and its measured result was suitable for the required frequency response. Therefore, we expect that the theory will be used to design the bandpass filter using the single dual-mode resonator.