Dual-narrowband bandpass filter with exact equations of scattering parameters

In this article, a new microstrip dual-narrowband bandpass filter employing parallel-coupled transmission lines and open stubs is presented, investigated, and fabricated. The proposed dual-narrowband bandpass filter is analyzed and its exact scattering parameters are calculated, simulated, and measured. So, calculated scattering parameters offer a deep inside view of the performance of the proposed filter. To analyze the proposed filter, the even- and odd-mode excitation are utilized. The input impedance under even- and odd-mode excitation are achieved by transmission line theory and inserted in the scattering parameter equations. Finally, the accurate scattering parameters are derived and compared with simulation results. Simulation results prove the theoretical results. Then, an optimized proposed filter is fabricated and matched with simulation results. The center frequency bands are 4.5 and 6.8 GHz. The optimized filter occupies 0.12 $ \times $ 0.096$\lambda _g^2$, which is small. Its fractional bandwidth of the first and second passband are 1.5 and 2.5%, respectively. Furthermore, wide and strong rejection levels in the stopbands are offered. The structure of the proposed filter provides many freedoms to design. There is an agreement between experimental and simulation results.