Equivalent circuit analysis of square-loop-resonator BPF with cross-shaped I/O coupling for X-band frequency application

The equivalent circuit of square-loop-resonator (SLR) bandpass filter (BPF) with cross-shaped I/O coupling is investigated to be analyzed and compared with the 3D electromagnetics (EM) simulator result. The proposed SLR BPF is designed for X-band frequency application with the center frequency of 9GHz and the -3dB fractional bandwidth larger than 3%. The analysis method is carried out by separating the proposed SLR BPF into few parts and then translating each part into RLC circuit to build all filter structures. From the analysis result, the proposed equivalent circuit of SLR BPF has the -3dB working bandwidth of 330MHz with the center frequency of 9GHz where this is slightly narrower than the result of 3D EM simulator. In addition, although the equivalent circuit of SLR BPF has a large number of lumped elements, however it is beneficial in obtaining high accuracy result of the filter characteristic which is useful for X-band frequency application.