Compact tri-band bandpass filter with controllable frequencies based on a novel quarter wavelength tri-section stepped impedance resonator

A compact microstrip line tri-band bandpass filter (BPF) with controllable working frequency bands is proposed in this paper. The proposed BPF is composed of two novel quarter wavelength (lambda(g)/4) tri-section stepped impedance resonators (TSSIRs). Meanwhile, for the first time, the electrical lengths for the first three modes of this proposed lambda(g)/4 TSSIR are mathematically' derived to determine the working frequency ratio. By replacing those conventional lambda(g)/4 uniform impedance resonators employed in an optimum BPF with fixed frequency ratio, the three working frequency bands in a BPF can be flexibly adjusted based on design specifications. The size of this lambda(g)/4 TSSIR is also smaller than existed lambda(g)/2 TSSIR, leading to a smaller size of the overall design. In order to verify this design approach, a tri-band bandpass filter with passbands centered at 1.0/3.5/6.0 GHz is designed, fabricated and measured. The minimum insertion loss of each passband is 0.07/0.52/1.14 dB, while the occupied size of the filter is only 31x21.5 mm(2) (0.17 lambda(g)x12 lambda(g)) .A good symmetry for each passband is also observed in this prototype.