Very thin multi-layered coplanar BPF with constant foot print

A new structure of BPF is proposed. In the case that each resonator is placed close and faced with broad sides, the coupling between resonators necessarily become strong. However, in the proposed filter structure, it is possible to design a narrow band BPF to say nothing of a wide band BPF. In addition, it has the advantage to be fabricated in the constant footprint. And then, a new parameter external k is proposed to substitute the external Q in the filter design. It helps to obtain the physically more understandable image that the coupling between the resonators should be proportional to that between the resonator and the external line for matching. In the last, a new method of spurious suppression is shown to improve the out-of-band characteristic. Then, the validity of the method is checked by applying it to the proposed filter.