Multiple-rings filter with dissociated transmission zeros

Cascaded-rings bandpass filter is presented with dissociated transmission zeros. While the position of the transmission zeros is largely depending on the coupled-line sections of the rings, less coupling level is required in some of the coupled-line sections, and the design will not be limited to some fixed values of impedance throughout the topology. This improves the degree of the liberty in designing cascaded rings filter for high selectivity applications. Three examples that employ three, four and five quarter-wavelength side-coupled ring resonator basic cells are given, where each of them leads to bandpass response of 8
^th
, 11
^th
and 14
^th
order, respectively. While very sharp bandpass response can be achieved, the different positions of transmission zeros also help in improving the out-of-band rejection. An example of realization is presented for a bandpass filter with three rings, on FR4 substrate.