Single-Band to Multiband Frequency Transformation for Multiband Filters

A method for the design of bandpass filters with multiple pass bands is presented. The key point of this method is a frequency map between single-band resonators and multiple-band networks formed by those resonators with additional resonators coupled to them. The mapping problem is a non-linear one and the mathematical treatment, based on mapping the cut-off frequencies, is not simple. However, the resulting method is quite straightforward: first, synthesize a single-band equivalent filter; then, couple to each resonator a set of as many resonators as pass bands minus one, being the sets identical between them. The method is illustrated by designing several microstrip prototypes with one to three bands. They consist of conventional parallel-coupled half-wavelength resonator filters with additional hairpin or meandered resonators.