A compact microstrip second-order lossy bandpass filter with improved simplified composite right-/left-handed zeroth-order resonator

A novel compact microstrip second-order lossy bandpass filter (BPF) based on an improved simplified composite right-/left-handed zeroth-order resonator (ISZOR) is presented in this paper. The microstrip ISZOR (MISZOR) features miniature topology and ample adjustable physical parameters accompanied by its easily controllable zeroth-order base mode and first harmonic. Its layout can be quickly generated by applying the implicit space mapping technique. By virtue of the lossy coupling matrix synthesis method, the finite unloaded quality factor of the MISZOR can be taken into account in advance to foretell the insertion loss level. A new definition of the external quality factor as well as its full-wave extraction method is introduced, enabling the targetted second-order lossy BPF to be directly implemented as in the classical lossless design, despite the existence of the parallel resistor loaded nonresonant node at each terminal. A succinct inductive coupled microstrip corner is conceived to achieve the relatively strong terminal coupling strength. The exemplified lossy BPF centers at 3.1 GHz with a fractional bandwidth of 5%, which is automatically optimized with the Nelder-Mead simplex algorithm. A prototype measurement is carried out, and good agreement is achieved with simulation, testifying the proposed design concept.