Geometrical structures and fundamental characteristics of microwave stepped-impedance resonators

λ_g/4-,λ_g/2-, and λ_g-type transmission-line stepped-impedance resonators (SIRs) have been proposed and various practical applications have been reported on the basis of the analysis related to each resonator. This paper standardizes these three types of SIRs and systematically summarizes their fundamental characteristics, such as resonance conditions, resonator length, spurious (higher order) responses, and equivalent circuits. Practical applications which employ features of three types of SIRs are investigated with demonstrations of specific structures. Original design formulas with respect to λ_g-type dual-mode resonators are analytically derived. Advanced SIR´s using composite material and multisteps are also introduced and their availability is discussed