Lumped and Line Resonators

This chapter presents the basic characteristics of lumped and line resonators. The physical dimensions of a resonator are expressed in terms of the wavelength, corresponding to the resonance frequency. The resonating structures, from the dimension point of view, are grouped into the following four categories: zero-dimensional resonator, one-dimensional resonator, two-dimensional resonator, and three-dimensional resonator. The series and parallel resonant circuits are complementary to each other and they are treated identically. The chapter discusses the one-port, two-port, and reaction-type resonators. It emphasizes on three fundamental characteristics of a practical resonator – resonance frequency, unloaded Q-factor, and coupling coefficient. The transmission line resonators are basic building blocks of the RF, microwave, and mm-wave circuits, as the lumped element-based resonators are normally not suitable for the frequency above 3 GHz. The chapter also presents a complete modal description of the λg/2 line resonators.