Resonators

Abstract

RESONATORSResonators are common and important components in radio frequency integrated circuits (RFICs). They are used in various circuits such as oscillators and filters. There are, in principle, two types of resonators: lumped-element and distributed resonators. In general, lumped-element resonators have a smaller size, but lower operating frequency and quality factor (Q) as compared to distributed resonators, which are made up of transmission lines or, in general, waveguide structures. 1 Advances in complementary metal oxide silicon (CMOS) technologies have made feasible good lumped-element resonators for RFICs. The compactness, particularly, makes lumped-element resonators popular in RFICs operating in the microwave regime. Lumped-element resonators also make their way into the millimeter-wave region. On the other hand, distributed resonators are attractive for RFIC design at millimeter-wave frequencies, particularly in the high millimeter-wave end, where lumped-element resonators either are not feasible or have lower quality than their distributed counterparts in current CMOS processes. In this chapter, we will present the analysis and design of both lumped-element and distributed resonators that can be implemented in the CMOS processes. FUNDAMENTALS OF RESONATORSResonators or resonant circuits, as the name implies, are used in principle to store the energy of signals. As signals contain both electric and magnetic energies, a resonator is electrically represented by a combination of an inductor and a capacitor (for ideal resonators) together with a resistor (for nonideal resonators), which account for the magnetic energy, electric energy, and loss in the resonator, respectively. A resonator is also sometimes called "tank circuit" in oscillators. A resonator type is dictated by its equivalent electrical representation as series or parallel resonator. As such, a resonator -whether lumped, distributed, or a combination of lumped and distributed structures -may be classified as a series or parallel resonator depending on its electrical equivalent circuit -not the actual constituent elements themselves or the resonator's configuration. Also, a general circuit consisting of multiple inductors, capacitors, and distributed elements may behave as a parallel or series resonator at a certain frequency depending on its equivalent-circuit representation at 1 Transmission lines are basically one class of waveguides or wave-guiding structures.Radio-Frequency Integrated-Circuit Engineering, First Edition. Cam Nguyen.