A Harmonic-Oscillator Design Methodology Based on Describing Functions

Doctoral thesis, 2006

Oscillators are present in most electronic equipment where they provide timing information, for example as sampling clocks in analog-to-digital converters or as radio carriers in wireless communications. To design an oscillator, we must have knowledge of the properties and the operation of oscillators. Since oscillators are inherently nonlinear and are subject to noise, we have a system that is difficult to analyze since the large wanted signal and the small unwanted signal interact. It is shown in this thesis that describing functions can be used to calculate not only the large-signal behavior, but also the small-signal behavior using the method of impulse sensitivity functions. Based on theoretical results from this method, a design methodology for harmonic oscillators is derived and analyzed. The design methodology aims at the design of harmonic oscillators fulfilling phase-noise requirements with minimized power consumption subject to constraints from the other requirements set by the specification and the technology used to implement the oscillator. The design methodology has been used to design oscillators meeting quite different specifications, both discrete and integrated implementations and with either inductors and capacitors or crystals as frequency-determining elements.