Chapter 10 - Survey on Two-Port Network-Based Fractional-Order Oscillators

Abstract

This chapter merges the fractional calculus and two-port networks in oscillator design. The fractional-order elements α and β add extra degrees of freedom that increase the design flexibility and frequency band while providing control over the phase difference. A prototype of the fractional-order two-port network oscillators is introduced. It consists of a general two-port network and three impedances distributed as input, output, and a feedback impedance. Three different two-port network classifications are obtained according to the ground location. This chapter focuses on one of these classifications from which two derived prototypes can be extracted. The general analytical formulas of the oscillation frequency and condition as well as the phase difference are derived in terms of the transmission matrix parameter of a general two-port network. Different active building blocks are used to serve as a two-port network. Numerical, Spice simulations, and experimental results are given to validate the presented analysis.