Injection-Locking of Nonharmonic Oscillators

  • Fei Yuan


This chapter investigates how Barkhausen criteria can be used to analyze ring oscillators. The modeling of harmonic oscillators and relaxation oscillators is explored with a special attention to the distinct nonlinear characteristics of relaxation oscillators. The representation of a nonharmonic oscillator with a set of harmonic oscillators is presented. The fundamentals of Volterra series are reviewed. The concept of the Volterra elements of a nonlinear element and the Volterra circuits of a nonlinear circuit are introduced and the process of how to obtain them is exemplified. The modeling of voltage comparators is studied. The Volterra circuits of an injection-locked nonharmonic oscillator are derived and the characteristics of the Volterra circuits are investigated. The chapter explores how the Volterra circuit approach can be used to analyze the dual-comparator relaxation oscillator under the injection of a pair of differential currents and how the high-order Volterra circuits of the oscillator contribute to the effective injection signals of the first-order Volterra circuit of the oscillator. Finally, the lock range of the dual-comparator relaxation oscillator is investigated.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Fei Yuan
    • 1
  1. 1.Electrical and Computer EngineeringRyerson UniversityTorontoCanada

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