Symbolic Calculation Of Oscillator Periodic Main Root-locus And Its Application In Circuit Optimization

Linearizing an oscillator around its periodic steady state (PSS) wouldgenerate a small-signal model with time-varying parameter value. Thetime-varying root-locus of this model can be plotted on the complex plane.This information explains how oscillator works during its PSS, which is ofbenefit to designers.Currently, there’s a numerical method to generate this root-locus, yetthe calculation process is repeated and inefficient. Also, this methodprovides limited information.In this paper, a symbolic main root-locus calculation method isproposed, which utilizes the advantage of both symbolic method andpolynomial root calculation methods to advance the calculation efficiency.Sensitivity information can be generated with ease with this method, whichcan provide further information to help with design.To lend more flexibility to symbolic method for comparison of similarcircuit topologies, a methodology to insert and delete devices withoutreconstruction of the data structure is proposed. Applying the method tostructural comparison of different circuits would bring about moreefficiency.