Abstract
This work presents new frequency-domain methods for the analysis and simulation of circuits based on a nonlinear resonator, with operation ranges delimited by turning points. Insightful analytical conditions fulfilled at these turning points are derived, which will enable an identification of the effect of each circuit element on their location in the solution curve. The cusp points, or co-dimension two bifurcations at which two turning points merge into one, thus delimiting the multivalued intervals, are directly calculated for the first time to our knowledge. In addition, a new numerical method, compatible with the use of commercial harmonic balance, is presented for the straightforward tracing of the multivalued solution curves, together with a new procedure to determine the locus of turning points in terms of any two analysis parameters. This relies on the use of a new mathematical condition to obtain a surface of turning points in the space defined by the two parameters and the input power. The methods have been applied to a wireless power-transfer system based on a recently proposed configuration, obtaining very good agreement with the experimental results.
Highlights
R ECENTLY, interesting applications of nonlinear resonators to improve the behavior of energy harvesters and wireless power-transfer systems have been proposed [1]–[7]
The oscillation frequency depends on the amplitude [8], [9], and when excited with a forcing signal, there is a folding of the resonance curve that typically exhibits two turning points (TPs), or infinite-slope points
A detailed frequency-domain analysis of circuits based on a nonlinear resonator has been presented, illustrated through its application to two configurations recently proposed in the literature for energy harvesting and wireless power transfer
Summary
R ECENTLY, interesting applications of nonlinear resonators to improve the behavior of energy harvesters and wireless power-transfer systems have been proposed [1]–[7]. A new analysis method is presented, which allows obtaining the solution curves and turning points loci in a single simulation with the aid of some equations introduced in commercial HB. The method is extended to obtain, for the first time to our knowledge, the locus of turning points versus any pair of arbitrary parameters without optimization/continuation procedures This relies on the use of a new mathematical condition to obtain a surface of turning points in the space defined by the two analysis parameters η1, η2 and the input power Pin. the intersection of this surface with planes defined by distinct Pin values will provide the corresponding turning point loci in terms of η1 and η2.
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