Considerations on the operating point of a planar parametric transformer based on the Mathieu equation

A planar parametric transformer using a laminated Si-Fe core has been proposed by the authors. The stable or unstable states of a parametric oscillation are represented by the Mathieu equation. The Mathieu equations under no-load and load conditions are obtained in this paper. The relationships between the stable-unstable state of a parametric oscillation and the operating point of the transformer are also obtained. Moreover, the stability chart of Mathieu equation is estimated. The obtained results can be useful for the optimum design of a planar parametric transformer. MATLAB is used for the theoretical analysis.