Frequency Derivatives of Eddy Current System Including Electric Scalar Potential

Frequency sensitivity analysis (FSA) is for evaluating the behavior of electromagnetic system as frequency variation. In this article, a higher order frequency sensitivity in linear eddy current system, which is expressed in terms of a magnetic vector potential A (MVP) and electrical scalar potential (ESP)
$\phi $
, is expressed in a variational form. The frequency sensitivity is derived in an analytical form by using the continuum approach not the discretized one. The frequency sensitivity is obtained up to the higher ones by repeating differentiation with respect to the angular frequency. The higher order frequency sensitivities are sequentially derived from the lower order one. Since these frequency sensitivities are expressed in an analytical closed form, their numerical values can be easily calculated using commercial finite element programs. Two numerical examples are presented to demonstrate validity and applicability of the FSA.