In a linear eddy current system excited by a current source, a high-order frequency sensitivity is derived in variational formulation instead of as a discretized state equation. An analytic sensitivity formulation of order ${n}$ is obtained by sequentially differentiating the variational eddy current system with respect to angular frequency. The high-order frequency sensitivity is implemented through a commercial finite element method. A frequency sensitivity analysis conducted based on two numerical examples verifies the results.

中文翻译：

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变涡流系统中的高阶频率导数

在由电流源激励的线性涡流系统中，高阶频率灵敏度是以变分形式导出的，而不是离散状态方程。阶的解析灵敏度公式 $ {n} $ 通过依次相对于角频率微分变涡流系统来获得Δω。高阶频率灵敏度是通过商业有限元方法实现的。根据两个数值示例进行的频率灵敏度分析验证了结果。