The modeling of coils with ferromagnetic cores is considered. An attempt is made at the application of fractional derivatives because of the success in the modeling of real phenomena in various other fields. Three coils with ferromagnetic cores have been selected for the analysis. In order to obtain a basis for the study, measurements have been taken on a specially designed setup including an arbitrary function generator and a data acquisition device. The measurement process has been controlled by an original algorithm written in C#. The studied model has been considered in several varieties (various numbers of fractional coil and capacitor branches) in a ladder-like structure. The estimation process has been performed in an original program written in C#, applying the COBYLA method for constrained optimization. The modeling and simulation results have been compared through their frequency characteristics. A more critical approach has also been applied, where the measurements and simulations are compared for both a non-sinusoidal waveform and a step function on the source output.

考虑了具有铁磁芯的线圈的建模。由于在其他各个领域对真实现象进行建模的成功，因此尝试了分数导数的应用。选择了三个带有铁磁芯的线圈进行分析。为了获得研究的基础，已对经过特殊设计的设置进行了测量，包括任意函数发生器和数据采集设备。测量过程已由用C＃编写的原始算法控制。所研究的模型已被考虑为梯形结构中的多种类型（分数线圈和电容器分支的数量不一）。估计过程已在用C＃编写的原始程序中执行，将COBYLA方法应用于约束优化。通过建模和仿真结果的频率特性进行了比较。还应用了一种更严格的方法，在该方法中，比较了非正弦波形和源输出上的阶跃函数的测量和仿真。