Abstract

A well-founded class of dependences, based on the theory of nonlinear electrical circuits, is proposed for the formal approximation of static characteristics for various electronic devices. The dependences are simple fractionally linear and fractionally quadratic expressions (a particular case of rational functions), convenient for engineering calculations. However, these expressions represent projective transformations in the sense of projective geometry. The projective transformations preserve an invariant in the form of a cross ratio (double proportion) of four samples of variable mode parameters (currents, resistances, voltage). The mutual reduction of measurement errors is an attractive practice property of the cross ratio. This leads to the direct formulas for recalculating the mode parameters that have group properties. An example of the approximation of the magnetization characteristic and relative magnetic permeability of the Nickel Steel Carpenter 49 is considered; invariants for the magnetic flux density and absolute permeability are established. The results are applicable in various fields of electronics and spintronics.

中文翻译：

---

镍钢木匠49磁化曲线的分数二次逼近和不变性

摘要

提出了一种基于非线性电路理论的有充分根据的依赖关系，用于形式上近似各种电子设备的静态特性。依存关系是简单的分数线性和分数二次表达式（有理函数的特殊情况），便于工程计算。但是，这些表达式代表射影几何意义上的射影变换。投影变换将可变模式参数（电流，电阻，电压）的四个样本的交叉比（双比例）形式的不变量保存下来。相互减少测量误差是交叉比率的一种有吸引力的实践特性。这将导致直接公式重新计算具有组属性的模式参数。考虑镍钢木匠49的磁化特性和相对磁导率的近似示例；但是，不限于此。建立了磁通密度和绝对磁导率的不变量。该结果适用于电子和自旋电子学的各个领域。