论文标题
Curie-von Schweidler法律的起源和来自时变电容的分数电容器
Origin of the Curie-von Schweidler law and the fractional capacitor from time-varying capacitance
论文作者
论文摘要
大多数实用目的的介电介质都表现出记忆，并由世纪以来的居里 - 冯·施韦德勒（Curie-Von Schweidler Law）描述。有趣的是，Curie-von Schweidler定律是一个非常规电路组件背后的动机，称为分数电容器，由于其幂律属性，它广泛用于复杂介电介质的建模。不幸的是，Curie-Von Schweidler法的经验性质困扰着分数电容器的应用。在这里，我们从电阻器和具有线性时变电容的电容器的一系列组合中得出了Curie-Von Schweidler定律。这可能是其物理原理的第一个派生。但是，这需要修改经典费用 - 电容器的电压关系以解释时间变化的电容。使用适当的电路建模证明了经典电荷 - 电压关系及其随后的修改的限制。因此，Curie-Von Schweidler定律和分数电容器的参数获得了物理解释。电介质的DEBYE响应自然来自幂律响应在短时间的限制案例。通过将其与已发布的实验报告相匹配来验证获得的结果。
Most dielectrics of practical purpose exhibit memory and are described by the century-old Curie-von Schweidler law. Interestingly, the Curie-von Schweidler law is the motivation behind an unconventional circuit component called fractional capacitor which due to its power-law property is extensively used in the modeling of complex dielectric media. Unfortunately, the empirical nature of the Curie-von Schweidler law plagues the applications of the fractional capacitor. Here, we derive the Curie-von Schweidler law from a series combination of a resistor and a capacitor with a linear time-varying capacitance. This may possibly be its first derivation from physical principles. However, this required a modification of the classical charge--voltage relation of a capacitor to account for the time-varying capacitance. The limitation of the classical charge-voltage relation and its subsequent modification are justified using appropriate circuit modeling. Consequently, the parameters of the Curie-von Schweidler law and the fractional capacitor gain physical interpretation. The Debye response of dielectrics emerges naturally from the limiting case of the power-law response at short timescales. The obtained results are validated by matching them with the published experimental reports.
