Curie–von Schweidler law
The Curie–von Schweidler law refers to the response of dielectric material to the step input of a direct current (DC) voltage first observed by Jacques Curie[1][2] and Egon Ritter von Schweidler.[3]
Overview
According to this law, the current decays according to a power law:
where is the current at a given charging time, , and is the decay constant such that . Given that the dielectric has a finite conductance, the equation for current measured through a dielectric under a DC electrical field is:
where is a constant of proportionality and is the decay constant (i.e., ). This stands in contrast to the Debye formulation, which states that the current is proportional an exponential function with a time constant, , according to:
- .
The Curie–von Schweidler behavior has been observed in many instances such as those shown by Andrzej K. Jonscher[4] and Jameson et al.[5] It has been interpreted as a many-body problem by Jonscher, but can also be formulated as an infinite number of resistor-capacitor circuits. This comes from the fact that the power law can be expressed as:
where is the Gamma function. Effectively, this relationship shows the power law expression to be equivalent to an infinite weighted sum of Debye responses.
References
- Curie, Jaques (1889). "Recherches sur le pouvoir inducteur spécifique et sur la conductibilité des corps cristallisés". Annales de Chimie et de Physique. 17: 384–434.
- Curie, Jaques (1889). "Recherches sur la conductibilité des corps cristallisés". Annales de Chimie et de Physique. 18: 203–269.
- Schweidler, Egon Ritter von (1907). "Studien über die Anomalien im Verhalten der Dielektrika (Studies on the anomalous behaviour of dielectrics)". Annalen der Physik. 329 (14): 711–770. Bibcode:1907AnP...329..711S. doi:10.1002/andp.19073291407.
- Jonscher, Andrzej K. (1983), Dielectric Relaxation in Solids, Chelsea Dielectrics Press Limited, ISBN 978-0-9508711-0-3
- Jameson, N. Jordan; Azarian, Michael H.; Pecht, Michael (2017). Thermal Degradation of Polyimide Insulation and its Effect on Electromagnetic Coil Impedance. Proceedings of the Society for Machinery Failure Prevention Technology 2017 Annual Conference.