Fractional RC and LC Electrical Circuits
In this paper we propose a fractional differential equation for the electrical RC and LC circuit in terms of the fractional time derivatives of the Caputo type. The order of the derivative being considered is 0 < γ ≤1. To keep the dimensionality of the physical parameters R, L, C the new parameter σ is introduced. This parameter characterizes the existence of fractional structures in the system. A relation between the fractional order time derivative γ and the new parameter σ is found. The numeric Laplace transform method was used for the simulation of the equations results. The results show that the fractional differential equations generalize the behavior of the charge, voltage and current depending of the values of γ. The classical cases are recovered by taking the limit when γ = 1. An analysis in the frequency domain of an RC circuit shows the application and use of fractional order differential equations.
| Main Authors: | , , , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Nacional Autónoma de México, Facultad de Ingeniería
2014
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| Online Access: | http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1405-77432014000200013 |
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| Summary: | In this paper we propose a fractional differential equation for the electrical RC and LC circuit in terms of the fractional time derivatives of the Caputo type. The order of the derivative being considered is 0 < γ ≤1. To keep the dimensionality of the physical parameters R, L, C the new parameter σ is introduced. This parameter characterizes the existence of fractional structures in the system. A relation between the fractional order time derivative γ and the new parameter σ is found. The numeric Laplace transform method was used for the simulation of the equations results. The results show that the fractional differential equations generalize the behavior of the charge, voltage and current depending of the values of γ. The classical cases are recovered by taking the limit when γ = 1. An analysis in the frequency domain of an RC circuit shows the application and use of fractional order differential equations. |
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