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Fractional order modeling of large three-dimensional RC networks

Galvão, R. K. H., Hadjiloucas, S., Kienitz, K. H., Paiva, H. M. and Afonso, R. J. M. (2012) Fractional order modeling of large three-dimensional RC networks. IEEE Transactions on Circuits & Systems I: regular papers, 60 (3). pp. 624-637. ISSN 1549-8328

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To link to this item DOI: 10.1109/TCSI.2012.2209733


An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Item Type:Article
Divisions:Life Sciences > School of Biological Sciences > Department of Bio-Engineering
ID Code:31538
Uncontrolled Keywords:Analog circuit simulation, circuit theory, fractional order system identification, RC circuits.

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