Fractional Order Modeling of Large Three-Dimensional RC Networks

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 cap...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on circuits and systems. I, Regular papers Regular papers, 2013-03, Vol.60 (3), p.624-637
Main Authors: Galvao, R. K. H., Hadjiloucas, S., Kienitz, K. H., Paiva, H. M., Afonso, R. J. M.
Format: Article
Language:English
Subjects:
Admittance
Analog circuit simulation
Approximation methods
Capacitors
circuit theory
Electrical impedance
fractional order system identification
Impedance
Mathematical model
Mathematical models
Networks
RC circuits
Reinforced concrete
Representations
Resistors
Studies
Three dimensional models
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2012.2209733