RC models of a constant phase element
SUMMARY The paper describes models of a constant‐phase element consisting of passive R and C components. The models offer any input impedance argument (phase) between −90° and 0° over a selectable frequency band covering several decades. The design procedure makes it possible to choose values of ave...
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| Published in | International journal of circuit theory and applications Vol. 41; no. 1; pp. 59 - 67 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
01.01.2013
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0098-9886 1097-007X |
| DOI | 10.1002/cta.785 |
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| Abstract | SUMMARY
The paper describes models of a constant‐phase element consisting of passive R and C components. The models offer any input impedance argument (phase) between −90° and 0° over a selectable frequency band covering several decades. The design procedure makes it possible to choose values of average phase, phase ripple, frequency bandwidth, and total number of R and C elements. The model can cover three frequency decades with as few as five resistors and five capacitors. The models can be used for practical realization of fractional analog differentiators and integrators, fractional oscillators, chaotic networks or for analog simulation of fractional control systems. Copyright © 2011 John Wiley & Sons, Ltd.
The described models consisting of several resistors and capacitors approximate an ideal constant phase element. Their input impedance phase is reasonably constant over several decades of frequency and can have any value between −90° and 0°. The models are much simpler and at the same time much more accurate than any other models of constant phase elements described so far. |
|---|---|
| AbstractList | The paper describes models of a constant‐phase element consisting of passive R and C components. The models offer any input impedance argument (phase) between −90
°
and 0° over a selectable frequency band covering several decades. The design procedure makes it possible to choose values of average phase, phase ripple, frequency bandwidth, and total number of R and C elements. The model can cover three frequency decades with as few as five resistors and five capacitors. The models can be used for practical realization of fractional analog differentiators and integrators, fractional oscillators, chaotic networks or for analog simulation of fractional control systems. Copyright © 2011 John Wiley & Sons, Ltd. SUMMARY The paper describes models of a constant-phase element consisting of passive R and C components. The models offer any input impedance argument (phase) between -90 degree and 0 degree over a selectable frequency band covering several decades. The design procedure makes it possible to choose values of average phase, phase ripple, frequency bandwidth, and total number of R and C elements. The model can cover three frequency decades with as few as five resistors and five capacitors. The models can be used for practical realization of fractional analog differentiators and integrators, fractional oscillators, chaotic networks or for analog simulation of fractional control systems. Copyright [copy 2011 John Wiley & Sons, Ltd. The described models consisting of several resistors and capacitors approximate an ideal constant phase element. Their input impedance phase is reasonably constant over several decades of frequency and can have any value between -90 degree and 0 degree . The models are much simpler and at the same time much more accurate than any other models of constant phase elements described so far. SUMMARY The paper describes models of a constant-phase element consisting of passive R and C components. The models offer any input impedance argument (phase) between -90° and 0° over a selectable frequency band covering several decades. The design procedure makes it possible to choose values of average phase, phase ripple, frequency bandwidth, and total number of R and C elements. The model can cover three frequency decades with as few as five resistors and five capacitors. The models can be used for practical realization of fractional analog differentiators and integrators, fractional oscillators, chaotic networks or for analog simulation of fractional control systems. Copyright © 2011 John Wiley & Sons, Ltd. [PUBLICATION ABSTRACT] SUMMARY The paper describes models of a constant‐phase element consisting of passive R and C components. The models offer any input impedance argument (phase) between −90° and 0° over a selectable frequency band covering several decades. The design procedure makes it possible to choose values of average phase, phase ripple, frequency bandwidth, and total number of R and C elements. The model can cover three frequency decades with as few as five resistors and five capacitors. The models can be used for practical realization of fractional analog differentiators and integrators, fractional oscillators, chaotic networks or for analog simulation of fractional control systems. Copyright © 2011 John Wiley & Sons, Ltd. The described models consisting of several resistors and capacitors approximate an ideal constant phase element. Their input impedance phase is reasonably constant over several decades of frequency and can have any value between −90° and 0°. The models are much simpler and at the same time much more accurate than any other models of constant phase elements described so far. |
| Author | Valsa, Juraj Vlach, Jiri |
| Author_xml | – sequence: 1 givenname: Juraj surname: Valsa fullname: Valsa, Juraj email: valsa@feec.vutbr.cz organization: Institute of Theoretical and Experimental Electrical Engineering, Brno University of Technology, Kolejní 4, Brno, Czech Republic – sequence: 2 givenname: Jiri surname: Vlach fullname: Vlach, Jiri organization: University of Waterloo, Department of Electrical and Computer Engineering, 200 University Avenue, Ontario, Waterloo, Canada |
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| Cites_doi | 10.1155/2008/369421 10.1109/TCT.1964.1082270 10.1023/A:1016556604320 10.1109/5.4388 10.1002/cta.453 10.1109/TCSII.2009.2020944 10.1109/TCSII.2008.2002571 10.1109/TCSI.2008.918196 10.1109/TCSII.2006.879102 10.1142/3779 |
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| References_xml | – reference: Hilfer R (ed.). Fractional Calculus in Physics. World Scientific Publishing Co: Singapore, 2000. – reference: Petras I. Method for simulation of the fractional order chaotic system. Acta Montanistica Slovaca 2006; 11(4):273-277. – reference: Carlson GE, Haliah CA. Approximation of fractional capacitors (1/s)1/n by a regular Newton process. IEEE Trans. on Circuit Theory 1964; 11(2):210-213. – reference: Podlubny I, Petras I, Vinagre BM, Leary PO, Dorcak L. Analogue realizations of fractional-order controllers. Nonlinear Dynamics, Kluwer Academic Publishers 2002; 29:281-296. – reference: Wen X-J, Wu Z-M, Lu J-G: Stability analysis of a class of nonlinear fractional-order systems. IEEE Trans. Circuits Syst II: Express Briefs 2008; 55:1178-1182. – reference: Biswas K, Sen S, Dutta P. Realization of a constant phase element and its performance study in a differentiator circuit. IEEE Trans. Circuits Syst. II, Exp. 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| Snippet | SUMMARY
The paper describes models of a constant‐phase element consisting of passive R and C components. The models offer any input impedance argument (phase)... The paper describes models of a constant‐phase element consisting of passive R and C components. The models offer any input impedance argument (phase) between... SUMMARY The paper describes models of a constant-phase element consisting of passive R and C components. The models offer any input impedance argument (phase)... |
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| SubjectTerms | Capacitors constant phase element fractance fractional control system Input impedance Mathematical models nanotechnology Networks Oscillators Reproduction Resistors Ripples Warburg diffusion element |
| Title | RC models of a constant phase element |
| URI | https://api.istex.fr/ark:/67375/WNG-WS4JS3XK-C/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fcta.785 https://www.proquest.com/docview/1269137330 https://www.proquest.com/docview/1439784930 |
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