Fractional‐order mutual inductance: analysis and design

Summary This paper introduces for the first time the generalized concept of the mutual inductance in the fractional-order domain where the symmetrical and unsymmetrical behaviors of the fractional-order mutual inductance are studied. To use the fractional mutual inductance in circuit design and simulation, an equivalent circuit is presented with its different conditions of operation. Also, simulations for the impedance matrix parameters of the fractional mutual inductance equivalent circuit using Advanced Design System and MATLAB are illustrated. The Advanced Design System and MATLAB simulations of the double-tuned filter based on the fractional mutual inductance are discussed. A great matching between the numerical analysis and the circuit simulation appears, which confirms the reliability of the concept of the fractional mutual inductance. Also, the analysis of the impedance matching using the fractional-order mutual inductance is introduced. Copyright © 2015 John Wiley & Sons, Ltd.

[1]  Kazuhiro Saito,et al.  Simulation of Power-Law Relaxations by Analog Circuits : Fractal Distribution of Relaxation Times and Non-integer Exponents , 1993 .

[2]  Lei He,et al.  An efficient inductance modeling for on-chip interconnects , 1999, Proceedings of the IEEE 1999 Custom Integrated Circuits Conference (Cat. No.99CH36327).

[3]  Khaled N. Salama,et al.  Passive and Active Elements Using Fractional ${\rm L}_{\beta} {\rm C}_{\alpha}$ Circuit , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  C. Pyo,et al.  Design of RFID tag antennas using an inductively coupled feed , 2005 .

[5]  Ali Hajimiri,et al.  Distributed active transformer-a new power-combining and impedance-transformation technique , 2002 .

[6]  Ahmed M. Soliman,et al.  General procedure for two integrator loops fractional order oscillators with controlled phase difference , 2013, 2013 25th International Conference on Microelectronics (ICM).

[7]  Ahmed S. Elwakil,et al.  First-Order Filters Generalized to the fractional Domain , 2008, J. Circuits Syst. Comput..

[8]  Debasmita Mondal,et al.  Design and performance study of phase‐locked loop using fractional‐order loop filter , 2015, Int. J. Circuit Theory Appl..

[9]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[10]  Costas Psychalinos,et al.  0.5‐V fractional‐order companding filters , 2015, Int. J. Circuit Theory Appl..

[11]  Saeid Abbasbandy,et al.  A comment on "Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations" , 2014, Commun. Nonlinear Sci. Numer. Simul..

[12]  Adel S. Sedra,et al.  Filter Theory and Design: Active and Passive , 1977 .

[13]  Les Thede,et al.  Practical Analog And Digital Filter Design , 2004 .

[14]  YangQuan Chen,et al.  ANALOGUE FRACTIONAL-ORDER GENERALIZED MEMRISTIVE DEVICES , 2009 .

[15]  Ahmed M. Soliman,et al.  Fractional order filter with two fractional elements of dependant orders , 2012, Microelectron. J..

[16]  Khaled N. Salama,et al.  The fractional-order modeling and synchronization of electrically coupled neuron systems , 2012, Comput. Math. Appl..

[17]  E. Sanchez-Sinencio,et al.  A GSM LNA using mutual-coupled degeneration , 2005, IEEE Microwave and Wireless Components Letters.

[18]  Khaled N. Salama,et al.  Passive and Active Elements Using Fractional Circuit , 2011 .

[19]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[20]  Ahmed S. Elwakil,et al.  Fractional-order sinusoidal oscillators: Design procedure and practical examples , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[21]  J.H. Sinsky,et al.  Design of an electronically tunable microwave impedance transformer , 1997, 1997 IEEE MTT-S International Microwave Symposium Digest.

[22]  G. Ablart,et al.  Influence of the electrical parameters on the input impedance of a fractal structure realised on silicon , 2005 .

[23]  Jan Terpak,et al.  On the mathematical properties of generalized fractional-order two-port networks using hybrid parameters , 2013, Proceedings of the 14th International Carpathian Control Conference (ICCC).

[24]  Khaled N. Salama,et al.  Microscale electrostatic fractional capacitors using reduced graphene oxide percolated polymer composites , 2013 .

[25]  A. Barrado,et al.  Transformer modeling for FRA techniques , 2002, IEEE/PES Transmission and Distribution Conference and Exhibition.

[26]  K. Biswas,et al.  Performance study of fractional order integrator using single-component fractional order element , 2011, IET Circuits Devices Syst..

[27]  S. Westerlund,et al.  Capacitor theory , 1994 .

[28]  Ahmed M. Soliman,et al.  CCII based KHN fractional order filter , 2013, 2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS).

[29]  B. T. Krishna,et al.  Active and Passive Realization of Fractance Device of Order 1/2 , 2008 .

[30]  David J. Perreault,et al.  Filters with inductance cancellation using printed circuit board transformers , 2003, IEEE 34th Annual Conference on Power Electronics Specialist, 2003. PESC '03..

[31]  Ahmed M. Soliman,et al.  CCII based fractional filters of different orders , 2013, Journal of advanced research.

[32]  I. Schäfer,et al.  Modelling of coils using fractional derivatives , 2006 .

[33]  K. Salama,et al.  Theory of Fractional Order Elements Based Impedance Matching Networks , 2011, IEEE Microwave and Wireless Components Letters.

[34]  Karabi Biswas,et al.  A constant phase element sensor for monitoring microbial growth , 2006 .

[35]  Pietro Andreani,et al.  Impact of mutual inductance and parasitic capacitance on the phase-error performance of CMOS quadrature VCOs , 2003, Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03..

[36]  B. T. Krishna.  Studies on fractional order differentiators and integrators: A survey , 2011, Signal Process..

[37]  A. Elwakil,et al.  Design equations for fractional-order sinusoidal oscillators: Four practical circuit examples , 2008 .

[38]  Ahmed M. Soliman,et al.  Fractional Order Butterworth Filter: Active and Passive Realizations , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[39]  Yoshiaki Hirano,et al.  Simulation of Fractal Immittance by Analog Circuits: An Approach to the Optimized Circuits , 1999 .

[40]  Ahmed S. Elwakil,et al.  Fractional Resonance-Based Filters , 2013 .

[41]  Muhammet Köksal,et al.  Realization of New Mutually Coupled Circuit Using CC-CBTAs , 2012, Circuits Syst. Signal Process..

[42]  Neeta Pandey,et al.  DVCCCTA-Based Implementation of Mutually Coupled Circuit , 2012 .

[43]  Yonghong Wu,et al.  The uniqueness of positive solution for a singular fractional differential system involving derivatives , 2013, Commun. Nonlinear Sci. Numer. Simul..

[44]  M. Nakagawa,et al.  Basic Characteristics of a Fractance Device , 1992 .

[45]  Yoshiaki Hirano,et al.  Frequency behavior of self-similar ladder circuits , 2002 .