Effect of boundary on controlled memristor-based oscillator

Recently, the applications of memristors have spread into many fields and especially in the circuit theory. Many models have been proposed for the HP-memristor based on the window functions. In this paper, we introduce a complete mathematical analysis of the controlled reactance-less oscillator for two different window functions of Joglekar's model (linear and nonlinear dopant drift) to discuss the effect of changing the window function on the oscillator's behavior. The generalized necessary and sufficient conditions based on the circuit elements and control voltages for both the linear and nonlinear models are introduced. Moreover, closed form expressions for the oscillation frequency and duty cycle are derived for these models and verified using PSPICE simulations showing an excellent matching. Finally a comparison between the linear and nonlinear models which shows their effect on the oscillation frequency and conditions of oscillation is introduced.

[1]  Mohammed Affan Zidan,et al.  HP Memristor mathematical model for periodic signals and DC , 2010, 2010 53rd IEEE International Midwest Symposium on Circuits and Systems.

[2]  Christofer Toumazou,et al.  Two centuries of memristors. , 2012, Nature materials.

[3]  P. Vontobel,et al.  Writing to and reading from a nano-scale crossbar memory based on memristors , 2009, Nanotechnology.

[4]  Earl E. Swartzlander,et al.  Memristor-based arithmetic , 2010, 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers.

[5]  Stephen J. Wolf,et al.  The elusive memristor: properties of basic electrical circuits , 2008, 0807.3994.

[6]  Khaled N. Salama,et al.  Memristor-based reactance-less oscillator , 2011 .

[7]  A. G. RADWAN,et al.  ON THE FRACTIONAL-ORDER MEMRISTOR MODEL , 2013 .

[8]  Uri C. Weiser,et al.  TEAM: ThrEshold Adaptive Memristor Model , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Kyungmin Kim,et al.  Memristor Applications for Programmable Analog ICs , 2011, IEEE Transactions on Nanotechnology.

[10]  Klaus Witrisal,et al.  A memristor-based multicarrier UWB receiver , 2009, 2009 IEEE International Conference on Ultra-Wideband.

[11]  Dalibor Biolek,et al.  SPICE Model of Memristor with Nonlinear Dopant Drift , 2009 .

[12]  L.O. Chua,et al.  Memristive devices and systems , 1976, Proceedings of the IEEE.

[13]  T. A. Wey,et al.  Amplitude modulator circuit featuring TiO2 memristor with linear dopant drift , 2009 .

[14]  Khaled N. Salama,et al.  Generalized model for Memristor-based Wien family oscillators , 2011, Microelectron. J..

[15]  Ahmed Gomaa Radwan,et al.  Stability and non-standard finite difference method of the generalized Chua's circuit , 2011, Comput. Math. Appl..

[16]  Mohammed Affan Zidan,et al.  On the mathematical modeling of memristors , 2010, 2010 International Conference on Microelectronics.

[17]  K.N. Salama,et al.  Non linear dynamics of memristor based 3rd order oscillatory system , 2012, Microelectron. J..

[18]  L. Chua.  Memristor-The missing circuit element , 1971 .