A memristor-based third-order oscillator: beyond oscillation
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This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.
KeywordsMemristor Linear time variant Oscillator
The three basic circuit elements have recently encountered the missing fourth element—‘memristor’, relating between the flux-linkage (φ) and the charge (q), when introduced experimentally by HP labs (Strukov et al. 2008) using a thin semiconductor film (TiO2) sandwiched between two metal contacts, after the visionary hypothesis given by Chua (1971). According to Strukov et al. (2008) the memristive property naturally appears in nanoscale devices and has the potential to replace conventional transistors in memory applications (Snider 2007; Yan et al. 2010; Manem et al. 2010), as well as in cross bar switching applications (Wang et al. 2010; Young et al. 2009).
Parametric oscillator is a well known phenomenon in linear time variant system in control theory which occurs only with externally applied periodical forces as in the case of a child on a swing or quartz oscillator (Komine et al. 2003). Such oscillation does not occur automatically, rather external oscillating inputs are required to pump the system. Previously, the oscillating nature of memristor was analytically modeled under sinusoidal input (Radwan et al. 2010a, b). In our recent work (Talukdar et al. 2010, 2011), the nonlinear dynamics of memristor having oscillating resistance and dynamic poles have been presented for memristor-based Wien oscillator, which requires no external input. This letter tries to generalize those concepts in third-order system with a new insight into realizing parametric oscillation by electrical circuit requiring no input force. Mathematical analyses are carried out showing close agreement with SPICE simulations.
Memristor-based phase shift oscillator
Frequency of oscillation, fM
In spite of having oscillating resistance of memristor, and dynamic behavior of poles, sustained oscillation is observed in this memristor-based third-orderoscillatory system. For the first time, these unprecedented behaviors of memristor in oscillation can become the circuit implementation of parametric oscillation without any external means. Memristor can be considered as a better candidate than resistor for low-frequency oscillator which is widely used in programmable frequency-based counter, random number generator, synthesizing bass, random number generator, and sophisticated portable system.
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