**2.5 Features of reactance-less memristor based oscillators in low frequency applications**

The model equation Eq. (5) describes an important feature of memristors - the property of inertia. Due to this property it is possible to construct the reactance-less oscillators or in other words oscillators without inductors and capacitors. In this case the charge and discharge of reactive components in conventional oscillators is replaced by changing the memristor resistance (Eq. (5)). The duration of these processes is determined by the inertial parameter *γ*. The typical times of switching of the memristor devices are determined by Eq. (6). Thus, typical current value 100 μA corresponds to oscillator frequency 10 Hz.

The prospects of application of such oscillators are associated primarily with the development of low-power low-frequency oscillator circuits for neuromorphic systems and biomedical equipment.

The low-frequency operation range is the main application area of memristor oscillators [21]. Low frequency oscillators are important for many applications but their design is connected with significant difficulties due to the large values of capacitors required for low oscillation frequencies [59]. Since the frequency of operation of conventional RC relaxation oscillators is inversely proportional to the time constant, τ = R � C, low-frequency operation requires high capacitance [21]. In this case the typical capacitance value may exceed 1 μF, capacitor occupies an area of more than mm<sup>2</sup> . Such an area size contradicts the implementation in integrated circuits. This leads often to off-chip placement of the capacitor [21]. The special-purpose techniques are developed to overcome this problem and to avoid the use of impractically large component values [59, 60]. Thus, relatively novel technique was used to implement the oscillator on-chip, but the capacitor consumed 77.8% of the total chip area [60].

It can be mentioned that the problem is solved automatically with applying reactance-less MBOs due to very small area of memristor devices. For the considered MBO circuits of type (**Figure 2**) the size of area is determined by the area occupied by CMOS comparator.

#### **2.6 Alternative circuitry**

In this type of MBO the comparator plays the role of control circuit in switching the direction of the memristor current. It can be noted that this function can be performed by other active circuit elements.

In particular, circuit with a series connected two devices can be considered: memristor and device with negative differential resistance (NDR). This circuit can generate relaxation oscillations when the generation conditions are satisfied.

There is no need for an active load in such circuits. This is advantage of oscillator circuits based on memristor with NDR. In particular, such two-terminal devices can specified by S-shaped I-V characteristics. In this case the memristor itself can have two state given by high and low resistance values [35]. The relaxation oscillations become possible when memristor is connected to a passive two-terminal circuit. Such oscillators can be connected to each other by resistive or resistive-capacitive couplings. This type of oscillators corresponds to circuits with the current input.

Various two-terminal devices can be used as the load in oscillators based on memristors with NDR. Among them, devices with a structure similar to memristors that exploit thin layers of insulators are promising. Creation of such devices based

### *Functional Capabilities of Coupled Memristor-Based Reactance-Less Oscillators DOI: http://dx.doi.org/10.5772/intechopen.97808*

on silicon oxides [36, 61] seems to be the most promising now. New emerging memristive technologies such as SiOx-based memristors are discussed in [61]. The compatibility with standard CMOS technology provides a good perspective for the implementation of hybrid CMOS-memristive designs in various applications.

Recent results [61] demonstrate advantages of the architecture of memory cell comprising memristor and selector. It is expected that under certain conditions such an emerging device architecture can act as an oscillator.

In the following text the consideration is limited by oscillator circuits based on memristor devices [3], although the results presented below for coupled oscillator elements can be extended to above mentioned circuit architecture.
