**2.2 Introducing the control of threshold parameters in memristor based oscillator circuits**

Standard control approach in memristor based oscillators (MBO) is the exploitation of input signal to control the rate of change in the state of the memristor.

In contrast from this, the main idea of considered controlling approach is to send the input signal not directly to the memristor device but to the comparator circuit and as result to control oscillator circuit behavior by change of interval of memristor resistor variation.

The possible schematic of memristor based oscillator with controlled threshold parameters [50] is given in **Figure 2**. This oscillator element provides the desired functionalities.

The purpose is to change the comparator thresholds using the input voltage *VIN* and to control the boundaries of range of memristor resistance variation by input voltage. In this case input voltage *VIN*ð Þ*t* , limited by the region *VOUT*ð Þ*t* ≥*VIN*ð Þ*t* ≥ 0, shifts the range of *R t*ð Þ change:

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

**Figure 2.**

*Schematic of memristor based oscillator with controlled threshold parameters. The oscillator circuit contains memristor* М*, two-threshold comparator (TTC), summing elements, attenuator* k *(Vr* ¼ *kVIN*Þ*, current source* IM*., logical element* NAND*.*

$$R\_m - r(t) \le R(t) \le R\_M - r(t). \tag{2}$$

Here *r t*ðÞ¼ *Vr*ð Þ*t =I* is conditional resistance. In order to avoid exceeding the limits of the range of changes in the memristor resistance, the following inequalities are supported:

$$r(t) < R\_m - R\_{ON} \text{ and } r(t) < R\_{OFF} - R\_M \tag{3}$$

The original comparator thresholds *Vm* and *VM* are converted into active thresholds in this case.

It can be mentioned that the state of the MBO can be characterized by phase. The phase is determined by the values of two variables: *R t*ð Þ and *sign dR* ð Þ *=dt :*

The fundamental difference between the proposed control approach and the conventional approach is following: the change of the memristor state does not depend on the time of the drive signal arrival under standard control and the state change depends on the time of arrival of the drive signal for proposed approach.

The different character of impact of driving pulses on MBO behavior is shown in **Figure 3**. The input current *iin* impacts on the rate of change in the memristor resistance (**Figure 3a**). In this case the speed increases at the same signs of the input

#### **Figure 3.**

*The different character of impact of driving pulses on varying memristor resistance* R(t)*: (a) excitation by input current* iin*, (b). excitation by input voltage* vin *to control thresholds.*

current and oscillator current and it decreases otherwise. The input voltage *VIN* is applied to the comparator to change its thresholds and to determine the range of resistance changes (**Figure 3b**).

The input current signal *iin* is integrated. Its effect on the waveforms depends on the duration of the signal and on the phase of the process, in other words on the sign of the resistance change. The long current pulses slow down or accelerate the transient process but short current pulses do not impact on the resistance value.

The input signal *VIN* applied to the input of the comparator directly before reaching the threshold can affect the switching process even with a small value of the coefficient *k*. At other times the comparator sensitivity to the input signals is reduced. This is illustrated in **Figure 3b**. The long-time pulses applied to the comparator input do not affect the trajectory *R(t).* But even a short positive pulse before reaching the upper threshold resistance *RM* leads to a decrease in the switching threshold and to earlier start of reducing memristor resistance. Similarly, a short negative pulse before reaching the lower threshold resistance *Rm* leads to an increase in the lower switching threshold. This leads to beginning of growth of the memristor resistance.
