## 3 Memristive Analog Design
### Oscillators  
A three-stage memristive PMOS ring oscillator is presented in [59; 60]. The memristive PMOS inverter utilizes the unique properties of memristors to create a stable and reliable oscillator. The three-stage design ensures proper amplification and feedback to maintain the output pulses' desired frequency and duty cycle. The memristive PMOS inverter is made up of a PMOS transistor in series with a memristor, which acts as a variable resistor to control the timing and amplitude of the output pulses. This combination allows precise control over the current flowing through the PMOS transistor, which determines the output waveform. Additionally, the memristor's ability to retain its resistance value even when power is removed ensures the stability and reliability of the oscillator. The simulation results indicate that the RO output signal frequency varies from 3 to 5 GHz when the memristance decreases from 308.2 \(\Omega\) to 55 \(\Omega\). The proposed memristive oscillator is used to generate ultra-wideband pulses. In this case, the oscillator can produce short-duration pulses with very high frequencies. The memristor is used to tune the frequency of the oscillator, allowing for flexibility in adjusting the output waveform. Furthermore, its simple design, low power consumption, compact size, and ease of implementation make it a cost-effective solution for high-frequency signal generation. In [61], a low-power hybrid CMOS-Memristor Ring Oscillator (RO) with a higher randomness value is discussed. The researchers propose a novel design that combines CMOS technology with memristor devices to achieve low power consumption in the ring oscillator. The higher randomness value of the RO makes it suitable for applications such as secure communication and random number generation. A comparison between conventional CMOS inverters, memristive load inverters, and a two-memristive inverter-based RO in terms of the frequency of oscillation, power consumption, and randomness is given. The results show that the two-memristive inverter-based RO outperformed both the conventional CMOS inverters and memristive load inverters in terms of the frequency of oscillation. Additionally, it exhibited significantly lower power consumption compared to the other two designs. The higher randomness value of the two-memristiveinverter-based RO also made it a promising candidate for applications requiring secure communication and random number generation. The proposed two memristor-based RO has a randomness of 51.16 \(\upmu\), significantly lower than CMOS and memristive load-based designs. The maximum power of the design is reported at 270 \(\upmu\)W. The lower power consumption of the proposed two memristor-based RO design makes it more energy efficient compared to CMOS and memristive load-based designs. Furthermore, the randomness value of 51.16 \(\upmu\) indicates a high level of unpredictability, making it suitable for cryptographic applications and enhancing security measures. A memristor-based oscillator designed for potential analog applications is implemented in [62]. The circuit is designed to emulate the operation of a relaxation oscillator by passing a constant current in both directions through a memristor, which induces voltage variations due to resistance changes. These voltage fluctuations are subsequently fed back to the memristor, forming a feedback loop that enables the oscillation to continue. The ability of the memristor to store and recall resistance values allows for precise control over the oscillation frequency and waveform shape. The circuit is implemented using Winbond 90-nm CMOS and HfO2-ReRAM technology, with an operating frequency range of 300-1150 kHz, a power consumption of 700-830 \(\upmu\)W, and a free-running oscillator jitter performance of 6.5 \(\times\) 10\({}^{-5}\). The proposed two-memristor inverter-based RO has a higher randomness value and improved power consumption. Additionally, the two-memristor inverter-based RO offers enhanced stability and reliability compared to traditional oscillators.