## 3 Memristive Analog Design
### Digital to Analog Converter  
A data converter circuit using memristors and a DAC circuit for common source connected transistors is discussed in [55]. This circuit design combines the unique properties of memristors with the functionality of a DAC circuit. The memristors provide non-volatile memory and can be used to store and manipulate data, while the DAC circuit converts digital signals into analog voltages for driving common-source connected transistors. Analytical formulas are introduced to relate digital input to analog output, including transistor dimensions. These analytical formulas and PSpice simulations allow for the accurate prediction and optimization of the performance of the DAC circuit using memristors. This integration of memristors and DAC circuits opens new possibilities for efficient data storage and manipulation, as well as improved analog signal generation in various applications such as communication systems and audio devices. A modified 2-bit DAC circuit is introduced for overlapped inputs. The proposed design eliminates the need for complex signal processing algorithms, making it a cost-effective solution. Additionally, the integration of memristors into the DAC circuit enhances its scalability and potential for future advancements in data storage and analog signal processing technologies. A memristor-based digital to analog converter (DAC) is proposed in [56] (Figure 7). The proposed memristive DAC offers improved performance and efficiency compared to traditional DACs. It utilizes the unique properties of memristors to achieve a higher resolution and lower power consumption. The proposed circuit utilizes two symmetric memristive DACs, enabling the design of both 4-bit and 8-bit DACs, as shown in Figure 8[56]. Furthermore, the memristive DAC eliminates the need for complex calibration techniques, resulting in simplified circuitry and reduced manufacturing costs. The design reduces the area by 40% and uses an 8-bit memristive DAC in a successive approximation register analog-to-digital converter approach (SAR-ADC). The SAR-ADC achieves a signal-to-noise and distortion ratio of 49.3 dB and a spurious free dynamic range of 61 dB with a power supply of 1.2 V and a consumption of 21 \(\upmu\)W. The figure of merit is 87.9 fj/Conv-step. The designs were simulated with optimized parameters using the VTEAM model. In [57], a memristor-based 4-bit digital-to-analog converter is presented. It uses a single input programmer with a deMultiplexer and reset switch to adjust the memristor's resistance. The reset switch ensures the proper adjustment of the resistance, while the demultiplexer facilitates the selection of the desired memristor. This configuration enables precise control over the output voltage levels of the digital-to-analog converter. The converter achieves a maximum error of \(\pm 1\%\) and achieves a DNL and INL of 0.075 LSB and 0.123 LSB, respectively. These low error values indicate the high accuracy and reliability of the digital-to-analog converter. The authors in [58] present a design for a single-bit continuous-time Delta-Sigma modulator (Kennesaw, GA, USA) using a memristive finite impulse response (FIR) DAC in the feedback. The proposed design aims to improve the performance of Delta-Sigma modulators by leveraging the unique properties of memristive FIR DACs. By incorporating  
Figure 8: Proposed successive approximation register (SAR)–analog-to-digital converter (ADC) using memristor [56]. Figure 7: An eight-level input memristor-based DAC (**a**) circuit and (**b**) simulation [56]. memristors in the feedback loop, the modulator can achieve higher linearity and lower power consumption compared to traditional designs. Additionally, the memristive FIR DAC offers greater flexibility in shaping the frequency response of the modulator, allowing for better noise shaping and improved overall performance. The 8-tap FIR filter coefficients are implemented using memristors with a programmable resistance ranging from 17.20 k\(\Omega\) to 55.63 k\(\Omega\).