## 3 Memristive Analog Design
### Programmable Circuits
The authors in [34] discuss the design and analysis of a memristor-based high-pass filter/amplifier topology for analog signal processing applications. The memristor serves as the negative feedback element, and a high-pass R-C filter is the input impedance. This configuration allows for the precise control of the cutoff frequency and the amplification of high-frequency signals. By tuning the memristor resistance, the circuit gain varies from 0.5 dB to 14 dB, allowing for a wide range of amplification levels to be achieved. This flexibility makes the circuit suitable for a variety of applications where variable gain is required. Additionally, the constant cut-off frequency ensures consistent performance across different input signals, further enhancing its reliability and versatility in various circuit designs. The authors in [35] propose a new method for hot-line adjusting cut-off frequencies using boundary values of memristance, integrating a preset DC voltage with the filtered signal to achieve the desired frequency adjustments. This approach eliminates the need for additional memristance write circuits, making it more suitable for integrated applications in various systems. A memristor emulator is implemented, allowing for the easy implementation and testing of the proposed approach. This emulator can accurately replicate the behavior of a memristor without the need for physical components, providing a cost-effective solution for researchers. Figure 4a [35] shows the proposed memrsitor low-pass filter design, which combines the connection nodes of a memristive circuit network Z with an op amp to achieve a low-pass filtering effect. The memristor network Z allows for programmable resistance values, providing flexibility in filter design and performance. The topology is divided into three parts: the feedback network, made up of two resistors \(Ra\) and \(Rb\); the four-terminal network Z, with two resistors \(R1\) and \(R2\); and the operational amplifier. The feedback network determines the gain of the amplifier. The inside circuit of network Z can be adjusted to create various filter configurations. Two configurations of the low-pass filter based on the circuit depicted in Figure 4b [35] are analyzed and tested to showcase the  
Figure 3: Tunable active memristor-based bandpass filter (**a**) schematic, and (**b**) measured amplitude response [33]. effectiveness of the suggested design. Theoretical analysis is conducted to determine the cut-off frequency and passband gain for each setting. The filter functionality is evaluated using square and sinusoidal voltage signals. The low-pass filter with positive feedback loop, named topology A, can be obtained by setting \(R2=0\) and replacing the resistor \(Ry\) with a memristor. Conversely, the low-pass filter without a positive feedback loop, named topology B, can be obtained by setting \(R1=\infty\) and \(R2=0\). For experimental verification, the feedback resistances are adjusted to \(Ra=5\) k\(\Omega\) and \(Rb=1\) k\(\Omega\), the capacitance is \(C=1\) uF, and the resistance is \(Rx=1\) k\(\Omega\). For topology A, the resistance \(Rx\) is set to 1 k\(\Omega\). Figure 5 [35] presents the experimental waveform magnitude-frequency characteristics of topologies A and B under the specified conditions. The memristor resistance varies between the boundary values Ron (lower memristance) and Roff (highest memristance). The filter's cut-off frequency varies depending on the topology. Topology A has a lower cut-off frequency of 198.94 Hz with Roff and a higher cut-off frequency of 771.91 Hz with Ron. Topology B has a cut-off frequency of 230.8 Hz at Roff and 803.7 Hz at Ron. As demonstrated by the experimental results, the resistance values of the memristors affect the cut-off frequency of the filter. This flexibility in design allows for the customization and optimization of filter circuits for various purposes. Table 1 summarizes the performances of the discussed memristor-based filters.