## 3 Memristive Analog Design
### Programmable Circuits  
The study in [32] showcases the use of a digital emulator to implement memristors in practical memristive programmable analog circuits. The memristor emulator allows the simulation of memristor behavior in programmable analog circuits, providing a cost-effective solution for testing and prototyping. The proposed circuits can be easily built using inexpensive components and program properties. The proposed memristor emulator consists of a digital potentiometer, an analog-to-digital converter (ADC), and a microcontroller. The microcontroller calculates the resistance of the digital potentiometer using a code, while the ADC provides voltage for code calculation. This enables a current-controlled memristive system. The proposed memristor-based digital potentiometer circuit operates in analog mode, with terminals connected to ground and field effect transistors (FETs). FETs program the memristor state using control voltages V\({}_{\mathrm{PP}}\) and V\({}_{\mathrm{pn}}\), allowing the resistance to vary in the direction of the applied voltage. FETs also enable memristor tuning when the programming voltage V\({}_{\mathrm{PP}}\) exceeds the memristor's threshold voltage V\({}_{\mathrm{T}}\). By controlling V\({}_{\mathrm{PP}}\), the memristor can be programmed to store and retain different resistance states. Different memristive analog circuits have been implemented to evaluate the performance and capabilities of these devices, including a programmable threshold comparator, a programmable gain amplifier, a programmable switching threshold Schmit trigger, and a frequency relaxation oscillator. The performance of these circuits using memristors has shown improved efficiency, lower power consumption, and enhanced functionality compared to circuits using conventional components. The authors in [33] present a solution for the automated programming of a commercially available memristor in a tunable active bandpass filter design. They demonstrate the effectiveness of their approach through simulations and experimental results, proving the feasibility of using memristors in practical electronic applications. Additionally, the central frequency can be programmed during filter operation, eliminating the need for memristor state-switching during operation and allowing for real-time adjustments to the filter characteristics. This flexibility opens new possibilities for the design of adaptive filtering systems. Figure 3a [33] displays the proposed design. It includes a memristor-based tunable active bandpass filter that removes the memristor-based programming signal from the output of the circuit. To achieve bandpass characteristics, the design incorporates a combination of passive and active components, allowing for efficient filtering while maintaining signal integrity within the desired bandwidth. The passive components, namely RC filters, help to attenuate frequencies outside of the desired range, while the active components, namely operational amplifiers, provide gain and stability to the signal within the passband. The filter is tuned for central frequency adjustments, with two target central frequencies of 19.5 kHz(1 st state) and 26 kHz (2 nd state), and a 3 dB bandwidth of 3.18 kHz. The capacitors C2 and C3, as well as the resistors R11 and R4, maintain their respective values of 200 pF, 200 pF, 5 k\(\Omega\), and 500 k\(\Omega\) for both target central frequencies. The memristor resistance (\(Z_{\text{m}}\)) in the first state is 10 k\(\Omega\), while in the second state it is 3 k\(\Omega\). The simulated and measured amplitude responses of the filter for the two states are presented in Figure 3b [33]. As shown in Figure 3b [33], there is good agreement between the simulated and measured results, indicating that the filter design is accurate and reliable. This consistency validates the effectiveness of the filter in both states. The measured gains of 29.3 dB at 19.5 kHz and 28.8 dB at 26 kHz are lower than the simulated value of 29 dB using LT-SPICE, owing to parasitic shunt capacitances.