## 3 Memristive Analog Design
### Memristive RF Circuits
#### 3.2.2 Tunable Inductors  
RFMSs have demonstrated promising high-frequency performance, making them suitable for integrated circuit applications. The authors in [49] present two novel topologies of tunable inductors using MEmristors (TIME): a memristive-via-switched tunable inductor and a multi-layer stacked inductor switched by an RFMS single-pole double-throw. These topologies offer the advantage of tunability, allowing for adjustable inductance values to meet specific circuit requirements. The memristive-via-switched tunable inductor provides a compact solution, while the multi-layer stacked inductor offers increased inductance values without sacrificing performance. These passive inductor topologies are tuned by electrochemical metallization memristors, improving tunable inductors' performance. As the memristor transitions from a low resistance state (LHS) to a high resistance state (HRS), the inductance changes from 2.43 nH to 9.6 nH, leading to a quality factor ranging from 12.4 to 18, respectively. The simulation results also show a maximum tunability of 296% and a self-resonant frequency above 8.4 GHz. These performance metrics make the memristive-via-switched tunable inductor and multi-layer stacked inductor highly desirable for applications requiring precise control over inductance values. Furthermore, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Features** & **[44]** & **[45]** & **[46]** & **[47]** & **[48]** \\ \hline
**Frequency Range (GHz)** & 10–40 & 0–40 & 0–6 & 0–10 & 0–3 \\ \hline
**OFF-State Isolation (dB)** & 36 & 35 & 30 & 26 & 16 \\ \hline
**On-State insertion Loss (dB)** & 0.26 & 0.33 & 0.5 & 0.54 & 1.1 \\ \hline
**Minimum Line Width (um)** & - & \textless{}1 & \textless{}1 & 50 & 100 \\ \hline
**Results type** & Simulation results & Simulation results & Measurement results & Simulation results & Measurement results \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of memristor-based RF switches. the electrochemical metallization memristors enable the dynamic tuning of the inductors, allowing real-time adjustments to meet changing circuit requirements. The authors in [50] explore the use of a memristor to control the biasing current of operational transconductance amplifiers (OTA) for gyrators. Gyrators are important components in electronic circuits that simulate inductors. By utilizing a memristor to control the biasing current of OTA, it is possible to enhance the performance and efficiency of gyrators. Additionally, this approach offers the advantage of flexibility and adaptability in adjusting the behavior of gyrators for various applications. The gyration constant is linearly controlled by the memristance state. This allows for precise control over the simulated inductance, making it easier to design circuits with specific frequency responses. Furthermore, the use of a memristor as a biasing current controller eliminates the need for external components, simplifies the circuit design, and reduces cost. The circuit is implemented using 0.18 \(\upmu\)m CMOS technology from TSMC and simulated using Cadence Virtuoso. The circuit's performance was evaluated through various simulations, including frequency response analysis and power consumption measurement. The off-chip memristor is a metal-oxide bi-layer with a non-volatile memristance range of 4.7 k\(\Omega\) to 170 k\(\Omega\). The active inductance range is 95 \(\upmu\)H to 1.55 mH, with an inductive bandwidth of 69 MHz and 18 MHz. The power consumption ranges from 0.21 mW to 1.95 mW, depending on the memristance and equivalent inductance. Based on the discussed works, the memristor exhibits promising results in designing tunable inductors for radio frequency applications, but further research is needed to optimize their performance and reliability for practical communication systems. One potential area of improvement is reducing the variability in memristor behavior, which can impact the consistency of inductor performance.