# The Dynamic Tunability of Memristor-Based Active Filters

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}memristors in tunable active filters are showcased in [22]. Here, memristors function as tunable loads in filter designs like the Sallen–Key active lowpass and bandpass filters. The underlying principle is that a specified memristance value allows for the tuning of filter characteristics such as passband frequencies and quality factors. Another instance of a tunable first-order active highpass filter employing a TiO

_{2}memristor is designed in [23]. Commercial KnowM memristors are recommended for RF passive filter implementations, as illustrated in [24], where the lowpass filter bandwidth can be adjusted by varying the memristance value.

## 2. Tunable Active RC Bandpass Filter with Memristor

_{p}, the quality factor of a complex-conjugate pole pair Q

_{p}, filter gain K, the capacitance C, and resistance ratio X = R

_{4}/R

_{1}, where R

_{1}= 1/(1/R

_{11}+ 1/Z

_{M}). Refer to Figure 1 for details. Parameter ${Z}_{\mathrm{M}}$ presents memristance value, which can be programmed to satisfy the filter specifications. Instead of parameter ${Q}_{\mathrm{p}}$ we can specify the filter bandwidth.

_{M}), while maintaining a constant filter bandwidth.

_{2}= 200 pF, C

_{3}= 200 pF, R

_{11}= 5 kΩ, R

_{4}= 500 kΩ. The filter amplitude response for these two cases is given in Figure 2.

## 3. Programming Signal Analysis

_{1}are set to zero.

## 4. Experimental Results

_{2}= 0.4 V pulse (Figure 3) at the input terminal of the circuit. For memristor programming from ON to OFF we apply the V

_{2}= −0.4 V at the same terminal. The other pulse parameters are selected using the criteria that ${f}_{\mathrm{z}5}\le {f}_{low,20\mathrm{dB}}=9.28\mathrm{kHz}$, i.e., ${T}_{\mathrm{w},\mathrm{min}}\approx 5/{f}_{low,20\mathrm{dB}}\approx 0.5\mathrm{ms}$ for ${T}_{\mathrm{r}}\ll {T}_{\mathrm{w}}$, which is the minimal pulse width in order to suppress the memristor programming signal at the filter output (see Figure 5). As we used the AD2 instrumentation tool, the rise and fall times are around 2 ms, which is greater than the minimal time. The pulse parameters used are ${T}_{\mathrm{r}}={T}_{\mathrm{f}}=2\mathrm{ms}$, ${T}_{\mathrm{w}}=250\mathrm{ms}$, ${T}_{\mathrm{d}}=0$, ${V}_{1}=0$.

_{2}= 0.4 V, while for programming for from 3 kΩ to 10 kΩ, the amplitude is V

_{2}= −0.4 V.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**Memristor programming from 10 kΩ to 3 kΩ and vice versa during operation of the tunable active bandpass filter. Insets represent short time intervals during memristance programming.

**Figure 7.**Measured amplitude response of the tunable active filter, from Figure 1, for the two memristor states.

Specification | Designed | ||||
---|---|---|---|---|---|

State | f_{p} [kHz] | K | C [pF] | X | Z_{M} [kΩ] |

1st | 19.5 | 50 | 200 | 150 | 10 |

2nd | 26 | 50 | 200 | 267 | 3 |

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**MDPI and ACS Style**

Marković, I.; Potrebić Ivaniš, M.; Tošić, D.
The Dynamic Tunability of Memristor-Based Active Filters. *Micromachines* **2023**, *14*, 2064.
https://doi.org/10.3390/mi14112064

**AMA Style**

Marković I, Potrebić Ivaniš M, Tošić D.
The Dynamic Tunability of Memristor-Based Active Filters. *Micromachines*. 2023; 14(11):2064.
https://doi.org/10.3390/mi14112064

**Chicago/Turabian Style**

Marković, Ivo, Milka Potrebić Ivaniš, and Dejan Tošić.
2023. "The Dynamic Tunability of Memristor-Based Active Filters" *Micromachines* 14, no. 11: 2064.
https://doi.org/10.3390/mi14112064