# Enhancing Q-Factor in a Biquadratic Bandpass Filter Implemented with Opamps

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## Abstract

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## 1. Introduction

## 2. Simulation and Signal Flow Graph Analysis

## 3. Sensitivity Analysis Performed in NI Multisim

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Biquadratic bandpass filter implemented with four opamps, ten resistors, and two capacitors.

**Figure 2.**Signal flow graph of the: (

**a**) opamp-RC filter shown in Figure 1, and (

**b**) augmenting one feedback loop labeled $-{K}_{1}$ from node ${V}_{out}$ to ${V}_{4}$.

**Figure 4.**Frequency response of the biquadratic bandpass filter shown in Figure 3.

**Figure 5.**Sensitivity analysis varying ${R}_{1}$ (red), ${R}_{2}$ (dark blue), ${R}_{3}$ (magenta), ${R}_{4}$ (gray), and ${R}_{5}$ (pink) in Figure 3.

**Figure 6.**Sensitivity analysis varying ${R}_{6}$ (purple), ${R}_{7}$ (orange), ${R}_{8}$ (yellow), ${R}_{9}$ (dark orange), ${R}_{10}$ (green), and ${R}_{11}$ (blue) in Figure 3.

**Figure 7.**Frequency response after updating the values of the resistances from sensitivity analysis.

Q Value | Pole 1 | Pole 2 |
---|---|---|

22.697 | −3.2629 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{8}$ | −0.0023 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{8}$ |

2920.06 | −3.2734 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{8}$ | −0.0025 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{8}$ |

122.79 | −3.2742 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{8}$ | −0.0022 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{8}$ |

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**MDPI and ACS Style**

Tlelo-Coyotecatl, E.; Díaz-Sánchez, A.; Rocha-Pérez, J.M.; Vázquez-González, J.L.; Sánchez-Gaspariano, L.A.; Tlelo-Cuautle, E.
Enhancing *Q*-Factor in a Biquadratic Bandpass Filter Implemented with Opamps. *Technologies* **2019**, *7*, 64.
https://doi.org/10.3390/technologies7030064

**AMA Style**

Tlelo-Coyotecatl E, Díaz-Sánchez A, Rocha-Pérez JM, Vázquez-González JL, Sánchez-Gaspariano LA, Tlelo-Cuautle E.
Enhancing *Q*-Factor in a Biquadratic Bandpass Filter Implemented with Opamps. *Technologies*. 2019; 7(3):64.
https://doi.org/10.3390/technologies7030064

**Chicago/Turabian Style**

Tlelo-Coyotecatl, Esteban, Alejandro Díaz-Sánchez, José Miguel Rocha-Pérez, Jose Luis Vázquez-González, Luis Abraham Sánchez-Gaspariano, and Esteban Tlelo-Cuautle.
2019. "Enhancing *Q*-Factor in a Biquadratic Bandpass Filter Implemented with Opamps" *Technologies* 7, no. 3: 64.
https://doi.org/10.3390/technologies7030064