# Single Drive Multi-Axis Gyroscope with High Dynamic Range, High Linearity and Wide Bandwidth

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## Abstract

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^{2}, making it one of the smallest multi-axis gyroscopes. A custom printed circuit board (PCB) was designed for the evaluation of the multi-axis gyroscope. The experimental results demonstrate that the gyroscope has a high sensitivity of $12.56\text{}\mathsf{\mu}\mathrm{V}/\mathrm{dps},\text{}17.13\text{}\mathsf{\mu}\mathrm{V}/\mathrm{dps}$ and $25.79\text{}\mathsf{\mu}\mathrm{V}/\mathrm{dps}$ in the roll (X-sense), pitch (Y-sense) and yaw (Z-sense) modes respectively. The scale-factor non-linearity of the gyroscope is less than $0.2\%$ for roll and pitch mode and $0.001\%$ for the yaw mode, in the full-scale range of $\pm 1500\text{}\mathrm{deg}/\mathrm{s}$. The multi-axis gyroscope demonstrates an angle random walk of $2.79\text{}\mathrm{dps}/\sqrt{\mathrm{Hz}}$, $2.14\text{}\mathrm{dps}/\sqrt{\mathrm{Hz}}$, and $\text{}1.42\text{}\mathrm{dps}/\sqrt{\mathrm{Hz}}$, for the roll, pitch and yaw rate with the in-run bias stability $1.62\text{}\mathrm{deg}/\mathrm{s}$, $1.14\text{}\mathrm{deg}/\mathrm{s}$ and $0.84\text{}\mathrm{deg}/\mathrm{s}$ respectively.

## 1. Introduction

## 2. Multi-Axis Gyroscope Design and Fabrication

#### 2.1. Mechanical Design

#### 2.2. Fabrication

## 3. Characterization

#### 3.1. Resonant Modes

#### 3.2. Angular Rate Response

#### 3.3. Allan Variance

## 4. Discussion

## 5. Conclusions and Future Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Simulated resonant modes of single drive multi-axis gyroscope (

**a**) Lateral drive mode. (

**b**) Out-of-plane X sense (Roll mode). (

**c**) Out-of-plane Y sense (Pitch mode). (

**d**) In-plane Z sense (Yaw mode).

**Figure 3.**Cross-sectional view of the fabrication process. (

**a**) Fabrication of the via wafer. (

**b**) Fabrication of cap and device wafer. (

**c**) Wafer level bonding and vacuum packaging.

**Figure 4.**Optical photograph (captured by EMI PHEMOS-1000, Hamamatsu Photonics, Hamamatsu, Japan) of the vacuum packaged single drive multi-axis gyroscope.

**Figure 6.**Meaured resonant characteristics of the single drive multi-axis gyroscope (

**a**) Drive mode. (

**b**) Roll mode. (

**c**) Pitch mode. (

**d**) Yaw mode.

**Figure 7.**(

**a**) Designed PCB for evaluation single drive multi-axis gyroscope. (

**b**) Test setup for evaluation of gyroscope.

Parameters | Values | |||
---|---|---|---|---|

Mechanical Structure size | 1428 × 1428 μm | |||

Structure thickness | 30 μm | |||

Drive | Roll | Pitch | Yaw | |

Electrode gap [μm] | 8 | 2 | 2 | 1.5 |

Static capacitance [fF] | 748 | 794 | 794 | 582 |

Measured resonant frequency [Hz] | 13,892 | 16,404 | 16,214 | 15,398 |

Measured Q-factor | 12,000 | 500 | 500 | 2000 |

Bandwidth [Hz] | - | 1200 | 1200 | 800 |

**Table 2.**Comparison of the designed multi-axis gyroscope with reported fabricated multi-axis gyroscopes.

Parameters | This Work | Ref [20] | Ref [12] | Ref [11] | |
---|---|---|---|---|---|

Size [mm] | 1.4 × 1.4 | – | 2 × 2 | 1.2 × 1.2 | |

Resonant Frequency [Hz] | Drive | 13,892 | 27,964 | 138,058 | 67,410 |

Roll | 16,404 | 25,901 | 139,140 | 63,260 | |

Pitch | 16,214 | 27,115 | 139,048 | 63,430 | |

Yaw | 15,398 | 30,559 | 138,043 | 65,000 | |

Scale Factor [µV/dps] | Roll | 12.5 | 28.5 | 1.40 [pA/dps] | 0.12 |

Pitch | 17.13 | 57.8 | 1.2 [pA/dps] | 0.09 | |

Yaw | 25.79 | 19.4 | 30.5 [pA/dps] | 0.3 | |

Measurement Range [dps] | 1500 | 300 | 150 | 50 | |

Theoretical Bandwidth (Hz) | Roll | 1357.56 | 1114.02 | 584.28 | 2241 |

Pitch | 1254.96 | 458.46 | 534.6 | 2149.2 | |

Yaw | 814.32 | 1401.3 | 8.1 | 1301.4 | |

Scale factor non-linearity (R^{2}) | Roll | 0.14% | - | - | - |

Pitch | 0.15% | - | - | - | |

Yaw | 0.0015% | - | - | - | |

Quality factor (Q) | drive | 12,000 | 9840 | 3910 | 34,000 |

Roll | 500 | 927 | 1181 | 53,000 | |

Pitch | 500 | 989 | 1360 | 45,000 | |

Yaw | 2000 | 6744 | 505 | 36,000 | |

Angle Random Walk (ARW) $\mathrm{dps}/\sqrt{\mathrm{Hz}}$ | Roll | 2.79 | 0.023 | 0.292 | 0.06 |

Pitch | 2.14 | 0.01 | 0.357 | 0.12 | |

Yaw | 1.42 | 0.036 | 0.028 | 0.048 | |

Bias instability deg/s | Roll | 1.62 | 0.043 | 0.226 | 0.033 |

Pitch | 1.14 | 0.016 | 0.166 | 0.039 | |

Yaw | 0.84 | 0.004 | 0.041 | 0.013 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Iqbal, F.; Din, H.; Lee, B.
Single Drive Multi-Axis Gyroscope with High Dynamic Range, High Linearity and Wide Bandwidth. *Micromachines* **2019**, *10*, 410.
https://doi.org/10.3390/mi10060410

**AMA Style**

Iqbal F, Din H, Lee B.
Single Drive Multi-Axis Gyroscope with High Dynamic Range, High Linearity and Wide Bandwidth. *Micromachines*. 2019; 10(6):410.
https://doi.org/10.3390/mi10060410

**Chicago/Turabian Style**

Iqbal, Faisal, Hussamud Din, and Byeungleul Lee.
2019. "Single Drive Multi-Axis Gyroscope with High Dynamic Range, High Linearity and Wide Bandwidth" *Micromachines* 10, no. 6: 410.
https://doi.org/10.3390/mi10060410