# Research on a Silicon Gyroscope Interface Circuit Based on Closed-Loop Controlled Drive Loop

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## Abstract

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## 1. Introduction

_{i}and K

_{p}were optimized according to the simulation results. According to the optimized parameters, the pre-stage circuit was adjusted. In order to verify the correctness of the model, a test system was established. The system’s start-up time and set-up time with different proportional integral controller (PI) parameters were compared by a transient response experiment for the silicon gyroscope. The performance of the silicon gyroscope interface circuit chip was tested and analyzed. According to the Allen variance method, the bias stability was 1.14°/hr, which met the requirements for high-precision silicon gyroscope sensors.

## 2. Drive Loop Modeling and Simulation

#### 2.1. Mechanical Motion Principle of Silicon Gyroscope

#### 2.2. The Establishment of the Closed-Loop Control Drive-Loop Model

_{v}ux in the driving loop, where k

_{v}is a displace to voltage conversion gain, u is the controller voltage.

_{d}ω

_{d}, the disturbance term $\ddot{\theta}/2({\omega}_{x}+\dot{\theta})$ could be ignored. k

_{v}ua is the envelope signal of u

_{x}, which could be redefined as u

_{a}. Therefore, the transfer function could be rewritten as:

_{ref}was used as the input, and the output of the low-pass filter was used as the output. The closed-loop transfer function of the entire loop system could be obtained as:

_{vga}is the gain of the variable gain amplifier, V

_{dc}is the driving direct current (DC) voltage, k is the spring constant, ω

_{lpf}is the cutoff frequency of the filter, K

_{p}and K

_{i}are the proportional and integral terms of the PI controller, and K

_{total}is the product of K

_{voltage-force}, K

_{displace-voltage}, and K

_{rectifier}.

#### 2.3. Simulation Result of the Model

_{i}, K

_{p}, ω

_{lpf}, and K

_{vga}on the system’s amplitude–frequency characteristics and unit step response was analyzed.

_{p}, the gain of the system remained unchanged, and the bandwidth increased. The setup time was the shortest when K

_{p}= 10. Therefore, considering the system comprehensively, K

_{p}= 10 was the optimal value for the system parameters. As shown in Figure 3b, the loop gain increased when K

_{i}increased, but the bandwidth did not change much. According to the step response of the system, K

_{i}= 200 was a suitable value. In Figure 3c, it can be observed that the cut-off frequency of the low-pass filter could be chosen. It could be observed that the cut-off frequency of the low-pass filter had little effect on the gain and bandwidth of the system, and the step response indicated that the choice of ω

_{lpf}should not be too small. As shown in Figure 3d, an increase in K

_{vga}would significantly increase the system gain and bandwidth.

_{i}and K

_{vga}to obtain a larger system gain, and then adjusting the value of K

_{p}to change the zero point of the complex plane and the loop stability, could be considered.

## 3. Circuit Design and Experiments

#### 3.1. Overall Design of the Drive Loop

#### 3.2. Circuit Implementation Details

#### 3.2.1. Charge–Voltage (CV) Conversion Circuit

_{17}and Q

_{19}were set so that Q

_{18}was in the linear region and had a larger equivalent resistance due to its smaller gate source voltage and smaller aspect ratio. This equivalent resistance was proportional to the bias resistance in the bias current source and was not affected by time and temperature variations [21]. The feedback capacitor C

_{f}was about 5 pF, and its resistance was matched to the silicon gyroscope sensitive structure to reduce the effect of parasitic capacitance. The equivalent resistance of the T-shaped network was:

_{M}was the equivalent resistance of the transistor Q

_{18}, and its resistance was about 1 MegΩ, which was much larger than R

_{1}and R

_{2}.

#### 3.2.2. Phase-Compensation Circuit

_{1}and the resistors R

_{1}, R

_{2}, and R

_{6}formed an adder, wherein the resistance values of R

_{1}, R

_{5}, and R

_{6}were equal, to realize negative feedback. The operational amplifier OP

_{2}, the resistor R

_{3}, and the capacitor C

_{1}formed a feedforward integrator. The operational amplifier OP

_{3}, resistor R

_{5}, and capacitors C

_{2}and C

_{3}formed a feedback integrator. A forward transfer integrator was used to achieve a 90° phase shift, and a feedback integrator was used to eliminate the continuously integrated forward transfer integrator detuning voltage.

#### 3.2.3. Automatic Gain Control Circuit

_{1}, and resistors R

_{1}and R

_{2}with two diodes; the full-wave rectification and low-pass filtering functions were completed with an integrator composed of the operational amplifier OP

_{2}and C

_{1}, C

_{2}and R

_{6}, and the resistors R

_{3}and R

_{4}. The inverting input of the integrator was connected to the voltage reference source through the resistor R

_{5}, and the integrator completed the closed-loop amplitude control function. The parameters in the circuit were R

_{1}= R

_{2}, R

_{3}= 2R

_{4}, R

_{7}= R

_{8}= R

_{9}, and R

_{10}= R

_{11}= R

_{12}. After the closed-loop feedback, the integrator automatically adjusted the output DC voltage V

_{dc}; the alternating current voltage amplitude, V

_{ac}, was:

_{3}with the resistors R

_{7}, R

_{8}, and R

_{9}, whose function was to superimpose the signals V

_{dc}and V

_{ac}. The multiplier consisted of the operational amplifier OP

_{4}with the transistors Q

_{1}and Q

_{2}, whose function was to complete the high frequency modulation of the driving voltage signal, with a function of (V

_{dc}+ V

_{ac}sinwt)U(t), to avoid coupling interference. In the multiplier, a switch consisted of the transistors Q

_{1}and Q

_{2}, whose gates were controlled by voltage square waves ±U(t) with a period of T

_{S}= 25 ms and a duty cycle of 50%, which was used to realize the square wave modulated signal.

#### 3.3. Verification of Closed-Loop Control Drive-Loop Model

_{p}, the transient waveforms were as shown in Figure 11. It could be observed that within about 0.2 s when the silicon gyroscope system was powered on, the driving loop did not start immediately, and the driving signal had not yet been established. Then the noise components were continuously selected and amplified by the closed-loop self-excited driving loop through frequency selection, a tiny driving signal was generated which was rapidly amplified by the multiplier. After a period of rise time, it was quickly stabilized at a fixed amplitude under the action of the closed-loop oscillation automatic gain control module in the driving loop as a sine wave. It could be observed that with K

_{p}increasing from 5 to 10, the overshoot signal was gradually smoothed, and the rise time and settling time were increased. When K

_{p}continued to be increased, the overshoot signal was increased again. The test result proved that, when K

_{p}= 10 and K

_{i}= 200, the stability optimization of the control loop was realized.

#### 3.4. Experimental Results for the Whole System

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Amplitude frequency characteristics of the driving loop when (

**a**) K

_{p}, (

**b**) K

_{i}, (

**c**) ω

_{lpf}, and (

**d**) K

_{vga}changed.

Kp | 5 | 10 | 15 | 20 |
---|---|---|---|---|

Rise time with simulation (s) | 0.16 | 0.21 | 0.06 | 0.04 |

Rise time of the test (s) | 0.15 | 0.19 | 0.04 | 0.02 |

Equipment | Type | Manufacturer |
---|---|---|

High-precision current source | PW36-1.5ADP | KENWOOD |

Current source | E3631A | Agilent |

Dynamic signal analyzer | 35670A | HP |

Oscilloscope | DSOX2002A | Agilent |

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**MDPI and ACS Style**

Li, Q.; Ding, L.; Liu, X.; Zhang, Q.
Research on a Silicon Gyroscope Interface Circuit Based on Closed-Loop Controlled Drive Loop. *Sensors* **2022**, *22*, 834.
https://doi.org/10.3390/s22030834

**AMA Style**

Li Q, Ding L, Liu X, Zhang Q.
Research on a Silicon Gyroscope Interface Circuit Based on Closed-Loop Controlled Drive Loop. *Sensors*. 2022; 22(3):834.
https://doi.org/10.3390/s22030834

**Chicago/Turabian Style**

Li, Qiang, Lifeng Ding, Xiaowei Liu, and Qiang Zhang.
2022. "Research on a Silicon Gyroscope Interface Circuit Based on Closed-Loop Controlled Drive Loop" *Sensors* 22, no. 3: 834.
https://doi.org/10.3390/s22030834