The force-to-rebalance (FTR) closed-loop detection method is commonly used to expand the bandwidth (BW) for micro-electro-mechanical system (MEMS) gyroscopes with low-frequency split and high-quality factors. However, the relationship between the BW and output noise is often incompatible; thus, reducing the detection accuracy of the gyroscope. This paper presents an analysis of the BW and noise spectra under modulation-demodulation FTR gyroscopes. The expressions for the BW and the noise-equivalent rate (NER) spectrum are derived to explore the effects of the loop gain on the BW and NER. It is demonstrated that the gain of the amplifier circuit is maximally transferred to the vibration displacement signal conversion part, which can reduce the output noise without affecting the BW. The simulation and experimental results on the Cobweb-like disk resonator gyroscope show that the derived expressions of BW and NER are correct, and the noise optimization method is effective, which provides an idea for the realization of a high-precision MEMS gyroscope.

力再平衡（FTR）闭环检测方法通常用于扩展具有低频分裂和高质量因子的微机电系统（MEMS）陀螺仪的带宽（BW）。然而，BW 和输出噪声之间的关系往往是不相容的；从而降低陀螺仪的检测精度。本文介绍了调制解调 FTR 陀螺仪下的带宽和噪声频谱分析。推导出 BW 和噪声等效率 (NER) 频谱的表达式，以探索环路增益对 BW 和 NER 的影响。结果表明，放大电路的增益最大程度地转移到振动位移信号转换部分，可以在不影响BW的情况下降低输出噪声。