Design of a Digitalized Microgyroscope System Using <inline-formula> <tex-math notation="LaTeX">$\Sigma \Delta $ </tex-math></inline-formula> Modulation Technology

Abstract

This paper presents a digitalized gyroscope system using $\Sigma \Delta $ modulation on ADC (Analog to Digital Converter) and DAC (Digital to Analog Converter) sections. Both discrete ADC and DAC chips are replaced with these $\Sigma \Delta $ sections. The $\Sigma \Delta $ ADC technology can convert signals between analog and digital domain using analog modulators on the printed circuit board circuit with different amplifiers and matched capacity couples and digital backend processing in field programmable gate array (FPGA). While the $\Sigma \Delta $ ADC technology are easily realized in FPGA by signal processing algorithms the major sections of the digital system, such as auto gain control and phase-lock loop are also implemented in FPGA, which have provided the programmable flexibility of the whole system. The signal-to-noise ratio of power spectrum density (PSD) and stability in both $\Sigma \Delta $ ADC and $\Sigma \Delta $ DAC are analyzed, respectively. Considering the sections of the $\Sigma \Delta $ ADC and DAC woks in different clock domain, the frequency characteristics of each section should be analyzed. In the drive mode of the gyroscope, the force feedback is applied through the direct bitstream of the modulator. To evaluate the gyroscope vibration stability of the $\Sigma \Delta $ modulation-based system, the Leeson-model phase noise characteristics of the drive mode detection signal are in-depth theoretically calculated with different parameters, including the noise models and the circuit components, which has been experimentally validated by the measured PSD analysis. Finally, the performance evaluation of the whole gyroscope system is demonstrated by time-domain sampling and Allan variance analysis. The digitalized system achieved a scale factor of 94LSB/°/s, with a linearity of 83.1 ppm, noise of 00054°/s/ $\sqrt {\rm Hz}$ , bandwidth of 75 Hz, and the bias instability of 2.94°/h.