A 27 $\mu \text{W}$ 0.06 mm2 Background Resonance Frequency Tuning Circuit Based on Noise Observation for a 1.71 mW CT- $\Delta \Sigma $ MEMS Gyroscope Readout System With 0.9 °/h Bias Instability

An Auto-Tuning Continuous-Time Bandpass Sigma-Delta Modulator with Signal Observation for MEMS Gyroscope Readout Systems

“…The measured IBN is about −100 dB and the SNDR is above 78 dB for each case. From these data, it can be seen that the circuit is stable in the temperature range of −45 to 60 • C. Similar to the definition of S.CF, a parameter SNDR coefficient with temperature (S.CT) is used to describe the relative change of the SNDR with temperature, as calculated in (11). The S.CT has been reduced from 0.091 to 0.023%/ • C. To verify that temperature variations can be compensated by filter tuning, the ASIC temperature was varied between -45 and 60 °C.…”

“…From these data, it can be seen that the circuit is stable in the temperature range of -45 to 60 °C. Similar to the definition of S.CF, a parameter SNDR coefficient with temperature (S.CT) is used to describe the relative change of the SNDR with temperature, as calculated in (11). The S.CT has been reduced from 0.091 to 0.023%/°C.…”

“…However, a CT circuit is sensitive to process, temperature, and voltage variations [10], as filter time constants are a function of resistances or transconductances. Since there is a narrow bandwidth signal in gyroscope readout systems, the relative matching requirements on the electronic filter are stringent [11]. As shown in Figure 1a, the actual signal is affected by the above factors and there is a frequency deviation from the ideal signal.…”

“…Furthermore, due to disturbance of the external environment and long-term drifts, it is only the initial calibration of the frequency matching that does not meet the work requirements. Therefore, it is necessary to tune the ΣΔ ADC center frequency in the whole operation process with an online calibration module that is able to work continuously [11]. To avoid the mismatch problems of RC times or transconductors, a method of using replica circuits is commonly used.…”

“…However, the module of signal tone generation is off-chip with extra area. Another tuning system is described in [11] based on noise observation, which adds an area to compare the noise power in two bands located symmetrically above and below the node point. However, the signal spectra cannot be of ideal symmetry and the correction method is composed of multiple modules that are complex to design.…”