Detailed Noise Analysis of Current-to-Frequency Converters for Precision Analog Accelerometers

This paper presents a detailed noise analysis of current-to-frequency converters (CFC) for current output precision analog accelerometers. In the proposed method, time domain approach is used instead of frequency domain approach and the standard deviation of the velocity error after a fixed period of time is calculated. The noise analysis demonstrates that the error caused by voltage noises does not increase with time. However, the standard deviation of the error due to the feedback current noise increases with time. It is proportional to the square root of time, when the noise is white (thermal). If the noise is of flicker type, the standard deviation depends on the average time constant of the flicker noise. If the current time is smaller than the average time constant of the flicker noise, it is proportional to time. However, if the current time is larger than the average time constant, it is proportional to square root of the time as in thermal noise. The detailed noise analysis also shows that the standard deviation of the velocity error depends on the input current (or acceleration). In the case of thermal noise, it is proportional to square root of the input current. On the other hand, in the case of flicker noise, it is proportional to input current. These results agree with simulations in which the analog operation of CFC is transformed into digital domain