Abstract
A wide range of measuring applications rely on phase estimation on sinusoidal signals. These systems, where the estimation is mainly implemented in the digital domain, can generally benefit from the use of undersampling to reduce the digitizer and subsequent digital processing requirements. This may be crucial when the application characteristics necessarily imply a simple and inexpensive sensor. However, practical limitations related to the phase stability of the band-pass filter prior digitization establish restrictions to the reduction of noise bandwidth. Due to this, the undersampling intensity is practically defined by noise aliasing, taking into account the amount of signal-to-noise ratio (SNR) reduction caused by it considering the application accuracy requirements. This work analyzes the relationship between undersampling frequency and SNR reduction, conditioned by the stability requirements of the filter that defines the noise bandwidth before digitization. The effect of undersampling is quantified in a practical situation where phase differences are measured by in-phase and quadrature (I/Q) demodulation for an infrared ranging application.
Highlights
Estimating the phase difference between two sinusoidal signals is a typical technique in a wide range of measurement applications such as: specification and calibration of electronic and sensor systems [1,2], interferometric applications [3], impedance spectroscopy [4], optical [5] or ultrasonic [6]
The conditioning stage of the system used for the analysis is formed by a single transimpedance amplifier that converts the generated photocurrent into a voltage plus an additional second order band-pass filter. This filtering stage is critical for the analysis presented in this document since it will define the noise bandwidth of the signals to be digitized, and the final performance defined by the sampling parameters will be strongly dependent on noise aliasing after the conversion and demodulation
The theoretical expression is compared with measurements with the digital implementation of the phasemeter on a PC, where signals with different signal-to-noise ratio (SNR) levels, directly generated in the digital domain, are introduced
Summary
Estimating the phase difference between two sinusoidal signals is a typical technique in a wide range of measurement applications such as: specification and calibration of electronic and sensor systems [1,2], interferometric applications [3], impedance spectroscopy [4], optical [5] or ultrasonic [6]time-of-flight ranging, near-field direction-of-arrival estimation [7], laser anemometry [8] or radio frequency control in synchrotrons [9,10]. Several techniques can be used to estimate the phase difference, such as quadrature phase detectors [11] and lock-in amplifiers [12], sine wave fits [13], cross-correlation [14] and methods based on the discrete Fourier transform [15]. These techniques are mainly implemented in the digital domain, from the data obtained from an analog-to-digital (A/D). This SNR depends on the original properties of the information and the effects suffered by it in the processing prior the estimation, : the frequency response of the analog channel and the features of the data acquisition system
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
