Random Errors in Time Interval Measurement Based on SAW Filter Excitation

Abstract

This paper deals with the time interval measurement method that makes use of a surface acoustic wave (SAW) filter as a time interpolator. The method is based on the fact that a transversal SAW filter excited by a short pulse can generate a finite signal with highly suppressed spectra outside a narrow frequency band. If the responses to two excitations are sampled at clock ticks, they can be precisely reconstructed from a finite number of samples and then compared to determine the time interval between the two excitations. We have analyzed noise contributions to the overall uncertainty of the interval measurement. The following four noise sources have been considered: (1) noise of excitation; (2) noise of amplifier; (3) quantization noise of the analog-to-digital converter; and (4) clock and sampling jitter. The main goal of the analysis was to determine the uncertainty of the measurement in dependence on the variances of contributing noises, and the magnitude of the frequency response of the filter. First, each uncertainty component has been analyzed under general assumptions. Second, a general narrow-band filter has been investigated. Finally, we have found the solution for an ideal narrow-band filter where we have obtained simple illustrative results. The results have been compared to Monte-Carlo simulations. Good agreement between theory and simulation has been demonstrated except for the outliers due to the false ambiguity solution that occurs with large measurement errors and small relative filter bandwidth.