A stochastic analysis of an anharmonic sensor phase response |
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Authors: | Shmaliy Y.S. Shkvarko Y.V. Torres-Cisneros M. Rojas-Laguna R. Ibarra-Manzano O.G. |
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Affiliation: | Guanajuato Univ., Salamanca, Mexico; |
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Abstract: | The probability density function (pdf) of a modulo 2/spl pi/ phase response slope of an intrinsic anharmonic sensor of a crystal oscillator is studied in detail. It is noted that without an external drive, the sensor is excited by the oscillator noise floor with a signal-to-noise ratio (SNR) of around unity. The slope pdf is provided both in the rigorous integral form and in the T-distribution-based approximation. It is shown that the slope mean value is estimated to be zero with SNR =0. It then gradually tends toward actual value as SNR rises so that with SNR >2 the bias of slope estimates is almost negligible. With 0/spl les/ SNR <0.7, the slope variance stays at a maximum and then asymptotically diminishes toward zero as the SNR rises. The importance of these studies resides in a shown fact that, practically, having SNR <2 in anharmonic sensors may result in substantial bias and variance for phase response slope mod 2/spl pi/ estimates. |
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