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On-Chip Accelerometers Using Bondwire Inertial Sensing
Published in Reza Mahmoudi, Krzysztof Iniewski, Low Power Emerging Wireless Technologies, 2017
Yu-Te Liao, William Biederman, Brian Otis
The Allan variance is often used to define a clock system and resonant sensor performance [19]. Figure 13.9(b) shows the measured Allan variance of the outputs of the sensing oscillator, PLL, and IF with a sample rate of 1 Hz. The Allan variance gradually flattens out as average time increases. The drift is most likely caused by the temperature and environment fluctuations, which can be removed with feedback control to VCO1. Furthermore, this plot reveals that the accelerometer has a resolution of 80 mg and a bias stability of 35 mg for a 10 s integration window. The noise floor of this accelerometer is limited by the phase noise of the sensing oscillator, not by mechanical noise sources. Accelerometer performance is summarized in Table 13.3.
Distributed Multi-Antenna SAR Time and Phase Synchronization
Published in Wen-Qin Wang, Multi-Antenna Synthetic Aperture Radar, 2017
The Allan variance is based on the average of the variance with N = 2 and adjacent samples (i.e, T = t). The Allan variance is defined as [5] σy2(τ)=12〈(y¯2−y¯1)2〉
Frequency Measurement
Published in John G. Webster, Halit Eren, Measurement, Instrumentation, and Sensors Handbook, 2017
For these reasons, frequency metrologists generally rely on nonclassical statistics to estimate and specify the frequency stability of oscillators [4]. The most common statistic employed for stability estimates is often called the Allan variance, but because it is actually the square root of the variance, its proper name is the Allan deviation (ADEV). Similar to the standard deviation, ADEV is better suited for frequency metrology because it has the advantage of being convergent for most types of oscillator noise. The equation for ADEV using frequency measurements and nonoverlapping samples is
Phase Noise Impact on the Short-Term Frequency Stability of a Frequency Source
Published in IETE Journal of Research, 2023
Md. Tosicul Wara, M. S. Bhuvaneshwari, M. R. Raghavendra, Usha Bhandiwad
For Random Walk FM Noise, For Flicker FM Noise, For White FM Noise, For Flicker PM Noise, For White PM Noise, Once the fractional frequency noise constants, and consequently, the Allan variance constants, are estimated from the measured phase noise data, the Allan deviations for the individual noise processes could be estimated from Equations (13a)–(13e). The overall Allan deviation due to all the noise processes, which is equal to the root sum square (RSS) of the individual Allan deviations could be estimated using Equation (12) as stated above.
Reactive oxidized nitrogen speciation and partitioning in urban and rural New York State
Published in Journal of the Air & Waste Management Association, 2021
Matthew Ninneman, Joseph Marto, Stephanie Shaw, Eric Edgerton, Charles Blanchard, James Schwab
where AV is the Allan variance, y is the chemical species of interest, ∆y is the change in concentration, represented here by y over the averaging period (i.e., ∆y = yt+1 – yt), and is the average of the square of each change of y over the averaging time period. Based on visual inspection of the initial Allan variance plots, a second Allan variance plot was generated for NO, HNO3, PNs, ANs, and NOy that showed only the stable periods that (1) exhibited a consistent relationship between the Allan variance and the averaging time, and (2) consisted of measurements that were likely above the method detection limit (MDL). For clarity, these stable periods were denoted as “selected stable periods.” Then, the percent error was computed using the following equations:
Trace methane gas detection by wavelength modulated off-axis integrated cavity output spectroscopy
Published in Journal of Modern Optics, 2019
Rong Lai, Chao He, Xin Li, Zhengguang Zhu
Allan variance is usually used to study some important performance parameters of the analytical instruments, such as system stability, sensitivity, and so on. Averaging spectral data can reduce White noise and improve measurement precision. The optimal average time can be determined by Allan variance analysis (19). In the present work, the optical cavity was flushed with 10 ppmv CH4 and 1450 successive measurements were recorded, each of which was averaged 100 times. The relationship between Allan variance and the average time is shown in Figure 8. With the increasing of average time, the Allan variance of 2f signal plot shows an optimum average time of ∼1644 s, and the Allan variance of 2f/1f value plot shows an optimum average time of ∼1660 s. Up to this point, the system of 2f signal and 2f /1f value had a very good stability. The average time of 80 s was selected as the compromise between fast time response and precision.