Statistical research of the measuring the frequency by coincidence method

Authors: Laptev D. V., Pasynkov Yu. A.

Annotation: The research represents the dependence of time frequency measurement by the coincidence method on a mathematical model of duty cycle and level of preset discrete maximum methodical relative peak error. Statistical modeling was carried out under the conditions that the measured frequency is less than reference frequency, frequency measurement process starts with zero phase between pulses reference and measured frequencies. We performed the comparison of the incremental method for speed measurement frequency (measured in an integer number of periods measured frequency [1–3]), and the measurement of frequency by coincidence method. We used the concept of «gain in performance» [8], which is defined as the ratio time of the frequency measurement by the incremental method to time of the frequency measurement by the coincidence method. According to the results of modeling there are the following conclusions. Measure frequency by coincidence method can be used over a wide frequency range. The frequency range in which there is «gain in performance», coincidence method for frequency measuring compared to the incremental method, increases with decreasing preset level of the discrete maximum methodical relative peak error. «Gain in performance» coincidence method for measuring the frequency increases with the increase of the measured frequency and decreasing preset level of the discrete methodical relative peak error. «Gain in performance» coincidence method for frequency measuring compared with the classical method depends on the duty cycle. As in [8] that there are optimums values of duty cycle, which achieves the highest «gain in performance» coincidence method for frequency measuring, compared to the incremental method. The optimal values depend on the duty cycle of a preset level of the discrete methodical relative peak error and measurable frequency range.

Keywords: statistical modeling, model of frequency measurement, measurement frequency, digital frequency meters, gain in performance, coincidence method, duty cycle, discrete methodical relative peak error