Mathematical analysis of the pulse coincidence process for applications on frequency sensors after the use of variable references

Abstract

In most cases, sensors are the means that enable a computer to get information from a process of interest. This requires that the information generated by the sensor can be processed by the computer in a timely manner. However, if accurate data from the sensor is required, an appropriate transduction process is required. There are sensors that generate a frequency-domain output. Since these sensors typically have a short response time, it is required to get the best approximation to their frequency within the shortest time possible. There are different methods for obtaining the frequency value generated by the sensor. Although such methods can be applied, their functioning characteristics are not suitable for application in sensors. The principle of rational approximations is a method that has proven plenty of improvements in comparison to other frequency measurement methods. In this work, the functioning of the principle of rational approximations is explored when different time references are used. After the computational analysis of the principle of rational approximations, it was found out how the reference frequency value affects the measurement process. It was found that if the magnitude of reference and unknown frequencies have an increment in their difference, then the relative error decreases.