Phase measurement and error analysis in the arc-tangent method using a novel phase-compensating algorithm

Many applications related to measurements use sinusoidal waves such as acoustic and electromagnetic waves. In particular, the phase information of sinusoidal waves is frequently used in several sensors. However, it is difficult to extract the phase information exactly, and many operations are consequently demanded. Among the operations, the arc-tangent method is very useful to measure the phase of a sinusoidal signal. This method, however, has a limitation that the initial phase difference between two sinusoidal signals must be essentially 90°, in some cases preventing its use. This paper proposes a novel algorithm to calculate the initial phase difference between two sinusoidal signals and to compensate the initial phase difference to exactly 90°. Several mathematical steps including equations are taken for the compensation. The mathematical equations are successfully simulated by using a numerical method to verify their availability in a computer simulation. In addition, experimental verification is also shown to confirm the performance of the algorithm by using a function generator and a data acquisition system. Finally, the phase measurement is also successfully performed by using the phase-compensating algorithm and the error of the phase measurement is analyzed.