Detection of resonant frequency of QCM by using Chirp Z-Transform

Abstract

One of the main working principles of the Quartz Crystal Microbalance (QCM) is the relationship between the series of resonance frequency and mass change. Commonly, the sensor works as an oscillator system, where the resonant frequency is measured using a frequency counter. For a heavy damped condition, the oscillator stops to operate. This paper deals with the use of the spectral analysis approach to detect the QCM resonant frequency. The scenario is that the QCM sensor is subject to an input signal consisting of multi-frequency components; its frequency and magnitude of the output signal are then analyzed. The resonant frequency must be within the signal frequency input range and have the largest magnitude in the output of signal spectrum. Using FFT, there would be a heavy burden of computation in finding the resonant frequency since the high sampling frequency is larger than at least twice of the required resonant frequency of QCM; while the required bin size of the output signal spectrum is expected as small as possible. Thus, a large portion of unwanted frequencies is computed in FFT yet then ignored. This paper elaborates the use of the Chirp Z-Transform (CZT) to overcome this problem since its computation is less costly and can focus on a limited desired range of the frequency spectrum with smaller bin size. For a case study, A BVD model of QCM of the AT-cut quartz crystal type in HC49/U standard package was numerically simulated and tuned at 10 MHz series resonant frequency. Using the CZT method, a fair estimation of the QCM's resonant frequency was obtained from the spectral analysis of the output signal of QCM, which was subject to the narrow range of the multi frequency input signal adjusted at 40 MHz frequency as a sample.