For ultrasonic systems, the resonance frequency tracking (RFT) is the most critical step. The rapid development in advanced material processing and microelectronics package has increased the demand of high speed RFT. Therefore, this paper proposes a fast RFT (FRFT) method according to the characteristics of piezoelectric transducers' (PT) admittance circle. In the proposed method, the PT is driven at two different frequencies, and the PT's admittance is collected and calibrated. Then, the PT's mechanical resonance frequency is derived using the admittance information after calibration. The proposed method is not affected by the parallel capacitor and the matching circuit. Additionally, the optimal initial values of the involved parameters are determined in order to improve the accuracy of the proposed method. Furthermore, an improved method based on multiple tracking is also provided. Simulations and experiments demonstrate that using the proposed FRFT method, the ultrasonic system can track the resonance frequency in a short time with high accuracy.
A universal method is proposed for fast tracking the peak wavelength of a fiber Bragg grating (FBG) reflection spectrum, which is the essential procedure of most FBG interrogators. Assuming the FBG reflection spectrum is sampled uniformly, we decompose the Moore–Penrose of the coefficient matrix into a formula that only contains a division and a dozen additions and multiplications; thereby, the cost of computation can be greatly reduced. Based on the analysis of the characteristics of the error introduced by the spectrum’s nonlinearity, we found and defined an error associated with the distance between the sampled peak and actual peak, and the compensating method for the error is also given. After compensation, the proposed method can speed up the tracking process 10 times or more without sacrificing the accuracy. An economical FBG interrogator with a commercial field programmable gate array (FPGA) and a microspectrometer was built up to verify the method, which was able to achieve a measurement frequency of 17 kHz.
Fluctuation of acoustic load significantly weakens the performance of ultrasonic system. To address this problem in a simple way, we consider the main input and output variables related to the ultrasonic transducer's performance and propose a detailed mathematical model based on the simplest LC matching network containing only one capacitor and one inductor. In this model, a new resonance frequency brought by matching components was found and defined. The optimum analysis method is used to solve the model, and a high-tolerance matching method against load fluctuation is obtained. Analysis indicates that when activated at the mechanical resonance frequency, the impedance and apparent power of the PT matched by the proposed method are constant no matter how the load changes, and thereby can significantly increase the stability and robustness of ultrasonic systems. For its simple structure and high performance, the proposed matching method can be widely applied in most ultrasonic systems. The tolerance of the proposed method against other environmental factors and high-order LC matching networks were also discussed. In addition, the feasibility and advantage of the proposed matching method are also verified by experiments.
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