基于零相位频率的晶体谐振器等效电参数测量方法

晶体谐振器等效参数的测量方法很多，工程上通常利用谐振频率和负载谐振频率来求解等效参数。该文推导了谐振频率、负载谐振频率、反谐振频率和负载反谐振频率的精确形式，并以此为基础求解晶体谐振器的等效参数。ADS仿真实验表明，该方法在理论上正确。利用相位-频率曲线在谐振点与反谐振点的导数构建非线性方程组，解决实测实验中的频率随机游动问题。采用二维搜索法求解非线性方程组。实测结果表明，该方法测量的等效参数和供应商提供的等效参数基本一致。该方法没有采用近似计算，不仅适用于高Q值晶体谐振器，也适用于低Q值谐振器，因此，该方法也能应用于传感器领域，如温度传感器、石英晶体微天平等。

Measurement of Quartz Crystal Resonator Parameters Based on the Precise Derivation of Zero Phase Frequency

There are a lot of methods to measure the equivalent parameters of the crystal resonator. In engineering, the resonant frequency and the load resonant frequency are usually used to calculate the equivalent parameters. In this paper, the precise form of the resonant frequency, the load resonant frequency, the anti-resonant frequency and the load anti-resonant frequency are deduced, which serve as the basis to calculate the equivalent parameters of crystal resonators. Advanced design system (ADS) simulation show that this method is correct in theory. In this paper, the nonlinear equations are constructed by the derivative of the phase-frequency-curve at the point of resonance and anti-resonance to solve the problem of random walk of frequency in the experiment. Then, the two-dimensional search method is used to solve those nonlinear equations. The experimental results show that the equivalent parameters measured by this way are basically the same as those provided by manufacturer. This method does not adopt approximate calculation, namely, it is not only suitable for high Q crystal resonators, but also suited to low Q resonators. Therefore, it can also be applied to the field of sensors, such as temperature sensors, quartz crystal microbalances, and so forth.