Admittance characteristics of piezoelectric ceramics

The admittance characteristics are further analyzed based on the obtained equivalent circuit diagram of the piezoelectric ceramics transducer. In order to simplify the derivation, it is assumed that the piezoelectric ceramic transducer has no electrical loss, that is, 0R=0, and the equivalent circuit is an LC circuit. For the analysis of the series branch, according to the definition of the resonant frequency, let 1B=0, 1G=0 or 111RG= can be obtained. Since the actual piezoelectric ceramic transducer's dynamic resistance 0R cannot be zero, the expression of 1G can be known that only 111RG satisfies the condition of series resonance. Then considering the situation after adding a static capacitor the static capacitance, the admittance of the transducer is equivalent to the susceptance of the series branch. In general, the mechanical quality factor of the piezoelectric ceramic transducer is large, that is, near the series resonant frequency, the value of 00CjY varies  with frequency and can be approximated as a constant. Therefore, it is only necessary to shift the ordinate of the admittance circle obtained by the series branch, and the abscissa remains unchanged to obtain the transducer after adding the static capacitor, and then consider the static resistance of the transducer. the actual admittance circle is unlikely to be tangent to the longitudinal axis, but to the positive direction of the horizontal axis by a certain amount (the amount of translational distance depends on the resistance of the static resistance),A brief analysis of the admittance chart shows that when sff< is s, the susceptance value is greater than zero. When sff is s, the susceptance value is less than zero. Therefore, as the frequency increases, the admittance circle changes in a clockwise direction. In addition, in the vicinity of the series resonant frequency, there are two frequency points so that the total susceptance of the transducer is zero. 

At this time, after the power signal passes through the transducer, only the amplitude changes, and there is no phase change, that is, The voltage and current signals are in phase of these two frequencies, the smaller value of the frequency rf is called the resonant frequency of hard material piezoelectric ceramics, and the larger af is called the anti-resonant frequency. In addition, there is a frequency mf which maximizes the admittance value of the transducer and a frequency nf at which the admittance value is the smallest. The frequency pf at the intersection of the origin and the series resonant frequency point and the admittance circle is called the parallel resonant frequency. In addition, it should be particularly pointed out that the above discussion is carried out within a small frequency variation range around a vibration mode resonance frequency. when the diameter of the admittance circle is much larger than the change of 0C in this frequency range. It is correct, otherwise the admittance curve of the transducer will become very complicated, with the characteristics of the vine curve.According to the derivation process of the above admittance chart, the relationship between each parameter and the admittance chart in the equivalent circuit of the piezoelectric ceramic transducer is introduced below, and the respective calculation formulas are given. In the admittance diagram of the transducer, the diameter is parallel to the longitudinal axis is made, and the admittance is rounded at two points, which are respectively denoted as 1f and 2f. At 1f, the dynamic conductance and susceptance values of the series branches are equal.

It can be seen from the above theoretical derivation of the correlation function method.measurement principle and phase difference of the Pzt4 piezoceramic cylinder measurement signal are independent of the frequency of the signal. That is to say, the correlation function method is not affected by the frequency and can be used to measure the phase difference of the signal of the unknown frequency. At the same time, the derivation of the correlation function method is based on a sinusoidal function. Therefore, it can only be used to measure sine or cosine signals, and it cannot measure general periodic signals.

Since the noise interference signal of column piezoelectric ceramic is not correlated with the original signal, the correlation function method can effectively suppress noise interference. However, if there is a strong correlation interference signal in the system, and the signal-to-noise ratio is relatively low, the correlation function method measurement error will be relatively large. It can be seen from the final calculation formula of the discrete sequence of the correlation function method that the calculation result is related to the number of points , that is, the magnitude of the measurement error is related to the number of sampling points, and the larger number of sampling points are closer for the calculation result is to the true value. The measurement error is smaller. Based on the above analysis of the characteristics of the correlation function method, it can be seen that the correlation function method has strong suppression ability for DC offset and noise in the sampled conversion signal. The error is mainly because the finite length sample is used instead of Gaussian white. The noise A/D quantization error make the detected sinusoidal signal not completely uncorrelated with the noise signal. Therefore, the measurement error of the correlation function method is related to the number of bits of the A/D conversion, the signal-to-noise ratio of the signal has the number of acquisition points.

The constrained least squares curve fitting of the admittance circle is that we have obtained the conductance and susceptance values of the piezoelectric transducer at each test frequency, and draw the admittance circle diagram, but this is not enough. 

It can be seen from the calculation formula of the various parameters of the piezoelectric discs piezo ceramic equivalent circuit that we also need to obtain the value of the center and radius of the admittance circle. To do this, it is necessary to perform a circular curve fitting on the obtained discrete points. There are many ways to fit a circle. Commonly used are the average method, the weighted average method, and the least squares method. The idea of the average method is to calculate the average value of the horizontal and vertical coordinates of each discrete point separately, and as the horizontal and vertical coordinates of the center of the circle, the average value of the distance from the center of the circle to each discrete point is taken as the radius. This method is simple to calculate and is suitable for the case where the discrete points are distributed more uniformly. However, for the case of uneven distribution, the calculated center position will be biased toward the side where the discrete points are densely distributed, and the calculated value of the radius will be too small. The weighted average method is an improvement of the average method. It adds a coefficient related to the arc length between two adjacent points when calculating the center coordinates, which reduces the influence of uneven distribution of discrete points and reduces the error. However, since the arc length between two adjacent points cannot be accurately obtained (in practice, the distance between two points is used ), the error is still large. In contrast, the least squares method has higher precision.