Equivalent Circuit Modeling Method of Piezoelectric Materials under the Principal Vibration Mode Based on SOMA

Abstract

The present invention discloses a method for modeling the equivalent circuit of a piezoelectric material in the main vibration mode based on SOMA, including the following steps: establishing an equivalent circuit model of the piezoelectric material in the main vibration mode; impedance extraction: extracting impedance data of the main vibration frequency band of the piezoelectric material through a vector network analyzer; listing the impedance expression of the equivalent circuit; obtaining the RLC parameters of the equivalent circuit by using the SOMA algorithm; extracting the parameters of the piezoelectric material in the main vibration mode; verifying the effectiveness of the equivalent circuit model and the material parameters. The technical solution of the present invention can improve the impedance characterization accuracy of the piezoelectric material and determine its impedance resonance characteristics.

Description

Technical Field

[0001] The present invention relates to a modeling method of piezoelectric materials in the main vibration mode, and specifically to an equivalent circuit modeling and parameter optimization method of piezoelectric materials in the main vibration mode based on SOMA. Background Art

[0002] Scholars at home and abroad have carried out extensive research on the modeling and characterization of piezoelectric materials and achieved many results. However, there is little research on the equivalent circuit modeling of piezoelectric materials concerned by the present invention, especially the circuit modeling research under multiple vibration modes has not been reported. In addition, there is no report on the research related to the model of the relationship between the geometric size and impedance of piezoelectric materials. In addition, the methods for extracting piezoelectric material parameters involved in various studies mostly require complex measurements and finite element simulations or iterative calculations of multi-parameter algorithm optimizations, and there are still great limitations in practical applications.

[0003] In summary, to achieve effective noise suppression using piezoelectric materials, an accurate impedance characterization method is required to determine its impedance resonance characteristics, and the equivalent circuit model and material parameters of piezoelectric materials are the key to impedance characterization. Usually, the calculation model provided in the IEEE piezoelectric material standard and the material parameters provided by the manufacturer are used to characterize its impedance, but the lack of accuracy of this method makes it unable to accurately characterize the impedance resonance characteristics. Therefore, it is very meaningful and necessary to study accurate equivalent circuit modeling of piezoelectric materials and material parameter extraction methods to improve the impedance characterization accuracy of piezoelectric materials and determine their impedance resonance characteristics. Summary of the Invention

[0004] Object of the Invention: The object of the present invention is to provide an equivalent circuit modeling and parameter optimization method of piezoelectric materials in the main vibration mode based on SOMA, which can improve the impedance characterization accuracy of piezoelectric materials and determine their impedance resonance characteristics.

[0005] Technical Solution: The equivalent circuit modeling and parameter optimization method of piezoelectric materials in the main vibration mode based on SOMA of the present invention includes the following steps:

[0006] (1) Establish an equivalent circuit model of piezoelectric materials in the main vibration mode;

[0007] (2) Impedance extraction: Extract the impedance data of the main vibration frequency band of piezoelectric materials through a vector network analyzer;

[0008] (3) List the impedance expression of the equivalent circuit;

[0009] (4) Use the SOMA algorithm to obtain the RLC parameters of the equivalent circuit;

[0010] (5) Extract the parameters of piezoelectric materials in the main vibration mode;

[0011] (6)Verify the effectiveness of the equivalent circuit model and material parameters.

[0012] In step (1), the topology of the equivalent circuit model of the piezoelectric material under the main vibration mode includes a capacitor C0, a capacitor C m , an inductor L m , and a resistor R m ; one end of the capacitor C0 is connected to one end of the capacitor C m , the other end of the capacitor C m is connected to one end of the inductor L m , the other end of the inductor L m is connected to one end of the resistor R m , and the other end of the resistor R m is connected to the other end of the capacitor C0.

[0013] In step (2), the impedance data is a data set containing N discrete frequencies (f1,..., f N ) and their corresponding impedances.

[0014] In step (3), the equivalent circuit impedance expression is as follows:

[0015]

[0016] In the formula, C m , R m , L m represent the capacitance, resistance, and inductance in the equivalent circuit.

[0017] In step (4), the specific steps to obtain the equivalent circuit RLC parameters using the SOMA algorithm are as follows:

[0018] Use the SOMA algorithm to obtain the equivalent circuit RLC parameters. Take Z PZT as the original function of the circuit RLC parameters to be extracted, and the measured impedance data Z m (f) as the sample, where

[0019]

[0020] Apply the SOMA algorithm to the extraction of RLC parameters, and establish the objective function Q as follows:

[0021]

[0022] Among them, Z m (f) is the measured impedance amplitude, and Z PZT (f)' is the calculated value of the impedance amplitude of the equivalent circuit; when the variable Q is the minimum value, the corresponding set of C0, C m , L m , R mThe value is the optimal parameter, thus realizing the extraction of the equivalent circuit RLC parameters of the piezoelectric material in the main vibration mode.

[0023] In step (6), the verification of the effectiveness of the equivalent circuit model and material parameters is specifically as follows: The equivalent circuit parameters and circuit impedance of the same piezoelectric material with different sizes are compared with the impedance measurement values in the main resonance, and the material parameter values are adjusted and optimized to verify the effectiveness of the material parameters.

[0024] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial effects: (1) According to the relationship between the circuit topology and material parameters, the present invention calculates the piezoelectric material parameters in the main vibration mode. Repeating the above method, multiple material parameter calculations are performed based on different sizes of the same piezoelectric material to select the optimal piezoelectric material parameters, and these parameters are used to replace the material parameters provided by the manufacturer to improve the impedance characterization accuracy of the piezoelectric material and determine its impedance resonance characteristics; (2) It has great practical significance for improving the utilization efficiency of piezoelectric materials, realizing the impedance resonance design of materials, and guiding the processing of piezoelectric materials. Description of the Drawings

[0025] Figure 1 is the flow chart of the present invention;

[0026] Figure 2 is the topology diagram of the main resonance equivalent circuit of the piezoelectric material;

[0027] Figure 3 is the flow chart of the SOMA algorithm;

[0028] Figure 4 is the example diagram of the polarization and vibration mode of the piezoelectric material geometry. Detailed Embodiments

[0029] The technical solution of the present invention will be introduced in detail below in combination with the specific embodiments and the drawings in the specification.

[0030] As Figure 1 shown, the method for modeling the equivalent circuit of the piezoelectric material in the main vibration mode based on SOMA of the present invention includes the following steps:

[0031] (1) Establish an equivalent circuit model of the piezoelectric material in the main vibration mode. As Figure 2 shown, the topology of this equivalent circuit model includes capacitor C0, capacitor C m , inductor L m and resistor R m ; One end of capacitor C0 is connected to one end of capacitor C m , the other end of capacitor C m is connected to one end of inductor L m , the other end of inductor L m is connected to one end of resistor R m and the other end of resistor Rm The other end of is connected to the other end of capacitor C0;

[0032] (2) Extract the impedance data Z of the main vibration frequency band of the piezoelectric material through a vector network analyzer (VNA) m (f), Z m (f) is a discrete frequency containing N frequencies (f1, ..., f N ) and their corresponding impedance datasets;

[0033] (3) According to the topology of the equivalent circuit model of piezoelectric material under the main vibration mode, the impedance expression can be obtained:

[0034]

[0035] (4) Figure 3 As shown, the SOMA algorithm is used to obtain the equivalent circuit RLC parameters. PZT As the original function of the circuit RLC parameters to be extracted, the impedance data Z is measured m (f) is a sample, where

[0036]

[0037] The SOMA algorithm is applied to RLC parameter extraction, and its objective function Q is established as follows:

[0038]

[0039] Among them, Z m (f) is the measured impedance amplitude, Z PZT (f)' is the calculated impedance amplitude of the equivalent circuit. When the variable Q is at its minimum value, the corresponding set of C0, C m , L m , R m The value is the optimal parameter, thus realizing the extraction of RLC parameters of the piezoelectric material equivalent circuit under the main vibration mode.

[0040] (5) Extraction of piezoelectric material parameters under the main vibration mode. Generally speaking, the small signal behavior of piezoelectric materials is numerically simulated based on the piezoelectric constitutive equations. Taking the d-form as an example, these equations are defined as:

[0041]

[0042] Where T and S represent the vectors of mechanical stress and mechanical deformation. The behavior of the material is determined by three tensors: 1) the elastic compliance constant tensor [s E ], 2) the dielectric constant tensor at constant mechanical stress [ε T, 3) Piezoelectric strain coefficient tensor [d]:

[0043]

[0044]

[0045] These three tensors contain 10 independent material parameters, which can characterize the impedance characteristics of piezoelectric materials, and these materials are related to the RLC parameters of the equivalent circuit. Taking a rectangular piezoelectric material as shown in Figure 4 as an example, p is the polarization direction and vibrates in the polarization direction. There are:

[0046]

[0047] Given the actual geometric dimensions 2a, 2b, 2c of the piezoelectric material, and the material density ρ, h refers to the h-th resonance. Here, only the first resonance in the main vibration mode is considered, h is 1, and C0, C m , L m obtained through equivalent circuit modeling, the material parameters corresponding to the main vibration mode of the material can be solved. For example, It should be noted that the main resonance corresponding to the main vibration is only a part of the impedance characteristics of the piezoelectric material. Therefore, only some material parameters can be obtained here. Of course, these material parameters can already characterize the impedance characteristics of the main resonance. Here, the extraction accuracy of material parameters can be improved by extracting parameters multiple times for the same material with different sizes and selecting the mean value of multiple parameters as the optimal parameter, and then replacing the parameters provided by the manufacturer with the optimal parameter to achieve parameter optimization. In addition, another advantage of this method is that piezoelectric materials have temperature sensitivity. By measuring the impedance and optimizing parameters at different temperatures, the impedance characteristics at different temperatures can be characterized.

[0048] (6) After obtaining the optimized parameters of a certain piezoelectric material, based on Equation (4), calculate the equivalent circuit parameters and circuit impedance of piezoelectric materials with different sizes, compare the main resonance with the impedance measurement values, and adjust and optimize the material parameter values to verify the effectiveness of the material parameters.

[0049] In summary, the technical solution of the present invention has great practical significance for improving the utilization efficiency of piezoelectric materials, realizing the impedance resonance design of materials, and guiding the processing of piezoelectric materials.

Claims

1. An equivalent circuit modeling method for piezoelectric materials under the main vibration mode based on SOMA, characterized in that, It includes the following steps: (1) Establish an equivalent circuit model of the piezoelectric material in the main vibration mode; (2) Impedance extraction: Extract the impedance data of the piezoelectric material in the main vibration frequency band through a vector network analyzer; (3) List the impedance expression of the equivalent circuit; (4) Use the SOMA algorithm to obtain the RLC parameters of the equivalent circuit; (5) Extract the parameters of the piezoelectric material in the main vibration mode; (6) Verify the effectiveness of the equivalent circuit model and material parameters; In step (1), the topology of the equivalent circuit model of the piezoelectric material in the main vibration mode includes a capacitor C0, a capacitor C m , an inductor L m , and a resistor R m ; one end of the capacitor C0 is connected to one end of the capacitor C m , the other end of the capacitor C m is connected to one end of the inductor L m , the other end of the inductor L m is connected to one end of the resistor R m , and the other end of the resistor R m is connected to the other end of the capacitor C0; In step (3), the impedance expression of the equivalent circuit is as follows: where C m , R m , L m represent capacitance, resistance, and inductance in the equivalent circuit; In step (4), the use of the SOMA algorithm to obtain the RLC parameters of the equivalent circuit is specifically as follows: The SOMA algorithm is used to obtain the equivalent circuit RLC parameters, and Z PZT is used as the original function of the circuit RLC parameters to be extracted, and the measured impedance data Z m (f) is used as a sample, where Apply the SOMA algorithm to the extraction of RLC parameters, and establish the following objective function Q: Among them, Z m (f) is the measured impedance amplitude, and Z PZT (f)' is the calculated value of the impedance amplitude of the equivalent circuit; when the variable Q is at its minimum value, the corresponding set of C0, C m , L m , R m values are the optimal parameters, thus realizing the extraction of the RLC parameters of the equivalent circuit of the piezoelectric material in the main vibration mode.

2. The equivalent circuit modeling method for piezoelectric materials under the main vibration mode based on SOMA according to claim 1, characterized in that: In step (2), the impedance data is a data set including N discrete frequencies (f1,..., f N ), and their corresponding impedances.

3. The equivalent circuit modeling method for piezoelectric materials under the main vibration mode based on SOMA according to claim 1, characterized in that, In step (6), the verification of the effectiveness of the equivalent circuit model and material parameters is specifically to compare the equivalent circuit parameters and circuit impedance of the same piezoelectric material with different sizes with the impedance measurement values at the main resonance, adjust and optimize the material parameter values, and realize the verification of the effectiveness of the material parameters.

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