A method for modeling and extracting parameters of piezoelectric material under multiple vibration modes

Abstract

The application discloses a piezoelectric material equivalent circuit modeling and parameter extraction method under multiple vibration modes, and comprises the following steps: establishing a piezoelectric material impedance equivalent circuit topology under multiple vibration modes; extracting impedance data of the piezoelectric material under corresponding vibration modes through a vector network analyzer; listing impedance expressions according to the piezoelectric material impedance equivalent circuit topology under corresponding vibration modes; extracting parameters of the equivalent circuit by using a differential evolution algorithm; obtaining optimal resistance, inductance and capacitance (RLC) parameter values of the equivalent circuit under corresponding vibration modes; and calculating piezoelectric material parameters corresponding to each vibration mode according to the relationship between the piezoelectric material equivalent circuit and the piezoelectric material parameters. The application realizes the equivalent circuit modeling of the piezoelectric material under multiple vibration modes, and realizes high-precision extraction of material parameters under corresponding vibration modes through the relationship between the piezoelectric material equivalent circuit and the piezoelectric material parameters.

Description

TECHNICAL FIELD

[0001] The application relates to a modeling method of piezoelectric materials under multiple vibration modes, and particularly relates to a piezoelectric material equivalent circuit modeling and parameter extraction method under multiple vibration modes. BACKGROUND

[0002] Switching power supply replaces linear power supply with its low manufacturing cost, low weight, small size and other advantages, and is widely used in various fields from small electronic devices to large industrial devices, but the serious electromagnetic interference caused by the high switching frequency of the switching power supply. Adding filters and related components in the switching power supply is the current mainstream measure to suppress electromagnetic interference, but this not only limits the design scheme of the switching power supply, but also increases the size and weight. Meanwhile, considering the application trend of wide band gap semiconductor technology (such as GaN and SiC) in the switching power supply, the problem will become more serious. On the one hand, the low switching loss and high switching frequency of the wide band gap semiconductor improve the power density of the switching power supply, and on the other hand, the technology leads to a larger voltage change rate du / dt, which aggravates electromagnetic interference and requires a larger size EMI filter for interference suppression. Therefore, reliable and effective electromagnetic interference suppression measures have attracted more and more attention, and especially new technologies that take into account the suppression effect and power density are particularly attractive to switching power supplies using wide band gap semiconductor technology.

[0003] The piezoelectric material can generate a low-impedance propagation path at its resonance frequency, realize the attenuation of discrete disturbance peaks, and has a similar impedance characteristic to a capacitor outside the resonance frequency, and therefore can be used instead of a capacitor. Meanwhile, the piezoelectric material often accompanies vibration in multiple directions during operation, and has multiple resonances, so that the suppression of multiple noise frequency points can be realized by using this characteristic. Therefore, the application of the piezoelectric material to the EMI noise suppression of the switching power supply helps to optimize the filter size and improve the power density of the switching power supply.

[0004] In summary, how to model the piezoelectric material equivalent circuit under multiple vibration modes and extract the material parameters is of great significance for further improving the utilization efficiency of the piezoelectric material, realizing the impedance resonance design of the piezoelectric material and guiding the piezoelectric material processing. SUMMARY

[0005] The purpose of the application is to provide a piezoelectric material equivalent circuit modeling and parameter extraction method under multiple vibration modes, which provides a piezoelectric material equivalent circuit model topology under multiple vibration modes, and extracts the piezoelectric material parameters corresponding to each vibration mode with high precision according to the relationship between the piezoelectric material equivalent circuit and the piezoelectric material parameters.

[0006] Technical scheme: The piezoelectric material equivalent circuit modeling and parameter extraction method under multiple vibration modes comprises the following steps:

[0007] (1)establishing the impedance equivalent circuit topology of piezoelectric material under multiple vibration modes;

[0008] (2) extracting the impedance data of piezoelectric material under corresponding vibration modes through a vector network analyzer;

[0009] (3) listing the impedance expression of piezoelectric material under corresponding vibration modes according to the impedance equivalent circuit topology of piezoelectric material under corresponding vibration modes;

[0010] (4) extracting the parameters of equivalent circuit by using differential evolution algorithm;

[0011] (5) obtaining the optimal RLC parameter values of equivalent circuit under corresponding vibration modes;

[0012] (6) calculating the piezoelectric material parameters corresponding to each vibration mode according to the relationship between the equivalent circuit of piezoelectric material and the parameters of piezoelectric material.

[0013] In step (1), the impedance equivalent circuit topology of piezoelectric material under multiple vibration modes is a plurality of series-connected equivalent circuit topologies with the same structure.

[0014] The i-th equivalent circuit topology in the plurality of equivalent circuit topologies comprises a capacitor C i , a capacitor C mi , a resistor R mi , and an inductor L mi ; one end of the capacitor C i is connected to one end of the resistor R mi , the other end of the capacitor C i is connected to one end of the capacitor C mi , one end of the resistor R mi is connected to one end of the inductor L mi , and the other end of the inductor L mi is connected to the other end of the capacitor C mi .

[0015] In step (2), the impedance data is a data set containing N discrete frequencies (f1,..., f N ) and their corresponding impedances.

[0016] In step (3), according to the impedance equivalent circuit topology of piezoelectric material under corresponding vibration modes, the impedance expression of piezoelectric material under corresponding vibration modes is obtained. Z PZT

[0017]

[0018] In the formula, Z PZT is the impedance of piezoelectric material under multiple vibration modes; R mi , C mi ​L mi Let ω represent the resistance, capacitance, and inductance parameters in the i-th series topology of the piezoelectric material equivalent circuit under multiple vibration modes; ω = 2πf, where ω is the angular frequency and f is the frequency.

[0019] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial effects: The present invention establishes the topology of the equivalent circuit model of piezoelectric materials under multiple vibration modes, and realizes high-precision extraction of material parameters under the corresponding vibration modes based on the relationship between the equivalent circuit of piezoelectric materials and the parameters of piezoelectric materials. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the process of the present invention;

[0021] Figure 2 This is the piezoelectric material multi-resonant equivalent circuit topology in this invention;

[0022] Figure 3 Here is a flowchart illustrating the principle of the differential evolution algorithm.

[0023] Figure 4 This is the topology after disassembling the equivalent topology of the piezoelectric material circuit in this invention;

[0024] Figure 5 This is an example diagram of the geometric polarization and vibration modes of the piezoelectric material in this invention. Detailed Implementation

[0025] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0026] like Figure 1 As shown, the method for modeling and extracting parameters of piezoelectric materials under multiple vibration modes according to the present invention includes the following steps:

[0027] (1) As Figure 2 As shown, an equivalent circuit topology for the piezoelectric material impedance under multiple vibration modes is established. This topology consists of multiple equivalent circuit topologies with identical structures connected in series. The i-th equivalent circuit topology has the following structure: including capacitor C i Capacitor C mi Resistance R mi Inductor L mi The capacitor C i One end is connected to a resistor R mi One end, capacitor C i The other end is connected to capacitor C. mi One end; the resistor R mi The other end is connected to inductor L mi One end is connected, inductor L mi The other end is connected to capacitor C mi The other end is connected.

[0028] (2) Extract the impedance data Z of piezoelectric material under corresponding vibration mode by vector network analyzer m (f), Z m (f) is a data set containing N discrete frequencies (f1,..., f N ) and their corresponding impedance;

[0029] (3) List the impedance expression according to the impedance equivalent circuit topology of piezoelectric material under corresponding vibration mode;

[0030] The impedance expression of piezoelectric material under corresponding vibration mode can be obtained from the equivalent circuit topology of piezoelectric material under multiple vibration modes Z PZT :

[0031]

[0032] In the formula, Z PZT Z is the impedance of piezoelectric material under multiple vibration modes, R mi , C mi , L mi are the resistance, capacitance, and inductance parameters in the i-th series topology in the equivalent circuit of piezoelectric material under multiple vibration modes, ω = 2πf, ω is the angular frequency, and f is the frequency.

[0033] (4) Extract the parameters of the equivalent circuit using differential evolution algorithm; as shown in the following figure, the specific steps are as follows: Figure 3

[0034] (4.1) Optimal parameter problem transformation: transform the impedance expression of piezoelectric material under corresponding vibration mode Z PZT into the expression of impedance amplitude Z x , and then take Z x as the original function of RLC parameters to be extracted, and the measured impedance data Z m (f) is a sample; let the expression of impedance amplitude Z x of piezoelectric material impedance equivalent circuit under corresponding vibration mode be:

[0035]

[0036] In the formula, D represents the spatial dimension, and respectively represent the maximum and minimum values of the j-th component x j ; f represents the independent variable; Z x represents the dependent variable; x1, x2, x3,.. x D ​represents the undetermined parameter; the RLC parameters of the equivalent impedance are extracted by using the DE algorithm, and the optimization criterion function is established by the minimum square sum of the system model residual error as follows:

[0037]

[0038] wherein, represents the measured impedance amplitude; represents the calculated impedance amplitude of the equivalent circuit; when the variable Q is the minimum value, the corresponding RLC parameter is the optimal parameter;

[0039] (4.2) initialization parameters: the following initial population is randomly generated

[0040]

[0041] wherein, N P represents the population size; x i (0) represents the i-th individual of the 0th generation in the population; x j,i (0) represents the j-th gene of the i-th individual of the 0th generation; rand(0,1) represents a random distribution number between 0 and 1;

[0042] (4.3) mutation operation: the DE algorithm takes the actual value parameter vector as the population of each generation, and takes the weighted difference value of two individuals in the population as the intermediate individual, i.e. the difference vector; then the difference vector is added to the third individual to produce mutation, as follows:

[0043]

[0044] wherein, F represents the mutagenic factor, x i (g) represents the i-th individual of the gth generation population;

[0045] (4.4) crossover operation: according to the rules, the part of the individual in the current population is exchanged with the corresponding part of the mutant individual, so as to generate the crossover population; the crossover operation of the gth generation population |x i (g) and its mutation amount {v i (g+1)} is as follows:

[0046]

[0047] wherein, j rand represents a random integer in [1, 2, 3…D]; C R represents the crossover probability;

[0048] (4.5) selection operation: if the objective function of the next generation individual is less than that of the current individual, the next generation individual will replace the current individual:

[0049]

[0050] (4.6) Convergence discrimination operation: let x i (g+1) be the optimal individual in (g+1) best (g+1); when DE runs to a predetermined number of times or the objective function value Q reaches a set accuracy, the operation ends, and the estimated result is the optimal value of the RLC parameter; if there is no convergence, return to step (4.2) to perform mutation, crossover and selection again.

[0051] (5) Obtain the optimal resistance inductance capacitance RLC parameter value of the equivalent circuit under the corresponding vibration mode; through the DE algorithm, the optimal solution of C i , C mi , L mi , R mi corresponding to the piezoelectric material equivalent circuit can be solved, so as to realize the piezoelectric material equivalent circuit modeling under the main vibration mode.

[0052] (6) According to the relationship between the piezoelectric material equivalent circuit and the piezoelectric material parameters, the piezoelectric material parameters corresponding to each vibration mode are calculated, which specifically includes the following:

[0053] As shown in Figure 4 , the material parameter extraction under multiple vibration modes will decompose the piezoelectric material equivalent circuit topology under the corresponding mode into multiple single topologies, and each topology after disconnection represents the equivalent circuit under a vibration mode. Taking d-form as an example, these equations are defined as:

[0054] D=[d]t+[ε t ]E

[0055] S=[s E ]t+[d] T E

[0056] In the formula, 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 ] under constant electric field, 2) the dielectric constant tensor [ε t ] under constant mechanical stress, and 3) the piezoelectric strain coefficient tensor [d]:

[0057]

[0058] These three tensors contain 10 independent material parameters, which can represent the impedance characteristics of the piezoelectric material, and these materials are related to the RLC parameters of the equivalent circuit. Taking the rectangular piezoelectric material as shown in Figure 5 , p is the polarization direction, and vibration occurs in the polarization direction, so:

[0059]

[0060] As shown in Figure 5 The actual geometric size 2a, 2b, 2c and material density p of the known piezoelectric material, and the optimal solution of C 0i , C mi , L mi under a certain vibration mode obtained by equivalent circuit modeling, based on the relationship between the piezoelectric material parameters under the vibration mode and the RLC parameters of its equivalent circuit, the material parameters corresponding to the vibration mode can be solved. Here, the average of multiple parameters can be selected as the optimal parameter to improve the extraction accuracy of the material parameters by extracting the parameters of the same material with different sizes multiple times. Through this way, the material parameters corresponding to all vibration modes of the piezoelectric material can be finally extracted. Of course, considering the practicability, the advantage of this method is that the material parameters corresponding to the impedance resonance of the desired application can be selectively extracted to reduce the workload.

[0061] It can be seen that the present scheme realizes the modeling of the equivalent circuit of the piezoelectric material under multiple vibration modes and the extraction of the material parameters under the corresponding state, which has great practical significance for improving the utilization efficiency of piezoelectric materials, realizing the design of material impedance resonance, and guiding the processing of piezoelectric materials.

Claims

1. A method for modeling and extracting parameters of equivalent circuits of piezoelectric materials under multiple vibration modes, characterized in that, Includes the following steps: (1) Establish the piezoelectric material impedance equivalent circuit topology under multiple vibration modes; (2) Impedance data of the piezoelectric material under the corresponding vibration mode were extracted using a vector network analyzer; (3) List the impedance expression based on the equivalent circuit topology of the piezoelectric material impedance under the corresponding vibration mode; (4) The parameters of the equivalent circuit are extracted using the differential evolution algorithm; (5) Obtain the optimal resistance, inductance, capacitance, and RLC parameter values ​​of the equivalent circuit under the corresponding vibration mode; (6) Based on the relationship between the equivalent circuit of the piezoelectric material and the piezoelectric material parameters, the piezoelectric material parameters corresponding to each vibration mode are calculated as follows: Material parameter extraction under multiple vibration modes involves decomposing the equivalent circuit topology of the piezoelectric material under the corresponding mode into multiple individual topologies. Each decomposed topology represents the equivalent circuit under a vibration mode. Taking the d-form as an example, these equations are defined as follows: In the formula, t and S represent the vectors of mechanical stress and mechanical deformation, and the behavior of the material is determined by three tensors: the elastic compliance constant tensor of the constant electric field [s E The dielectric constant tensor [ε] of constant mechanical stress t and the piezoelectric strain coefficient tensor [d]:

2. The method for modeling and extracting parameters of piezoelectric materials under multiple vibration modes according to claim 1, characterized in that: In step (1), the piezoelectric material impedance equivalent circuit topology under the multiple vibration modes is a series connection of multiple equivalent circuit topologies with the same structure.

3. The method for modeling and extracting parameters of piezoelectric materials under multiple vibration modes according to claim 2, characterized in that: The i-th equivalent circuit topology among the multiple equivalent circuit topologies includes capacitor C. i Capacitor C mi Resistance R mi Inductor L mi The capacitor C i One end is connected to a resistor R mi One end, capacitor C i The other end is connected to capacitor C. mi One end; the resistor R mi The other end is connected to inductor L mi One end is connected, inductor L mi The other end is connected to capacitor C mi The other end is connected.

4. The method for modeling and extracting parameters of piezoelectric materials under multiple vibration modes according to claim 1, characterized in that: In step (2), the impedance data consists of N discrete frequencies (f1, ..., f2). N ) and its corresponding impedance dataset.

5. The method for modeling and extracting parameters of piezoelectric materials under multiple vibration modes according to claim 1, characterized in that, In step (3), the impedance of the piezoelectric material under the corresponding vibration mode is obtained based on the equivalent circuit topology of the piezoelectric material impedance under the corresponding vibration mode. Z PZT expression: In the formula, Z PZT The impedance of the piezoelectric material under multiple vibration modes; R mi C mi L mi Let ω represent the resistance, capacitance, and inductance parameters in the i-th series topology of the piezoelectric material equivalent circuit under multiple vibration modes; ω = 2πf, where ω is the angular frequency and f is the frequency.

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