Double-branch parallel composite structure high-frequency ultrasonic transducer and design method thereof

Abstract

The invention discloses a high-frequency ultrasonic transducer with a double-branch parallel composite structure and a design method of the high-frequency ultrasonic transducer. The high-frequency ultrasonic transducer comprises a first branch transducer and a second branch transducer, the first branch transducer and the second branch transducer are connected to two vertical end surfaces of the Y-shaped connecting piece in a 90-degree V shape; each of the first branch transducer and the second branch transducer comprises a rear cover plate, a piezoelectric ceramic crystal stack and an amplitude-change pole; a clamping mechanism is arranged on the amplitude-change pole; the high-frequency ultrasonic transducer further comprises a global equivalent circuit model, and the global equivalent circuit model is composed of a first equivalent circuit model, a second equivalent circuit model and a third equivalent circuit model. The output stability and the power bearing capacity of the high-frequency ultrasonic transducer are remarkably improved, the problem of resonant frequency deviation caused by independent design of each branch is effectively solved, and errors caused by design of a traditional design method are greatly reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of precision machining, and in particular relates to a double-branch parallel composite structure high-frequency ultrasonic transducer and a design method thereof. Background Art

[0002] 1. Piezoelectric ultrasonic transducers with sandwich structures are widely used in thermosonic bonding of upper electrical connections of microelectronic packages. At present, the operating frequency of most piezoelectric ultrasonic transducers used in related fields can be above 100kHz, because high-frequency ultrasonic energy can improve bonding, shorten bonding time, reduce bonding temperature, and reduce thermal stress and joint drift. As IC chips develop towards high density, multi-lead and fine pitch, bonders must complete more electrical connections than before in the same time. At the same time, thermosonic bonding has also been extended to electrical connections of heavy wires, which require more energy than traditional fine gold wire bonding due to higher mechanical and thermal stresses. In order to meet the new requirements, improving the electrical power and bonding force of piezoelectric ultrasonic transducers is the most direct way. However, the electromechanical properties of the transducer are very sensitive to external electrical energy and acoustic loads, because too much electrical energy will significantly increase the self-heating of the piezoelectric ceramic stack, resulting in deterioration of its electromechanical properties. Excessive bonding force will increase the acoustic load and interface stress in the bonding area, destroy the bonding electrical connection, and cause substrate delamination and voids in the metal interface. Faced with new challenges, multi-dimensional piezoelectric ultrasonic transducers are gaining more and more attention.

[0003] 2. For traditional single-branch ultrasonic transducers, a complete set of design methods has been established, such as equivalent circuit method, four-terminal network method, finite element analysis method, etc. Considering that multidimensional ultrasonic transducers usually have a more complex structure, in order to simplify the design, a popular strategy is to first complete the structural and parameter design of the structural unit, including branch transducers, coupling units and other auxiliary structures. Let them all have the same resonant frequency. Since the composite structure transducer is a mechanical combination of structural units, if all structural units have the same resonant frequency, it can be considered that the mechanical resonant frequency of the entire transducer is close to the mechanical resonant frequency of the structural unit. However, there is usually a large error between the actual resonant frequency and the expected frequency, which makes the transducer not work as we imagined. In extreme cases, the expected resonant mode may even disappear. From the perspective of structural dynamics, the resonance of the structure is not only related to the distribution of mass and stiffness, but also to the support conditions, shape and damping. Although the above strategy ensures the consistency of the resonant frequency between all structural units, changes in mass and stiffness distribution are inevitable due to the mutual cooperation of these structural units. Therefore, the traditional design method cannot guarantee the effectiveness and rationality of the design results. Summary of the invention

[0004] In view of the difficulties in the prior art, the present invention provides a dual-branch parallel composite structure high-frequency ultrasonic transducer and a design method thereof. The transducer can reduce the risk of output performance deterioration of the traditional single-branch transducer due to increased power and long-term operation, and also helps to reduce the bonding temperature and bonding force, and improve the adaptability of soft material substrates for ultrasonic bonding. The method proposed in the present invention effectively solves the problem of resonant frequency deviation caused by the separate design of each branch transducer, and can efficiently and accurately design the dual-branch parallel composite structure high-frequency ultrasonic transducer.

[0005] In order to solve the problems of the prior art, the present invention adopts the following technical solutions:

[0006] A dual-branch parallel composite structure high-frequency ultrasonic transducer, the high-frequency ultrasonic transducer comprises a first branch transducer and a second branch transducer; the first branch transducer and the second branch transducer are connected to two vertical end surfaces of a Y-shaped connector in a 90° V-shape; the first branch transducer and the second branch transducer both comprise a rear cover plate, a piezoelectric ceramic crystal pile, and a horn; the horn is provided with a clamping mechanism; wherein: the high-frequency ultrasonic transducer also comprises a global equivalent circuit model,

[0007] Right now:

[0008] Z=Z C0 ||Z eq1 / n 2 ||Z eq2 / n 2 ||Z C0

[0009] Where: Z eq1 is the mechanical impedance of the piezoelectric ceramic crystal stack of the first branch transducer, Z eq2 is the mechanical impedance of the piezoelectric ceramic crystal stack of the second branch transducer, Z C0 is the static capacitance impedance of two groups of piezoelectric ceramic crystal stacks:

[0010]

[0011] Among them: U1 and U2 are the excitation voltages of the two groups of piezoelectric ceramic crystal stacks, I1 and I2 are the currents of each branch, n is the electromechanical conversion coefficient of the piezoelectric ceramic crystal stack, C0 is the static capacitance of the piezoelectric ceramic crystal stack, ω is the angular frequency, and P is the number of piezoelectric ceramic pieces.

[0012] Further, the global equivalent circuit model includes a first equivalent circuit model, a second equivalent circuit model and a third equivalent circuit model; wherein;

[0013] The piezoelectric ceramic crystal stack constructs a first equivalent circuit model through the following formula, namely:

[0014]

[0015] Where: p represents the density of piezoelectric ceramics, and k e =ω / c e are the equivalent wave velocity and wave number of longitudinal vibration in piezoelectric ceramics, A p is the cross-sectional area of ​​the piezoelectric ceramic, l p for

[0016] Piezoelectric ceramic thickness;

[0017] The rear cover plate and the horn are used to construct a second equivalent circuit model through the following formula, namely:

[0018]

[0019] Where: i Indicates the density of the rear cover and horn, and k i =ω / c i Respectively represent the wave velocity and wave number of the longitudinal vibration of the rear cover and the horn, A i is the cross-sectional area of ​​the rear cover and the horn, l i is the length of each segment.

[0020] The Y-type connector constructs a third equivalent circuit model through the following formula, namely:

[0021]

[0022] Where: ρ5 represents the density of the Y-type connector, and k5=ω / c5 respectively represent the wave velocity and wave number of the longitudinal vibration in the Y-type connector, A5 is the cross-sectional area of ​​the Y-type connector, and l5 is the length of the Y-type connector.

[0023] Furthermore, the clamping mechanism is composed of a fixed part and a flexible arm; one end of the flexible arm is connected to the amplitude changing rod, and the other end of the flexible arm is connected to the fixed part; the flexible arm adopts a parallelogram hinge.

[0024] In order to solve the problems existing in the prior art, the present invention also adopts the following technical solutions:

[0025] A design method for a dual-branch parallel composite structure high-frequency ultrasonic transducer comprises the following steps:

[0026] Step S1: construct a three-dimensional model of the high-frequency ultrasonic transducer according to claim 1, and

[0027] Initialize the parameters of the components in;

[0028] Step S2: construct a first equivalent circuit for the piezoelectric ceramic crystal stack using the following formula, namely:

[0029]

[0030] Where: p represents the density of piezoelectric ceramics, and k e =ω / c e are the equivalent wave velocity and wave number of longitudinal vibration in piezoelectric ceramics, A p is the cross-sectional area of ​​the piezoelectric ceramic, l p is the thickness of piezoelectric ceramics;

[0031] Step S3, constructing a second equivalent circuit for the rear cover plate and the horn using the following formula, namely:

[0032]

[0033] Where: i Indicates the density of the rear cover and horn, and k i =ω / c i Respectively represent the wave velocity and wave number of the longitudinal vibration of the rear cover and the horn, A i is the cross-sectional area of ​​the rear cover and the horn, l i The length of each segment.

[0034] Step S4: construct a third equivalent circuit model for the Y-type connector using the following formula, namely:

[0035]

[0036] Where: ρ5 represents the density of the Y-type connector, and k5=ω / c5 respectively represent the wave velocity and wave number of the longitudinal vibration in the Y-type connector, A5 is the cross-sectional area of ​​the Y-type connector, and l5 is the length of the Y-type connector.

[0037] Step S4, combining the first equivalent circuit model, the second equivalent circuit model and the third equivalent circuit model to obtain a global equivalent circuit model;

[0038] Step S5: Optimize the global equivalent circuit model using the following formula:

[0039] Z=Z C0 ||Z eq1 / n 2 ||Z eq2 / n 2 ||Z C0

[0040] Where: Z eq1is the mechanical impedance of the piezoelectric ceramic crystal stack of the first branch transducer, Z eq2 is the mechanical impedance of the piezoelectric ceramic crystal stack of the second branch transducer, Z C0 is the static capacitance impedance of two groups of piezoelectric ceramic crystal stacks:

[0041]

[0042] Among them: U1 and U2 are the excitation voltages of the two groups of piezoelectric ceramic crystal stacks, I1 and I2 are the currents of each branch, n is the electromechanical conversion coefficient of the piezoelectric ceramic crystal stack, C0 is the static capacitance of the piezoelectric ceramic crystal stack, ω is the angular frequency, and P is the number of piezoelectric ceramic pieces.

[0044] Beneficial Effects

[0045] Compared with the traditional technical solution, the beneficial effects brought by the present invention are:

[0046] 1. The flexible hinge parallelogram clamping mechanism described in the present invention can provide a rotational motion pair and a translational motion pair, which can effectively suppress the disturbance torque from the mounting bracket, improve the motion decoupling ability of the mounting clamp, and improve the ultrasonic energy transmission efficiency of the branch transducer.

[0047] 2. The design method of a dual-branch parallel composite structure high-frequency ultrasonic transducer and the method for solving related parameters described in the present invention is based on the vibration mode of the dual-branch parallel composite structure high-frequency ultrasonic transducer, and realizes the design of the dual-branch parallel composite structure high-frequency ultrasonic transducer and the solution of related parameters based on the equivalent circuit of each structural unit of the transducer;

[0048] 3. The dual-branch parallel composite structure high-frequency ultrasonic transducer provided by the present invention can reduce the risk of output performance deterioration of the traditional single-branch transducer due to increased power and long-term operation, and also helps to reduce the bonding temperature and bonding force, and improve the adaptability of ultrasonic bonding to soft material substrates. It is an effective way to solve the outstanding problems of ultrasonic bonding technology in occasions such as thick wire diameter, multiple wires, and dissimilar metal bonding;

[0049] 4. The present invention takes into account the relationship between the resonance of the structure and the mass and stiffness distribution, and proposes a design method for a dual-branch parallel composite structure high-frequency ultrasonic transducer, which greatly reduces the error caused by the traditional design method, so that the designed dual-branch parallel composite structure high-frequency ultrasonic transducer has a better vibration effect. It provides a new idea for efficiently and accurately obtaining the design parameters of the dual-branch parallel composite structure high-frequency ultrasonic transducer; it has important engineering significance for the design of the dual-branch parallel composite structure high-frequency ultrasonic transducer. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1It is a schematic diagram of the structure of the high-frequency ultrasonic transducer with a dual-branch parallel composite structure of the present invention;

[0051] Figure 2 It is the equivalent circuit model of each structural unit of the double-branch parallel composite structure high-frequency ultrasonic transducer;

[0052] Figure 3 It is the overall equivalent circuit model of the high-frequency ultrasonic transducer with a dual-branch parallel composite structure;

[0053] Figure 4 A simplified equivalent circuit model of a dual-branch parallel composite structure high-frequency ultrasonic transducer.

[0054] Figure numerals: 101, first branch transducer; 102, first branch transducer; 103, Y-type connector 201, rear cover; 202, amplitude rod; 203, piezoelectric ceramic crystal pile; 204 clamping mechanism; 241, fixing part; 242, flexible arm; 231, first equivalent circuit model; 221, second equivalent circuit model; 131, third equivalent circuit model; 323, global equivalent circuit model DETAILED DESCRIPTION

[0055] The following is combined with Figure 1 The present invention is described as follows:

[0056] like Figure 1 As shown, the present invention provides a dual-branch parallel composite structure high-frequency ultrasonic transducer, the high-frequency piezoelectric ultrasonic transducer comprises a first branch transducer 101 and a second branch transducer 102; the first branch transducer 101 and the second branch transducer 102 are connected to two vertical end surfaces of a Y-shaped connector 103 in a 90° V-shape; the first branch transducer 101 and the second branch transducer 101 both comprise a rear cover plate 201, a piezoelectric ceramic crystal stack 203, and an amplitude transformer 202; the amplitude transformer 202 consists of a primary cylindrical section and a secondary conical section; the rear cover plate 201 is connected to the amplitude transformer by bolts 202, piezoelectric ceramic crystal pile 203; a clamping mechanism 204 is provided on the amplitude rod 202; the clamping mechanism is composed of a fixed part 241 and a flexible arm 242; one end of the flexible arm 242 is connected to the amplitude rod 202, and the other end thereof is connected to the fixed part 241; the flexible arm 242 adopts a parallelogram flexible hinge, which can effectively rotate and translate the first branch transducer 101 and the second branch transducer 102; and more effectively suppress the disturbance torque from other equipment, improve the motion decoupling ability of the clamping mechanism, and ensure the ultrasonic energy transmission efficiency between the first branch transducer and the second branch transducer.

[0057] In order to better ensure the ultrasonic energy transmission efficiency between the first branch transducer and the second branch transducer, the present invention constructs a first equivalent circuit 231 model, a second equivalent circuit 221 and a third equivalent circuit 131 for the piezoelectric ceramic crystal stack 203, the rear cover plate 201, the amplitude transformer 202 and the Y-type connector 103 respectively; Figure 2 shown.

[0058] The piezoelectric ceramic crystal stack 203 constructs a first equivalent circuit model 231 by the following formula to ensure the ultrasonic energy transmission efficiency between the first branch transducer 101 and the second branch transducer 102:

[0059]

[0060] Where: p represents the density of piezoelectric ceramics, and k e =ω / c e are the equivalent wave velocity and wave number of longitudinal vibration in piezoelectric ceramics, A p is the cross-sectional area of ​​the piezoelectric ceramic, l p is the thickness of piezoelectric ceramics;

[0061] The rear cover plate 201 and the horn 202 construct a second equivalent circuit model 221 through the following formula to ensure the ultrasonic energy transmission efficiency between the first branch transducer 101 and the second branch transducer 102:

[0062]

[0063]

[0064] Where: i Indicates the density of the rear cover and horn, and k i =ω / c i Respectively represent the wave velocity and wave number of the longitudinal vibration of the rear cover and the horn, A i is the cross-sectional area of ​​the rear cover and the horn, l i The length of each segment.

[0065] The Y-shaped connector 103 constructs a third equivalent circuit model 131 through the following formula. The third equivalent circuit model 131 is to project the Y-shaped connector 103 onto the horizontal axis. The Y-shaped connector 103 is a cylindrical segment. According to the vector decomposition principle, the external force, vibration speed, and connector length are decomposed to ensure the ultrasonic energy transmission efficiency between the first transducer branch 101 and the second transducer branch 102: That is:

[0066]

[0067] Where: ρ5 represents the density of the Y-type connector, and k5=ω / c5 respectively represent the wave velocity and wave number of the longitudinal vibration in the Y-type connector, A5 is the cross-sectional area of ​​the Y-type connector, and l5 is the length of the Y-type connector.

[0068] like Figure 3 As shown, the present invention combines the first equivalent circuit model 231, the second equivalent circuit model 221 and the third equivalent circuit model 131 to obtain a global equivalent circuit model 323;

[0069] like Figure 4 As shown, the global equivalent circuit model is optimized by the series combination of triangle-star circuit conversion and impedance to obtain an efficient and accurate dual-branch parallel composite structure high-frequency ultrasonic transducer; the triangle-star circuit conversion and the series combination of impedance use the impedance equation at mechanical resonance to optimize the global equivalent circuit model, that is:

[0070] Z=Z C0 ||Z eq1 / n 2 ||Z eq2 / n 2 ||Z C0

[0071] Where: Z eq1 is the mechanical impedance of the piezoelectric ceramic crystal stack of the first branch transducer, Z eq2 is the mechanical impedance of the piezoelectric ceramic crystal stack of the second branch transducer, Z C0 is the static capacitance impedance of two groups of piezoelectric ceramic crystal stacks:

[0072]

[0073] Among them: U1 and U2 are the excitation voltages of the two groups of piezoelectric ceramic crystal stacks, I1 and I2 are the currents of each branch, n is the electromechanical conversion coefficient of the piezoelectric ceramic crystal stack, C0 is the static capacitance of the piezoelectric ceramic crystal stack, ω is the angular frequency, and P is the number of piezoelectric ceramic pieces.

[0074] The present invention also adopts the following steps to design a dual-branch parallel composite structure high-frequency ultrasonic transducer, including the following steps:

[0075] Step S1, establishing a three-dimensional model of a dual-branch parallel composite structure high-frequency ultrasonic transducer, the three-dimensional model including a rear cover plate, a piezoelectric ceramic crystal stack, a horn, a Y-shaped connector and a clamping mechanism; and initializing the parameters of the above components including: measuring the sound velocity, density, acoustic impedance and dielectric constant of the materials of each part of the ultrasonic transducer in the equivalent circuit model of the dual-branch parallel composite structure high-frequency ultrasonic transducer; the materials and material parameters used by the dual-branch parallel composite structure high-frequency ultrasonic transducer of the present invention are shown in Table 1.

[0076] Table 1 Materials and parameters

[0077]

[0078] Step S2: construct a first equivalent circuit for the piezoelectric ceramic crystal stack using the following formula, namely:

[0079]

[0080] where ρ p represents the density of piezoelectric ceramics, and k e =ω / c e are the equivalent wave velocity and wave number of longitudinal vibration in piezoelectric ceramics, A p is the cross-sectional area of ​​the piezoelectric ceramic, l p is the thickness of the piezoelectric ceramic; Step S3, constructing a second equivalent circuit model for the rear cover plate and the amplitude transformer by the following formula, namely:

[0081]

[0082] Where: i Indicates the density of the rear cover and horn, and k i =ω / c i Respectively represent the wave velocity and wave number of the longitudinal vibration of the rear cover and the horn, A i is the cross-sectional area of ​​the rear cover and the horn, l i Step S4: construct a third equivalent circuit model for the Y-type connector using the following formula, namely:

[0083]

[0084] Where: ρ5 represents the density of the Y-type connector, and k5=ω / c5 respectively represent the wave velocity and wave number of the longitudinal vibration in the Y-type connector, A5 is the cross-sectional area of ​​the Y-type connector, and l5 is the length of the Y-type connector.

[0085] Step S4, combining the first equivalent circuit model, the second equivalent circuit model and the third equivalent circuit model to obtain a global equivalent circuit model;

[0086] Step S5: Optimize the global equivalent circuit model using the following formula:

[0087] Z=Z C0 ||Z eq1 / n 2 ||Z eq2 / n 2 ||Z C0

[0088] Where: Z eq1 is the mechanical impedance of the piezoelectric ceramic crystal stack of the first branch transducer, Z eq2 is the mechanical impedance of the piezoelectric ceramic crystal stack of the second branch transducer, Z C0 is the static capacitance impedance of two groups of piezoelectric ceramic crystal stacks:

[0089]

[0090] Among them: U1 and U2 are the excitation voltages of the two groups of piezoelectric ceramic crystal stacks, I1 and I2 are the currents of each branch, n is the electromechanical conversion coefficient of the piezoelectric ceramic crystal stack, C0 is the static capacitance of the piezoelectric ceramic crystal stack, ω is the angular frequency, and P is the number of piezoelectric ceramic pieces.

[0091] According to the design method of the double-branch parallel composite structure high-frequency ultrasonic transducer of the present invention, the size parameters of the double-branch parallel composite structure high-frequency ultrasonic transducer are calculated as shown in Table 2:

[0092] Table 2 Design size parameters of dual-branch parallel composite structure high-frequency ultrasonic transducer (unit: mm)

[0093] <![CDATA[l1]]> <![CDATA[l2]]> <![CDATA[l3]]> <![CDATA[l4]]> <![CDATA[l5]]> <![CDATA[l6]]> <![CDATA[l p ]]> <![CDATA[d1]]> <![CDATA[d2]]> <![CDATA[d3]]> 5.8 20.2 28.7 19.9 6.1 3.0 4.0 15.0 7.0 3.0

[0094] The present invention uses COMSOL simulation software to carry out modal analysis on the established model. In COMSOL simulation software, the corresponding material properties of different components are first assigned, and the model is adaptively meshed, and finally the model is modally solved.

[0095] From the above results, it can be found that a reliable approach is provided for the design method of a dual-branch parallel composite structure high-frequency ultrasonic transducer.

[0096] Although the present invention has been described above, the present invention is not limited to the above-mentioned specific embodiments. The above-mentioned specific embodiments are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can make many modifications without departing from the purpose of the present invention, which are all within the protection of the present invention.

Claims

1. A dual-branch parallel composite structure high-frequency ultrasonic transducer, characterized in that: The high-frequency ultrasonic transducer comprises a first branch transducer and a second branch transducer; the first branch transducer and the second The branch transducers are connected to two vertical end surfaces of the Y-shaped connector in a 90° V-shape; the first branch transducer and the second branch transducer both include a rear cover plate, a piezoelectric ceramic crystal stack, and a horn; The horn is provided with a clamping mechanism; wherein: the high-frequency ultrasonic transducer also includes a global equivalent circuit model, namely: Z=Z C0 ||From eq1 / n 2 ||From eq2 / n 2 ||From C0 Where: Z eq1 is the mechanical impedance of the piezoelectric ceramic crystal stack of the first branch transducer, Z eq2 is the mechanical impedance of the piezoelectric ceramic crystal stack of the second branch transducer, Z C0 is the static capacitance impedance of two groups of piezoelectric ceramic crystal stacks: Among them: U1 and U2 are the excitation voltages of the two groups of piezoelectric ceramic crystal stacks, I1 and I2 are the currents of each branch, n is the electromechanical conversion coefficient of the piezoelectric ceramic crystal stack, C0 is the static capacitance of the piezoelectric ceramic crystal stack, ω is the angular frequency, and P is the number of piezoelectric ceramic pieces.

2. The dual-branch parallel composite structure high-frequency ultrasonic transducer according to claim 1, characterized in that: The global equivalent circuit model includes a first equivalent circuit model, a second equivalent circuit model and a third equivalent circuit model; wherein; The piezoelectric ceramic crystal stack constructs a first equivalent circuit model through the following formula, namely: Where: p represents the density of piezoelectric ceramics, and k e =ω / c e are the equivalent wave velocity and wave number of longitudinal vibration in piezoelectric ceramics, A p is the cross-sectional area of ​​the piezoelectric ceramic, l p is the thickness of piezoelectric ceramics; The rear cover plate and the amplitude transformer construct a second equivalent circuit model through the following formula, namely: Where: i Indicates the density of the rear cover and horn, and k i =ω / c i Respectively represent the wave velocity and wave number of the longitudinal vibration of the rear cover and the horn, A i is the cross-sectional area of ​​the rear cover and the horn, l i is the length of each segment; The Y-type connector constructs a third equivalent circuit model through the following formula, namely: Where: ρ5 represents the density of the Y-type connector, and k5=ω / c5 represent Y A5 is the wave velocity and wave number of the longitudinal vibration in the Y-type connector, l5 is the cross-sectional area of ​​the Y-type connector, and 3. The dual-branch parallel composite structure high-frequency ultrasonic transducer according to claim 1, characterized in that: The clamping mechanism is composed of a fixed part and a flexible arm; one end of the flexible arm is connected to the amplitude changing rod, and the other end is connected to the fixed part; the flexible arm adopts a parallelogram hinge.

4. A design method for a dual-branch parallel composite structure high-frequency ultrasonic transducer, characterized in that: The steps include: Step S1, constructing a three-dimensional model of the high-frequency ultrasonic transducer according to claim 1, and initializing parameters of components in the three-dimensional model; Step S2: construct a first equivalent circuit for the piezoelectric ceramic crystal stack using the following formula, namely: where ρ p represents the density of piezoelectric ceramics, and k e =ω / c e are the equivalent wave velocity and wave number of longitudinal vibration in piezoelectric ceramics, A p is the cross-sectional area of ​​the piezoelectric ceramic, l p is the thickness of piezoelectric ceramics; Step S3, constructing a second equivalent circuit for the rear cover plate and the horn using the following formula, namely: Where: i Indicates the density of the rear cover and horn, and k i =ω / c i Respectively represent the wave velocity and wave number of the longitudinal vibration of the rear cover and the horn, A i is the cross-sectional area of ​​the rear cover and the horn, l i The length of each segment. Step S4: construct a third equivalent circuit model for the Y-type connector using the following formula, namely: Where: ρ5 represents the density of the Y-type connector, and k5=ω / c5 respectively represent the wave velocity and wave number of the longitudinal vibration in the Y-type connector, A5 is the cross-sectional area of ​​the Y-type connector, and l5 is the length of the Y-type connector. Step S4, combining the first equivalent circuit model, the second equivalent circuit model and the third equivalent circuit model to obtain a global equivalent circuit model; Step S5: Optimize the global equivalent circuit model using the following formula: Z=Z C0 ||From eq1 / n 2 ||From eq2 / n 2 ||From C0 Where: Z eq1 is the mechanical impedance of the piezoelectric ceramic crystal stack of the first branch transducer, Z eq2 is the mechanical impedance of the piezoelectric ceramic crystal stack of the second branch transducer, Z C0 is the static capacitance impedance of two groups of piezoelectric ceramic crystal stacks: Among them: U1 and U2 are the excitation voltages of the two groups of piezoelectric ceramic crystal stacks, I1 and I2 are the currents of each branch, n is the electromechanical conversion coefficient of the piezoelectric ceramic crystal stack, C0 is the static capacitance of the piezoelectric ceramic crystal stack, ω is the angular frequency, and P is the number of piezoelectric ceramic pieces.

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