CN117770912B - Ultrasonic simulation load calibration method of ultrasonic surgical instrument - Google Patents
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Abstract
The invention provides an ultrasonic simulation load calibration method of an ultrasonic surgical instrument, which relates to the technical field of ultrasonic surgical instruments and constructs an equivalent circuit of an ultrasonic vibrator load model of the ultrasonic surgical instrument; constructing an equivalent circuit of a transducer load model of the ultrasonic surgical instrument based on the equivalent circuit of the ultrasonic vibrator load model; constructing a calibration circuit, and connecting the calibration circuit with an equivalent circuit of an ultrasonic vibrator load model; and calculating the inductance and the filter capacitance of the calibration circuit required by the equivalent circuit of the calibration transducer load model, and obtaining the correction inductance and the correction filter capacitance of the calibration circuit according to the target inductance and the target filter capacitance of the calibration circuit.
Description
Technical Field
The invention relates to the technical field of ultrasonic surgical instruments, in particular to an ultrasonic simulation load calibration method of an ultrasonic surgical instrument.
Background
Ultrasonic surgical instruments are widely used in surgical operations, such as ultrasonic knife systems, for tissue cutting and coagulation hemostasis, and are implemented by converting an electrical signal into an ultrasonic signal by an ultrasonic transducer and transmitting the ultrasonic signal to a knife tip, so that high-frequency vibration is generated at the knife tip, proteins in tissue of the knife tip are denatured to form viscous coagulum, and a hemostasis seal is formed by the coagulum.
The ultrasonic knife can simultaneously cut and coagulate tissues by setting different output power gears, and can stop bleeding when cutting, so that the operation efficiency is improved. The high power gear may cut tissue more quickly and the low power gear may better coagulate tissue. The current with ultrasonic frequency in the host machine is conducted to the transducer, the transducer converts electric energy into longitudinal vibration mechanical energy of front-back vibration, the tail end of the cutter head vibrates at a certain frequency through the transmission and amplification of the cutter head, the heat generated by friction causes vaporization of water in tissue cells contacted with the cutter head, protein hydrogen bonds are broken, cell disintegration and recombination are carried out, and the tissue is cut after solidification; when cutting blood vessels, the cutter head is contacted with tissue protein, heat is generated through mechanical vibration, so that the collagen structure in the tissue is damaged, the protein is solidified, the blood vessels are further sealed, and the hemostatic purpose is achieved.
The existing problems are that the increase of impedance value of the ultrasonic transducer causes the increase of heating when the ultrasonic transducer vibrates, the increase of quality factor Q value, the decrease of frequency bandwidth of the ultrasonic transducer, the decrease of effective electromechanical coupling coefficient Keff value, and the like. The change of the performances can lead the amplitude of the terminal of the ultrasonic transducer to be gradually increased under the same current excitation after the ultrasonic transducer is used for a long time, so that the amplitude of the cutter head output to the ultrasonic surgical instrument is increased, the cutting hemostasis effect of the cutter head on tissues is further changed, and the performance stability of the ultrasonic surgical system is affected.
Disclosure of Invention
In order to solve the technical problems, the invention provides an ultrasonic simulation load calibration method of an ultrasonic surgical instrument, which comprises the following steps:
S1, constructing an equivalent circuit of an ultrasonic vibrator load model of an ultrasonic surgical instrument, and calculating the output impedance of the equivalent circuit of the ultrasonic vibrator load model;
s2, constructing an equivalent circuit of a transducer load model of the ultrasonic surgical instrument based on the equivalent circuit of the ultrasonic vibrator load model, and constructing a frequency equation of a piezoelectric transduction circuit of the transducer load model based on output impedance of the equivalent circuit of the ultrasonic vibrator load model;
s3, constructing a calibration circuit, connecting the calibration circuit with an equivalent circuit of the ultrasonic vibrator load model, and calculating inductance and filter capacitance of the equivalent circuit of the calibration transducer load model;
S4, calculating a target value of the output voltage of the driving part of the ultrasonic vibrator load model of the current ultrasonic surgical instrument, and calculating a target inductance and a target filter capacitance of the calibration circuit to obtain a correction inductance and a correction filter capacitance of the calibration circuit.
Further, in step S1, the equivalent circuit of the ultrasonic vibrator load model includes: a driving part, an adjusting part; the output impedance Z i of the equivalent circuit of the ultrasonic vibrator load model is as follows:
Wherein R i and X i are respectively the output resistance and the output reactance of an equivalent circuit of an ultrasonic vibrator load model, Z m is the impedance of the adjusting part, n F is the electromechanical coupling coefficient of the driving part, C F is the cut-off capacitance of the driving part, R F is the dielectric loss resistance of the driving part, For ultrasonic resonance frequency, j is the imaginary part,/>Is the ultrasonic phase angle.
Further, in step S2, the equivalent circuit of the transducer load model includes a horn circuit, a front-end circuit, a back-end circuit, and a piezoelectric transduction circuit, where the input impedance Z a of the horn circuit is expressed as:
Wherein: z x is the impedance of the horn, For the impedance of the large end face of the amplitude transformer,/>For the length of the large end face of the amplitude transformer, k 1 is the longitudinal wave number of the amplitude transformer.
Further, the impedances Z F and Z B before and after the piezoelectric transduction circuit are expressed as:
Wherein, Z 2 and Z 4 are the impedance of the front-end circuit and the back-end circuit, L 2 and L 4 are the lengths of the front-end circuit and the back-end circuit, k 4 is the longitudinal wave number of the back-end circuit, and k 2 is the longitudinal wave number of the front-end circuit.
Further, when the transducer is operated at a resonant frequency, the frequency equation of the piezoelectric transduction circuit is:
Wherein k 3 and k 4 are longitudinal wave numbers of the piezoelectric transduction circuit and the back-end circuit respectively, L 3 is the length of the piezoelectric transduction circuit, Z 3 is the impedance of the piezoelectric transduction circuit, and Z i is the output impedance of an equivalent circuit of the ultrasonic vibrator load model.
Further, in step S3, the calibration circuit includes: the circuit comprises an inductor L, a boost diode VD, a circuit switching tube VT, a filter capacitor C and a calibration equivalent chip connected with the circuit switching tube VT; and connecting an input voltage port in the calibration circuit with two ends of a dielectric loss resistor of a driving part of an equivalent circuit of the ultrasonic vibrator load model, and receiving output voltage of the driving part of the equivalent circuit of the ultrasonic vibrator load model.
Further, in step S4, the circuit inductance L of the equivalent circuit of the calibration ultrasonic vibrator load model is:
Wherein U in is the output voltage of the driving part of the equivalent circuit of the ultrasonic vibrator load model, D is the on duty ratio, For the current flowing through the calibration circuit inductance, f is the circuit switching tube switching frequency.
Further, the method is characterized in that the filter capacitor C of the equivalent circuit of the calibration ultrasonic vibrator load model is as follows:
Wherein T S is the switching period of the circuit switching tube VT, For the maximum value of the current flowing through the inductance of the calibration circuit,Is a pulse frequency coefficient.
Further, in step S4, the target inductance L T of the calibration circuit is calculated according to the target value U f of the output voltage of the driving portion of the equivalent circuit of the ultrasonic vibrator load model, as:
Wherein D T is the target on duty cycle;
Then the inductance is corrected ；
The target filter capacitance C T of the calibration circuit is calculated as:
Wherein, For maximum value of current flowing through the inductance of the calibration circuit,/>Pulse frequency coefficients;
then correct the filter capacitance 。
Compared with the prior art, the invention has the following beneficial technical effects:
Constructing an equivalent circuit of an ultrasonic vibrator load model of the ultrasonic surgical instrument, and calculating the output impedance of the equivalent circuit of the ultrasonic vibrator load model; constructing an equivalent circuit of a transducer load model of the ultrasonic surgical instrument based on the equivalent circuit of the ultrasonic vibrator load model, and constructing a frequency equation of a piezoelectric transduction circuit of the transducer load model based on the output impedance of the equivalent circuit of the ultrasonic vibrator load model; constructing a calibration circuit, connecting the calibration circuit with an equivalent circuit of an ultrasonic vibrator load model, and calculating inductance and filter capacitance of the equivalent circuit of the calibration transducer load model; and calculating a target value of the output voltage of a driving part of an ultrasonic vibrator load model of the current ultrasonic surgical instrument, and calculating a target inductance and a target filter capacitance of a calibration circuit to obtain a correction inductance and a correction filter capacitance of the calibration circuit. After correction of the filter capacitor and the inductor, the output impedance of the equivalent circuit of the ultrasonic vibrator load model and the frequency equation of the piezoelectric transduction circuit brought into the transducer load model are calculated again, and whether the left end and the right end of the frequency equation are matched is checked, so that the stability of the transducer load model is evaluated. Effectively solves the technical problem that the ultrasonic surgical tool can safely work when the ultrasonic load of the existing ultrasonic surgical instrument works.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort to a person skilled in the art.
FIG. 1 is a flow chart of a method for ultrasonic simulated load calibration of an ultrasonic surgical instrument of the present invention;
Fig. 2 is an equivalent circuit schematic diagram of an ultrasonic vibrator load model of the present invention;
FIG. 3 is a schematic diagram of an equivalent circuit of a transducer load model of the present invention;
Fig. 4 is a schematic diagram of a calibration circuit according to the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments of the present application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
In the drawings of the specific embodiments of the present invention, in order to better and more clearly describe the working principle of each element in the system, the connection relationship of each part in the device is represented, but only the relative positional relationship between each element is clearly distinguished, and the limitations on the signal transmission direction, connection sequence and the structure size, dimension and shape of each part in the element or structure cannot be constructed.
The ultrasonic simulation load calibration structure comprises an equivalent circuit of an ultrasonic vibrator load model, an equivalent circuit of a transducer load model and a calibration circuit.
Referring to fig. 1, a flow chart of an ultrasonic simulated load calibration method of an ultrasonic surgical instrument according to the present invention includes the following steps:
S1, constructing an equivalent circuit of an ultrasonic vibrator load model of the ultrasonic surgical instrument, and calculating the output impedance of the equivalent circuit of the ultrasonic vibrator load model.
As shown in fig. 2, the equivalent circuit of the ultrasonic vibrator load model includes: a driving part and an adjusting part. The adjusting portion includes an impedance Z m, and the driving portion includes a cut-off capacitance C F01, a dielectric loss resistance R F01.
Calculating the output impedance Z i of an equivalent circuit of the ultrasonic vibrator load model:
Wherein R i and X i are respectively the output resistance and the output reactance of an equivalent circuit of an ultrasonic vibrator load model, Z m is the impedance of the adjusting part, n F is the electromechanical coupling coefficient of the driving part, C F is the cut-off capacitance of the driving part, R F is the dielectric loss resistance of the driving part, For ultrasonic resonance frequency, j is the imaginary part,/>Is the ultrasonic phase angle.
The electromechanical coupling coefficient is used for representing the parameter of the mutual coupling relation between the mechanical energy and the electric energy, reflects the size of the part of mechanical energy which can be extracted from the total energy of the equivalent circuit of the ultrasonic vibrator load model and provides driving, and is also an important factor for determining the bandwidth.
Electromechanical coupling coefficient n F and maximum ultrasonic resonant frequencyAnd minimum ultrasonic resonant frequency/>
The calculation relation between the two is as follows:
The mean value of the electromechanical coupling coefficient N F of the equivalent circuit of the ultrasonic vibrator load model calculated under N adjusting conditions of the adjusting part is used as an electromechanical conversion evaluation model V:
Where n F (I) denotes the calculated electromechanical coupling coefficient for the seed adjustment.
S2, constructing an equivalent circuit of a transducer load model of the ultrasonic surgical instrument based on the equivalent circuit of the ultrasonic vibrator load model, and constructing a frequency equation of a piezoelectric transduction circuit of the transducer load model based on output impedance of the equivalent circuit of the ultrasonic vibrator load model.
The resonance frequency of the transducer is affected by load, and an equivalent circuit of a transducer load model comprises an amplitude transformer circuit, a front-end circuit, a rear-end circuit and a piezoelectric transduction circuit, so that the transducer can work only when reaching a certain amplitude, and therefore, the front-end circuit is externally connected with an amplitude transformer, energy is concentrated on the small end face of the amplitude transformer, and the output amplitude is amplified. The back-end circuitry of the transducer may be considered empty, but the impedance of the front-end circuitry cannot be ignored.
The equivalent circuit of the ultrasonic vibrator load model is connected with the piezoelectric transduction circuit part of the equivalent circuit of the transducer load model, as shown in fig. 3.
The output impedance Z a of the horn circuit is represented as:
Wherein: z x is the impedance of the horn, For the impedance of the large end face of the amplitude transformer,/>For the length of the large end face of the amplitude transformer, k 1 is the longitudinal wave number of the amplitude transformer.
The impedance Z x of the amplitude transformer has the following calculation formula:
In the method, in the process of the invention, For the impedance of the small end face of the amplitude transformer,/>For the length of the small end of the horn, Z fl is the reaction impedance of the transducer load to the transducer.
The impedances Z F and Z B before and after the piezoelectric transduction circuit are expressed as:
Wherein the load Z FL=jZfl of the front-end circuit; the load Z BL =0 of the back-end circuit.
Wherein, Z 2 and Z 4 are the impedance of the front-end circuit and the back-end circuit respectively, L 2 and L 4 are the lengths of the front-end circuit and the back-end circuit respectively, and k 4 is the longitudinal wave number of the back-end circuit.
When the transducer is operated at a resonant frequency, the frequency equation of the piezoelectric transduction circuit is:
Wherein k 3 and k 4 are longitudinal wave numbers of the piezoelectric transduction circuit and the back-end circuit respectively, L 3 is the length of the piezoelectric transduction circuit, Z 3 is the impedance of the piezoelectric transduction circuit, and Z i is the output impedance of an equivalent circuit of the ultrasonic vibrator load model.
S3, constructing a calibration circuit, connecting the calibration circuit with an equivalent circuit of the ultrasonic vibrator load model, and calculating inductance L and filter capacitance C of the equivalent circuit of the calibration transducer load model.
The calibration circuit is shown in fig. 4. The calibration circuit includes: the circuit comprises an inductor L, a boost diode VD, a circuit switching tube VT, a filter capacitor C and a calibration equivalent chip connected with the circuit switching tube VT. And connecting an input voltage U in port in the calibration circuit with two ends of a dielectric loss resistor R F01 of a driving part of an equivalent circuit of the ultrasonic vibrator load model, and receiving output voltage of the driving part of the equivalent circuit of the ultrasonic vibrator load model.
The specific working process is as follows: after the calibration circuit is electrified, the alternating current power supply charges the total filter capacitor C through the direct current voltage U dc through the calibration circuit inductor L and the boosting diode VD, and then the circuit switching tube VT is turned on or off at a certain switching frequency and duty ratio.
When the circuit switching tube VT is conducted, the calibration circuit inductance L starts to store energy, and when the circuit switching tube VT is cut off, the calibration circuit inductance L charges the total filter capacitance C through the boosting diode VD.
And calculating a calibration circuit inductance L and a filter capacitance C required for calibrating an equivalent circuit of the transducer load model.
When the circuit switching tube VT is conducted, the voltage U L (t) at two ends of the inductance L of the calibration circuit at the moment t is as follows:
UL(t)=Uin；
the current i L (t) flowing through the inductance L of the calibration circuit at time t is:
i L (0) is the current flowing through the calibration circuit inductance L at the initial time.
When t=t on=DTS, T on is on time, D is on duty, and T S is switching period. From the above formula:
When the circuit switching tube VT is cut off, the voltage U L (t) at the two ends of the calibrating circuit inductance at the moment t is as follows:
The current flowing through the calibration circuit inductance at this time is:
When t=t S, it is obtainable by:
According to the working mode of the calibration circuit, the inductance L of the calibration circuit is calculated as follows:
Wherein U in is the output voltage of the driving part of the equivalent circuit of the ultrasonic vibrator load model, D is the on duty ratio, For the current flowing through the calibration circuit inductance, f is the circuit switching tube switching frequency. The filter capacitance C of the calibration circuit is calculated as follows:
Wherein T S is the switching period of the circuit switching tube VT, For the maximum value of the current flowing through the inductance of the calibration circuit,Is a pulse frequency coefficient.
It can be seen that the circuit inductance L and the filter capacitance C of the calibration circuit are both associated with the output voltage U in of the driving portion of the equivalent circuit of the ultrasound transducer load model.
S4, calculating a target value of the output voltage of the driving part of the ultrasonic vibrator load model of the current ultrasonic surgical instrument, and calculating a target inductance and a target filter capacitance of the calibration circuit to obtain a correction inductance and a correction filter capacitance of the calibration circuit.
A target value U f of the output voltage of the driving portion of the equivalent circuit of the ultrasonic vibrator load model of the current ultrasonic surgical instrument is determined.
Wherein Δf represents an equivalent circuit output impedance margin value of the ultrasonic vibrator load model, F S represents a resonance frequency value of an equivalent circuit of the current ultrasonic vibrator load model, C 0 represents an instantaneous capacitance value on a cut-off capacitance of the driving portion, a 1 represents a balance factor, and B 0 represents an offset constant.
The expression balance factor a 1 is calculated according to the following formula:
Wherein Q represents an electric quantity value corresponding to a resonance frequency value of an equivalent circuit of the current ultrasonic vibrator load model, and M represents an equivalent mass value corresponding to a resonance frequency value of the equivalent circuit of the current ultrasonic vibrator load model.
According to a target value U f of the output voltage of the driving part of the equivalent circuit of the ultrasonic vibrator load model, calculating a target inductance L T of the calibration circuit as follows:
wherein U f is a target value of the output voltage of the driving part of the equivalent circuit of the ultrasonic vibrator load model, For the current flowing through the calibration circuit inductance, D T is the target on-duty, and f is the circuit switching tube switching frequency.
Then the inductance is corrected
The target filter capacitance C T of the calibration circuit is calculated as:
Wherein T S is the switching period of the circuit switching tube VT, For the maximum value of the current flowing through the inductance of the calibration circuit,Pulse frequency coefficient.
Then correct the filter capacitance。
After correction of the filter capacitor and the inductor, the output impedance of the equivalent circuit of the ultrasonic vibrator load model and the frequency equation of the piezoelectric transduction circuit brought into the transducer load model are calculated again, and whether the left end and the right end of the frequency equation are matched is checked, so that the stability of the transducer load model is evaluated.
By using the ultrasonic simulation load calibration method of the ultrasonic surgical instrument, when the ultrasonic surgical instrument leaves the factory, various parameters of an ultrasonic vibrator load circuit of the current ultrasonic surgical instrument are set. The ultrasonic vibrator load circuits of different ultrasonic surgical instruments correspond to different initial parameter values. Therefore, when the target circuit inductance and the circuit filter capacitance of the current ultrasonic surgical instrument are set, initial parameter values corresponding to voltages at two ends of the target calibration circuit inductance of the current ultrasonic transducer are calibrated. Further, the initial parameter values corresponding to the target circuit inductance and the circuit filter capacitance are correlated and stored in the current ultrasonic surgical instrument. The target circuit inductance and the circuit filter capacitance set by the current ultrasonic surgical instrument can be multiple, and each target amplitude value is marked in the current ultrasonic transducer to correspond to an initial driving current value.
In the above embodiments, it may be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When loaded and executed on a computer, produces a flow or function in accordance with embodiments of the present application, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a computer network, or other programmable apparatus. The computer instructions may be stored in or transmitted across a computer-readable storage medium. The computer readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. that contains an integration of one or more available media. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid State Disk (SSD)), etc.
While the application has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made and equivalents will be apparent to those skilled in the art without departing from the scope of the application. Therefore, the protection scope of the application is subject to the protection scope of the claims.
Claims (4)
1. An ultrasonic simulated load calibration method of an ultrasonic surgical instrument, comprising the steps of:
S1, constructing an equivalent circuit of an ultrasonic vibrator load model of an ultrasonic surgical instrument, and calculating the output impedance of the equivalent circuit of the ultrasonic vibrator load model; the equivalent circuit of the ultrasonic vibrator load model comprises: a driving part, an adjusting part; the output impedance Z i of the equivalent circuit of the ultrasonic vibrator load model is as follows:
;
Wherein R i and X i are respectively the output resistance and the output reactance of an equivalent circuit of an ultrasonic vibrator load model, Z m is the impedance of the adjusting part, n F is the electromechanical coupling coefficient of the driving part, C F is the cut-off capacitance of the driving part, R F is the dielectric loss resistance of the driving part, For ultrasonic resonance frequency, j is the imaginary part,/>Is the ultrasonic phase angle;
s2, constructing an equivalent circuit of a transducer load model of the ultrasonic surgical instrument based on the equivalent circuit of the ultrasonic vibrator load model, and constructing a frequency equation of a piezoelectric transduction circuit of the transducer load model based on output impedance of the equivalent circuit of the ultrasonic vibrator load model;
s3, constructing a calibration circuit, connecting the calibration circuit with an equivalent circuit of the ultrasonic vibrator load model, and calculating inductance and filter capacitance of the equivalent circuit of the calibration transducer load model;
the calibration circuit includes: the circuit comprises an inductor L, a boost diode VD, a circuit switching tube VT, a filter capacitor C and a calibration equivalent chip connected with the circuit switching tube VT; connecting an input voltage port in the calibration circuit with two ends of a dielectric loss resistor of a driving part of an equivalent circuit of the ultrasonic vibrator load model, and receiving output voltage of the driving part of the equivalent circuit of the ultrasonic vibrator load model;
The circuit inductance L of the equivalent circuit of the calibration ultrasonic vibrator load model is as follows:
;
Wherein U in is the output voltage of the driving part of the equivalent circuit of the ultrasonic vibrator load model, D is the on duty ratio, F is the switching frequency of a switching tube of the circuit;
the filter capacitor C of the equivalent circuit of the calibration ultrasonic vibrator load model is as follows:
;
Wherein T S is the switching period of the circuit switching tube VT, For maximum value of current flowing through the inductance of the calibration circuit,/>Is a pulse frequency coefficient;
s4, calculating a target value of the output voltage of a driving part of an ultrasonic vibrator load model of the current ultrasonic surgical instrument, and calculating a target inductance and a target filter capacitance of a calibration circuit to obtain a correction inductance and a correction filter capacitance of the calibration circuit;
according to a target value U f of the output voltage of the driving part of the equivalent circuit of the ultrasonic vibrator load model, calculating a target inductance L T of the calibration circuit as follows:
;
Wherein D T is the target on duty cycle;
Then the inductance is corrected ；
The target filter capacitance C T of the calibration circuit is calculated as:
;
Wherein, For maximum value of current flowing through the inductance of the calibration circuit,/>Pulse frequency coefficients;
then correct the filter capacitance 。
2. The ultrasonic simulated load calibration method of claim 1, wherein in step S2, the equivalent circuit of the transducer load model comprises a horn circuit, a front-end circuit, a back-end circuit, and a piezoelectric transduction circuit, and the input impedance Z a of the horn circuit is represented as:
;
Wherein: z x is the impedance of the horn, For the impedance of the large end face of the amplitude transformer,/>For the length of the large end face of the amplitude transformer, k 1 is the longitudinal wave number of the amplitude transformer.
3. The ultrasonic simulated load calibration method of claim 2, wherein the impedances Z F and Z B before and after the piezoelectric transduction circuit are represented as:
;
Wherein, Z 2 and Z 4 are the impedance of the front-end circuit and the back-end circuit, L 2 and L 4 are the lengths of the front-end circuit and the back-end circuit, k 4 is the longitudinal wave number of the back-end circuit, and k 2 is the longitudinal wave number of the front-end circuit.
4. A method of calibrating an ultrasonic analog load according to claim 3, wherein when the transducer is operating at a resonant frequency, the frequency equation of the piezoelectric transduction circuit is:
;
Wherein k 3 and k 4 are longitudinal wave numbers of the piezoelectric transduction circuit and the back-end circuit respectively, L 3 is the length of the piezoelectric transduction circuit, Z 3 is the impedance of the piezoelectric transduction circuit, and Z i is the output impedance of an equivalent circuit of the ultrasonic vibrator load model.
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