CN106021174A - Device and method for tracking frequency of ultrasound knife - Google Patents

Abstract

The invention provides a device and a method for tracking the frequency of an ultrasound knife, which solve the problems of low frequency tracking speed and low efficiency in the existing ultrasound equipment. The device comprises a processor, an FPGA (field programmable gate array) unit, a power supply module, an adjustable power supply module, a storage module, a display module, a sound module, a key and indication lamp module, a fault detection module, a safety detection module, a signal conditioning module, a power amplifying and output module, a control module, an ADC (analogue to digital converter) module I, an ADC module II, a voltage feedback module, a current feedback module and a piezoelectric transducer. The device has the advantages that the finding speed is fast, the operation efficiency is high, the continuously changed resonance frequency of the piezoelectric transducer system can be quickly tracked, and the piezoelectric transducer is enabled to be in resonance frequency state; the device can be widely applied to the ultrasound knife.

Description

Ultrasound knife frequency tracking apparatus and method

Technical field

The present invention relates to a kind of medical apparatus and instruments, be specifically related to a kind of ultrasound knife, a kind of ultrasonic Cutter frequency tracking apparatus and method.

Background technology

It is known that ultrasound knife is increasingly widely applied in surgical operation, according to specifically The structure of apparatus and operation principle, ultrasound knife can carry out blood coagulation while cutting tissue, its work Not having electric current to pass through human body during work, tissue eschar is little, thus the damage to patient is little.Ultrasonic Cutter can be used for open surgery, peritoneoscope or endo-surgical, including robot assisted Operation in；Ultrasound knife generally comprises ultrasound knife main frame, driving handle, cutter head and controls switch, Cutter head is made up of piezoelectric transducer, knife bar and point of a knife；During ultrasonic instrument work, ultrasound knife main frame is sent out Going out pumping signal driving pressure electric transducer, piezoelectric transducer controls knife bar and the point of a knife of ultrasound knife cutter head Carry out high-frequent reciprocating motion, thus realize cutting tissue, reach the effect of hemostasis simultaneously.

When ultrasound knife main frame is by sending the work of pumping signal driving pressure electric transducer, only make piezoelectricity Transducer is under resonant frequency state and works, the amplitude output maximum of the ultrasonic cutter head of guarantee, And the efficiency of now ultrasound knife cutting tissue just can be the highest, therefore, the driving electricity of ultrasonic transducer Road should be encouraged with its resonant frequency signal.And in actual operation, load can be along with cutting people The difference of soma and be continually changing so that the resonant frequency of whole system also changes, this Time be accomplished by changing driving frequency and be allowed to the resonant frequency with system and reach consistent.

As it is shown in figure 1, be the equivalent circuit diagram of piezoelectric transducer, Fig. 2 is the resistance of piezoelectric transducer Anti-frequency curve, Fig. 3 is the Phase-Frequency curve of piezoelectric transducer, it can be seen that press in figure Electric transducer has the most precipitous resonance curve, and piezoelectric transducer is only operated in resonant frequency point Having the mechanical activation amplitude of maximum and the highest motor conversion efficiency, therefore the excitation of ultrasound knife main frame is driven Dynamic signal should keep consistent with the resonant frequency point of piezoelectric transducer, could realize ultrasound knife head height effect Work.

But in real work, along with change and the change of extraneous load impedance, the pressure of temperature The resonance point of electric transducer system can offset, in order to make piezoelectric transducer system always work in At resonant frequency, it is necessary to the resonant frequency of piezoelectric transducer system constantly followed the tracks of by ultrasound knife main frame, And feed back to ultrasound knife main frame, ultrasound knife main frame constantly adjusts the frequency of the pumping signal of driving source, Ensure that piezoelectric transducer system is in resonant frequency state, thus ensure the amplitude output of ultrasonic cutter head Maximum, and the efficiency of now ultrasound knife cutting tissue just can be the highest.

Ultrasound knife frequency tracking apparatus and method at present, it is slow that its frequency tracking algorithm searches speed, fortune Line efficiency is low, along with change and the change of extraneous load impedance, the piezoelectric transducer system of temperature Resonance point when there is skew, it is impossible to quickly follow the tracks of the resonance frequency that piezoelectric transducer system is continually changing Rate, can not can not adjust driving source to ultrasound knife main frame, ultrasound knife main frame by rapid feedback in time The frequency of pumping signal, it is impossible to ensure that piezoelectric transducer system is in resonant frequency state, thus not Can guarantee that the amplitude output maximum of ultrasonic cutter head, just cannot ensure that efficiency that ultrasound knife cutting organizes is High.

Summary of the invention

The present invention is directed to current ultrasound knife frequency tracking apparatus and method, its frequency tracking algorithm is searched Speed is slow, and operational efficiency is low, along with change and the change of extraneous load impedance, the piezoelectricity of temperature When there is skew in the resonance point of transducer system, it is impossible to quickly follow the tracks of piezoelectric transducer system and constantly become The resonant frequency changed, can not can not adjust to ultrasound knife main frame, ultrasound knife main frame by rapid feedback in time The frequency of the pumping signal of whole driving source, it is impossible to ensure that piezoelectric transducer system is in resonant frequency shape State, thus it cannot be guaranteed that the amplitude output maximum of ultrasonic cutter head, ultrasound knife cutting group just cannot be ensured The technical problem that the efficiency knitted is the highest, it is provided that it is fast that its frequency tracking algorithm a kind of searches speed, runs Efficiency is high, along with change and the change of extraneous load impedance of temperature, piezoelectric transducer system When resonance point occurs skew, can quickly follow the tracks of the resonant frequency that piezoelectric transducer system is continually changing, Also the pumping signal of driving source can be adjusted in time to ultrasound knife main frame, ultrasound knife main frame by rapid feedback Frequency, can guarantee that piezoelectric transducer system is in resonant frequency state, thus ensure ultrasonic cutter head Amplitude output maximum, it is ensured that ultrasound knife cutting tissue efficiency the highest ultrasound knife frequency-tracking dress Put and method.

The technical scheme is that, a kind of ultrasound knife frequency tracking apparatus, including processor, can Program logic circuit FPGA unit, power module, adjustable source module, memory module, display Module, sound module, button and indicating lamp module, fault detection module, safety detection module, Signal-regulated kinase, power amplification output module, control module, ADC one, ADC two, Voltage feedback module, current feedback module and piezoelectric transducer；

Processor is connected with memory module, display module, sound module, processor and control module, Signal-regulated kinase connect, control module, Signal-regulated kinase respectively with power amplification output module Connecting, power amplification output module is connected with adjustable source module, adjustable source module and electricity Source module connects, and power amplification output module is connected with piezoelectric transducer；

Processor is connected with Programmable Logic Device FPGA unit, and Programmable Logic Device FPGA is mono- Unit is connected with safety detection module, and the safety detection module other end is connected with power amplification output module；

Programmable Logic Device FPGA unit is connected with ADC, ADC one, ADC Two are connected with voltage feedback module and current feedback module respectively；

Programmable Logic Device FPGA unit and button and indicating lamp module and fault detection module are connected.

Preferably, processor is dsp processor.

Preferably, memory module is EEPROM.

Preferably, ADC is that DSP carries module or outside high-speed ADC module, ADC At least two passage.

The present invention also provides for the tracking of a kind of ultrasound knife frequency tracking apparatus, comprises the following steps:

(1) impedance and the phase angle expression formula of transducer is obtained by the equivalent circuit of transducer, andTable Reach formula.

(2) simulation transducer is in different operating state, and measures its characteristic under this duty Parameter C₀, L_S, C_S, R_S, and calculate impedance corresponding at a certain frequency, phase angle andBy phase At inphase angle, scan resistance value corresponding to each dot frequency andValue is depicted as point-like figure.

(3) at according to step (2) not inphase angle,With the change curve of impedance, matching obtains Matched curve.

(4) the matched curve numerical value that step (3) is obtained by processor is stored in as subfunction and deposits In reservoir.

(5) processor gathers Voltage Feedback and current feedback signal, and thus signal calculates piezoelectricity and changes The impedance Z of energy device system and phase angle θ.

(6) size of the phase angle θ that processor calculates according to step (5), selects step (4) The corresponding subfunction of storage, then the resistance value Z that will be calculated by step (5) is as parameter meter The functional value of the subfunction called, i.e. obtainsSize.

(7) step (6) is calculated by processorThe phase angle θ calculated with step (5), It is updated to formulaIn, obtain the frequency values needing to adjust.

(8) processor is according to the frequency values needing to adjust calculated, and regulates the frequency of output signal, The resonant frequency making driving frequency and transducer system self is consistent.

Preferably, the computational methods of step (1) comprise the following steps:

A () by the equivalent circuit of transducer, the expression formula of the mould calculating transducer impedance is:

$\left|Z\right|=\sqrt{\frac{C_s^2{L}_s^2{w}^4+C_s^2{R}_s^2{w}^2-2C_s{L}_s{w}^2+1}{w^2(C_0^2{C}_s^2{L}_s^2{w}^4+C_0^2{C}_s^2{R}_s^2{w}^2-2C_0^2{C}_s{L}_s{w}^2-2C_0{C}_s^2{L}_s{w}^2+C_0^2+2C_0{C}_s+C_s^2)}}---\left(1\right);$

B () by the equivalent circuit of transducer, the expression formula of the phase angle calculating transducer impedance is:

$\mathrm{\θ}=-{\tan }^{-1}\frac{C_0{C}_s^2{L}_s^2{w}^4-C_s^2{L}_s{w}^2+C_0{C}_s^2{R}_s^2{w}^2-2C_0{C}_s{L}_s{w}^2+C_0+C_s}{C_s^2{R}_{s}w}\×\frac{180}{\mathrm{\π}}---\left(2\right);$

C () can be obtained equation below by the phase angle expression formula of the phase angle expression formula of formula (2):

$\frac{dw}{d\mathrm{\θ}}=\frac{-k_1{k}_2{\mathrm{wsec}}^2\left(k_2\mathrm{\θ}\right)}{4k_3{w}^3+2k_{4}w+k_1\tan \left(k_2\mathrm{\θ}\right)}---\left(3\right)$

$k_1=C_s^2{R}_s---\left(4\right)$

$k_2=\frac{\mathrm{\π}}{180}---\left(5\right)$

$k_3=C_0{C}_s^2{L}_s^2---\left(6\right)$

$k_4=-C_s^2{L}_s+C_0{C}_s^2{R}_s^2-2C_0{C}_s{L}_s---\left(7\right);$

D () can be obtained the variable quantity of frequency when phase place has minor variations by formula (3), byAlso The most availableExpression formula.

Preferably, the approximating method of step (3) be method of least square, Lagrange's interpolation or The curve-fitting methods such as Newton interpolating method.

Preferably, the fitting function of step (3) is multinomial, exponential function or logarithmic function.

The invention has the beneficial effects as follows, owing to taking dsp processor and Programmable Logic Device FPGA Unit, it is fast that its frequency tracking algorithm searches speed, and operational efficiency is high, along with temperature change and The change of extraneous load impedance, when there is skew in the resonance point of piezoelectric transducer system, can quickly with The resonant frequency that track piezoelectric transducer system is continually changing, also can rapid feedback to ultrasound knife main frame, Ultrasound knife main frame can adjust the frequency of the pumping signal of driving source in time, can guarantee that piezoelectric transducer system System is in resonant frequency state, thus ensures the amplitude output maximum of ultrasonic cutter head, it is ensured that ultrasound knife The efficiency of cutting tissue is the highest.

Accompanying drawing explanation

Fig. 1 is piezoelectric transducer equivalent circuit diagram；

Fig. 2 is the frequency versus impedance curve chart of piezoelectric transducer；

Fig. 3 is the frequency-phase curve chart of piezoelectric transducer；

Fig. 4 is the structured flowchart of ultrasound knife frequency tracking apparatus of the present invention；

Fig. 5 is the logic control block diagram of ultrasound knife frequency tracking method of the present invention；

Fig. 6 be piezoelectric transducer of the present invention under out of phase, Δ f/ Δ θ is with the change curve of impedance And matched curve figure.

Symbol description in figure

1. power module；2. adjustable source module；3. control module；4. power amplification output module； 5. piezoelectric transducer；6. Signal-regulated kinase；7. memory module EEPROM；8. display module；9. Sound module；10.DSP processor；11. buttons and indicating lamp module；12. fault detection module； 13. Programmable Logic Device FPGA unit；14. safety detection module；15.ADC module one；16. Voltage feedback module；17.ADC module two；18. current feedback modules.

Detailed description of the invention

Below in conjunction with embodiment, the present invention is described further.

As shown in Figure 1, Figure 2, shown in Fig. 3, Fig. 4, Fig. 5, Fig. 6, it is a kind of embodiment of the present invention, A kind of ultrasound knife frequency tracking apparatus, including processor, Programmable Logic Device FPGA unit 13, Power module 1, adjustable source module 2, memory module, display module 8, sound module 9, Button and indicating lamp module 11, fault detection module 12, safety detection module 14, signal condition mould Block 6, power amplification output module 4, control module 3, ADC 1, ADC 2 17, Voltage feedback module 16, current feedback module 18 and piezoelectric transducer 5；

Processor is connected with memory module 2, display module 8, sound module 9, processor and control Module 3, Signal-regulated kinase 6 connect, control module 3, Signal-regulated kinase 6 respectively with power Amplifying output module 4 to connect, power amplification output module 4 is connected with adjustable source module 2, Adjustable source module 2 is connected with power module 1, power amplification output module 4 and piezoelectric energy-conversion Device 5 connects；

Processor is connected with Programmable Logic Device FPGA unit 13, Programmable Logic Device FPGA Unit 13 is connected with safety detection module 14, and safety detection module 14 other end is defeated with power amplification Go out module 4 to connect；

Programmable Logic Device FPGA unit 13 is connected with ADC, ADC 1, ADC Module 2 17 is connected with voltage feedback module 16 and current feedback module 18 respectively；

Programmable Logic Device FPGA unit 13 and button and indicating lamp module 11 and fault detect mould Block 12 connects.

It can be seen that processor is dsp processor 10 in Fig. 4, memory module is memory module EEPROM7, ADC is two-way ADC, including ADC 1 and ADC two 17, ADC can also use DSP to carry module, and the processor of this scheme has only to containing two ADC that road precision comparison is high or a piece of high-precision two passage ADC of exterior arrangement, Hardware circuit design is simple, system will be caused unstable because of reasons such as device agings, processor Flexibly and easily.

The frequency tracking method of a kind of ultrasound knife device of this embodiment, comprises the following steps:

(1) impedance and the phase angle expression formula of transducer is obtained by the equivalent circuit of transducer, andTable Reach formula.

As it is shown in figure 1, be the equivalent transformation circuit diagram of piezoelectric transducer.Wherein C₀For piezoelectric energy-conversion The direct capacitance of device, is primarily referred to as piezoelectric transducer because of the electric capacity produced when trapping human organizes；R₀ For the medium electrical loss in piezoelectric transducer potsherd, because being connected in parallel on C₀Two ends, can be by R₀It is considered as Infinity, generally can ignore its impact (R not shown in figure₀, directly ignore)；L_SFor dynamic electric Sense, is produced by piezoelectric transducer quality；C_SThe dynamic capacity produced for piezoelectric transducer；R_SIt is super During sound cutter cutting tissue, the dynamic electric resistor that load produces.

A () by the equivalent circuit of the transducer of Fig. 1, the expression formula of the mould calculating transducer impedance is:

$\left|Z\right|=\sqrt{\frac{C_s^2{L}_s^2{w}^4+C_s^2{R}_s^2{w}^2-2C_s{L}_s{w}^2+1}{w^2(C_0^2{C}_s^2{L}_s^2{w}^4+C_0^2{C}_s^2{R}_s^2{w}^2-2C_0^2{C}_s{L}_s{w}^2-2C_0{C}_s^2{L}_s{w}^2+C_0^2+2C_0{C}_s+C_s^2)}}---\left(1\right);$

B () by the equivalent circuit of the transducer of Fig. 1, the expression formula of the phase angle calculating transducer impedance is:

$\mathrm{\θ}=-{\tan }^{-1}\frac{C_0{C}_s^2{L}_s^2{w}^4-C_s^2{L}_s{w}^2+C_0{C}_s^2{R}_s^2{w}^2-2C_0{C}_s{L}_s{w}^2+C_0+C_s}{C_s^2{R}_{s}w}\×\frac{180}{\mathrm{\π}}---\left(2\right);$

Wherein θ is phase place, and | Z | is transducer impedance, and w is angular frequency, w=2 π f.

C () can be obtained equation below by phase angle expression formula above:

$\frac{dw}{d\mathrm{\θ}}=\frac{-k_1{k}_2{\mathrm{wsec}}^2\left(k_2\mathrm{\θ}\right)}{4k_3{w}^3+2k_{4}w+k_1\tan \left(k_2\mathrm{\θ}\right)}---\left(3\right)$

$k_1=C_s^2{R}_s---\left(4\right)$

$k_2=\frac{\mathrm{\π}}{180}---\left(5\right)$

$k_3=C_0{C}_s^2{L}_s^2---\left(6\right)$

$k_4=-C_s^2{L}_s+C_0{C}_s^2{R}_s^2-2C_0{C}_s{L}_s---\left(7\right);$

D () can be obtained the variable quantity of frequency when phase place has minor variations by formula (3), byAlso The most availableExpression formula.

(2) processor simulation transducer is in different operating state, and measures it under this duty Characterisitic parameter C₀, L_S, C_S, R_S, and calculate impedance corresponding at a certain frequency, phase angle and At phase inphase angle, scan resistance value corresponding to each dot frequency andValue is depicted as point-like figure.

The characterisitic parameter C measured under different operating state according to transducer₀, L_S, C_S, R_S, and Parameter will be measured and substitute into formula (1), (2), (3), can obtain impedance corresponding at a certain frequency, Phase angle andCurve as shown in Figure 6, phase angle is respectively-20^°、0^°、20^°Time,With impedance Change curve, same method can obtain at other phase angles correspondingChange with impedance is bent Line, draws the most one by one.

(3) at according to step (2) not inphase angle,With the change curve of impedance, matching obtains Matched curve.

As shown in Figure 6, phase angle be respectively-20 °, 0 °, 20 ° time,Change with impedance is bent Line, it can be seen that when angle is between-20 °～20 °,With impedance change curve substantially Overlap, with a matched curve, therefore, it can approximation represents that phase angle is in-20 °～20 ° of intervals With the matched curve in the change of impedance, i.e. Fig. 6.The transducer system of other different models is permissible Characteristic according to self obtains corresponding phase place interval and matched curve.

Approximating method here uses method of least square, but is not limited to method of least square, it is also possible to Using Lagrange's interpolation, Newton interpolating method etc. curve-fitting method, fitting function uses many Item formula, but it is not limited to multinomial, other can use as exponential function, logarithmic function etc..

Transducer is under out of phase, and Δ f/ Δ θ is with the change curve of impedance and matched curve, matching The function expression of curve is:

$\frac{df}{d\mathrm{\θ}}=P_n{Z}^n+P_{n-1}{Z}^{n-1}+\mathrm{...}+P_1{Z}^1+P_0---\left(8\right)$

The wherein highest index of the n matched curve by being taken, P₀... P_nCoefficient for matched curve.

Can obtain according to the method described above with the change curve of impedance for the Δ f/ Δ θ at other phase places Go out.Phase bit comparison is big when, curve can offset up.In actual application, can be according to tool The transducer of body obtains the matched curve under several phase place interval, the phase value detected according to system Call different matched curve functions and obtain correspondenceValue.

If the matched curve in Fig. 6 is to obtain after matchingChange curve with impedance.

(4) the matched curve numerical value that step (3) is obtained by processor is stored in as subfunction and deposits In reservoir.

The matched curve i.e. formula (8) that step (3) obtains stores in memory as subfunction, If curve difference is relatively big at each phase angle, a series of curve can be obtained by phase angle demarcation interval, These curves are stored in memorizer.

(5) processor gathers Voltage Feedback and current feedback signal, and thus signal calculates piezoelectricity and changes The impedance Z of energy device system and phase angle θ.

(6) size of the phase angle θ that processor calculates according to step (5), selects step (4) The corresponding subfunction of storage, then the resistance value Z that will be calculated by step (5) is as parameter meter The functional value of the subfunction called, i.e. obtainsSize.

(7) step (6) is calculated by processorThe phase angle θ calculated with step (5), It is updated in formula (9), obtains the frequency values needing to adjust.

$f=\mathrm{\α}\×\frac{df}{d\mathrm{\θ}}\×\mathrm{\θ}---\left(9\right)$

In formula (9), α is the regulatory factor close to 1.

(8) processor is according to the frequency values needing to adjust calculated, and regulates the frequency of output signal, The resonant frequency making driving frequency and transducer system self is consistent.

Take above way, it is possible to ensure that ultrasonic cutter head is operated in optimum state.Above controlling party Method, it is fast that its frequency tracking algorithm searches speed, and operational efficiency is high, along with the change of temperature and outer The change of boundary's load impedance, when the resonance point of piezoelectric transducer system occurs skew, can quickly follow the tracks of The resonant frequency that piezoelectric transducer system is continually changing, also can rapid feedback to ultrasound knife main frame, super Sound cutter main frame can adjust the frequency of the pumping signal of driving source in time, can guarantee that piezoelectric transducer system It is in resonant frequency state；For different ultrasonic transducers, it is only necessary to according to ultrasonic transduction Device characterisitic parameter under different operating state adjust the constant factor of fitting function can realize right The accurate control of piezoelectric transducer, thus control the amplitude output maximum of ultrasonic cutter head, ultrasound knife is cut The efficiency cutting tissue is the highest.

Only as described above, the only specific embodiment of the present invention, when not limiting this with this The scope that invention is implemented, therefore the displacement of its equivalent assemblies, or made according to scope of patent protection of the present invention Equivalent variations and amendment, all should still belong to the category that claims of the present invention is contained.

Claims (8)

1. a ultrasound knife frequency tracking apparatus, it is characterised in that: include processor, able to programme patrol Volume circuit FPGA unit, power module, adjustable source module, memory module, display module, Sound module, button and indicating lamp module, fault detection module, safety detection module, signal are adjusted Reason module, power amplification output module, control module, ADC one, ADC two, voltage Feedback module, current feedback module and piezoelectric transducer；

Described processor is connected with described memory module, described display module, described sound module, Described processor is connected with described control module, described Signal-regulated kinase, described control module, Signal-regulated kinase is connected with described power amplification output module respectively, described power amplification output mould Block is connected with described adjustable source module, and described adjustable source module is with described power module even Connecing, described power amplification output module is connected with described piezoelectric transducer；

Described processor is connected with described Programmable Logic Device FPGA unit, described FPGA Circuit FPGA unit is connected with described safety detection module, the described safety detection module other end and institute State power amplification output module to connect；

Described Programmable Logic Device FPGA unit is connected with described ADC, described ADC One, described ADC two is connected with described voltage feedback module and described current feedback module respectively；

Described Programmable Logic Device FPGA unit and described button and indicating lamp module and described fault Detection module connects.

Ultrasound knife frequency tracking apparatus the most according to claim 1, it is characterised in that: described Processor is dsp processor.

Ultrasound knife frequency tracking apparatus the most according to claim 1, it is characterised in that: described Memory module is EEPROM.

Ultrasound knife frequency tracking apparatus the most according to claim 1, it is characterised in that: described ADC is that DSP carries module or outside high-speed ADC module, described ADC at least two Passage.

5. a tracking for any one ultrasound knife frequency tracking apparatus as described in claim 1-4, It is characterized in that: comprise the following steps:

(1) impedance and the phase angle expression formula of transducer is obtained by the equivalent circuit of transducer, andTable Reach formula；

(2) simulation transducer is in different operating state, and measures its characteristic under this duty Parameter C₀, L_S, C_S, R_S, and calculate impedance corresponding at a certain frequency, phase angle andBy phase At inphase angle, scan resistance value corresponding to each dot frequency andValue is depicted as point-like figure；

(3) at according to step (2) not inphase angle,With the change curve of impedance, matching obtains Matched curve；

(4) the described matched curve numerical value that described step (3) is obtained by processor is as subfunction Storage is in memory；

(5) processor gathers Voltage Feedback and current feedback signal, and thus signal calculates piezoelectricity and changes The impedance Z of energy device system and phase angle θ；

(6) size of the phase angle θ that processor calculates according to described step (5), selects step Suddenly the corresponding subfunction that (4) store, then the resistance value Z that will be calculated by described step (5) Calculate the functional value of the subfunction called as parameter, i.e. obtainSize；

(7) described step (6) is calculated by processorThe phase place calculated with step (5) Angle θ, is updated to formulaIn, obtain the frequency values needing to adjust；

(8) processor according to described in the frequency values needing to adjust that calculates, regulation output signal Frequency, the resonant frequency making driving frequency and transducer system self is consistent.

Tracking the most according to claim 5, it is characterised in that: in described step (1) The impedance of described transducer and phase angle expression formula, andThe calculating of expression formula, comprises the following steps:

A () by the equivalent circuit of transducer, the expression formula of the mould calculating transducer impedance is:

$\left|Z\right|=\sqrt{\frac{C_s^2{L}_s^2{w}^4+C_s^2{R}_s^2{w}^2-2C_s{L}_s{w}^2+1}{w^2(C_0^2{C}_s^2{L}_s^2{w}^4+C_0^2{C}_s^2{R}_s^2{w}^2-2C_0^2{C}_s{L}_s{w}^2-2C_0{C}_s^2{L}_s{w}^2+C_0^2+2C_0{C}_s+C_s^2)}}---\left(1\right);$

B () by the equivalent circuit of transducer, the expression formula of the phase angle calculating transducer impedance is:

$\mathrm{\θ}=-{\tan }^{-1}\frac{C_0{C}_s^2{L}_s^2{w}^4-C_s^2{L}_s{w}^2+C_0{C}_s^2{R}_s^2{w}^2-2C_0{C}_s{L}_s{w}^2+C_0+C_s}{C_s^2{R}_{s}W}\×\frac{180}{\mathrm{\π}}---\left(2\right);$

C () by step (b), the phase angle expression formula of described formula (2) can obtain equation below:

$\frac{dw}{d\mathrm{\θ}}=\frac{-k_1{k}_2{\mathrm{wsec}}^2\left(k_2\mathrm{\θ}\right)}{4k_3{w}^3+2k_{4}w+k_{1}tan\left(k_2\mathrm{\θ}\right)}---\left(3\right)$

$k_1=C_s^2{R}_s---\left(4\right)$

$k_2=\frac{\mathrm{\π}}{180}---\left(5\right)$

$k_3=C_0{C}_s^2{L}_s^2---\left(6\right)$

$k_4=-C_s^2{L}_s+C_0{C}_s^2{R}_s^2-2C_0{C}_s{L}_s---\left(7\right);$

D () can be obtained there is minor variations time-frequency in phase place by the formula (3) in described step (b) The variable quantity of rate, byNamely it is availableExpression formula.

Tracking the most according to claim 5, it is characterised in that: in described step (3) Described approximating method be the curves such as method of least square, Lagrange's interpolation or Newton interpolating method Approximating method.

Tracking the most according to claim 5, it is characterised in that: in described step (3) Described fitting function be multinomial, exponential function or logarithmic function.