CN108920808A - The LC of piezoelectric ultrasonic transducer matches modeling method - Google Patents

The LC of piezoelectric ultrasonic transducer matches modeling method Download PDF

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CN108920808A
CN108920808A CN201810680605.8A CN201810680605A CN108920808A CN 108920808 A CN108920808 A CN 108920808A CN 201810680605 A CN201810680605 A CN 201810680605A CN 108920808 A CN108920808 A CN 108920808A
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CN108920808B (en
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王金栋
段发阶
蒋佳佳
彭呈祥
黄婷婷
程沁蕊
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Tianjin University
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    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
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    • B06B1/06—Methods or apparatus for generating mechanical vibrations of infrasonic, sonic, or ultrasonic frequency making use of electrical energy operating with piezoelectric effect or with electrostriction
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    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10—Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes

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Abstract

本发明涉及超声换能技术领域，为提出压电超声换能器的LC匹配系统。为此，本发明采用的技术方案是，压电超声换能器的LC匹配建模方法，步骤如下：1)模型准备；2)模型假设；3)模型构成：确定各个常量、变量之间的约束关系，并简化，根据设计初衷，选择模型输入量、输出量，根据约束关系，推导输入量、输出量之间的函数关系；4)模型求解；5)模型分析；6)模型检验；7)模型应用：根据上述分析，分析上述优化的匹配方式的应用领域，并给出相应的器件选择、频率跟踪时的建议和策略。本发明主要应用于压电超声换能器设计制造场合。

The invention relates to the technical field of ultrasonic transducers, and provides an LC matching system for piezoelectric ultrasonic transducers. For this reason, the technical scheme that the present invention adopts is, the LC matching modeling method of piezoelectric ultrasonic transducer, and the steps are as follows: 1) model preparation; 2) model hypothesis; 3) model constitutes: determine each constant, variable between Constraint relationship, and simplify, according to the original intention of the design, select the input quantity and output quantity of the model, and deduce the functional relationship between the input quantity and output quantity according to the constraint relationship; 4) Model solution; 5) Model analysis; 6) Model inspection; 7 ) model application: According to the above analysis, analyze the application field of the above optimized matching method, and give corresponding suggestions and strategies for device selection and frequency tracking. The invention is mainly used in the design and manufacture of piezoelectric ultrasonic transducers.

Description

The LC of piezoelectric ultrasonic transducer matches modeling method
Technical field
The present invention relates to ultrasonic technique field, the LC matching modeling method and one kind of especially a kind of piezoelectric ultrasonic transducer The matching way of optimization.
Background technique
Ultrasonic transducer is the core component of ultrasonic wave generating system, is to convert machinery for the energy of driving signal Can converter, in order to improve the power output efficiency of energy converter, generally require between ultrasound-driven power supply and energy converter into Row matching, including resonance matching and impedance matching.When energy converter series resonance, equivalent circuit be not in purely resistive, but At capacitive, supply voltage will be divided by capacitive load, lead to the output power degradation of energy converter, it is therefore necessary to be adjusted The capacitive in circuit is offset in humorous matching, to make circuit that purely resistive be presented.In addition, the output of switching power semiconductor is side Wave, which contains the reasonable matching network of a large amount of harmonic components, can effectively filter out harmonic components raising electroacoustic efficiency.Resonance matching is big It is all to be realized by capacitor, inductance network, while there is tuning and a degree of filter action.In addition, to make load impedance It is more nearly with the internal resistance of source to improve power efficiency, impedance matching is carried out to energy converter, impedance matching is mainly by transformer It realizes, capacitor, inductance network for tuning also have certain impedance matching function.
Match circuit has series connection matching, matching in parallel, LC matching, T-type matching, double-T shaped matching etc..LC matching is inductance electricity Hold matching, structure is simple, convenience of calculation, and can further decrease equivalent load impedance, therefore be widely used.Matching Inductance L, matching capacitance C value directly affect the performance of system after matching, but domestic and foreign scholars are less refers to one at present The good analysis of kind and obtaining value method.
The value of match circuit depends on system parameter, including series resonance frequency fsDirect capacitance C0, dynamic load resistance R1, environmental change, the aging of energy converter, fever, load variation can all cause energy converter series resonance frequency fsChange, load electricity Hinder R1Even more change and acute variation with load, results in the failure of match circuit above.In order to solve this problem, currently, Domestic and foreign scholars mainly propose two kinds of solutions, are respectively：
1) more complicated matching network, such as T-type matching, double-T shaped matching are used, more complicated was proposed there are also scholar With circuit, such match circuit adjustable parameter is more, therefore can keep stablizing in the certain fluctuation range of system.No It crosses, this solution system is complicated, value and when analysis are more complicated, and excessive power component can also occupy more skies Between, increase cost.
2) adjustable component is added, adjustable inductance or capacitor, then logical its size of feedback control is added, such as to realize Dynamic Matching avoids the failure of match circuit.Likewise, this solution system is complicated, higher cost, and adjustment speed It is relatively slow, load can not be adapted to and change violent working environment.
To overcome the shortcomings of above-mentioned solution, the present invention is directed to establish model to the LC match circuit of ultrasonic transducer into The accurate assessment of row and quantitative analysis, and obtain a kind of LC matching process of optimization, to use fairly simple LC match circuit It solves the above problems, improves the stability and robustness of system after matching.
Summary of the invention
In order to overcome the deficiencies of the prior art, the present invention is directed to propose the LC matching system of piezoelectric ultrasonic transducer.For this purpose, this Invention the technical solution adopted is that, the LC of piezoelectric ultrasonic transducer matches modeling method, and steps are as follows：
1) model preparation：Specify the original design intention of LC match circuit, the i.e. purpose of Match circuits, it is desirable to the function of realization The effect that can and reach；
2) model hypothesis：Circuit model after establishing matching, and simplify, determine the constant, variable and ginseng to be determined of model Number carries out symbol definition；
3) model is constituted：It determines the constraint relationship between each constant, variable, and simplifies, according to original design intention, select mould Type input quantity, output quantity derive the functional relation between input quantity, output quantity according to the constraint relationship；
4) model solution：The functional relation of above-mentioned establishment is solved, using the zero of function, pole as characteristic point, weight Point analysis chooses the best value of parameter to be determined, obtains a kind of matching way of optimization according to original design intention；
5) model analysis：The matching way of above-mentioned optimization is substituted into system model, analyzes influence of its dependent variable to model, The advantage and disadvantage for analyzing the matching way of above-mentioned optimization further determine that the reasonability of above-mentioned value；
6) model testing：The match circuit of ultrasonic transducer is built by the matching way of above-mentioned optimization, is surpassed after detection matching The frequency and load response characteristic of sonic transducer；
7) model application：According to above-mentioned analysis, the application field of the matching way of above-mentioned optimization is analyzed, and is provided corresponding Suggestion and strategy when device selection, frequency-tracking.
Specific steps further refine as follows：
Step 1：Model preparation：The original intention for determining LC matched design is the following aspects：
Original intention 1) power factor：It is tuned in Several Typical Load resistance value, makes system at purely resistive, power factor 1；
Original intention 2) power is larger：In the work of series resonance point, system output power, that is, active power is maximum or larger；
Original intention 3) power stability：System is set more to adapt to load resistance R1Variation, in R1Effective power fluctuation is small when fluctuation, And maintain higher level；
Original intention 4) protection circuit：In extreme circumstances：Unloaded or load R1It is smaller, so that system power is unlikely to excessive, To protect circuit；
Step 2：Model hypothesis：Circuit model after establishing matching, and simplify, determine the constant of model, variable and to true Determine parameter, carries out symbol definition；
Converter circuitry model after LC matching, L is matching inductance, C2For matching capacitance, C0Transducer static capacitor, R1 For energy converter load resistance, C1Energy converter dynamic capacity, L1For energy converter dynamic inductance, VinFor driving voltage, Vo is energy converter The voltage at both ends, wherein C0For constant, driving voltage VinCorresponding angular frequencys2Frequency fs2, R1、C1、L1It is with load and ring The variable of border variation, energy converter correspond to angular frequencysSeries resonance frequency fsBy C1、L1It determines,Work as fs2 =fsWhen, C1、L1Resonance is ignored, L, C2For parameter to be determined, then enable C=C1+C2, C C1And C2The sum of, dependent variable has Power factor η, apparent energy S, active-power P, then system model is defined as：
(η, S, P)=f (Vin,L,C,R1,fs)
(y1,y2,y3...)=f (x1,x2,x3...) indicate by x1,x2,x3... arrive y1,y2,y3... mapping relations；
Step 3：Model is constituted：It determines the constraint relationship between each constant, variable, and simplifies, according to original design intention, choosing Mode input amount, output quantity are selected, according to the constraint relationship, derives the functional relation between input quantity, output quantity；
System complex impedance Z (w at this times) be：
Circuit to be made is pure configuration, i.e. imaginary part is equal to 0, in driving angular frequencys2=ωs, R1=R0Shi Jinhang matching, then The relationship of matching inductance L and C is：
In addition, matching inductance L, matching capacitance C2Addition, new resonance frequency f is added to system0, i.e. L and C's is humorous Vibration frequency f0：
L, C value is worked as f by formula (2), formula (3) constraint0When determining, L, C are uniquely determined, and are enabled：
Then ρ and R0When determining, the value of L, C are also uniquely determined, and system model is at this time：
(η, S, P)=f (Vin,ρ,R0, R1,fs)
It is obtained by formula (3), formula (4)：
Substitution formula (2) obtains：
By the nodal method of analysis：It obtains:
The then active power that energy converter obtainsAnd R1Functional relation be：
Step 4：Model solution：The functional relation of above-mentioned establishment is solved, using the zero of function, pole etc. as feature Point, selective analysis choose the best value of parameter to be determined, obtain a kind of matching way of optimization according to original design intention；
The functional relation established by formula (7), in R1>In the range of 0, function has and only one pole, is maximum Point, is easy to get and works asWhen, active powerObtain maximum value
According to original design intention 1), original intention 2) when output power is very big, power factor should be 1, therefore, enables R1max=R0, I.e.It solves：
TakeBest value as ρ；Formula (8) substitution formula (6) is obtained：
Formula (9) is the preliminary optimization value of undetermined parameter；
Step 5：Model analysis：The matching way that step 4 is optimized substitutes into system model, analyzes its dependent variable to model It influences, analyzes the advantage and disadvantage of the matching way of above-mentioned optimization, further determine that the reasonability of above-mentioned value；
Step 6：Model testing：The match circuit of ultrasonic transducer, detection matching are built by the matching way of above-mentioned optimization The frequency of ultrasonic transducer and load response characteristic afterwards；Above-mentioned emulation sufficiently simulates actual state, demonstrates above-mentioned excellent The feasibility and good characteristic of the matching way of change；
Step 7：Model application：According to above-mentioned analysis, the application field of the matching way of above-mentioned optimization is analyzed, and provides phase Answer device selection, frequency-tracking when suggestion and strategy.
Step 5 specifically, driving frequency fs2Equal to energy converter series resonance frequency fs, as load resistance R1Fluctuation, R1For allusion quotation Offset R0When, the active power of system is very big, and power factor be 1, meet original design intention 1) and original design intention 2), below it is right System performance at this time is further analyzed：
Formula (9) are substituted into formula (1), are obtained：
The then impedance of system | Z (jws) | it is：
It is obtained by formula (11), as load resistance R1When variation, the impedance of system | Z (jws) | it remains unchanged, perseverance is Then the apparent energy S of system is：
It is obtained by formula (12), the apparent energy S (ω of the system after optimizing values) remain unchanged, it is a constant；
Further, if R1Fluctuation, by formula (10), the power factor η for obtaining system is：
The active power of systemFor：
IfIt is fluctuated in the range of [0.63,1.6], substitutes into formula (13), formula (14) obtains, power factor η and wattful power RateFluctuation range be [0.9,1]；
In conclusion when takingOptimization value as LC match circuit； Consider fs1、fs2Influence, enableIt is same to enable
Firstly, enabling ρ2=1, i.e. analysis ρ1Influence to system, system model at this time are：
(η, S, P)=f (Vin,R0,ρ1,ρ3)
By formula (9), actual match parameter is：
At this point, the complex impedance of system is：
If Vin=200V, R0=200 Ω draw active power and ρ according to formula (13), formula (14), formula (15)1、ρ3Between Function curve P=f (ρ1、ρ3) and power factor η and ρ1、ρ3Between function curve η=f (ρ1、ρ3)；
Further, ρ is enabled1=1, analyze frequency tracking error ρ2Influence to system, frequency tracking error ρ2To system Influence direct and energy converter quality factor qmIt is related, it is necessary to take into account, QmBigger bandwidth is smaller, gets over to frequency tracking error It is sensitive.System model at this time is：
(η, S, P)=f (Vin,R0,ρ2,ρ3, Qm)
Energy converter quality factor qmFor：
The series resonance angular frequency of energy converter is：
Joint type (17), formula (16)：
Complex impedance Z (jw at this times2) be：
If Vin=200V, R0=200 Ω, Qm=50, according to formula (13), formula (14), formula (18) draws active power and ρ2、 ρ3Between function curve P=f (ρ2、ρ3) and power factor and ρ2、ρ3Between function curve n=f (ρ2、ρ3)。
Should be a little higher than series resonance frequency of driving frequency in frequency-tracking, if carry out frequency sweep, need from high frequency to Low frequency carries out, to avoid high-power point.
The features of the present invention and beneficial effect are：
1) present invention establishes the ultrasound transducer system mathematical model after LC matching, quantifies to each parameter in system Analysis, realizes comprehensive, the accurate analysis and assessment to the matched transducer system of LC.
2) one embodiment of the present of invention, the angle new from one, with matching inductance L2, matching capacitance C2The resonance of introducing Frequency f0With energy converter series resonance frequency fsThe ratio between ρ analyzed as input quantity, simplify system model, can it is more succinct, Intuitively obtain influence of the different LC values to system.
3) one embodiment of the present of invention proposes a kind of LC matching way of optimization, has the following advantages that：A) phase is used To simple LC matching network, do not increase adjustable element, reduces system cost, volume and design difficulty；B) it is typically bearing Under load, the output power of energy converter is very big, and power factor is 1, when being supported on the fluctuation of biggish range (0.6~1.5 times), It is still able to maintain biggish output power (more than 0.9 times of rated power), and power factor is improved in higher range (0.9 or more) The stability and robustness of ultrasonic system；C) the LC matching way of a kind of optimization, when the load, total view of system is in function Rate remains unchanged, even if in load resistance R1Under minimum extreme case, still ensure that the apparent energy of system is constant, thus It solves ultrasonic technique field " system is burnt in zero load " this technical problem, improves the safety of system.
4) present invention has done further analysis of uncertainty to the circuit after above-mentioned optimization LC matching, proposes corresponding Suggestion and strategy when device selection, frequency-tracking, can further improve system performance；
Detailed description of the invention：
Fig. 1 is that a kind of LC of piezoelectric ultrasonic transducer of the invention matches the flow chart of modeling method.
Fig. 2 is the circuit model and simplified electricity involved in one embodiment of the present of invention, after energy converter LC matching Road model.
Fig. 3 is active-power P, power factor η and ρ involved in one embodiment of the present of invention1、ρ3Between relationship Figure.
Fig. 4 is active-power P, power factor η and ρ involved in one embodiment of the present of invention2、ρ3Between relationship Figure.
In Fig. 2, L is matching inductance, C2For matching capacitance, C0Transducer static capacitor, R1For energy converter load resistance, C1Energy converter dynamic capacity, L1For energy converter dynamic inductance, VinFor driving voltage, Vo is the voltage at energy converter both ends, C C1With C2The sum of.
In Fig. 3, ρ1To match when institute selected frequency fs1With series resonance frequency fsThe ratio between, ρ2For the driving frequency of energy converter fs2With the series resonance frequency f of energy convertersThe ratio between, ρ3For dynamic electric resistor R1With the selected resistance R of matching0The ratio between, ρ2=1, driving electricity Press Vin=200V matches selected resistance R0=200 Ω, Fig. 3 a are active-power P and ρ1、ρ3Between functional relation, Fig. 3 b be function Rate factor η and ρ1、ρ3Between functional relation.
In Fig. 4, ρ1To match when institute selected frequency fs1With series resonance frequency fsThe ratio between, ρ2For the driving frequency of energy converter fs2With the series resonance frequency f of energy convertersThe ratio between, ρ3For dynamic electric resistor R1With the selected resistance R of matching0The ratio between, ρ1=1, driving electricity Press VinResistance R is chosen in=200V, matching0=200 Ω, Fig. 3 a are active-power P and ρ2、ρ3Between functional relation, Fig. 3 b be function Rate factor η and ρ2、ρ3Between functional relation.
Specific embodiment
To achieve the goals above, the technical solution adopted by the present invention is that, a kind of LC matching of piezoelectric ultrasonic transducer is built Mould method and a kind of matching way of optimization, include the following steps：
1) model preparation：Specify the original design intention of LC match circuit, the i.e. purpose of Match circuits, it is desirable to the function of realization The effect that can and reach；
2) model hypothesis：Circuit model after establishing matching, and simplify, determine the constant, variable and ginseng to be determined of model Number carries out symbol definition；
3) model is constituted：It determines the constraint relationship between each constant, variable, and simplifies, according to original design intention, select mould Type input quantity, output quantity derive the functional relation between input quantity, output quantity according to the constraint relationship；
4) model solution：The functional relation of above-mentioned establishment is solved, using the zero of function, pole etc. as characteristic point, Selective analysis chooses the best value of parameter to be determined, obtains a kind of matching way of optimization according to original design intention；
5) model analysis：The matching way of above-mentioned optimization is substituted into system model, analyzes influence of its dependent variable to model, The advantage and disadvantage for analyzing the matching way of above-mentioned optimization further determine that the reasonability of above-mentioned value；
6) model testing：The match circuit of ultrasonic transducer is built by the matching way of above-mentioned optimization, is surpassed after detection matching The frequency and load response characteristic of sonic transducer；
7) model application：According to above-mentioned analysis, the application field of the matching way of above-mentioned optimization is analyzed, and is provided corresponding Suggestion and strategy when device selection, frequency-tracking；
Specific implementation process is as follows：
Step 1：Model preparation：Specify the original design intention of LC match circuit, the i.e. purpose of Match circuits, it is desirable to realize Function and the effect that reaches；The matched main purpose of LC is tuning, while original design intention should include the stability of realization system And safety, comprehensively consider, determines that the original intention of LC matched design is the following aspects：
Original intention 1) power factor：It is tuned in Several Typical Load resistance value, makes system at purely resistive, power factor 1；
Original intention 2) power is larger：In the work of series resonance point, system output power, that is, active power is maximum or larger；
Original intention 3) power stability：System is set more to adapt to load resistance R1Variation, in R1Effective power fluctuation is small when fluctuation, And maintain higher level；
Original intention 4) protection circuit：(unloaded or load R in extreme circumstances1It is smaller), so that system power is unlikely to excessive, To protect circuit；
Step 2：Model hypothesis：Circuit model after establishing matching, and simplify, determine the constant of model, variable and to true Determine parameter, carries out symbol definition；
Converter circuitry model after LC matching is as shown in Figure 2 a, and L is matching inductance, C2For matching capacitance, C0Energy converter is quiet State capacitor, R1For energy converter load resistance, C1Energy converter dynamic capacity, L1For energy converter dynamic inductance, VinFor driving voltage, Vo For the voltage at energy converter both ends.Wherein C0For constant, driving voltage VinFrequency fs2(corresponding angular frequencys2), R1、C1、L1It is With the variable of load and environmental change, the series resonance frequency f of energy converters(corresponding angular frequencys) by C1、L1It determines,Work as fs2=fsWhen, C1、L1Resonance can be ignored, and circuit model is as shown in Figure 2 b at this time, L, C2For Parameter to be determined, then enable C=C1+C2, simplified circuit model is as shown in Figure 2 c, C C1And C2The sum of.System because become Power factor η, apparent energy S, active-power P etc. are measured, then system model can be defined as：
(η, S, P)=f (Vin,L,C,R1,fs)
(y1,y2,y3...)=f (x1,x2,x3...) indicate by x1,x2,x3... arrive y1,y2,y3... mapping relations.
Step 3：Model is constituted：It determines the constraint relationship between each constant, variable, and simplifies, according to original design intention, choosing Mode input amount, output quantity are selected, according to the constraint relationship, derives the functional relation between input quantity, output quantity；
In figure 2 c, system complex impedance Z (w at this times) be：
Circuit to be made is pure configuration, i.e. imaginary part is equal to 0, in driving angular frequencys2=ωs, R1=R0Shi Jinhang matching, then The relationship of matching inductance L and C is：
In addition, matching inductance L, matching capacitance C2Addition, new resonance frequency f is added to system0, i.e. L and C's is humorous Vibration frequency f0：
L, C value is worked as f by formula (2), formula (3) constraint0When determining, L, C are uniquely determined, and are enabled：
Then ρ and R0When determining, the value of L, C are also uniquely determined, and system model is at this time：
(η, S, P)=f (Vin,ρ,R0, R1,fs)
It is obtained by formula (3), formula (4)：
Substitution formula (2) obtains：
By the nodal method of analysis：It obtains:
The then active power that energy converter obtainsAnd R1Functional relation be：
Step 4：Model solution：The functional relation of above-mentioned establishment is solved, using the zero of function, pole etc. as feature Point, selective analysis choose the best value of parameter to be determined, obtain a kind of matching way of optimization according to original design intention；
The functional relation established by formula (7), in R1>In the range of 0, function has and only one pole, is maximum Point, is easy to get and works asWhen, active powerObtain maximum value
According to original design intention 1), original intention 2) when output power is very big, power factor should be 1, therefore, enables R1max=R0, I.e.It solves：
TakeBest value as ρ.
Formula (8) substitution formula (6) is obtained：
Formula (9) is the preliminary optimization value of undetermined parameter.
Step 5：Model analysis：The matching way of above-mentioned optimization is substituted into system model, analyzes its dependent variable to model It influences, analyzes the advantage and disadvantage of the matching way of above-mentioned optimization, further determine that the reasonability of above-mentioned value；
If driving frequency fs2Equal to energy converter series resonance frequency fs, as load resistance R1Fluctuation, R1For representative value R0When, The active power of system is very big, and power factor be 1, meet original design intention 1) and original design intention 2), below at this time be System performance is further analyzed.
Formula (9) are substituted into formula (1), are obtained：
The then impedance of system | Z (jws) | it is：
It is obtained by formula (11), as load resistance R1When variation, the impedance of system | Z (jws) | it remains unchanged, perseverance is Then the apparent energy S of system is：
It is obtained by formula (12), the apparent energy S (ω of the system after optimizing values) remain unchanged, it is a constant, explanation In load resistance R1When variation, the size of current of major loop is remained unchanged, even if under the extreme cases such as zero load, it will not be because of mistake It flows and burns circuit, to ensure that the safety of system, realize original intention 4).
Further, if R1Fluctuation, by formula (10), the power factor η for obtaining system is：
The active power of systemFor：
IfIt is fluctuated in the range of [0.63,1.6], substitutes into formula (13), formula (14) obtains, power factor η and wattful power RateFluctuation range be [0.9,1], i.e. load resistance R1In larger range variation, system active power and power because Number fluctuation is smaller, and keeps higher level, realizes original design intention 3.
In conclusion when takingOptimization value as LC match circuit When, system can satisfy every original design intention in step 1.
As described above, working asSystem after matching has every excellent performance, but this premise is：1) selected when matching Frequency fs1The as series resonance frequency f of energy converters；2) the driving frequency f of energy converters2Equal to the series resonance frequency of energy converter fs.But in fact, above-mentioned two premise cannot achieve, because of the series resonance frequency f of rate energy convertersIt can change at any time, And the frequency-tracking of energy converter certainly exists certain error.
Consider fs1、fs2Influence, enableIt is same to enable
Firstly, enabling ρ2=1, i.e. analysis ρ1Influence to system, system model at this time are：
(η, S, P)=f (Vin,R0,ρ1,ρ3)
By formula (9), actual match parameter is：
At this point, the complex impedance of system is：
If Vin=200V, R0=200 Ω draw active power and ρ according to formula (13), formula (14), formula (15)1、ρ3Between Function curve P=f (ρ1、ρ3) and power factor η and ρ1、ρ3Between function curve η=f (ρ1、ρ3), respectively such as Fig. 3 a and Shown in Fig. 3 b.By Fig. 3 a and Fig. 3 b as it can be seen that when the error of matching frequency presence ± 5%, i.e. ρ1∈ [0.95,1.05], in ρ1∈ When [0.7,1.5], the power factor of system is maintained at 0.9 or more, is in higher level, it is seen then that (the ρ when frequency-tracking is accurate2 =1), the error (ρ of matching frequency1) smaller to systematic influence, system still keeps preferable stability.
Further, ρ is enabled1=1, analyze frequency tracking error (ρ2) influence to system, frequency tracking error (ρ2) to being System influences direct and energy converter quality factor qmIt is related, it is necessary to take into account, QmBigger bandwidth is smaller, misses to frequency-tracking Difference is more sensitive.System model at this time is：
(η, S, P)=f (Vin,R0,ρ2,ρ3, Qm)
The tracking of energy converter series resonance frequency is always the hot and difficult issue of ultrasound field, and numerous scholars propose locking phase The frequency-trackings modes such as method, maximum current method, be continuously improved ultrasonic transducer frequency-tracking precision, but due to energy converter quality because Number QmIt is larger, there are precipitous mechanical admittance curves, tremendous influence can be caused to system lesser frequency departure, therefore divide Analyse frequency tracking error (ρ2) influence to system is very necessary.Energy converter quality factor qmFor：
The series resonance angular frequency of energy converter is：
Joint type (17), formula (16)：
Complex impedance Z (jw at this times2) be：
If Vin=200V, R0=200 Ω, Qm=50, according to formula (13), formula (14), formula (18) draws active power and ρ2、 ρ3Between function curve P=f (ρ2、ρ3) and power factor and ρ2、ρ3Between function curve n=f (ρ2、ρ3), respectively such as Shown in Fig. 4 a and Fig. 4 b.Ideally, at series resonance frequency, obtain maximum power is energy converterBy scheming 4a is as it can be seen that when frequency-tracking is there are when error, and energy converter obtains active power, and there are larger fluctuations, in ρ3=0.5, ρ2=0.98 Place, or even there is the active power of up to 1400w, it is extremely dangerous.Under comparing, in ρ3>1 and ρ2>In the range of 1, power Variation is steady, and no high-power point of crossing occurs.From fig. 4b, it can be seen that working as Qm=50, in load resistance R1When fluctuation, to keep 0.9 with On power factor, frequency tracking error will be within ± 0.5%, within even ± 0.3%, and the energy converter of corresponding 40k allows Frequency tracking error be ± 120hz, the frequency tracking error that the energy converter of higher quality factor allows can be smaller.
Step 6：Model testing：The match circuit of ultrasonic transducer, detection matching are built by the matching way of above-mentioned optimization The frequency of ultrasonic transducer and load response characteristic afterwards；Above-mentioned emulation sufficiently simulates actual state, demonstrates above-mentioned excellent The feasibility and good characteristic of the matching way of change；
Step 7：Model application：According to above-mentioned analysis, the application field of the matching way of above-mentioned optimization is analyzed, and provides phase Answer device selection, frequency-tracking when suggestion and strategy；The LC matching way of energy converter optimization proposed in this paper, circuit letter Clean, calculation method is simple, does not increase adjustable element, while improving system output power, avoids because of dynamic electric resistor R1Variation Bring is detuning and power flash-up, has many advantages, such as high security, high power stability, High Power Factor, is widely used in surpassing The fields such as sound processing, ultrasonic cleaning, ultrasonic welding.Fig. 4 shows that the precision of frequency-tracking directly influences the performance of system, and Due to various reasons, frequency-tracking precision can not further increase, therefore should select the lesser ultrasound of broader bandwidth, quality factor Energy converter, to reduce influence of the frequency tracking error to system.In addition, Fig. 4 is shown, driving frequency is larger and smaller than practical series connection When resonance frequency, the influence to system is different, works as ρ2<When 1, power swing is larger, or even occurs being up to the power of 1400w, right System causes larger threat, and in ρ2>In the range of 1, changed power is steady, it is no cross high-power point occur, therefore frequency with It should be a little higher than series resonance frequency of driving frequency when track, if carrying out frequency sweep, need to carry out from high frequency to low frequency, to avoid High-power point.
The present invention is described in detail with reference to the accompanying drawings and detailed description.
A kind of LC matching modeling method flow chart of piezoelectric ultrasonic transducer as shown in Figure 1, modeling analysis process according to this Flow chart executes, and one embodiment of the present of invention process is as follows：
Step 1：Model preparation：Specify the original design intention of LC match circuit, the i.e. purpose of Match circuits, it is desirable to realize Function and the effect that reaches；The matched main purpose of LC is tuning, while original design intention should include the stability of realization system And safety, comprehensively consider, determines that the original intention of LC matched design is the following aspects：
Original intention 1) power factor：It is tuned in Several Typical Load resistance value, makes system at purely resistive, power factor 1；
Original intention 2) power is larger：In the work of series resonance point, system output power, that is, active power is maximum or larger；
Original intention 3) power stability：System is set more to adapt to load resistance R1Variation, in R1Effective power fluctuation is small when fluctuation, And maintain higher level；
Original intention 4) protection circuit：(unloaded or load R in extreme circumstances1It is smaller), so that system power is unlikely to excessive, To protect circuit；
Step 2：Model hypothesis：Circuit model after establishing matching, and simplify, determine the constant of model, variable and to true Determine parameter, carries out symbol definition；
Converter circuitry model after LC matching is as shown in Figure 2 a, and L is matching inductance, C2For matching capacitance, C0Energy converter is quiet State capacitor, R1For energy converter load resistance, C1Energy converter dynamic capacity, L1For energy converter dynamic inductance, VinFor driving voltage, Vo For the voltage at energy converter both ends.Wherein C0For constant, driving voltage VinFrequency fs2(corresponding angular frequencys2), R1、C1、L1It is With the variable of load and environmental change, the series resonance frequency f of energy converters(corresponding angular frequencys) by C1、L1It determines,Work as fs2=fsWhen, C1、L1Resonance can be ignored, and circuit model is as shown in Figure 2 b at this time, L, C2For to Determining parameter, then enable C=C1+C2, simplified circuit model is as shown in Figure 2 c, C C1And C2The sum of.The dependent variable of system Power factor η, apparent energy S, active-power P etc., then system model can be defined as：
(η, S, P)=f (Vin,L,C,R1,fs)
(y1,y2,y3...)=f (x1,x2,x3...) indicate by x1,x2,x3... arrive y1,y2,y3... mapping relations.
Step 3：Model is constituted：It determines the constraint relationship between each constant, variable, and simplifies, according to original design intention, choosing Mode input amount, output quantity are selected, according to the constraint relationship, derives the functional relation between input quantity, output quantity；
In figure 2 c, system complex impedance Z (w at this times) be：
Circuit to be made is pure configuration, i.e. imaginary part is equal to 0, in driving angular frequencys2=ωs, R1=R0Shi Jinhang matching, then The relationship of matching inductance L and C is：
In addition, matching inductance L, matching capacitance C2Addition, new resonance frequency f is added to system0, i.e. L and C's is humorous Vibration frequency f0：
L, C value is worked as f by formula (2), formula (3) constraint0When determining, L, C are uniquely determined, and are enabled：
Then ρ and R0When determining, the value of L, C are also uniquely determined, and system model is at this time：
(η, S, P)=f (Vin,ρ,R0, R1,fs)
It is obtained by formula (3), formula (4)：
Substitution formula (2) obtains：
By the nodal method of analysis：It obtains:
The then active power that energy converter obtainsAnd R1Functional relation be：
Step 4：Model solution：The functional relation of above-mentioned establishment is solved, using the zero of function, pole etc. as feature Point, selective analysis choose the best value of parameter to be determined, obtain a kind of matching way of optimization according to original design intention；
The functional relation established by formula (7), in R1>In the range of 0, function has and only one pole, is maximum Point, is easy to get and works asWhen, active powerObtain maximum value
According to original design intention 1), original intention 2) when output power is very big, power factor should be 1, therefore, enables R1max=R0, I.e.It solves：
TakeBest value as ρ.
Formula (8) substitution formula (6) is obtained：
Formula (9) is the preliminary optimization value of undetermined parameter.
Step 5：Model analysis：The matching way of above-mentioned optimization is substituted into system model, analyzes its dependent variable to model It influences, analyzes the advantage and disadvantage of the matching way of above-mentioned optimization, further determine that the reasonability of above-mentioned value；
If driving frequency fs2Equal to energy converter series resonance frequency fs, as load resistance R1Fluctuation, R1For representative value R0When, The active power of system is very big, and power factor be 1, meet original design intention 1) and original design intention 2), below at this time be System performance is further analyzed.
Formula (9) are substituted into formula (1), are obtained：
The then impedance of system | Z (jws) | it is：
It is obtained by formula (11), as load resistance R1When variation, the impedance of system | Z (jws) | it remains unchanged, perseverance is Then the apparent energy S of system is：
It is obtained by formula (12), the apparent energy S (ω of the system after optimizing values) remain unchanged, it is a constant, explanation In load resistance R1When variation, the size of current of major loop is remained unchanged, even if under the extreme cases such as zero load, it will not be because of mistake It flows and burns circuit, to ensure that the safety of system, realize original intention 4).
Further, if R1Fluctuation, by formula (10), the power factor η for obtaining system is：
The active power of systemFor：
IfIt is fluctuated in the range of [0.63,1.6], substitutes into formula (13), formula (14) obtains, power factor η and wattful power RateFluctuation range be [0.9,1], i.e. load resistance R1In larger range variation, system active power and power because Number fluctuation is smaller, and keeps higher level, realizes original design intention 3.
In conclusion when takingOptimization value as LC match circuit When, system can satisfy every original design intention in step 1.
As described above, working asSystem after matching has every excellent performance, but this premise is：1) selected when matching Frequency fs1The as series resonance frequency f of energy converters；2) the driving frequency f of energy converters2Equal to the series resonance frequency of energy converter fs.But in fact, above-mentioned two premise cannot achieve, because of the series resonance frequency f of rate energy convertersIt can change at any time, And the frequency-tracking of energy converter certainly exists certain error.
Consider fs1、fs2Influence, enableIt is same to enable
Firstly, enabling ρ2=1, i.e. analysis ρ1Influence to system, system model at this time are：
(η, S, P)=f (Vin,R0,ρ1,ρ3)
By formula (9), actual match parameter is：
At this point, the complex impedance of system is：
If Vin=200V, R0=200 Ω draw active power and ρ according to formula (13), formula (14), formula (15)1、ρ3Between Function curve P=f (ρ1、ρ3) and power factor η and ρ1、ρ3Between function curve η=f (ρ1、ρ3), respectively such as Fig. 3 a and Shown in Fig. 3 b.By Fig. 3 a and Fig. 3 b as it can be seen that when the error of matching frequency presence ± 5%, i.e. ρ1∈ [0.95,1.05], in ρ1∈ When [0.7,1.5], the power factor of system is maintained at 0.9 or more, is in higher level, it is seen then that (the ρ when frequency-tracking is accurate2 =1), the error (ρ of matching frequency1) smaller to systematic influence, system still keeps preferable stability.
Further, ρ is enabled1=1, analyze frequency tracking error (ρ2) influence to system, frequency tracking error (ρ2) to being System influences direct and energy converter quality factor qmIt is related, it is necessary to take into account, QmBigger bandwidth is smaller, misses to frequency-tracking Difference is more sensitive.System model at this time is：
(η, S, P)=f (Vin,R0,ρ2,ρ3, Qm)
The tracking of energy converter series resonance frequency is always the hot and difficult issue of ultrasound field, and numerous scholars propose locking phase The frequency-trackings modes such as method, maximum current method, be continuously improved ultrasonic transducer frequency-tracking precision, but due to energy converter quality because Number QmIt is larger, there are precipitous mechanical admittance curves, tremendous influence can be caused to system lesser frequency departure, therefore divide Analyse frequency tracking error (ρ2) influence to system is very necessary.Energy converter quality factor qmFor：
The series resonance angular frequency of energy converter is：
Joint type (17), formula (16)：
Complex impedance Z (jw at this times2) be：
If Vin=200V, R0=200 Ω, Qm=50, according to formula (13), formula (14), formula (18) draws active power and ρ2、 ρ3Between function curve P=f (ρ2、ρ3) and power factor and ρ2、ρ3Between function curve n=f (ρ2、ρ3), respectively such as Shown in Fig. 4 a and Fig. 4 b.Ideally, at series resonance frequency, obtain maximum power is energy converterBy scheming 4a is as it can be seen that when frequency-tracking is there are when error, and energy converter obtains active power, and there are larger fluctuations, in ρ3=0.5, ρ2=0.98 Place, or even there is the active power of up to 1400w, it is extremely dangerous.Under comparing, in ρ3>1 and ρ2>In the range of 1, power Variation is steady, and no high-power point of crossing occurs.From fig. 4b, it can be seen that working as Qm=50, in load resistance R1When fluctuation, to keep 0.9 with On power factor, frequency tracking error will be within ± 0.5%, within even ± 0.3%, and the energy converter of corresponding 40k allows Frequency tracking error be ± 120hz, the frequency tracking error that the energy converter of higher quality factor allows can be smaller.
Step 6：Model testing：The match circuit of ultrasonic transducer, detection matching are built by the matching way of above-mentioned optimization The frequency of ultrasonic transducer and load response characteristic afterwards；Above-mentioned emulation sufficiently simulates actual state, demonstrates above-mentioned excellent The feasibility and good characteristic of the matching way of change；
Step 7：Model application：According to above-mentioned analysis, the application field of the matching way of above-mentioned optimization is analyzed, and provides phase Answer device selection, frequency-tracking when suggestion and strategy；The LC matching way of energy converter optimization proposed in this paper, circuit letter Clean, calculation method is simple, does not increase adjustable element, while improving system output power, avoids because of dynamic electric resistor R1Variation Bring is detuning and power flash-up, has many advantages, such as high security, high power stability, High Power Factor, is widely used in surpassing The fields such as sound processing, ultrasonic cleaning, ultrasonic welding.Fig. 4 shows that the precision of frequency-tracking directly influences the performance of system, and Due to various reasons, frequency-tracking precision can not further increase, therefore should select the lesser ultrasound of broader bandwidth, quality factor Energy converter, to reduce influence of the frequency tracking error to system.In addition, Fig. 4 is shown, driving frequency is larger and smaller than practical series connection When resonance frequency, the influence to system is different, works as ρ2<When 1, power swing is larger, or even occurs being up to the power of 1400w, right System causes larger threat, and in ρ2>In the range of 1, changed power is steady, it is no cross high-power point occur, therefore frequency with It should be a little higher than series resonance frequency of driving frequency when track, if carrying out frequency sweep, need to carry out from high frequency to low frequency, to avoid High-power point.

Claims (4)

1.一种压电超声换能器的LC匹配建模方法，其特征是，步骤如下：1. a kind of LC matching modeling method of piezoelectric ultrasonic transducer, it is characterized in that, step is as follows: 1)模型准备：明确LC匹配电路的设计初衷，即匹配电路设计的目的，想要实现的功能和达到的效果；1) Model preparation: clarify the original intention of the design of the LC matching circuit, that is, the purpose of the matching circuit design, the function to be realized and the effect to be achieved; 2)模型假设：建立匹配后的电路模型，并简化，确定模型的常量、变量和待确定参数，进行符号定义；2) Model assumption: establish the matched circuit model, simplify it, determine the constants, variables and parameters to be determined of the model, and define symbols; 3)模型构成：确定各个常量、变量之间的约束关系，并简化，根据设计初衷，选择模型输入量、输出量，根据约束关系，推导输入量、输出量之间的函数关系；3) Model composition: determine the constraint relationship between each constant and variable, and simplify it. According to the original intention of the design, select the input and output of the model, and deduce the functional relationship between the input and output according to the constraint relationship; 4)模型求解：对上述确立的函数关系进行求解，以函数的零、极点作为特征点，重点分析，根据设计初衷，选取待确定参数的最佳取值，得出一种优化的匹配方式；4) Model solution: Solve the function relationship established above, take the zero and pole points of the function as feature points, focus on analysis, and select the best value of the parameters to be determined according to the original design intention, and obtain an optimized matching method; 5)模型分析：将上述优化的匹配方式代入系统模型，分析其他变量对模型的影响，分析上述优化的匹配方式的优缺点，进一步确定上述取值的合理性；5) Model analysis: Substituting the above-mentioned optimized matching method into the system model, analyzing the influence of other variables on the model, analyzing the advantages and disadvantages of the above-mentioned optimized matching method, and further determining the rationality of the above-mentioned values; 6)模型检验：按上述优化的匹配方式搭建超声换能器的匹配电路，检测匹配后超声换能器的频率和负载响应特性；6) Model inspection: Build the matching circuit of the ultrasonic transducer according to the above-mentioned optimized matching method, and detect the frequency and load response characteristics of the ultrasonic transducer after matching; 7)模型应用：根据上述分析，分析上述优化的匹配方式的应用领域，并给出相应的器件选择、频率跟踪时的建议和策略。7) Model application: According to the above analysis, analyze the application field of the above optimized matching method, and give corresponding suggestions and strategies for device selection and frequency tracking. 2.如权利要求1所述的压电超声换能器的LC匹配建模方法，其特征是，具体步骤进一步细化如下：2. the LC matching modeling method of piezoelectric ultrasonic transducer as claimed in claim 1 is characterized in that, concrete steps are further refined as follows: 步骤1：模型准备：确定LC匹配设计的初衷为以下几个方面：Step 1: Model preparation: Determine the original intention of LC matching design for the following aspects: 初衷1)功率因数：在典型负载阻值时进行调谐，使系统成纯阻性，功率因数为1；Original intention 1) Power factor: Tuning is performed at typical load resistance to make the system purely resistive and the power factor is 1; 初衷2)功率较大：在串联谐振点工作时，系统输出功率即有功功率最大或较大；Original intention 2) Larger power: when working at the series resonance point, the system output power is the largest or larger active power; 初衷3)功率稳定：使系统更适应负载电阻R1的变化，在R1波动时有效功率波动小，且维持在较高水平；Original intention 3) Power stability: to make the system more adaptable to the change of load resistance R1, and the effective power fluctuation is small when R1 fluctuates, and it is maintained at a relatively high level; 初衷4)保护电路：在极端情况下：空载或者负载R1较小，使系统功率不至于过大，以保护电路；Original intention 4) Protect the circuit: In extreme cases: no load or load R 1 is small, so that the system power will not be too large to protect the circuit; 步骤2：模型假设：建立匹配后的电路模型，并简化，确定模型的常量、变量和待确定参数，进行符号定义；Step 2: Model assumption: establish the matched circuit model, simplify it, determine the constants, variables and parameters to be determined of the model, and define symbols; LC匹配后的换能器电路模型，L为匹配电感，C2为匹配电容，C0换能器静态电容，R1为换能器负载电阻，C1换能器动态电容，L1为换能器动态电感，Vin为驱动电压，Vo为换能器两端的电压，其中C0为常量，驱动电压Vin对应角频率ωs2的频率fs2，R1、C1、L1是随负载和环境变化的变量，换能器对应角频率ωs的串联谐振频率fs由C1、L1决定，当fs2＝fs时，C1、L1谐振，忽略不计，L、C2为待确定的参数，再令C＝C1+C2，C为C1和C2之和，因变量有功率因数η、视在功率S、有功功率P，则系统模型定义为：The circuit model of the transducer after LC matching, L is the matching inductance, C 2 is the matching capacitance, C 0 is the static capacitance of the transducer, R 1 is the load resistance of the transducer, C 1 is the dynamic capacitance of the transducer, L 1 is the transducer The dynamic inductance of the transducer, V in is the driving voltage, Vo is the voltage across the transducer, where C 0 is a constant, the driving voltage V in corresponds to the frequency f s2 of the angular frequency ω s2 , R 1 , C 1 , and L 1 are random The variable of load and environment changes, the series resonance frequency f s of the transducer corresponding to the angular frequency ω s is determined by C 1 and L 1 , When f s2 = f s , C 1 and L 1 resonate and are ignored, L and C 2 are parameters to be determined, and let C=C 1 +C 2 , C is the sum of C 1 and C 2 , the dependent variable With power factor η, apparent power S, and active power P, the system model is defined as: (η,S,P)＝f(Vin,L,C,R1,fs)(η,S,P)=f(V in ,L,C,R 1 ,f s ) (y1,y2,y3...)＝f(x1,x2,x3...)表示由x1,x2,x3...到y1,y2,y3...的映射关系；(y 1 ,y 2 ,y 3 ...)=f(x 1 ,x 2 ,x 3 ...) means from x 1 ,x 2 ,x 3 ... to y 1 ,y 2 ,y 3 The mapping relationship of ...; 步骤3：模型构成：确定各个常量、变量之间的约束关系，并简化，根据设计初衷，选择模型输入量、输出量，根据约束关系，推导输入量、输出量之间的函数关系；Step 3: Model composition: Determine the constraint relationship between each constant and variable, and simplify it. According to the original design intention, select the input quantity and output quantity of the model, and deduce the functional relationship between the input quantity and output quantity according to the constraint relationship; 此时的系统复阻抗Z(ws)为：The system complex impedance Z(w s ) at this time is: 欲使电路为纯组态，即虚部等于0，在驱动角频率ωs2＝ωs，R1＝R0时进行匹配，则匹配电感L和C的关系为：To make the circuit a pure configuration, that is, the imaginary part is equal to 0, and the matching is performed when the driving angular frequency ω s2 = ω s , R 1 = R 0 , then the relationship between the matching inductance L and C is: 另外，匹配电感L、匹配电容C2的加入，给系统添加了新的谐振频率f0，即L和C的谐振频率f0：In addition, the addition of matching inductance L and matching capacitor C 2 adds a new resonant frequency f 0 to the system, that is, the resonant frequency f 0 of L and C: L、C的取值受式(2)，式(3)约束，即当f0确定时，L、C唯一确定，令：The values of L and C are constrained by formula (2) and formula (3), that is, when f 0 is determined, L and C are uniquely determined, so that: 则ρ和R0确定时，L、C的取值也唯一确定，此时系统模型为：Then when ρ and R 0 are determined, the values of L and C are also uniquely determined. At this time, the system model is: (η,S,P)＝f(Vin,ρ,R0，R1,fs)(η,S,P)=f(V in ,ρ,R 0 ,R 1 ,f s ) 由式(3)、式(4)得到：From formula (3) and formula (4): 代入式(2)得到：Substitute into formula (2) to get: 由节点电压法：得到: By the node voltage method: get: 则换能器获得的有功功率和R1的函数关系为：The active power obtained by the transducer is The functional relationship with R 1 is: 步骤4：模型求解：对上述确立的函数关系进行求解，以函数的零、极点等作为特征点，重点分析，根据设计初衷，选取待确定参数的最佳取值，得出一种优化的匹配方式；Step 4: Model solution: Solve the above-established functional relationship, use the zero and pole points of the function as feature points, focus on analysis, and select the best value of the parameters to be determined according to the original design intention to obtain an optimized matching Way; 由公式(7)确立的函数关系，在R1>0的范围内，函数有且只有一个极点，为极大值点，易得当时，有功功率取得最大值 According to the functional relationship established by formula (7), in the range of R 1 >0, the function has one and only one pole, which is the maximum value point, which is easy to get , active power get the maximum 根据设计初衷1)，初衷2)在输出功率极大时，功率因数应当为1，因此，令R1max＝R0，即解得：According to the original design intention 1) and original intention 2) when the output power is extremely large, the power factor should be 1, so let R 1max = R 0 , that is Solutions have to: 即取作为ρ的最佳取值；将式(8)代入式(6)得到：instant As the optimal value of ρ; Substituting Equation (8) into Equation (6) to get: 式(9)即为待定参数的初步最优化取值；Equation (9) is the initial optimal value of the undetermined parameters; 步骤5：模型分析：将步骤4优化的匹配方式代入系统模型，分析其他变量对模型的影响，分析上述优化的匹配方式的优缺点，进一步确定上述取值的合理性；Step 5: Model analysis: Substitute the matching method optimized in step 4 into the system model, analyze the influence of other variables on the model, analyze the advantages and disadvantages of the above optimized matching method, and further determine the rationality of the above values; 步骤6：模型检验：按上述优化的匹配方式搭建超声换能器的匹配电路，检测匹配后超声换能器的频率和负载响应特性；上述仿真已经充分模拟了实际状况，验证了上述优化的匹配方式的可行性和优良特性；Step 6: Model inspection: build the matching circuit of the ultrasonic transducer according to the above optimized matching method, and detect the frequency and load response characteristics of the ultrasonic transducer after matching; the above simulation has fully simulated the actual situation and verified the above optimized matching The feasibility and excellent characteristics of the method; 步骤7：模型应用：根据上述分析，分析上述优化的匹配方式的应用领域，并给出相应的器件选择、频率跟踪时的建议和策略。Step 7: Model application: According to the above analysis, analyze the application field of the above optimized matching method, and give corresponding suggestions and strategies for device selection and frequency tracking. 3.如权利要求1所述的压电超声换能器的LC匹配建模方法，其特征是，步骤5具体地，驱动频率fs2等于换能器串联谐振频率fs，当负载电阻R1波动，R1为典型值R0时，系统的有功功率极大，且功率因数为1，满足了设计初衷1)和设计初衷2)，下面对此时的系统性能进一步分析：3. The LC matching modeling method of piezoelectric ultrasonic transducer as claimed in claim 1, it is characterized in that, step 5 specifically, driving frequency f s 2 equals transducer series resonant frequency f s , when load resistance R 1 When R 1 is the typical value R 0 , the active power of the system is extremely large, and the power factor is 1, which meets the original design intention 1) and design intention 2). The following further analyzes the system performance at this time: 将式(9)代入式(1)，得：Substituting formula (9) into formula (1), we get: 则系统的阻抗|Z(jws)|为：Then the impedance |Z(jw s )| of the system is: 由公式(11)得出，当负载电阻R1变化时，系统的阻抗|Z(jws)|保持不变，恒为则系统的视在功率S为：According to the formula (11), when the load resistance R 1 changes, the impedance |Z(jw s )| of the system remains unchanged and is constant as Then the apparent power S of the system is: 由公式(12)得到，优化取值后的系统的视在功率S(ωs)保持不变，为一常量；Obtained from formula (12), the apparent power S(ω s ) of the system after optimizing the value remains unchanged and is a constant; 进一步的，若R1波动，由式(10)，得到系统的功率因数η为：Further, if R fluctuates, the power factor η of the system can be obtained from formula (10): 系统的有功功率为：active power of the system for: 若在[0.63,1.6]的范围内波动，代入式(13)、式(14)得出，功率因数η和有功功率的波动范围为[0.9,1]；like Fluctuating within the range of [0.63,1.6], substituting formula (13) and formula (14) to get, power factor η and active power The fluctuation range of is [0.9,1]; 综上所述，当取作为LC匹配电路的优化取值；In summary, when taking As an optimized value of LC matching circuit; 考虑fs1、fs2的影响，令同样令 Considering the influence of f s1 and f s2 , let same order 首先，令ρ2＝1，即分析ρ1对系统的影响，此时的系统模型是：First, let ρ 2 =1, that is to analyze the influence of ρ 1 on the system, the system model at this time is: (η,S,P)＝f(Vin,R0,ρ1,ρ3)(η,S,P)=f(V in ,R 0 ,ρ 1 ,ρ 3 ) 由式(9)，实际的匹配参数为：According to formula (9), the actual matching parameters are: 此时，系统的复阻抗为：At this point, the complex impedance of the system is: 设Vin＝200V，R0＝200Ω，根据式(13)、式(14)、式(15)，绘出有功功率和ρ1、ρ3之间的函数曲线P＝f(ρ1、ρ3)以及功率因数η和ρ1、ρ3之间的函数曲线η＝f(ρ1、ρ3)；Assuming V in =200V, R 0 =200Ω, according to formula (13), formula (14), formula (15), draw the function curve between active power and ρ 1 , ρ 3 P=f(ρ 1 , ρ 3 ) and the function curve between power factor η and ρ 1 , ρ 3 η=f(ρ 1 , ρ 3 ); 进一步的，令ρ1＝1，分析频率跟踪误差ρ2对系统的影响，频率跟踪误差ρ2对系统的影响直接和换能器的品质因数Qm有关，必须考虑在内，Qm越大带宽越小，对频率跟踪误差越敏感。此时的系统模型是：Further, set ρ 1 =1 to analyze the influence of the frequency tracking error ρ 2 on the system. The influence of the frequency tracking error ρ 2 on the system is directly related to the quality factor Q m of the transducer, which must be taken into account. The larger the Q m The smaller the bandwidth, the more sensitive to frequency tracking error. The system model at this point is: (η,S,P)＝f(Vin,R0,ρ2,ρ3，Qm)(η,S,P)=f(V in ,R 0 ,ρ 2 ,ρ 3 ,Q m ) 换能器品质因数Qm为：The transducer quality factor Q m is: 换能器的串联谐振角频率为：The series resonant angular frequency of the transducer is: 联立式(17)、式(16)得：Simultaneous formula (17) and formula (16) get: 此时的复阻抗Z(jws2)为：The complex impedance Z(jw s2 ) at this time is: 设Vin＝200V，R0＝200Ω，Qm＝50，根据式(13)、式(14)，式(18)绘出有功功率和ρ2、ρ3之间的函数曲线P＝f(ρ2、ρ3)以及功率因数和ρ2、ρ3之间的函数曲线n＝f(ρ2、ρ3)。Assuming V in =200V, R 0 =200Ω, Q m =50, according to formula (13), formula (14), formula (18), draw the function curve between active power and ρ 2 , ρ 3 P=f( ρ 2 , ρ 3 ) and the function curve n=f(ρ 2 , ρ 3 ) between the power factor and ρ 2 , ρ 3 . 4.如权利要求1所述的压电超声换能器的LC匹配建模方法，其特征是，在频率跟踪时，应是驱动频率稍高于串联谐振频率，若进行扫频，则需要从高频向低频进行，以避开高功率点。4. the LC matching modeling method of piezoelectric ultrasonic transducer as claimed in claim 1 is characterized in that, when frequency tracking, should be that drive frequency is slightly higher than series resonance frequency, if carry out frequency sweep, then need from High frequencies are carried towards low frequencies to avoid high power points.
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CN110221123A (en) * 2019-05-30 2019-09-10 西安交通大学 CMUTSThe frequency tracking circuit of resonant mode biochemical sensor
CN110542794A (en) * 2019-08-28 2019-12-06 华南理工大学 A Method and Device for Measuring Equivalent Circuit Impedance Based on Constrained Optimization Problem
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CN113351459A (en) * 2021-06-07 2021-09-07 上海工程技术大学 Method for accurately setting matching inductance of self-excitation driving circuit of piezoelectric transducer
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CN113922698A (en) * 2021-09-14 2022-01-11 深圳爱芯怡科技有限公司 Piezoelectric ceramic drive circuit and ultrasonic atomizer
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CN113934137B (en) * 2021-10-20 2022-07-15 江南大学 Method and system for tracking resonant frequency of ultrasonic power supply
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