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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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B06—GENERATING OR TRANSMITTING MECHANICAL VIBRATIONS IN GENERAL
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    • B06B1/00—Methods or apparatus for generating mechanical vibrations of infrasonic, sonic, or ultrasonic frequency
    • B06B1/02—Methods or apparatus for generating mechanical vibrations of infrasonic, sonic, or ultrasonic frequency making use of electrical energy
    • 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

The present invention relates to ultrasonic transduction technical fields, for the LC matching system for proposing piezoelectric ultrasonic transducer.For this purpose, the technical solution adopted by the present invention is that, the LC of piezoelectric ultrasonic transducer matches modeling method, and steps are as follows：1) model preparation；2) model hypothesis；3) model is constituted：It determines the constraint relationship between each constant, variable, and simplifies, according to original design intention, preference pattern input quantity, output quantity derive the functional relation between input quantity, output quantity according to the constraint relationship；4) model solution；5) model analysis；6) model testing；7) model application：According to above-mentioned analysis, the application field of the matching way of above-mentioned optimization is analyzed, and provides suggestion when corresponding device selection, frequency-tracking and strategy.Present invention is mainly applied to piezoelectric ultrasonic transducers to manufacture and design occasion.

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. a kind of LC of piezoelectric ultrasonic transducer matches modeling method, characterized in that 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 and The effect reached；
2) model hypothesis：Circuit model after establishing matching, and simplify, determine the constant, variable and parameter to be determined of model, into Row symbol definition；
3) model is constituted：It determines the constraint relationship between each constant, variable, and simplifies, according to original design intention, preference pattern is defeated Enter amount, output quantity, according to the constraint relationship, derives the functional relation between input quantity, output quantity；
4) model solution：The functional relation of above-mentioned establishment is solved, using the zero of function, pole as characteristic point, emphasis point Analysis, according to original design intention, chooses the best value of parameter to be determined, obtains a kind of matching way of optimization；
5) model analysis：The matching way of above-mentioned optimization is substituted into system model, analyzes influence of its dependent variable to model, is analyzed The advantage and disadvantage of 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, ultrasound is changed after detection matching The frequency and load response characteristic of energy device；
7) model application：According to above-mentioned analysis, the application field of the matching way of above-mentioned optimization is analyzed, and provides corresponding device Suggestion and strategy when selection, frequency-tracking.
2. the LC of piezoelectric ultrasonic transducer as described in claim 1 matches modeling method, characterized in that specific steps are further It refines 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 ties up It holds in higher level；
Original intention 4) protection circuit：In extreme circumstances：Unloaded or load R1It is smaller, so that system power is unlikely to excessive, with protection Circuit；
Step 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；
Converter circuitry model after LC matching, L is matching inductance, C2For matching capacitance, C0Transducer static capacitor, R1To change Energy device load resistance, C1Energy converter dynamic capacity, L1For energy converter dynamic inductance, VinFor driving voltage, Vo is energy converter both ends Voltage, wherein C0For constant, driving voltage VinCorresponding angular frequencys2Frequency fs2, R1、C1、L1It is to become with load and environment The variable of change, energy converter correspond to angular frequencysSeries resonance frequency fsBy C1、L1It determines,Work as fs2=fs When, C1、L1Resonance is ignored, L, C2For parameter to be determined, then enable C=C1+C2, C C1And C2The sum of, dependent variable is active Rate 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, select mould Type input quantity, output quantity derive the functional relation between input quantity, output quantity according to the constraint relationship；
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 match The relationship of inductance L and C is：
In addition, matching inductance L, matching capacitance C2Addition, new resonance frequency f is added to system0, i.e. the resonance frequency of L and C Rate 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 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；
The functional relation established by formula (7), in R1>In the range of 0, function has and only one pole, is maximum point, easily It is properWhen, 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 the shadow of model It rings, 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 is built by the matching way of above-mentioned optimization, is surpassed after detection matching The frequency and load response characteristic of sonic transducer；Above-mentioned emulation sufficiently simulates actual state, demonstrates above-mentioned optimization The feasibility and good characteristic of matching way；
Step 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.
3. the LC of piezoelectric ultrasonic transducer as described in claim 1 matches modeling method, characterized in that step 5 specifically, is driven Dynamic frequency fs2Equal to energy converter series resonance frequency fs, as load resistance R1Fluctuation, R1For representative value R0When, the wattful power of system Rate is very big, and power factor is 1, meets original design intention 1) and original design intention 2), it is further to system performance at this time below Analysis：
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 isThen it is 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 active powerFluctuation 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 letter Number 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 ρ2Influence to system Direct and energy converter quality factor qmIt is related, it is necessary to take into account, QmBigger bandwidth is smaller, more sensitive to frequency tracking error. 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、ρ3It Between function curve P=f (ρ2、ρ3) and power factor and ρ2、ρ3Between function curve n=f (ρ2、ρ3)。
4. the LC of piezoelectric ultrasonic transducer as described in claim 1 matches modeling method, characterized in that in frequency-tracking, It should be a little higher than series resonance frequency of driving frequency, if carrying out frequency sweep, need to carry out from high frequency to low frequency, to avoid high power Point.
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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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