Mechanical quality factor of high-overtone bulk acoustic resonator

Mechanical quality factor Qm is a key characteristic parameter of High-overtone bulk acoustic resonator(HBAR). The effects of structure parameter(thickness) and perfor?mance parameters(characteristic impedance and mechanical attenuation factor) of substrate,piezoelectric film and electrode constituting HBAR on Qm are carried out. The relationships between Qm and these parameters are obtained by a lumped parameter equivalent circuit instead of distributed parameter equivalent circuit near the resonance frequency, and the an?alytical expressions oi Qm are given. The results show that Qm increases non-monotonically with the continuous increase of the substrate thickness for HBAR with certain piezoelectric film thickness, and it approaches to the substrate material mechanical quality factor as the substrate thickness is large. Qm decreases wavily with the continuous increase of the piezoelectric film thickness for HBAR with certain substrate thickness. Sapphire and YAG with low mechanical loss are appropriate as the substrate to get a larger Qm- The electrode loss must be considered since it can reduce Qm- Compared with Au electrode, A1 electrode with lower loss can obtain higher Qm when the appropriate electrode thickness is selected. In addition, Qm decreases with the increase of frequency. These results provide the theoretical basis for optimizing the parameters of HBAR and show that trade-oflFs between Qm and must be considered in the design because their changes are often inconsistent.     

Optimal design of resonant piezoelectric buzzer from a perspective of vibration-absorber theory

In this paper, an optimization technique is presented for the design of piezoelectric buzzers. This design technique aims at finding the optimal configuration of the coupled cavity and diaphragm structure to maximize the sound pressure output. Instead of measuring the material constants of the piezoelectric ceramic and the metal diaphragm, an "added-mass method" is developed to estimate the equivalent electromechanical parameters of the system on which an analogous circuit can be established. The electrical impedance and on-axis sound pressure level of the piezoelectric buzzer can be simulated by solving the loop equations of the electromechanoacoustical analogous circuit. An interesting finding of this research is that the nature of the piezoelectric buzzer bears remarkable resemblance to that in the dynamic vibration absorber theory. Much physical insight can be gained by exploiting this resemblance in search of the optimal configuration. According to the system characteristic equation, a design chart was devised to "lock" the critical frequency at which the system delivers the maximal output. On the basis of the analogous circuit and the vibration absorber theory, an optimal design was found with constrained optimization formalism. Experiments were conducted to justify the optimal design. The results showed that the performance was significantly improved using the optimal design over the original design. Design guidelines for the piezoelectric buzzers are summarized.     

Excitation of bulk elastic waves at the surfaces of piezoelectric crystals with 422,622 symmetry

The problem of exciting bulk elastic waves at the surface of a piezoelectric with symmetries 422,622 has been solved by a successive approximation method. In the approximation of a fixed electric field, created at the surface of the piezoelectric crystal by a two-electrode transducer, the distributions are found for the shear wave stress and the energy flux density in the far zone. The equivalent circuit parameters for a two-electrode radiator are determined taking account of the dynamic piezoelectric correction obtained in the second approximation. The equivalent circuit parameters and the transducer loss are treated for TeO₂ crystals. A realistic possibility of using surface transducers in the development of acousto-optic modulators in the s.h.f. region is shown. Tomsk State Academy of Control Systems and Radio Electronics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 8–15, January, 1997.     

Study on the radial composite piezoelectric ceramic transducer in radial vibration

A new type of radial composite piezoelectric transducer in radial vibration is developed and analyzed. The radial composite transducer consists of a piezoelectric ceramic thin ring polarized in the thickness direction and a metal thin circular ring. They are connected together and excited to vibrate in the radial direction. The radial vibrations of a piezoelectric ceramic thin ring and a metal thin circular ring are analyzed, respectively. Their radial electro-mechanical equivalent circuits are obtained. Based on the electro-mechanical equivalent circuits and using the boundary conditions between the piezoelectric ceramic thin ring and the metal thin circular ring in the radial direction, the electro-mechanical equivalent circuit of the radial composite piezoelectric transducer is derived out and the resonance frequency equation is obtained. The relationship between the resonance frequency and the geometrical dimensions of the transducer is analyzed. Some radial composite piezoelectric transducers are designed and manufactured. The resonance frequencies and the anti-resonance frequencies, the electro-mechanical equivalent circuit parameters are measured. The effective electro-mechanical coupling coefficient and the mechanical quality factor are calculated. It is illustrated that the measured radial resonance frequencies are in good agreement with the theoretical results from the resonance frequency equation.     

Definition and measurement of the normalized electrical impedance of lossy piezoelectric resonators for ultrasonic transducers

Relevant equivalent circuit parameters and values of material constants of a piezoelectric resonator can be determined from measurements of its electrical input impedance as a function of frequency. The complex electrical impedance curves and the associated critical frequencies are the basis of this characterization by the piezoelectric resonance method. In this paper, the previously introduced concept of normalized electrical impedance of the lossy resonator, extended to include piezoelectric losses, is applied to the analysis of the effects of different types of intrinsic losses on peak values, bandwidths and characteristic frequencies. The resulting impedance patterns depend solely on the electromechanical coupling coefficient and the loss tangents, providing a useful tool for the analysis of low-Q resonators. The normalized impedance is experimentally evaluated from the basic data provided by an HP 4194A impedance analyser by means of specifically developed ASP programs.     

压电换能器导纳的研究

本对压电换能器的等效电路及导纳圆测定方法进行了介绍．对于提供压电换能器与所在电路间的阻抗匹配有重要意义。     

一种新型Cymbal换能器的研究

提出并研究了一种新型的Cymbal换能器.与传统的Cymbal换能器相比,该换能器中的压电陶瓷圆盘由一个金属圆环和压电陶瓷圆盘的径向组合体所代替.论文首先探讨了压电陶瓷圆盘和金属圆环组合体的径向振动,用解析方法得出了其径向振动的机电等效电路.在此基础上,得出了新型Cymbal换能器的机电等效电路,并得出了其共振及反共振...     

Investigations of thickness-shear mode elastic constant and damping of shunted piezoelectric materials with a coupling resonator

Shear-mode piezoelectric materials have been widely used to shunt the damping of vibrations where utilizing surface or interface shear stresses. The thick-shear mode(TSM) elastic constant and the mechanical loss factor can change correspondingly when piezoelectric materials are shunted to different electrical circuits. This phenomenon makes it possible to control the performance of a shear-mode piezoelectric damping system through designing the shunt circuit. However, due to the difficulties in directly measuring the TSM elastic constant and the mechanical loss factor of piezoelectric materials, the relationships between those parameters and the shunt circuits have rarely been investigated. In this paper, a coupling TSM electro–mechanical resonant system is proposed to indirectly measure the variations of the TSM elastic constant and the mechanical loss factor of piezoelectric materials. The main idea is to transform the variations of the TSM elastic constant and the mechanical loss factor into the changes of the easily observed resonant frequency and electrical quality factor of the coupling electro–mechanical resonator. Based on this model, the formular relationships are set up theoretically with Mason equivalent circuit method and they are validated with finite element(FE) analyses. Finally, a prototype of the coupling electro–mechanical resonator is fabricated with two shear-mode PZT5 A plates to investigate the TSM elastic constants and the mechanical loss factors of different circuit-shunted cases of the piezoelectric plate. Both the resonant frequency shifts and the bandwidth changes observed in experiments are in good consistence with the theoretical and FE analyses under the same shunt conditions. The proposed coupling resonator and the obtained relationships are validated with but not limited to PZT5 A.     

考虑损耗的磁致/压电层合材料谐振磁电响应分析

运用等效电路法，对磁致/压电层合材料谐振状态下的磁电响应进行分析，得到了材料在谐振状态下的磁电电压转换系数理论计算公式. 详细地分析了磁致/压电层合材料在谐振点附近的磁损耗、机械损耗、电损耗，并给出了各种损耗相应的计算方法和大小，发现谐振状态下，材料的主要损耗来源于机械损耗. 分析结论较好地解释了磁电层合材料在不同偏置磁场下磁电响应的实验结果. 关键词： 磁致/压电层合材料 磁电效应 谐振 损耗分析     

利用等效电路模型快速分析加载集总元件的微型化频率选择表面

为了提高频率选择表面(FSS)设计优化速度, 利用等效电路方法对基于集总元件加载的微型化FSS结构进行了分析. 根据FSS物理结构建立了相应的等效电路模型, 通过ADS软件对全波分析曲线进行拟合提取了等效电路模型参数, 通过延长曲线范围增加极值点个数提高拟合参数精度. 利用所提取的等效电路参数计算了不同LC 参数下FSS的传输特性, 与全波分析精确结果相对比, 电路模型计算的透过率略高, 中心频点及-3 dB带宽与全波分析结果的相对误差均小于10%. 证明了利用等效电路模型分析复杂FSS结构的可行性, 为FSS设计和快速优化提供了参考. 关键词： 频率选择表面 等效电路 集总元件     

高次谐波体声波谐振器的机械品质因数

机械品质因数Q_M是高次谐波体声波谐振器(High-overtone Bulk Acoustic Resonator,HBAR)一个关键的特性参数。首次较系统地研究了Q_M随构成HBAR的3个组成部分(基底、压电薄膜和电极)的结构参数(厚度)和性能参数(特性阻抗与机械衰减因子)的变化规律。在谐振频率附近,将HBAR的分布参数等效电路简化为集总参数等效电路,首次用解析表达式给出它们的变化规律,分析了Q_M在给定频率最近谐振点的变化情况。结果表明,固定压电层厚度,Q_M随基底厚度的连续增加略呈振荡(非单调)上升,当基底厚度很大时趋于基底材料的机械品质因数;固定基底厚度,Q_M随压电层厚度的连续增加呈波浪式下降;选择低损耗的蓝宝石或YAG作为基底可以获得较大的Q_M值;电极的损耗必须考虑,它会降低Q_M值;与Au电极相比,具有较低损耗的A1电极选择适当厚度可以获得较高的Q_M值;此外,Q_M随频率的增加呈下降趋势。上述的结果为HBAR的优化设计提供了相应的理论依据。根据我们对K_eff2的研究,Q_M与K_eff2的变化规律往往是相悖的,因此在设计HBAR时要在这两者作适当的权衡。      

Slotted piezoelectric ring deep ocean hydrophone

Based on the energy method,the underwater resonance frequency equation and electrical admittance curve of the slotted piezoelectric ring are derived.By establishing the equivalent circuit of slotted piezoelectric ring in low-frequency receiving condition,the lowfrequency open circuit voltage sensitivity of slotted piezoelectric ring is deduced.Compared the low-frequency receiving sensitivity of the slotted piezoelectric ring and the complete ring,the thought to design the deep ocean hydrophone is presented,which combines the slotted piezoelectric ring and the free flooded structure.By establishing finite element simulation model of free flooded slotted piezoelectric ring,the relationship between ring structure parameters and low-frequency open circuit voltage sensitivity are discussed.Through the simulation and optimization,the deep-sea slotted piezoelectric ring hydrophone with the resonance frequency of 600 Hz is fabricated.The acoustic and pressure tests results indicated that the low-frequency open circuit voltage sensitivity of free flooded slotted piezoelectric ring hydrophone in work bandwidth 100-300 Hz is-193.2 dB and the least value is-197.9 dB with the-4.7 dB fluctuation.Hydrostatic pressure resistance of 30 Mpa is obtained.Compared with the same structure size free flooded piezoelectric ring hydrophone,the low-frequency open circuit voltage sensitivity of slotted piezoelectric ring hydrophone raised 20 dB.The results verify the practicability of deep ocean hydrophone presented here with free flooded slotted piezoelectric ring structure.     

Effective electromechanical coupling coefficient of high-overtone bulk acoustic resonator

A high-overtone bulk acoustic resonator(HEAR) is composed of a substrate,a piezoelectric film and upper and lower electrodes,the influences of their structure parameter(thickness) and performance parameter(characteristic impedance) on effective electromechanical coupling coefficient K_(eff)~2 are investigated systematically.The relationship between K_(eff)~2 and these parameters is obtained by a lumped parameter equivalent circuit instead of distributed parameter equivalent circuit near the resonant frequency,and K_(eff)~2 at the resonance frequency closest to the given frequency is analyzed.The results show that K_(eff)~2 declines rapidly and oscillatorily with the continuous increase of the substrate thickness when the piezoelectric film thickness is fixed,and decreases inversely proportion to the thickness when the substrate thickness is greater than a certain value.With the ratio of the characteristic impedance of the substrate to the piezoelectric layer increasing,the maximum of K_(eff)~2 obtained from the variation curve of K_(eff)~2 with the continuous increase of the piezoelectric film thickness decreases rapidly before reaching the minimum value,and later increases slowly.Fused silica with low impedance is appropriate as the substrate of HBAR to get a larger K_(eff)~2.Compared with Al electrode,Au electrode can obtain larger K_(eff)~2 when the appropriate electrode thickness is selected.The revealed laws above mentioned provide the theoretical basis for optimizing parameters of HBAR.     

Two new designs of lamp-type piezoelectric metamaterials for active wave propagation control

A major limitation of current metamaterials is that they control the wave propagation depending on their structure. Active metamaterials in this paper are designed whose physical structure is fixed, yet the position where they control the wave propagation can be changed by piezoelectric conditions. Two kinds of lamp-type piezoelectric metamaterials were assembled from an aluminum base, rubber plate and steel column, the piezoelectric patches were attached on both sides of the steel column, which can change the equivalent elastic modulus of the whole structure when the pair of patches are accessed by an LC circuit. The equivalent elastic modulus becomes zero or negative when the frequency of the circuit varies between 29,000 Hz and 30,000 Hz, in this case the two kinds of lamp-type piezoelectric metamaterials behave as a wave localization and a wave guide, respectively. The advantage of the lamp-type piezoelectric metamaterials is that we can control the wave propagation actively, as long as we change the position of the piezoelectric patches or choose the kind of lamp-type piezoelectric metamaterial. This is more flexible than a traditional passive metamaterial and provides a new way for us to design some acoustic equipment, such as acoustic cloaking, an acoustic black hole, filter or wave guide.     

Study of the sandwiched piezoelectric ultrasonic torsional transducer

The sandwiched piezoelectric ultrasonic torsional transducer was studied. The transducer consists of front and back metal cylinders, and coaxially segmented, tangentially polarized, piezoelectric ceramic tubes. The torsional vibration of the tangentially polarized piezoelectric ceramic slender tube was studied first and its electromechanical equivalent circuit was derived. Based on the network theory and the electromechanical equivalent circuit, the torsional vibration of the piezoelectric ceramic cylinder, formed by stacking a number of identical short piezoelectric ceramic rings, was analysed and the electromechanical equivalent circuit of the piezoelectric ceramic stack in torsional vibration was developed. Finally, the sandwiched ultrasonic torsional transducer was studied and resonance frequency equations were derived which can be used to design and calculate the torsional transducers for different applications.     

多匹配层空气耦合压电超声换能器*

该文针对超声无损检测与成像功能空气耦合换能器开展了分析计算和研制。为解决压电材料与空气间巨大的阻抗失配问题,进行了多匹配层设计,并基于有限元技术仿真设计了1-3压电复合材料参数。借助复数压电方程,导出考虑损耗的多匹配层压电复合材料换能器厚度振动等效电路,获得其等效导纳,以此计算电导谱,同时基于有限元技术数值计算相应电导谱,二者有较好的一致性。在此基础上分别设计制作复合压电材料,多匹配层材料以及由此构成的空气耦合超声换能器。换能器的实测电导谱与数值仿真结果一致。进一步的换能器回波信号测试及其谱分析结果表明,所研制的160 k Hz中心频率空气耦合换能器样品有较好灵敏度和带宽。这些结果说明,该文研制的空气耦合超声换能器的初样是成功的。     

外接LC电路的可调压电换能器的频率特性

压电换能器往往因受到温度与负载的影响,导致其谐振频率、反谐振频率和机械品质因数等特征参数发生变化。通过在压电换能器中设计用于调节的压电陶瓷片,并在调节压电陶瓷片两端外接电负载,可以实现压电换能器的频率调节,修正由于温度和负载导致的频率漂移。基于压电换能器的Mason等效电路,建立外接LC调节电路的压电换能器的谐振频率、反谐振频率模型,分析LC调节电路中调节电感对频率调节特性的影响;通过实验研究外接LC调节电路对可调压电换能器机械品质因数的影响,并验证调节电感对频率调节特性的影响。理论分析和实验研究的结果表明:随着调节电感的增大,调节电容对频率的调节灵敏度提高,可调压电换能器的频率调节宽度拓宽,但也会使压电换能器的机械品质因数降低。合理选择调节电感和调节电容能兼顾频率调节宽度和机械品质因数的要求。此研究可为后续自适应压电换能器的频率调节系统设计提供指导。      

压电陶瓷薄圆环振子径向振动的机电等效电路及其分析

本文对轴向极化压电陶瓷薄圆环的径向振动进行了研究，推出了其机电等效电路，得出了振子的共振和反共振频率方程并进行了实验验证。探讨了振子的共振和反共振频率与其材料和几何尺寸之间的依赖关系。     

Lumped modeling with circuit elements for nonreciprocal magnetoelectric tunable band-pass filter

This paper presents a lumped equivalent circuit model of the nonreciprocal magnetoelectric tunable microwave bandpass filter.The reciprocal coupled-line circuit is based on the converse magnetoelectric effect of magnetoelectric composites,includes the electrical tunable equivalent factor of the piezoelectric layer,and is established by the introduced lumped elements,such as radiation capacitance,radiation inductance,and coupling inductance,according to the transmission characteristics of the electromagnetic wave and magnetostatic wave in an inverted-L-shaped microstrip line and ferrite slab.The nonreciprocal transmission property of the filter is described by the introduced T-shaped circuit containing controlled sources.Finally,the lumped equivalent circuit of a nonreciprocal magnetoelectric tunable microwave band-pass filter is given and the lumped parameters are also expressed.When the deviation angles of the ferrite slab are respectively 0° and45°,the corresponding magnetoelectric devices are respectively a reciprocal device and a nonreciprocal device.The curves of S parameter obtained by the lumped equivalent circuit model and electromagnetic simulation are in good agreement with the experimental results.When the deviation angle is between 0° and 45°,the maximum value of the S parameter predicted by the lumped equivalent circuit model is in good agreement with the experimental result.The comparison results of the paper show that the lumped equivalent circuit model is valid.Further,the effect of some key material parameters on the performance of devices is predicted by the lumped equivalent circuit model.The research can provide the theoretical basis for the design and application of nonreciprocal magnetoelectric tunable devices.     

引入界面耦合系数的长片型磁电层状复合材料的等效电路模型

针对长片型磁电层状复合材料,提出了一种适用于准静态和动态磁场激励的引入界面耦合系数的等效电路模型,旨在为基于长片型磁电层状复合材料的传感器、换能器等器件的设计、制作和应用提供理论指导.考虑到磁电层状复合材料实际工作过程中磁致伸缩层和压电层的应变并不相同,首先利用运动方程分别对磁致伸缩层和压电层进行建模,提出了一个从物理上反映相间应变传递的界面耦合系数表达式,然后利用一个变比恰为界面耦合系数的理想变压器将两层材料的等效电路耦合,构成改进的磁电层状复合材料的等效电路模型,得到包含界面耦合系数的磁电电压系数和最佳层合比的表达式.对12个具有不同尺寸和负载条件的样品进行实验,制作过程中承受500g砝码负载的样品的界面耦合系数为0.15,最佳层合比为0.57;承受100g砝码负载的样品的界面耦合系数为0.10,最佳层合比为0.50.磁电电压系数和最佳层合比的实验值与各自包含界面耦合系数的理论值基本符合,证明了改进的等效电路模型的合理性和正确性.