Elastic, dielectric, and piezoelectric losses in piezoceramics: how it works all together

The quality factor along with electromechanical coupling coefficient (CEMC) is commonly used as a measure of the energy efficiency of a piezoelectric transducer (PT) working as an energy converter. Losses in piezoceramics are phenomenologically considered to have three coupled mechanisms: dielectric, elastic, and piezoelectric. Their cumulative performance first of all determines the PT quality factor characterizing the efficiency of vibrational energy accumulation, and related to it dissipative effects. The extended definition of the PT electromechanical quality factor (EMQ) with permanent energy exchange between electrical source of excitation and PT was proposed. The EMQ analysis has been conducted on the basis of complex material constants for both stiffened and unstiffened canonical vibrational modes. The efficiency of mechanically free and electrically excited piezoceramic transducers in a wide frequency range of PT harmonics, especially between the fundamental resonance and antiresonance frequencies, was investigated, and the effect of piezoelectric loss anomaly with extremely low total losses was predicted. Particularly, optimization of PT excitation with connected reactive (capacitive) element was conducted to provide higher PT mechanical vibrational characteristics with less total losses. The requirements to the piezoceramic material parameters, types of transducer vibrations, and especially to the piezoelectric loss factor in the range of physically valid values were established to provide maximal EMQ.     

Loss mechanisms in piezoelectrics: how to measure different losses separately

Losses in piezoelectrics are considered in general to have three different mechanisms: dielectric, mechanical, and piezoelectric losses. This paper deals with the phenomenology of losses first, then how to measure these losses separately in experiments. We found that heat generation at off-resonance is caused mainly by dielectric loss tan delta' (i.e., P-E hysteresis loss), not by mechanical loss, and that a significant decrease in mechanical Qm with an increase of vibration level was observed in resonant piezoelectric ceramic devices, which is due to an increase in the extensive dielectric loss, not in the extensive mechanical loss. We propose the usage of the antiresonance mode rather than the conventional resonance mode, particularly for high power applications because the mechanical quality factor QB at an antiresonance frequency is larger than QA at a resonance frequency.     

Effect of electric load impedances on the performance of sandwich piezoelectric transducers

Based on the electromechanical equivalent circuit, the sandwich piezoelectric transducer with adjustable resonance frequency is studied. The underlying theory of frequency adjustment is its piezoelectric effect. In this paper, the influence of electric load impedance (including electric resistance, electric inductance, and electric capacitance) on the resonance frequency, the antiresonance frequency, and the effective electromechanical coupling coefficient is analyzed theoretically and experimentally. It is demonstrated that the electric load impedance can change the resonance frequency, the antiresonance frequency, and the effective electromechanical coupling coefficient. When the electric load resistance is increased, the resonance frequency and the antiresonance frequency are increased; the effective electromechanical coupling coefficient has a maximum value when the electric load resistance changes. When the electric load resistance becomes large, the effect of the electric load resistance on the effective electromechanical coupling coefficient is negligible. When the electric load inductance is increased, the resonance frequency and the antiresonance frequency are decreased, whereas the effective electromechanical coupling coefficient is increased. When the electric load capacitance is increased, the resonance frequency, the antiresonance frequency, and the effective electromechanical coupling coefficient are all decreased. It should be noted that when the electric load impedance becomes large, the effect of the electric load impedance on the resonance frequency, the antiresonance frequency, and the effective electromechanical coupling coefficient of a sandwich piezoelectric transducer becomes negligible.     

Vibration of piezoelectric/elastic laminated trimorph ring transducer

This article describes the vibration characteristics of the trimorph ring transducer that consists of an isotropic elastic ring laminated between two identical piezoelectric rings under mechanical traction-free and constant electric voltage boundary conditions. The electro-elasticity theory with Kirchhoff-Love plate theory was applied to formulate the electromechanical solution. The resonance, antiresonance frequencies with corresponding mode shapes were verified by the measured impedance frequency responses. And, the design of maximized electromechanical coupling coefficients (EMCC) is proceeded.     

基于机械品质因数的全波压电超声换能器设计

针对全波压电超声换能器常规设计方法存在的尺寸参数较多、计算较复杂等问题,研究了一种利用机械品质因数设计全波压电超声换能器的方法.基于压电超声理论推导了全波压电超声换能器的频率方程,利用电学理论推导了全波压电超声换能器各组成部分的等效电路,利用等效电路求取了在任意等效截面处的等效机械阻抗,进而推导出全波压电超声换能器各部...     

Ultrasound transducer modeling--general theory and applications to ultrasound reciprocal systems

A tutorial presentation on the theory of reciprocal ultrasound systems is given, and a complete set of modeling equations for one-dimensional multi-layer ultrasound transducers is derived from first principles. The model includes dielectric losses and mechanical losses in the transducer material layers as well as sound absorption in the transmission medium. First, the so-called constitutive relations of a piezoelectric body are derived based on general thermodynamic considerations, assuming that transducer operation takes place under almost isentropic conditions. Second, full attention is given to transducers oscillating in the thickness mode, discarding all other vibration modes. Dynamic transducer equations are determined using Newton's Second Law, Poisson's equation, and the definition of strain applied to a piezoelectric transducer with one or more non-piezoelectric layers on the front surface (multilayer transducer). Boundary conditions include continuity of normal velocity and stress across material interfaces as well as a subsidiary electrical condition over the piezoceramic electrodes. Sound transmission is assumed to take place in a water bath such that the Rayleigh equation can be used to obtain the incoming pressure at the receiver aperture from the acceleration of the opposing transmitter. This allows, e.g., a detailed treatment of receiver signal variations as the receiver moves from the near-field zone to the far-field zone of the transmitter. In the remaining part of the paper, receiver voltage and current signals are obtained by solving the full set of dynamic equations numerically. Special attention is given to transducers consisting of a) a pure piezoceramic layer only, b) a piezoceramic layer and a quarter-wavelength matching layer of polyphenylensulphide (PPS), c) a piezoceramic layer and a half-wavelength matching layer of stainless steel, and d) a piezoceramic layer and a half-wavelength matching layer of stainless steel tuned to resonance by a parallel inductance. Results are also given for receiver incoming pressure and receiver voltage signals when sound reception takes place in the near-field and far-field zones of the transmitter.     

Ultrasonic piezoceramic transducers with a magnetoacoustic layer

We describe the design and present the results of calculations of the properties of an ultrasonic transducer based on a piezoceramic plate in mechanical contact with a layer of a magnetoacoustic material. The transducer is characterized by strong dependence of the velocities of both transverse and longitudinal waves on the magnetic field. This allows the resonance frequency and the bandwidth to be effectively controlled even in the case of low-Q piezoelectric ceramics and makes it possible to create a tunable frequency standard based on a high-Q piezoelectric material.     

Modeling and fabrication of a piezoelectric vibration‐induced micro power generator

Abstract

In this paper, theoretical and experimental study on a piezoelectric vibration‐induced micro power generator that can convert mechanical vibration energy into electrical energy is presented. The mechanical‐electrical energy conversion mechanism is a voltage between two capacitors, which belong to the mechanical and the piezoelectric equivalent circuits, respectively. To verify the theoretical analysis, two clusters of transducer structures are fabricated. Piezoelectric lead zirconate titanate (PZT) material is chosen to make the energy conversion transducer. The desired shape of the piezoelectric generator with its resonance frequency in accordance with the ambient vibration source is designed by finite element analysis (FEA).

Experimental results show that the maximum output voltages are generated at the first mode resonance frequencies of the structure. The overall conversion efficiency is measured to be 33%. The experimental results coincide with the theoretical analysis.     

SPICE model for lossy piezoceramic transducers

A transmission line equivalent circuit for piezoelectric transducers has been modified to provide modeling of lossy piezoceramic transducers. A lossy transmission line is used to model the mechanical losses. The equivalent circuit parameters are derived from analogies between electrical transmission lines and acoustic wave propagation. Implementation of the equivalent circuit model in SPICE is shown. Simulations and measurements in the time and frequency domain of a low-Q material and a multilayered ultrasonic sensor using a low-Q piezoceramic transducer are presented.     

Performance analysis of ultrasono-therapy transducer with contact detection

The performance of ultrasono-therapy transducer with contact detection by using the impedance phase change is described. Usually a therapy transducer is designed with a /spl lambda//2 frontal plate glued to a PZT-4 piezoceramic. This plate ensures a good mechanical protection of the piezoceramic with a corresponding high-transmission energy. Normally this transducer is operated at the minimum at the frequency of the impedance module of its input electric impedance, but this operation point is affected by the shift caused by the expected temperature increase. This shift could be higher than the narrow bandwidth presented. As a result we obtain a decrease in the power level for medical treatment. Usually electronic drivers with automatic control that follow the frequency change are designed, however, the relatively narrow bandwidth introduces difficulty in the design. Another frequency operation point is presented here and analyzed using the criteria of the maximum of the impedance phase with a wider bandwidth than in the previous case. Simulation with mechanical losses are presented with experimental results that show the convenience of this criteria for practical application.     

Strong ultrasonic microwaves in ferroelectric ceramics

It is well known that ferroelectric materials have piezoelectric properties which allow the transformation of electrical signals into mechanical signals and vice versa. The transducer action normally is restricted to frequencies up to the mechanical resonance frequency of the sample. There are, however, two mechanisms which allow transducer action in ferroelectric ceramics at much higher frequencies: one is the normal piezoelectric effect in a ferroelectric ceramic in which the crystallites have periodic domain structures, the other is a domain wall effect in which ferroelastic domain walls in a periodic domain structure are powerful shear wave emitters. Both mechanisms give rise to extensive dielectric losses in ceramics at microwave frequencies.     

Modeling for temperature compensation and temperature characterizations of BAW resonators at GHz frequencies

This paper deals with the temperature dependence of electrical and physical features of various kinds of solidly mounted resonators (SMR). The presented bulk acoustic wave (BAW) devices are designed for the 2 GHz application. The temperature coefficient of frequency (TCF) is determined from measurements well above the temperature range defined for wireless telecommunication system specifications. Therefore, evolution of electromechanical coupling factors and quality factors at resonance and antiresonance are also monitored. Results of characterizations show the trend for a subsequent theoretical temperature compensation study by using analytical modeling. To improve accuracy of modeling, an attempt to extract temperature dependence of dielectric permittivity epsilon(33) and piezoelectric coefficient e(33) is made. Finally, a well-known analytical model is modified to take into account the temperature dependence of length, density, stiffness coefficient, dielectric permittivity, and piezoelectric coefficient. Modeling highlights the need to deposit a material with positive temperature coefficient of stiffness on the top electrode. Realistic thickness of such a layer is determined. At the same time, it is necessary to adjust piezoelectric and electrode thin film thicknesses for simultaneously keeping a constant antiresonance frequency, reaching a zero temperature coefficient of frequency for antiresonance, and minimizing the decrease in the coupling factor because of the mass-loading deposition.     

Radiation impedance and equivalent circuit for piezoelectric ultrasonic composite transducers of vibrational mode-conversion

The piezoelectric ultrasonic composite transducer, which can be used in either gas or liquid media, is studied in this paper. The composite transducer is composed of a longitudinal sandwich piezoelectric transducer, a mechanical transformer, and a metal circular plate in flexural vibration. Acoustic radiation is produced by the flexural circular plate, which is excited by the longitudinal sandwich transducer and transformer. Based on the classic flexural theory of plates, the equivalent lumped parameters for a plate in axially symmetric flexural vibration with free boundary conditions are obtained. The radiation impedance of the plate is derived and the relationship between the radiation impedance and the frequency is analyzed. The equivalent circuits for the plate in flexural vibration and the composite transducer are given. The vibrational modes and the harmonic response of the composite piezoelectric transducer are simulated by the numerical method. Based on the theoretical and numerical analysis, two composite piezoelectric ultrasonic transducers are designed and manufactured, their admittance-frequency curves are measured, and the resonance frequency is obtained. The flexural vibrational displacement distribution of the transducer is measured with a laser scanning vibrometer. It is shown that the theoretical results are in good agreement with the measured resonance frequency and the displacement distribution.     

多方向压电振动能量收集装置及其优化设计

摘要：为实现对不同方向环境振动能量的收集,提出了一种新颖的多方向振动能量收集装置的设计结构,装置的换能部分采用了一种Rainbow型压电结构。为提高多方向振动能量收集装置收集能量的效果,以多方向振动能量收集装置输出的总电能为目标函数,综合考虑金属弹性基片的强度、装置振动的固有频率及装置的尺寸空间要求等多种因素,采用序列二次规划法对能量收集装置的结构参数进行了优化。该多方向振动能量收集装置经过优化后,在Y向激励时,其输出的总电能为37.146μJ,比优化前提高了30.82%,当沿装置体对角线方向激励时,结构装置输出的总电能为58.715μJ,比优化前提高了29.24%,装置的能量收集效果得到了明显提高。分析结果为多方向振动能量收集装置的设计、制造及应用提供了技术依据。     

压电陶瓷堆位置对郎之万换能器内部损耗的影响

压电陶瓷堆位置是郎之万换能器优化设计的一个重要对象,人们对其研究较多但结论并不一致。文章主要考虑压电陶瓷的机械损耗及介电损耗,分析了恒振幅输出时这两种损耗与压电陶瓷堆位置的关系,并通过引入负载系数探讨了不同负载情况下压电陶瓷堆位置对郎之万换能器内部损耗的影响。分析结果表明,对于不同的负载,压电陶瓷堆均对应一个最佳位置,此时换能器的内部损耗最小,且随着负载的增大,这一最佳位置逐渐向换能器的节点位置靠近。可见,压电陶瓷堆位置的优化设计与实际负载密切相关,以往关于该问题的不同结论源于其仅针对某种特定负载分析而得。     

Characterization of sol-gel Pb(Zr0.53Ti0.47O3) in thin film bulk acoustic resonators

The behavior of {f111g}-textured Pb(Zr(0.53Ti0.47O3) (PZT) deposited by the sol-gel technique in thin film bulk acoustic resonators (TFBAR's) was investigated at a resonance frequency of about 1 GHz. The resonators were fabricated on Si wafers using deep silicon etching to create a membrane structure and using platinum as top and bottom electrodes. The best response of the resonators was observed at a bias voltage of -15 kV/cm with values of about 10% for the coupling constant and about 50 for the quality factor. This voltage corresponds to optimal values of piezoelectric constant d33 and dielectric constant measured as a function of the electric field. The influence of a bias voltage on the resonance frequency, antiresonance frequency, and coupling constant were observed. Both the resonance and antiresonance frequency show a hysteretic change with applied bias. This effect can be used to shift the whole band of a filter by applying a voltage. The TFBAR structure also allowed us to extract values for materials parameters of the PZT film. Dielectric, piezoelectric, and elastic properties of the f111g-textured PZT film are reported and compared to direct measurements and to literature values.     

Piezoelectric ceramic rectangular transducers in flexural vibration

Based on the equivalent elastic method and coupled vibration theory, an analytic method is presented to study the flexural vibration of rectangular transducers consisting of piezoelectric ceramic thin plates. By introducing a mechanical coupling coefficient, the flexural vibration of the piezoelectric ceramic rectangular thin plate is reduced to two simple, one-dimensional flexural vibrations of narrow piezoelectric ceramic strips. The resonance frequency equations for the piezoelectric ceramic rectangular thin-plate transducers in flexural vibration are derived under the free and simply supported boundary conditions analytically. The relationship between the resonance frequency and the flexural vibrational order, the geometrical shape, and the dimensions of the piezoelectric ceramic rectangular thin-plate transducer is analyzed. It is demonstrated that the one-dimensional vibrational theory for the flexural vibration of a narrow piezoelectric ceramic strip and the stripe-mode flexural vibrational theory for the piezoelectric ceramic rectangular thin plate can be derived directly from the theory obtained in this paper. Experimental results show that the measured resonance frequencies of the piezoelectric ceramic rectangular thin-plate transducers in flexural vibration under free-boundary conditions are in good agreement with the calculated results. The method presented in this paper can be used in the resonance frequency analysis of vibrating systems in coupled vibration.     

Analysis of a disk-type piezoelectric ultrasonic motor using impedance matrices

The dynamic behavior and the performance characteristics of the disk-type traveling wave piezoelectric ultrasonic motors (USM) are analyzed using impedance matrices. The stator is divided into three coupled subsystems: an inner metal disk, a piezoelectric annular actuator with segmented electrodes, and an outer metal disk with teeth. The effects of both shear deformation and rotary inertia are taken into account in deriving an impedance matrix for the piezoelectric actuator. The impedance matrices for each subsystem then are combined into a global impedance matrix using continuity conditions at the interfaces. A comparison is made between the impedance matrix model and the three-dimensional finite element model of the piezoelectric stator, obtaining the resonance and antiresonance frequencies and the effective electromechanical coupling factors versus circumferential mode numbers. Using the calculated resonance frequency and the vibration modes for the stator and a brush model with the Coulomb friction for the stator and rotor contact, stall torque, and no-load speed versus excitation frequencies are calculated at different preloads. Performance characteristics such as speed-torque curve and the output efficiency of the USM also are estimated using the current impedance matrix and the contact model. The present impedance model can be shown to be very effective in the design of the USM.     

Determination of electromechanical coupling factors of low Q piezoelectric resonators operating in stiffened modes

The electromechanical coupling coefficient is usually determined from the relative spacing of the frequencies of resonance and antiresonance. The conventional formula is derived from equations describing the electrical behavior of an ideal piezoelectric resonator in the absence of losses. In this paper, the influence of the intrinsic material losses on the shift of the resonance/antiresonance frequencies, and therefore on the accuracy of the standard formula to determine k, is analyzed. The exact one-dimensional model of the piezoelectric resonator vibrating in a pure stiffened mode, with a rigorous account of the internal mechanical losses, has been taken as a reference, instead of the frequently used lumped approximate equivalent circuit (Butterworth-Van Dyke). It is shown that the coupling coefficient determined from the frequencies f(s) and f(p) is less than the intrinsic coupling coefficient, and that the error increases for highly attenuating materials with weak electromechanical coupling. The error due to the effect of attenuation, which increases with the decrease of the product Q(m)k of the resonator intrinsic parameters, has been systematically evaluated and plotted for 0.5相似文献