Theoretical modeling and equivalent electric circuit of a bimorph piezoelectric micromachined ultrasonic transducer

An electric circuit model for a circular bimorph piezoelectric micromachined ultrasonic transducer (PMUT) was developed for the first time. The model was made up of an electric mesh, which was coupled to a mechanical mesh via a transformer element. The bimorph PMUT consisted of two piezoelectric layers of the same material, having equal thicknesses, and sandwiched between three thin electrodes. The piezoelectric layers, having the same poling axis, were biased with electric potentials of the same magnitude but opposite polarity. The strain mismatches between the two layers created by the converse piezoelectric effect caused the membrane to vibrate and, hence, transmit a pressure wave. Upon receiving the echo of the acoustic wave, the membrane deformation led to the generation of electric charges as a result of the direct piezoelectric phenomenon. The membrane angular velocity and electric current were related to the applied electric field, the impinging acoustic pressure, and the moment at the edge of the membrane using two canonical equations. The transduction coefficients from the electrical to the mechanical domain and vice-versa were shown to be bilateral and the system was shown to be reversible. The circuit parameters of the derived model were extracted, including the transformer ratio, the clamped electric impedance, the spring-softening impedance, and the open-circuit mechanical impedance. The theoretical model was fully examined by generating the electrical input impedance and average plate displacement curves versus frequency under both air and water loading conditions. A PMUT composed of piezoelectric material with a lossy dielectric was also investigated and the maximum possible electroacoustical conversion efficiency was calculated.     

Accurately modeling EI core inductors using a high-fidelity magnetic equivalent circuit approach

We present a high-fidelity magnetic equivalent circuit (HFMEC) inductor model that reduces the inaccuracies associated with a traditional MEC approach. The model can accurately predict the flux linkage versus current characteristic in a fraction of the time needed for finite-element analysis. The accuracy, computational efficiency, and simple inputs (consisting of only geometry and material specifications) make the model ideal for automated inductor design.     

利用等效的方法对调谐器输入电路进行讨论

从电路等效和参数等效两面方面出发 ,将调谐器的高放输入电路等效于简单的LC并联谐振电路 ,然后对该电路进行讨论。     

参量激励的非线性电路

非线性电路作为一种孤立波的实验系统,具有设计灵活,容易测量等特点,弥补了一些机械系统的不足.本文在前人工作基础上,利用乘法器,设计了一种带参量激励的非线性电路,克服了电路耗散.数值计算中观察到不衰减的电路孤立波.     

High-power CMUTs: design and experimental verification

Capacitive micromachined ultrasonic transducers (CMUTs) have great potential to compete with piezoelectric transducers in high-power applications. As the output pressures increase, nonlinearity of CMUT must be reconsidered and optimization is required to reduce harmonic distortions. In this paper, we describe a design approach in which uncollapsed CMUT array elements are sized so as to operate at the maximum radiation impedance and have gap heights such that the generated electrostatic force can sustain a plate displacement with full swing at the given drive amplitude. The proposed design enables high output pressures and low harmonic distortions at the output. An equivalent circuit model of the array is used that accurately simulates the uncollapsed mode of operation. The model facilities the design of CMUT parameters for high-pressure output, without the intensive need for computationally involved FEM tools. The optimized design requires a relatively thick plate compared with a conventional CMUT plate. Thus, we used a silicon wafer as the CMUT plate. The fabrication process involves an anodic bonding process for bonding the silicon plate with the glass substrate. To eliminate the bias voltage, which may cause charging problems, the CMUT array is driven with large continuous wave signals at half of the resonant frequency. The fabricated arrays are tested in an oil tank by applying a 125-V peak 5-cycle burst sinusoidal signal at 1.44 MHz. The applied voltage is increased until the plate is about to touch the bottom electrode to get the maximum peak displacement. The observed pressure is about 1.8 MPa with -28 dBc second harmonic at the surface of the array.     

动磁式直线压缩机的电磁力及其等效电路模型

推导了动磁式直线压缩机中电磁力的表达式,并利用简化分析式和有限元分析方法模拟分析了直线电机主要结构参数对电磁力的影响。研究表明,电磁力随直线电机气隙高度的增大而减小,随环状永磁体的半径和厚度的增大而增大。分析式和有限元模拟结果具有合理的一致性。同时,建立了动磁式直线压缩机的等效电路模型,推导了获得压缩机整机最大能量转换效率的表达式及各个参数对该转换效率的影响,并得到了最大能量转换效率下的活塞面积。     

Linear AC magnetic circuit theory

A theory is presented for linear, AC magnetic circuits. The theory develops real and imaginary reluctance terms, which are used in the same manner as real and imaginary impedance terms in linear, AC electrical circuit theory. The reluctance terms can be manipulated through coil-coupled resistances and capacitances. The theory is applied to a parallel magnetic-circuit configuration to show the limits of applicability for the particular materials from which the circuit is constructed     

Nonstationary equivalent linearization of nonlinear continuous systems

This paper presents a technique for obtaining the nonstationary stochastic response of a nonlinear continuous system. The method of equivalent linearization is generalized to continuous systems subjected to nonstationary random excitation. This technique allows replacement of the original nonlinear system with a time-varying linear continuous system. A numerical implementation is also described. In this procedure, the linear replacement system is discretized by the finite element method. Application to systems satisfying the one-dimensional wave equation with a constitutive nonlinearity is discussed. Results are presented for nonlinear stress-strain laws of a strain-hardening type.     

New equivalent lumped electrical circuit for piezoelectric transformers

A new equivalent circuit is proposed for a contour-vibration-mode piezoelectric transformer (PT). It is shown that the usual lumped equivalent circuit derived from the conventional Mason approach is not accurate. The proposed circuit, built on experimental measurements, makes an explicit difference between the elastic energies stored respectively on the primary and secondary parts. The experimental and theoretical resonance frequencies with the secondary in open or short circuit are in good agreement as well as the output "voltage-current" characteristic and the optimum efficiency working point. This circuit can be extended to various PT configurations and appears to be a useful tool for modeling electronic devices that integrate piezoelectric transformers.     

Resistance of pollution in equivalent electric circuit of flashover

In flashover-modelling literature, researchers only take into account, the resistance of the pollution on the insulator, assuming that the current takes part in its totality and that the geometrical shape of its lines in the pollution does not have an influence on the phenomenon. In the paper, and after presentation of the equivalent electric circuit of flashover used in the literature, an experimental study and physical analysis are presented concerning this assumption in two sets of laboratory models: multidirectional models and circular-sector models. The results obtained allow us to confirm first that the form of the pollution and the distribution of leakage current lines are indispensable to flashover modelling; and secondly that flashover criteria and critical conditions in the literature are unjustified.     

Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.     

An equivalent circuit model for dielectrics: polymeric materials

Multiple-arc analysis is used in conjunction with a generalized relaxation time distribution (GRTD) to derive an equivalent electric circuit model for dielectric materials that exhibit frequency dispersion. The validity of this new methodology is examined by comparing reported measurements of a.c. conductance and capacitance of a polymeric dielectric with those obtained from the equivalent circuit prediction. The values are shown to agree satisfactorily over the frequency range 100 to 850 kHz.     

Electric equivalent circuit for flexural vibrations in piezoelectric materials

General expressions for the values of the components of an electric equivalent circuit are derived for flexural vibrations. These expressions are applied to some interesting electrode configurations. The obtained values are in good agreement with experimental values and values specified by manufacturers of watch crystals. It is noted that solving Laplace's equation for the dielectric field is sufficient in order to obtain the values of the vibration amplitude, the piezoelectric current, and the equivalent components. The piezoelectric part of the electric field need only be considered if very accurate values of the resonance frequencies are desired. It is shown how accurate estimates can be obtained without the need of advanced calculation tools.     

Determining the equivalent circuit parameters of canned solid-rotor induction motors

For designing canned solid-rotor induction motors, the conventional induction motor circuit is inadequate. Here we present an alternative equivalent circuit, one that reflects the eddy currents in all regions (cans and rotor body). The proposed model operates on a per-phase basis at a single frequency. We confirm the validity of the new equivalent circuit with numerical and analytical solutions. This analysis has shown that the classical equivalent circuit for conventional induction motors is not sufficient to obtain the circuit parameters for the canned solid rotor induction motors. We also consider certain assumptions that make the analytical approach simpler.     

An improved equivalent circuit model of radial mode piezoelectric transformer

In this paper, both the equivalent circuit models of the radial mode and the coupled thickness vibration mode of the radial mode piezoelectric transformer are deduced, and then with the Y-parameter matrix method and the dual-port network theory, an improved equivalent circuit model for the multilayer radial mode piezoelectric transformer is established. A radial mode transformer sample is tested to verify the equivalent circuit model. The experimental results show that the model proposed in this paper is more precise than the typical model.     

Influence of electrodes arrangement on the quartz resonator equivalent circuit

The strip electrodes deposited on the main surfaces of the rotated Y-cut quartz plate in the Z' direction and overlapping only in the central part of the plate excite a non-negligible electric field parallel to the surface of the plate. The influence of this field on the parameters of the electrical equivalent circuit and frequency-temperature characteristic of the AT-cut quartz plates is examined. The influence of this electric field parallel to the surface depends on the orientation of electrodes in the rectangular coordinate system of quartz.     

The a.c. equivalent circuit of dielectric materials

An equivalent circuit for dielectrics exhibiting frequency dispersion has been obtained using a new multiple-arc analysis in conjunction with relaxation time distribution (RTD). Subsequently, an equivalent network was derived for a zinc oxide (ZnO)-based ceramic varistor at low electric fields. Reported measurements of ZnO varistor resistivity and permittivity were found to correspond satisfactorily to those obtained from the network over the frequency range 30 Hz–10 MHz. The new methodology is, in principle, applicable to any analysable dielectric data.     

On a driven nonlinear circuit and chaotic behaviour

Abstract

The chaotic behaviour of the sinusoidally driven nonlinear circuit proposed by Hunt is investigated. The results are compared with those from other driven nonlinear circuits.     

On nonlinear feedforward shift register and its linear equivalent system

Abstract

In this paper we shall show how we can find a linear system equivalent to a running key generator consisting of a maximum length (ML), a linear feedback shift register (LFSR), and a nonlinear feedforward state filter function. At the same time, a new analysis, which uses a Walsh orthogonal expansion of the state filter function and its relation to the crosscorrelation function (CCF) between the ML‐sequence and the produced running key sequence, is introduced.