Michio Ohki

Calculation Principle of Stored Energy and Effective Power in Piezoelectric Transducer using Infinite Series of a Complex Dynamical Variable and Its Finite Difference

Both effective power and stored energy in a piezoelectric transducer can be calculated by a simple mathematical method using infinite geometric series of a complex dynamical variable η instead of solving an ordinary or partial differential equation; this differs from the conventional methods which deal with the concept of complex power based on the theory of alternating-current phenomenon. The stored energy can be obtained by a superposition of η, in which the method of superposition reflects the electrical and mechanical boundary conditions in the transducer. By considering the finite difference of η, the effective power can also be evaluated using a method of superposition and the uncertainty principle. This method can deal with the system having an infinite number of degrees of freedom along with dissipative process, simply and easily, and is consistent with the second law of thermodynamics.

Equivalent Representation of Mode Coupling in Two-Dimensional Bulk Waves Using Unitary Matrix with 4*4 Elements.

Mode coupling in two-dimensional bulk waves confined in a two-dimensional rectangular resonator is discussed using a 4 ×4 unitary matrix and Neumann series; this differs from the conventional methods which involve a coupling between N resonance systems solved as an eigenvalue problem of an N ×N matrix, which becomes complicated when the loss phenomenon is included or when the value of N increases. The coupling is dealt with by considering the energy distribution between the two modes with unitarity or energy conservation. The 4 ×4 unitary matrix is adopted to distinguish between self-coupling and mutual coupling, and the confinement of wave energy due to the multiple reflection is represented by the Neumann series. Simple and unified matrix algebra gives the resonance characteristics when the mode coupling occurs in an infinite number of degrees of freedom.

Resonance Patterns of Piezoelectric Partial-Drive Systems without Mechanical Impedance Matching

The mathematical rules about resonance frequencies and intensities are investigated for partially-driven piezoelectric transducers with mechanical impedance-mismatch layers inside the transducer. The concepts of (arithmetic) location rules, density and period of resonance pattern are introduced, and some mathematical rules with regard to these quantities are found out, which should be considered when the transducer is designed and analyzed.

Mathematical Treatment of Mode Coupling between Two Plane Waves Using Unitary Matrix and Neumann Series

Mode coupling between two plane waves through a spatial periodic structure is discussed using a unitary matrix and Neumann series; this differs from the conventional methods which deal with a difference or differential equation as an eigenvalue problem. The two modes are represented by a two-component quantity, which does not correspond to the power flow as is involved in the conventional theory, but to stored energy. Phenomenon due to multiple reflection or transmission inside the periodic structure is expressed by a simple and unified matrix algebra, which leads to the resonance characteristics after the mode coupling.

Estimation of Piezoelectric Equivalent Circuit Parameters Using Principle of Least Variance

The estimates of equivalent circuit parameters of a piezoelectric transducer, observed from the admittance circle near resonance in a conventional manner, are improved on two types of lumped-parameter circuits, namely, L- and T-type circuits, which are consistent with Marutakes approximation formula for estimating electromechanical coupling coefficient, using the principle of least variance with regard to the physical quantities observed in more than one resonance mode. First, the electrically observed frequencies of resonance and antiresonance are corrected using the T- and L-type circuits, respectively. Secondly, whether the transducer is actually driven in the L- or T-effect is distinguished using the principle of least variance introduced in this study. Next, the inductance components of the circuit are re-estimated using this principle again, and finally other circuit components are also adjusted in a self-consistent manner.

Impulse Response of Piezoelectric Transducer by Multiresolution Analysis of Energy Modes

The impulse response of a piezoelectric transducer with an inhomogeneous structure is calculated in a simple and systematic manner without using a Laplace transform of an electrically equivalent circuit model. The inhomogeneous structure is wavelet-analyzed to construct a 2L+1-layered structure (L=0,1,2,...), and 2L+1 energy modes are introduced in the respective layers and superposed in a probabilistic manner. The 2L+1 layers are classified into the odd- and even-numbered layers, and the superposition of energy modes is performed at odd and even time steps separately. The calculation precision in the time domain improves as the wavelet level L increases. Using this methodology, the calculation of the impulse response of the transducer becomes as simple as that of the frequency response, in which the uncertainty principle between time and frequency is involved.

Distributed-Parameter Based Treatment of Interaction Process between Elastic and Dielectric Energy in Piezoelectric Transducer

The interaction process between elastic and dielectric energy in a piezoelectric transducer, which has been treated on the basis of lumped parameters in the framework of electrical equivalent circuit, is treated on a distributed-parameter basis. The concept of coupling between elastic and dielectric energy modes is introduced, and the superposition of the energy mode after the coupling is considered, which allows us to determine the frequency characteristics of the transducer with an electromechanical coupling. Mathematically, the coupling effect is represented by the exponential of a matrix, and the superposition of the energy mode is calculated with the infinite geometric series of a matrix, Neumann series, which provides physically reasonable results.

Optical Measurement of Piezoelectric Vibration in Circular Rod and Disk Ceramics

The fiber-optic measurement and evaluation of piezoelectric vibration of circular rod and disk ceramics are described. The values corresponding to the piezoelectric d- and g-constants can be obtained locally by measuring amplitude and Q- value at the first-resonance frequency under appropriate electric conditions. The results are analyzed numerically by using the theory of coupled resonance

Application of Complex Series Dynamics to Electromechanical Coupling System

The characteristics of an electromechanical transducer are expressed in a distributed-parameter basis without using any lumped-parameter components. Two energy modes, elastic mode and dielectric mode, are considered, which interact with each other in some mathematical regularities. Physical processes on the two modes are represented with some matrix operation, and the infinite geometric series of the matrices, reflecting the boundary conditions of transducer, provides frequency characteristics from the viewpoint of locally stored energy in the transducer. The sum of the local characteristics provides the global characteristics of the transducer. The energy transfer and the shift of resonance frequency owing to the electromechanical coupling can be calculated by this method.

Frequency characteristics of an acoustooptic modulator with two interdigital transducers

An acoustooptic (AO) modulator with two interdigital transducers (IDTs) is investigated from the viewpoint of frequency characteristics of the modulation. The 1st IDT is used for driving an acoustic wave in a piezoelectric substrate and the 2nd IDT is used for controlling the reflection and the radiation of the acoustic wave propagating in the substrate. Light intensity modulation using Raman-Nath diffraction is controlled by changing the electrical terminal condition at the 2nd IDT. The modulation characteristics are found to be periodic functions of the frequency of acoustic wave, which suggests that the interference of acoustic waves in the substrate influences the modulation. In the present AO modulator, the interference of fields is utilized effectively and the electrical terminal condition with regard to not only the amplitude but also the phase can control the modulation.