Sergey V. Biryukov

Derivation of COM equations using the surface impedance method

The surface impedance method is used for the consistent derivation of coupling of modes equations which describe the interaction of SAW with a periodical system of electrodes of finite thickness. The exact analytic solution of the electrostatic problem in the presence of an arbitrary external electric field for a plane system of electrodes is applied to the calculation of the charge and electric field distributions. Mechanical perturbations are taken into account to first order of the thickness of the electrodes. As a result the scalar self-consistent equation for the electric potential of acoustic waves in the gratings is obtained. For the periodic structure this equation is reduced to the form of COM equations for slowly varying amplitudes. Analytical expressions for all coefficients of the COM equations connecting them with geometrical and material parameters are found. The NSPUDT effect can be considered. Dissipation and energy storage terms can be introduced empirically. The solution of the COM equations is represented in the form of a P matrix with elements written in a convenient form. A simple formula for calculating the location of maximum transducer frequency response is proposed, The balance of energy is considered. Some new relations among the elements of P matrix are found.<<ETX>>

The effective permittivity in the complex plane and a simple estimation method for leaky wave slowness

The well-known effective permittivity function is defined for complex values of slowness, using the procedure of analytical continuation from the real axis of slowness. An approximate estimation for a complex-value leaky wave slowness is given. Both parts of the slowness are expressed in terms of the real and imaginary parts of effective permittivity and the derivatives of them, which are calculated on the real axis only. This estimation may be as a simple indicator of possible existence of leaky waves. Lithium tetraborate and lithium niobate crystals are considered.

Gyroscopic effect for SAW in common piezoelectric crystals

In the present work, using the well-known numerical procedure for SAW calculation in arbitrary crystals the gyroscopic effect is investigated. To take into account the medium rotation the Coriolis and centrifugal forces are introduced into the piezoelectric medium equations of motion. As a result of the standard procedure, the SAW velocity is calculated as a function of the medium rotation rate about each coordinate axis. A shift of such velocity due to rotation is determined for isotropic Al, STX-quartz, 128°YX-LiNbO3, YZ-LiNbO3, X112°Y-LiTaO3, and Z-cut of AlN substrates.

The electrostatic problem for the SAW interdigital transducers in an external electric field. II. Periodic structures

For pt.I see ibid., vol.43, no.6, pp.1150-9 (1996). An exact solution of the electrostatic problem for calculating the surface charge and electric field distributions in an arbitrary periodic interdigital transducer (IDT) is given using the results of our companion paper. An arbitrary external electric field may be specified along the electrode structure with the unit cell containing one electrode, or several electrodes, of different widths. The potentials of the electrodes that may be specified are also arbitrary. It is shown that in the case without an external field, the solution includes all the known results as special cases. The case of shorted electrodes in the external electric field is investigated in detail. The surface charge and electric field distributions are calculated for a spatially harmonic external field with an arbitrary wavenumber. The results of the calculations are represented graphically for various ratios between the period of the electrode structure and the wavelength of the external field for the case of a unit cell containing one or two electrodes of different widths.

Consistent generalization of COM equations to three-dimensional structures and the theory of the SAW transversely coupled waveguide resonator filter

An analytical theory for calculating the response of a transversely coupled waveguide resonator filter (TCF) is derived consistently from the analytical model for the description of two-dimensional structures. The COM equations for slowly varying amplitudes of the SAW electric potential as functions of the longitudinal coordinate are derived. The coefficients of these equations such as reflectivity, phase delay and transduction coefficient are calculated for each mode. The theory connects the material and geometrical parameters of the structure with the characteristics of the TCF. The frequency dependence of the admittance matrix and insertion loss for one and two cascaded filters are considered. The splitting of the resonance peaks due to cascading is investigated. Good agreement between theoretical and experimental results is found.<<ETX>>

Fast variation method for elastic strip calculation

A new, fast, variation method (FVM) for determining an elastic strip response to stresses arbitrarily distributed on the flat side of the strip is proposed. The remaining surface of the strip may have an arbitrary form, and it is free of stresses. The FVM, as well as the wellknown finite element method, starts with the variational principle. However, it does not use the meshing of the strip. A comparison of FVM results with the exact analytical solution in the special case of shear stresses and a rectangular strip demonstrates an excellent agreement.

Ring waveguide resonator on surface acoustic waves

A simple regular electrode structure for surface acoustic wave (SAW) devices is proposed. The structure consists of an interdigital transducer in the form of a ring placed on the Z cut of a hexagonal piezoelectric crystal. Finite thickness electrodes produce the known slowing effect for a SAW in comparison with this SAW on a free surface. The closed “slow” electrode region with the “fast” surrounding region forms an open waveguide resonator structure with the acoustic field concentrated in the electrode region. If the radius of the structure is large enough for a given wavelength, an acceptable level of radiation losses can be reached. The electrical admittance of such resonator does not have sidelobes.

CTGS material parameters obtained by versatile SAW measurements

Recently big size high quality piezoelectric single crystals of Ca3TaGa3Si2O14 (CTGS) have been grown. This temperature durable crystal is very promising for future application in different devices based on surface acoustic waves (SAW) due to its high electromechanical coupling compared to quartz. In contrast to the popular langasite, CTGS is a more ordered compound and therefore stands for better characteristics at both, high temperatures and high frequencies. During the last decade several sets of material constants for CTGS were published extracted from bulk acoustic wave measurements on small samples, but these results are strongly different from each other. Moreover, all published constant sets lead to unacceptable numerical differences for calculated SAW velocities when compared to recent measurements of SAW velocities on large CTGS wafers. In this work we present a new set of room temperature CTGS material constants, extracted by combination of high-precision SAW phase velocity measurements with proprietary numerical procedures developed in-house.

Harmonic admittance and dispersion equations-the theorem [SAWs in periodic electrode arrays]

The harmonic admittance is known as a powerful tool for analyzing the excitation and propagation of surface acoustic waves (SAWs) in periodic electrode arrays. In particular, the dispersion relationships for open- and short-circuited systems are indicated, respectively, by the zeros and poles of the harmonic admittance. Here, we show that a strict reverse relationship also exists: the harmonic admittance of a periodic system of electrodes may always be expressed as the ratio of two determinants, which have been specifically constructed to describe the eigenmodes of the open- and short-circuited systems. There is no need to solve these equations to find the admittance. The existence of a connection between the excitation and propagation problems was recognized within the coupling-of-modes theory by Chen and Haus (1985) and was recently used to model surface transverse waves by Koskela et al. (1998), but a rigorous mathematical proof was only found later by Biryukov (2000). Here, we reproduce this theorem in detail, give some examples of calculations based on this theorem, and compare the results with measured admittance curves.

Two-finger (TF) SPUDT cells [Correspondence]

SPUDT cells including two fingers only are hitherto known for so-called NSPUDT directions. In this case, usual solid-finger cells are used. The purpose of the present paper is to find SPUDT cell types consisting of two fingers only for pure mode directions. Moreover, SPUDT cells composed of two fingers suited to complete imperfect NSPUDT behavior or to compensate that are to be found. TF cells for pure mode directions on substrates like 128degYX LiNbO3, YZ LiNbO3 and STX quartz were found by means of an optimization procedure. The forward direction of a TF-cell SPUDT on 128degYX LiNbO3 was determined experimentally. The properties of the new cells are compared with those of conventional SPUDT cells. The reflectivity of TF cells on 128degYX LiNbO3 turns out to be two up to three times larger than that of DART and Hanma-Hunsinger cells at the same metal layer thickness. Furthermore, properties of TF cells on STX and SST quartz are reported. Examples for completing and compensating imperfect NSPUDT behavior are given.