Finite Transducers Research Articles

Self-Consistent Theory of Interdigital Transducers

The generation and absorption of surface waves by an interdigital transducer with uniform finger spacing are calculated with the aid of a surface dielectric constant related to the TM-wave impedance. It is found that the response of an infinite transducer can be calculated with complete consistency, i.e., the field due to the distortion of the piezoelectric medium is correctly included in the determination of the distortion. For a finite transducer, the solutions given are in error only at lines on the surface at either end of the transducer, and are therefore accurate when the transducer is long. It is found that the parallel equivalent circuit derived in the weak coupling approximation is a reasonably accurate representation of the transducer when the coupling is strong and the transducer long, but that the central resonance is then distorted.

A Note on the Solution of Sequential Boolean Equations

The problem of solving sequential Boolean equations is examined in terms of nondeterministic finite transducers. An upper bound for the delay is established and a method for obtaining a deterministic equivalent is described.

Measurements of the wave-number/phase velocity spectrum of wall pressure beneath a turbulent boundary layer

Measurements are presented of the wave-number/frequency and wave-number/phase velocity spectrum of wall pressure for a two-dimensional turbulent boundary layer in zero pressure gradient, obtained from a Fourier transform of experimental filtered spatial correlations. This method allows the results to be corrected for acoustic disturbances in the wind tunnel, and for finite transducer size. An empirical form for the pressure field is proposed, based on the measurements, and is used to predict a frequency spectrum correction for transducer size which agrees well with measured values.

The resolution of turbulent pressures at the wall of a boundary layer

This paper is a discussion of the resolution by a piezo-electric transducer of the local pressure fluctuations at the wall of a turbulent boundary layer. The first part applies to transducers whose sensing area is large in comparison with the boundary layer thickness, and the second part to transducers whose sensing area is either of the order of, or smaller than, the boundary layer thickness. For large transducers, the main result, derived for a sensing surface of arbitrary shape and with an arbitrary spatial sensitivity distribution, is that under circumstances which are perhaps unrealistically stringent, the attenuation of a given frequency component will increase as the cube of the transducer face linear dimension. In general, it should be expected to increase only as the square of the dimension. In the second part, the probable dependence of the resolution on frequency and on transducer size is indicated by using both recent experimental evidence and physical reasoning bearing on the nature of the pressure cross-spectral density. Both approaches suggest that in a co-ordinate system translated downstream at an appropriate velocity, as the streamwise wave number increases, the spectral density in wave number-frequency space is associated with proportionately increasing spanwise wave numbers and almost proportionately increasing frequencies. Experimental evidence suggests departure from this finding if the fixed axis longitudinal wave length is very large (of the order of the boundary layer thickness) in which case both the characteristic time in convected axes and the characteristic lateral coherence length appear to reach asymptotic finite values. For shorter waves, the strong relationship between the two space scales and the convective time scale necessarily implies that the resolution of the frequency spectral density by a finite transducer continues to deterioriate as the frequency increases. It is concluded that the attenuation predictions previously published by the author are not likely to be seriously in error.

Diffraction Corrections for Ultrasonic Attenuation and Velocity Measurements in Crystals

The echo train in a pulse-echo ultrasonic measurement does not decay exponentially but displays irregular variations in the Fresnel region. Similarly, the apparent travel time of the wave will be slightly nonlinear as a function of distance. These variations are caused by diffraction from the finite transducer, and cause errors in attenuation and velocity measurements. The incremental diffraction loss and delay can be computed from the radiation pattern of the transducer by considering both amplitude and phase in finding the integrated pressure at a receiver, and corrections can be applied to the measurements. The loss goes through several peaks and troughs versus S=zλ/a2, the distance normalized by the Fresnel length, while the phase climbs toward π/2 through the same number of slopes and plateaus. A phase plateau is located at a loss peak. The loss finally becomes monotonic, increasing with a monotonic decreasing slope. The location of a loss peak along S is a strong function of the anisotropy of the crystal under study. Computed curves of the diffraction-loss/distance and phase/distance characteristics are presented, and data from pulse-echo measurements on several crystals are shown to verify the theory. The method of making diffraction corrections for attenuation and velocity is outlined, and the effect of these corrections on experimental data is shown.

A remark on finite transducers

Abstract : A very restricted class of transducers, i.e. of autthe transformation consisting in the replacement of every input letter x by an output word (x) which is eventually the empty word e sub Y. (Author)