Abstract-It is an accepted fact that transverse Doppler effects of the first order in v/c are nonexistent for all physical wave phenomena, including acoustics, i.e., the Doppler effect is zero for radiation normal to the direction of motion. However, this statement assumes that the incident field is a plane wave, which is not true in general for finite aperture sources. Consequently, the probing of flows transverse to the axis of finite diameter beams, particularly focused beams, is feasible. This geometry will be advantageous in many applications where the classical orientation of the sound beam, oblique to the flow, is not possible. With this motivation in mind, the theory and experimental feasibility of measuring Doppler spectra in transverse geometries is presently investigated.The comparison of flow flux measurements, and measurements performed using a standard ultrasound pulsed Doppler system, show that flow normal to the axis of a focused transducer can be measured with an accuracy comparable to that obtained with the conventional oblique orientation. The measured Doppler spectra are shown to agree well with theory.Although the experiments have been performed for acoustical waves, the present results should also be applicable to electromagnetic systems.

Abstract-In conventional ultrasound Doppler systems, the velocity component along the beam axis is derived from the observed frequency shift. Recently, it was verified that by using a pulsed-Doppler system with the beam transversely oriented with respect to the flow, the velocity component transverse to the beam can be derived from the edges of the spectrum. Presently, these results are generalized to take into account arbitrary angles of incidence, effects of velocity gradients, arbitrary apertures, and arbitrary source pulses. For uniform apertures and transverse flow, it has been previously shown that the Doppler output spectrum is symmetrical about zero frequency, with its width depending on the Doppler effect due to the transverse velocity and the geometry of the problem. For a beam direction oblique to the velocity, it is shown that the spectrum is now shifted, and is centered about the classical Doppler frequency. It is shown here that for velocity gradients and transverse flows the spectrum remains symmetrical, with the edges corresponding to the maximal velocity; however, the profile becomes peaked at the center. For oblique incidence, an asymmetrical spectrum is obtained and its edges are related to the maximal and minimal velocities within the sampling volume.For the simple case of a long strip transducer discussed previously, it was shown that the Doppler system output spectrum is essentially obtained by convolving the transmitter and receiver aperture functions. The general discussion given here, even for the single particle, is more complicated. Nevertheless, using the reciprocity theorem it is shown that the output spectrum is obtained by convolving the particle excitation spectrum due to monochromatic excitation, with the receiver input spectrum due to a moving monochromatic source, all this shifted to the classical Doppler frequency mentioned above. It is shown that when the excitation possesses an arbitrary (narrow band) spectrum, this spectrum, replicated in a prescribed manner, has to be convolved with the spectra derived above. Following the single scatterer analysis, the effects produced by an ensemble of particles are considered. Numerical computations of theoretical results are given, supporting the semi-quantitative graphical interpretations for various configurations. To further substantiate the results analytical treatments of simplified models are given.The results contribute to our understanding of Doppler spectra and their use, mainly in medical ultrasound diagnostics.

Piezoelectric transformers have a high potential for use in power supplies due to large power density and flexibility in design. A lot of work has been done in piezoelectric transformer design and analysis of their operation in different regimes and in different electronic circuits. In this paper an attempt has been made to investigate the influence of temperature, mechanical and electrical field stress, properties of piezoceramic material and regimes of piezoelectric transformer operation on the value of its power density. The results of the presented calculations of piezoelectric transformer parameters show a good correlation with measured data on experimental transformers. A substantial improvement of piezoelectric transformer power density seems feasible, making them more attractive for a wider range of applications in power supplies. In addition, useful guidelines for piezoelectric transformer design and selection criteria for piezoelectric materials for transformers have been established.