Ele c tric a l c o up ling e ffe c ts in a n ultra so nic tra nsd uc e r a rra y C. BRUNEEL, B. DELANNOY, R. TORGUET, E. BRIDOUX and H. LASOTA Ultrasonic imaging devices often use transducer arrays for sampling the incoming acoustic field and converting it into electrical signals. After some convenient processing (amplification, dephasing, summing, etc), the electrical signals are used to modulate the brightness of a cathode ray tube (crt) monitor on which the ultrasonic image becomes visible. The quality of the imaging apparatus depends critically on the transducer array design and implementation. Each individual transducer would, ideally, produce an electrical signal related exclusively to the ultrasonic field arriving at its surface; the reciprocal would also be true for transmission. In all practical cases, however, numerous effects lead to some coupling between nearby transducers, especially for very narrow transducers, The subsequent perturbations may be described as a narrowing of the radiation (or reception) pattern of the individual transducers, with respect to the theoretical predictions. To understand the mechanism for these couplings and to minimize them, their possible origins have been systematically studied. One of the most important sources of coupling is electrical leakage, which is reported here. Since no simple analytical calculation can be performed, diagrams have been established that enable evaluation of the electrical coupling against the dimensional characteristics of the array. Some means for reducing this coupling are suggested and comparative experimental results are given. introduction Transducers are often machined in piezoelectric ceramic platelets, typically one half an acoustic wavelength in thick- ness, say We. The spatial period II of the array must be chosen to correctly sample the acoustic field, an optimum value being one half a wavelength in the acoustic propaga- tion medium, according to Shannon’s sampling criterion. For biomedical’+ applications, the velocity in tissues, which are water-like media, is nearly equal to 1500 ms-’ , that is, three times lower than in the piezoelectric ceramic (for which the velocity is typically 4200 ms-r). The a/W,, ratio may therefore be equal to about l/3. If the transducer array is machined simply by cutting the metallization over one face of the piezoelectric platelet, the other face remaining uniformly metallized and playing the role of a ground electrode, the driving electric field is not very well confined to the theoretically active area of the individual transducers. The piezoelectric effect is therefore responsible for the launching of ultrasonic waves over a wider-than-wished active area. For large transducers, this effect may be of no importance, but it increases drastically as the ratio a/W,, is reduced. The The authors are at the Laboratoire d’Otoacoustoelectronique ERA, CNRS No 593, Universite de Valenciennes, 59326 Valenciennes, France. Paper received 30 July 1970. purpose of the present study is then to evaluate the relative effectiveness of this phenomenon, and to see under what conditions the simple metallization cutting process proves satisfactory, a feature which greatly simplifies the technolo- gical production and reduces probe failures. As the physical dimensions considered are much lower than the electromagnetic wavelength at the operating frequency, say some megahertz, study of the electric field map may be performed using the static approximation. The problem is then reduced to the solution of Laplace’s equation, with additional simplifications arising from the translational symmetry along the z axis (see Fig. 1) and the periodicity along the x axis. The electrical potential must fulfil the partial derivative equation: a* v 2 + a2 = 0 aY* together with the boundary conditions: V(x, - We) = 0 for all x (2) i VO for 1x1 <b (3) V(x, 0) = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ Vn for Ix - ~a1 <b (4) where V, is the electrical potential imposed on the central transducer, V, is that which is induced through electrical zyxwvutsrqpo ULTRASONICS. NOVEMBER 1979 0041-624X/79/060255-06/$02.00 0 1979 IPC Business Press 255