Effects of mutual impedance on the radiation characteristics of transducer arrays

Abstract

The mutual resistance of transducer arrays is investigated in order to design arrays with improved performance for high intensity sounds at a given frequency. This work proposes the theory that the mutual resistance is related to the loading effects of pressure waves propagated from a piston driver on the surface of another driver. Using this interpretation, the important characteristics of the mutual resistance of two piston drivers are explained and the conditions for local maxima in the mutual resistance are easily determined. On the basis of analyses of the interactions between a driver and acoustic pressure waves, we propose a method to determine the driver radius and the distance between two drivers that give maximum mutual radiation resistance. To evaluate the proposed method, the total resistance of a transducer array is calculated using the formulas for mutual and self-resistance established by Pritchard. The results of the calculations of the total resistances of arrays with many drivers show that a transducer array with drivers arranged sparsely can achieve a larger value of the radiation power per unit area as well as better radiation efficiency than an array in which the drivers are in a closely packed arrangement at a given frequency.

Radiation impedance of an array of circular capacitive micromachined ultrasonic transducers

“…For kd < 5, R r of the cMUT cell shows a behavior similar to that of an array of pistons [17] except for the vertical scale. as kd increases, the positive loading on the each cell increases and R r becomes maximum at around kd = 7.5, where the loading reaches an optimum point [28]. as N increases, the maximum value of radiation resistance, R max , also increases, although the corresponding kd value, kd opt , is not significantly affected.…”

“…3 as a function of ka. as ka → ∞, the mutual effects vanish and the normalized radiation resistance for both radiators converges to unity [27], [28]. For the same case, the radiators do not generate reactive power, hence, 971 senlik et al: radiation impedance of an array of circular cMUTs the radiation reactances of both radiators approach zero.…”

Dynamic response of an array of flexural plates in acoustic medium

“…5 Based on these theoretical backgrounds, focusing on the calculation method of the mutual impedance of two transducers, Lee recently introduced the lumped acoustic impedance of a piston transducer array and the optimal parameters of the array design. 6 The mutual acoustic impedance has a significant impact on flexural mode transducers, such as piezoelectric micromachined ultrasound transducers (PMUTs), and capacitive micromachined ultrasonic transducers (CMUTs). Compared to piston transducers, the flexural mode transducers have much lower mechanical impedance with respect to the liquid medium.…”

Implementation of master curves for cMUT arrays design

“…For cMUT devices, the key feature when vibrating in fluid medium is the mechanical radiation impedance, which frequency dependence greatly depends on the cell layout periodicity. Radiation impedance computation has received numerous attentions in the literature on account of its importance in the analysis of a lot of acoustical systems [3][4][5]. On the base of equations published in [4], we have developed a simple model to compute the mechanical radiation impedance of one cMUT cell that take into account shape and periodic distribution.…”

“…Radiation impedance computation has received numerous attentions in the literature on account of its importance in the analysis of a lot of acoustical systems [3][4][5]. On the base of equations published in [4], we have developed a simple model to compute the mechanical radiation impedance of one cMUT cell that take into account shape and periodic distribution. Results are then used for complete transducer simulation through the equivalent electromechanical scheme proposed in reference [1].…”