Parametric linear modeling of circular cMUT membranes in vacuum

Abstract

Abstract-We present a lumped element parametric model for the clamped circular membrane of a capacitive micromachined ultrasonic transducer (cMUT). The model incorporates an electrical port and two sets of acoustic ports, through which the cMUT couples to the medium. The modeling approach is based on matching a lumped element model and the mechanical impedance of the cMUT membrane at the resonance frequencies in vacuum. Very good agreement between finite element simulation results and model impedance is obtained. Equivalent circuit model parameters can be found from material properties and membrane dimensions without a need for finite element simulation.

P2P-5 Radiation Impedance and Equivalent Circuit for Immersed CMUT Array Element

“…1 reduces to the one in Fig. 2 [5]. This equivalent circuit models the membrane when loaded with water, up to the vicinity of first parallel resonance frequency.…”

“…The inductive loading represents the mass of the water moved by the membrane apart from the piston motion. This mass is approximately equal to the mass of water in one half of the hemispherical volume above the membrane [5],…”

“…However, when immersed in fluid medium, modelling approaches fail in the explanation of the radiation impedance that cMUT experiences. In this work, using the results obtained in [5], the designs of various cMUT array elements are presented. Practical considerations such as parasitic capacitances are included in all design examples.…”

“…In [6], it is shown that the model depicted in Fig. 1, which is derived from Mason's impedance equation [7], represents the mechanical impedance of cMUT exactly up to the third parallel resonance when operated in vacuum.…”

“…1, which is derived from Mason's impedance equation [7], represents the mechanical impedance of cMUT exactly up to the third parallel resonance when operated in vacuum. Although, the mechanical impedance of the membrane deviates from Mason's expression as it gets thicker, this affect is accurately taken into account in [6]. The model has one electrical port and two sets of symmetric acoustics ports corresponding to the two faces of the membrane.…”