Rayleigh-Bloch waves in CMUT arrays.

Using the small-signal electrical equivalent circuit of a capacitive micromachined ultrasonic transducer (CMUT) cell, along with the self and mutual radiation impedances of such cells, we present a computationally efficient method to predict the frequency response of a large CMUT element or array. The simulations show spurious resonances, which may degrade the performance of the array. We show that these unwanted resonances are due to dispersive Rayleigh-Bloch waves excited on the CMUT surface-liquid interface. We derive the dispersion relation of these waves for the purpose of predicting the resonance frequencies. The waves form standing waves at frequencies where the reflections from the edges of the element or the array result in a Fabry-Pérot resonator. High-order resonances are eliminated by a small loss in the individual cells, but low-order resonances remain even in the presence of significant loss. These resonances are reduced to tolerable levels when CMUT cells are built from larger and thicker plates at the expense of reduced bandwidth.

An improved lumped element nonlinear circuit model for a circular CMUT cell.

This paper describes a correction and an extension in the previously published large signal equivalent circuit model for a circular capacitive micromachined ultrasonic transducer (CMUT) cell. The force model is rederived so that the energy and power is preserved in the equivalent circuit model. The model is able to predict the entire behavior of CMUT until the membrane touches the substrate. Many intrinsic properties of the CMUT cell, such as the collapse condition, collapse voltage, the voltage-displacement interrelation and the force equilibrium before and after collapse voltage in the presence of external static force, are obtained as a direct consequence of the model. The small signal equivalent circuit for any bias condition is obtained from the large signal model. The model can be implemented in circuit simulation tools and model predictions are in excellent agreement with finite element method simulations.

High-power CMUTs: design and experimental verification.

Capacitive micromachined ultrasonic transducers (CMUTs) have great potential to compete with piezoelectric transducers in high-power applications. As the output pressures increase, nonlinearity of CMUT must be reconsidered and optimization is required to reduce harmonic distortions. In this paper, we describe a design approach in which uncollapsed CMUT array elements are sized so as to operate at the maximum radiation impedance and have gap heights such that the generated electrostatic force can sustain a plate displacement with full swing at the given drive amplitude. The proposed design enables high output pressures and low harmonic distortions at the output. An equivalent circuit model of the array is used that accurately simulates the uncollapsed mode of operation. The model facilities the design of CMUT parameters for high-pressure output, without the intensive need for computationally involved FEM tools. The optimized design requires a relatively thick plate compared with a conventional CMUT plate. Thus, we used a silicon wafer as the CMUT plate. The fabrication process involves an anodic bonding process for bonding the silicon plate with the glass substrate. To eliminate the bias voltage, which may cause charging problems, the CMUT array is driven with large continuous wave signals at half of the resonant frequency. The fabricated arrays are tested in an oil tank by applying a 125-V peak 5-cycle burst sinusoidal signal at 1.44 MHz. The applied voltage is increased until the plate is about to touch the bottom electrode to get the maximum peak displacement. The observed pressure is about 1.8 MPa with -28 dBc second harmonic at the surface of the array.

Nonlinear modeling of an immersed transmitting capacitive micromachined ultrasonic transducer for harmonic balance analysis.

Finite element method (FEM) is used for transient dynamic analysis of capacitive micromachined ultrasonic transducers (CMUT) and is particularly useful when the membranes are driven in the nonlinear regime. One major disadvantage of FEM is the excessive time required for simulation. Harmonic balance (HB) analysis, on the other hand, provides an accurate estimate of the steady-state response of nonlinear circuits very quickly. It is common to use Mason's equivalent circuit to model the mechanical section of CMUT. However, it is not appropriate to terminate Mason's mechanical LC section by a rigid piston's radiation impedance, especially for an immersed CMUT. We studied the membrane behavior using a transient FEM analysis and found out that for a wide range of harmonics around the series resonance, the membrane displacement can be modeled as a clamped radiator. We considered the root mean square of the velocity distribution on the membrane surface as the circuit variable rather than the average velocity. With this definition, the kinetic energy of the membrane mass is the same as that in the model. We derived the force and current equations for a clamped radiator and implemented them using a commercial HB simulator. We observed much better agreement between FEM and the proposed equivalent model, compared with the conventional model.