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.