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

Date
2010
Advisor
Instructor
Source Title
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Print ISSN
1525-8955
Electronic ISSN
Publisher
IEEE
Volume
57
Issue
2
Pages
438 - 447
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

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.

Course
Other identifiers
Book Title
Keywords
Finite element analysis, Instrumentation, Microtechnology, Nonlinear system, Transducer, Ultrasound
Citation
Published Version (Please cite this version)