Equivalent Circuit Models for Large Arrays of Curved and Flat Piezoelectric Micromachined Ultrasonic Transducers.

Equivalent circuit models of large arrays of curved (spherical shape) and flat piezoelectric micromachined ultrasonic transducers (pMUTs) have been developed for complex pMUT arrays design and analysis. The exact solutions for circuit parameters in the electromechanical domain, such as mechanical admittance, input electrical impedance, and electromechanical transformer ratio, were analytically derived. By utilizing the array solution methods previously established for the thickness-mode piezoelectric devices and capacitive micromachined ultrasonic transducers (cMUTs), the single pMUT circuit model can be extended to models for array structures.

An analytical solution for curved piezoelectric micromachined ultrasonic transducers with spherically shaped diaphragms.

An analytical solution for piezoelectrically actuated spherically shaped diaphragms has been developed to study their dynamic behavior with targeted applications in piezoelectric micromachined ultrasonic transducers (pMUT). The analytical model starts with a curved pMUT composed of a piezoelectric diaphragm with a nominal radius in size, a radius of curvature in shape, and under both possible actuation sources of radial pressure and electric potential. The diaphragm has the piezoelectric material polarized in the direction perpendicular to its surface and sandwiched between two metal electrodes.

Analytic solution for N-electrode actuated piezoelectric disk with application to piezoelectric micromachined ultrasonic transducers.

In this work, the deflection equation of a piezoelectrically-driven micromachined ultrasonic transducer (PMUT) is analytically determined using a Green's function approach. With the Green's function solution technique, the deflection of a circular plate with an arbitrary circular/ring electrode geometry is explicitly solved for axisymmetric vibration modes. For a PMUT with one center electrode covering ≈60% of the plate radius, the Green's function solution compares well with existing piece-wise and energy-based solutions with errors of less than 1%.

An equivalent network representation of a clamped bimorph piezoelectric micromachined ultrasonic transducer with circular and annular electrodes using matrix manipulation techniques.

An electric circuit model for a clamped circular bimorph piezoelectric micromachined ultrasonic transducer (pMUT) was developed for the first time. The pMUT consisted of two piezoelectric layers sandwiched between three thin electrodes. The top and bottom electrodes were separated into central and annular electrodes by a small gap.

Optimizing the electrode size of circular bimorph plates with different boundary conditions for maximum deflection of piezoelectric micromachined ultrasonic transducers.

The effect of plate electrode area on the deflection of a symmetric circular bimorph piezoelectric micromachined ultrasonic transducer (pMUT) with clamped and simply supported boundary conditions was studied for the first time. Distinct plate displacement shape functions were defined for the regions underneath and outside the active electrodes. The plate shape functions were solved analytically using classic plate theory in conjunction with the external boundary conditions and the internal ones between the two regions in order to calculate the exact plate displacement under both external voltage stimulus and acoustic pressure.

Theoretical modeling and equivalent electric circuit of a bimorph piezoelectric micromachined ultrasonic transducer.

An electric circuit model for a circular bimorph piezoelectric micromachined ultrasonic transducer (PMUT) was developed for the first time. The model was made up of an electric mesh, which was coupled to a mechanical mesh via a transformer element. The bimorph PMUT consisted of two piezoelectric layers of the same material, having equal thicknesses, and sandwiched between three thin electrodes.