An analytical study of capacitive micromachined ultrasonic transducers (CMUTs) with circular microplates has been carried out. The study comprises one-sided (single electrode back-plate) and two-sided (double electrode back-plate) systems, and derives universal correction factors for pull-in voltage and critical displacement to be used in lumped element model (LEM) analysis. We employ von Karman plate theory and the single-mode Galerkin decomposition method to solve the equations. Consequently, voltage–deflection relations have been derived. By comparing results from plate theory with LEM, it is concluded: (1) for the one-sided CMUT by neglecting geometrical nonlinearity, we find \(\frac{{{V_{\text {Pull in - P}}}}}{{{V_{\text {Pull in - LEM}}}}} = 1.327\) and the ratio of critical displacement derived from plate theory over critical displacement from LEM is always 1.882. (2) For the one-sided CMUT including geometrical nonlinearity \(\frac{{{V_{\text {Pull in} - P}}}}{{{V_{\text {Pull in - LEM}}}}} = 1.45\) and critical displacement from plate theory over critical displacement from LEM is 1.792, for a specific set of parameters. (3) For the two-sided CMUT, there is no differences in using linear nor nonlinear analysis and \(\frac{{{V_{\text {Pull in - P}}}}}{{{V_{\text {Pull in - LEM}}}}} = 1.276\). For all studied cases, finite element (FE) analysis has been performed to validate the analytical outcomes.

对带有圆形微板的电容式微加工超声换能器（CMUT）进行了分析研究。该研究包括单侧（单电极背板）和双面（双电极背板）系统，并得出了用于集总元件模型（LEM）分析的引入电压和临界位移的通用校正因子。 。我们采用冯卡曼板理论和单模Galerkin分解方法求解方程。因此，得出了电压-偏转关系。通过比较板理论和LEM的结果，得出以下结论：（1）对于单侧CMUT，忽略了几何非线性，我们发现\（\ frac {{{V _ {\ text {Pull in-P}}}}} {{{V _ {\ text {Pull in-LEM}}}}} = 1.327 \）板理论得出的临界位移与LEM得出的临界位移之比始终为1.882。（2）对于包含几何非线性的单侧CMUT \（\ frac {{{V _ {\ text {Pull in}-P}}}} {{{V _ {\ text {Pull in-LEM}}}}}} = 1.45 \）从板理论和临界位移超过临界位移从LEM是1.792，对于一组特定的参数。（3）对于双向CMUT，使用线性或非线性分析和\（\ frac {{{V _ {\ text {Pull in-P}}}}}} {{{V _ {\ text {拉入-LEM}}}}} = 1.276 \）。对于所有研究的案例，已经执行了有限元（FE）分析以验证分析结果。