This page summarizes the non-linear model for a circular CMUT cell operating in uncollapsed mode. Refer to the paper by Koymen, for details.

Parameters of the circular CMUT cell (all in MKS units):

  • a : Radius of the cell
  • tg : gap height of the cell
  • ti : thickness of the insulator
  • tm : thickness of the top plate
  • εr : relative permitivity of the insulator
  • Y0 : Young’s modulus of the top plate
  • σ : Poisson’s ratio of the top plate
  • ρ : density of the top plate

Input signals and parameters for the model (all in MKS units):

  • P0 : Ambient static pressure
  • pIN(t) : Incident instantaneous pressure
  • V(t) : Applied instantaneous voltage (including DC)
  • ZRR : Complex radiation impedance of the immersion medium specified in the frequency domain.


To utilize the model, one can use a harmonic-balance simulator, like ADS, AWR or Spectre. If the simulator allows conditional nonlinear equations, Eq.’s (6) and (10) should be used for small values of u, while for larger u values, Eq.’s (5) and (9) should be utilized. If the simulator allows only one nonlinear equation, then Eq.’s (6) and (10) can be used, possibly with more terms added.