The radiation impedance seen by a single circular CMUT cell in the absence of any neighboring cells is shown in figure as a function of ka, where k is the wavenumber in the immersion medium and a is the radius of the top plate. The radiation impedance shown is normalized with respect to Sρ0c0 where S is the area of the top plate of the CMUT cell, ρ0 is the density and c0  is the sound velocity of the immersion medium.

In the equations below

  • Z : normalized complex radiation impedance
  • k : wavenumber in the immersion medium
  • kp : wavenumber of the second order circularly symmetric mode of the CMUT top plate
  • a : radius of the CMUT top plate

RadImpEqns

RadImpSingleCellMutual Impedance between two neighboring CMUT cells

The mutual impedance (normalized with respect to Sρ0c0) between two circular CMUT cells with a center-to-center distance of d:

Z=(sin kd +j cos kd)/(kd)