Acoustics Capacitive Sensing: The Analogy (Mechanical)


Acoustics Capacitive Sensing: The Analogy (Mechanical)
By: Mohd Faizal Abd Rahman

In sensing technology, capacitive sensing is one of the techniques applied in detecting some physical variables. The basic structure design of such sensor consists of two parallel plate with a dielectric medium sandwiched between these plates. The top plate is normally referred as membrane or diaphragm which will be acting as an active sensing element. In acoustic engineering, the vibration of the medium particles carrying the signal will cause the membrane to vibrate accordingly, changing the initial gap thickness and thus producing the variation in capacitance according to the well known equation: mac 4a The variation then will be detected by a specific circuit to reflect the measured variable[1]. In order to understand the behaviour of such sensor, researchers are working based on the equivalent model that closely resembles the actual operation. In [1]-[2], the sensor is considered as analogous to spring-mass-damper, while in [3], the sensor is modelled in the form of electrical equivalent circuit.


CMUT can be thought of as having the same working principles as SMD system. So, the mechanical equation for SMD system (a) is a valid representation for CMUT as explained in [1].

mac 4b


m is the mass in kg, k is the spring constant in N/m, and c is the viscous damping coefficient in N-s/m. The time dependent variables, x(t) and u(t) represents the position and displacement component. Analytical representation of this parameter has been discussed in detail in [1]-[2] and are summarised below:

mac 4c

mac 4d and Q is the resonance frequency and the quality factor of the system respectively.


[1] D Ozewin, D.W Grewe, I.J Oppenheim, S.P Pessiki, Resonant Capacitive MEMS Acoustic Emission Transducers Smart Mater. Struct., 15, 2006, 1863-1871.,

[2] G.G Yaralioglu, A.S Ergun and B.T Khuri-Yakub ,Finite Element Analysis of CMUT,IEEE Trans. on Ultrasonics, Ferroelectric and Frequency Controls, Vol 52,No 12, Dec 2005

[3] G.Caliano et al, PSpice Modeling of CMUT, Ultrasonics Symposium 40 (2002),449-455