VHDL-AMS Behavioural Modelling of a CMUT Element Samuel Frew University of British Columbia frews@ece.ubc.ca Hadi Najar University of British Columbia motieian@ece.ubc.ca Edmond Cretu University of British Columbia edmondc@ece.ubc.ca ABSTRACT This paper reports the development, implementation and simulation of a behavioural model written in VHDL-AMS for a capacitive micromachined ultrasonic transducer (CMUT). Unlike previous behavioural models, this model incorporates the non-linear electro-mechanical relations of the CMUT. VHDL-AMS was chosen for the ease with which it can be used to implement these relations, and for its portability between software platforms. To the best of the authors’ knowledge, this is the first reported VHDL-AMS model of a CMUT. The simulation results demonstrate that the model can be used to simulate a number of scenarios, including frequency responses, time responses and effects of DC bias voltage. Results are compared to a finite element method model, and show excellent agreement in resonant frequency and a 16 % error in pull-in voltage. 1. ITRODUCTIO Capacitive micromachined ultrasonic transducers (CMUT) are a relatively new transducer technology that has emerged from the ultrasonics and micro-electro-mechanical systems (MEMS) research communities. A CMUT element is made up of numerous cells, each of which consists of a thin membrane suspended above a substrate. An electrostatic force generated by a voltage applied between membrane and substrate perturbs the membrane from its resting position. By applying a suitable time-varying voltage superimposed on a fixed DC bias, the membrane can be made to vibrate at its resonance in the ultrasonic frequency range, thus emitting a pressure wave into the surrounding medium. Conversely, pressure waves from the medium incident on the membrane cause it to vibrate, which, if the fixed DC bias is maintained, generates a time-varying current that can be measured electronically. CMUT are therefore a viable substitute for piezoelectric transducers used currently in most ultrasound imaging systems. CMUT have two primary advantages over piezoelectric transducers. Firstly, research literature (e.g. [1]) shows that CMUT can perform better than piezoelectric transducers in terms of bandwidth and sensitivity, giving them the ability to generate ultrasound images of greater resolution and thus discern smaller structures. This would be a fundamental improvement for ultrasonic imaging, and particularly beneficial for its use in cancer diagnosis and treatment. The second advantage lies in the ability of CMUT to be fabricated using technologies similar to those used to make integrated circuits (IC). This allows CMUT to be potentially fabricated together with CMOS driving, receiving and signal processing electronics on a single IC, and could greatly reduce the wiring needs between the ultrasound probe, containing the IC, and the rest of the ultrasound system. The wiring requirements of large 2D transducer arrays are currently a significant limitation in the development of high-resolution, real-time 3D ultrasonic imaging systems [2]. Using standard IC fabrication methods could also reduce the cost of fabricating ultrasonic imaging systems. In this work, a behavioural model is developed for a CMUT element. Such a model allows the characteristics and performance of CMUT designs to be quickly tested and optimised, before performing lengthy simulation of finite- element method (FEM) models or investing in fabrication. It can also be incorporated into a macromodel along with models of the driving and receiving electronics. This is a particular advantage in the case where the CMUT and the electronics are to be fabricated on the same IC, as it allows the whole IC to be simulated together and gives the ability to optimise the parameters of the CMOS layout of the electronics along with those of the CMUT. Previous behavioural models of CMUT [1, 3] have been based on a small-signal linearisation of the electro- mechanical relations about a DC bias point, allowing a 2- port electrical equivalent circuit to be formulated. Generally, in these models, a fixed capacitor represents the capacitance of the parallel electrodes of the CMUT, an ideal transformer performs the conversion of energy from the electrical to the mechanical domain, and a complex impedance models the mechanical impedance of the membrane. The work of Mason [4] is typically used to obtain an expression for this mechanical impedance. The approach was extended in [5] to account for the effects of mechanical interactions between the membrane and the gap beneath it. A PSpice (Cadence OrCAD, San Jose, CA, USA) implementation of this model was also developed [6]. The behavioural model developed in this work differs from previous models in that it does not rely on a linearised small-signal model. The inherently non-linear relations of the electro-mechanical coupling are preserved. The model is also bi-directional, allowing it to be used as a transmitter and a receiver. This is an advantage of the energy-domain