H. Kagan Oguz

An improved lumped element nonlinear circuit model for a circular CMUT cell

This paper describes a correction and an extension in the previously published large signal equivalent circuit model for a circular capacitive micromachined ultrasonic transducer (CMUT) cell. The force model is rederived so that the energy and power is preserved in the equivalent circuit model. The model is able to predict the entire behavior of CMUT until the membrane touches the substrate. Many intrinsic properties of the CMUT cell, such as the collapse condition, collapse voltage, the voltage–displacement interrelation and the force equilibrium before and after collapse voltage in the presence of external static force, are obtained as a direct consequence of the model. The small signal equivalent circuit for any bias condition is obtained from the large signal model. The model can be implemented in circuit simulation tools and model predictions are in excellent agreement with finite element method simulations.

Equivalent circuit-based analysis of CMUT cell dynamics in arrays

Capacitive micromachined ultrasonic transducers (CMUTs) are usually composed of large arrays of closely packed cells. In this work, we use an equivalent circuit model to analyze CMUT arrays with multiple cells. We study the effects of mutual acoustic interactions through the immersion medium caused by the pressure field generated by each cell acting upon the others. To do this, all the cells in the array are coupled through a radiation impedance matrix at their acoustic terminals. An accurate approximation for the mutual radiation impedance is defined between two circular cells, which can be used in large arrays to reduce computational complexity. Hence, a performance analysis of CMUT arrays can be accurately done with a circuit simulator. By using the proposed model, one can very rapidly obtain the linear frequency and nonlinear transient responses of arrays with an arbitrary number of CMUT cells. We performed several finite element method (FEM) simulations for arrays with small numbers of cells and showed that the results are very similar to those obtained by the equivalent circuit model.

Analysis of mutual acoustic coupling in CMUT arrays using an accurate lumped element nonlinear equivalent circuit model

We use an accurate nonlinear equivalent circuit model to analyze CMUT arrays with multiple cells, where every cell in the array is coupled to other cells at their acoustic terminals through a mutual radiation impedance matrix. We get results comparable to finite element analysis accuracy. Hence, the analysis of a large array becomes a circuit theory problem and can be scrutinized with circuit simulators. We study the mutual acoustic interactions that arise through the immersion medium due to the influence of the generated pressure field by each cell on the others. We compare the performance of different 1D cMUT arrays, where each element is half-wavelength wide and 10 and 20 wavelengths long at the resonance frequency of a single cell.

Designing circular CMUT cells using CMUT biasing chart

A very accurate equivalent circuit model for circular CMUT cell is recently proposed. As a consequence of this model, the operating characteristics of the cell is derived and presented as a biasing chart for CMUTs. We discuss these operating characteristics and show how the coupling coefficient can be derived from the model. We present an analysis of receiver performance of a CMUT cell. We also demonstrate how to design cells for fixed bias voltage but for different static depression.

A novel equivalent circuit model for CMUTs

A nonlinear equivalent circuit for immersed transmitting capacitive micromachined ultrasonic transducers (CMUTs) is presented. The velocity profile across the CMUT surface maintains the same form over a wide frequency range. This property and the profile are used to model both the electromechanical conversion and the mechanical section. The model parameters are calculated considering the root mean square of the velocity distribution on the membrane surface as the through variable. The new model is compared with the FEM simulation results. The new model predicts the CMUT performance very accurately.

Lumped element model of single CMUT in collapsed mode

In this study, an equivalent electrical circuit model for a single circular CMUT in both uncollapsed and collapsed modes is obtained. In order to model the collapsed mode mechanics, the governing differential equation is solved semi-analytically for a large number of normalized cases. Then the calculations are adapted to the equivalent electrical circuit model. The model uses the self radiation impedance of both uncollapsed and collapsed modes. The model is fully parametric in such a way that a CMUT cell of given dimensions and parameters can be simulated under an arbitrary large signal excitation. Transient simulations can be performed in less than a minute with a circuit simulator. Transient and frequency domain simulations are consistent with finite element analysis results.

Nonlinear equivalent circuit model for circular CMUTs in uncollapsed and collapsed mode

An equivalent electrical circuit model valid for collapsed mode operation of CMUT is described. The across and through variables of the circuit model are chosen to be rms force and rms displacement over the surface of the CMUT membrane. The relation between rms displacement and applied voltage is obtained through analytical calculations utilizing the exact force distribution. The radiation impedance of collapsed mode CMUT is included as a load impedance in the circuit model. The resulting equivalent circuit is merged with uncollapsed mode model, to obtain a simulation tool that covers the whole operation range of CMUT.

Electrically unbiased driven airborne capacitive micromachined ultrasonic transducer design

We present a design method for airborne capacitive micromachined ultrasonic transducers (CMVT). We use an equivalent lumped element circuit to model both electrical and mechanical properties of CMUT and analyze it in frequency domain using harmonic balance approach. We use this method to design CMUTs for large transmitted power generation at low drive voltage amplitude. We determine the dimensions of an airborne CMUT using the proposed method that works at 30 kHz with 5 rum radius, 240 11m membrane thickness and 11.8 11m effective gap height. The CMUT is designed such that an atmospheric depression of 70% of effective gap height is maintained.

Circuit theory based analysis of CMUT arrays with very large number of cells

We have recently developed a circuit theory based method to analyze large CMUT arrays and shown that mutual acoustic interactions significantly influence the transducer performance. We connect each cell in the array to a radiation impedance matrix that contains the mutual radiation impedance between every pair of cells, in addition to their self radiation impedances. However, efficient analysis of very large arrays is challenging, which may become computationally cumbersome. To partition the problem, we electrically drive a single element in the array and keep the rest undriven but biased and with their electrical ports terminated with a load. The radiation impedance matrix can be partitioned and rearranged to represent these loads in a reduced form. In this way, only the driven element can be simulated by coupling its cells through this reduced impedance matrix. This method considerably reduces the number of cells and the size of the original radiation impedance matrix at the expense of calculating the inverse of a large complex symmetric matrix.