Radiation Impedance of Collapsed Capacitive Micromachined Ultrasonic Transducers

Cataloged from PDF version of article.The radiation impedance of a capacitive micromachined ultrasonic transducer (CMUT) array is a critical parameter to achieve high performance. In this paper, we present a calculation of the radiation impedance of collapsed, clamped, circular CMUTs both analytically and using finite element method (FEM) simulations. First, we model the radiation impedance of a single collapsed CMUT cell analytically by expressing its velocity profile as a linear combination of special functions for which the generated pressures are known. For an array of collapsed CMUT cells, the mutual impedance between the cells is also taken into account. The radiation impedances for arrays of 7, 19, 37, and 61 circular collapsed CMUT cells for different contact radii are calculated both analytically and by FEM simulations. The radiation resistance of an array reaches a plateau and maintains this level for a wide frequency range. The variation of radiation reactance with respect to frequency indicates an inductance-like behavior in the same frequency range. We find that the peak radiation resistance value is reached at higher kd values in the collapsed case as compared with the uncollapsed case, where k is the wavenumber and d is the center-to-center distance between two neighboring CMUT cells

Radiation Impedance of an Array of Circular Capacitive Micromachined Ultrasonic Transducers

Cataloged from PDF version of article.The radiation impedance of a capacitive micromachined ultrasonic transducer (cMUT) with a circular membrane is calculated analytically using its velocity profile for the frequencies up to its parallel resonance frequency for both the immersion and the airborne applications. The results are verified by finite element simulations. The work is extended to calculate the radiation impedance of an array of cMUT cells positioned in a hexagonal pattern. A higher radiation resistance improves the bandwidth as well as the efficiency of the cMUT. The radiation resistance is determined to be a strong function of the cell spacing. It is shown that a center-to-center cell spacing of 1.25 wavelengths maximizes the radiation resistance, if the membranes are not too thin. It is also found that excitation of nonsymmetric modes may reduce the radiation resistance in immersion applications

Improved performance of cMUT with nonuniform membranes

When capacitive micromachined ultrasonic transducers are immersed in water, the bandwidth of the device is limited by the membrane's second resonance frequency. At this frequency no mechanical power to immersion medium can be transferred. We present a membrane shape to shift the second resonance frequency to a higher value. The structure consists of a very thin membrane at the outer rim with a rigid mass at the center. The stiffness of the central region moves the second resonance to a higher frequency. This membrane configuration is shown to work better in terms of gain and bandwidth as compared to conventional uniform membranes in both transmission and reception. © 2005 IEEE

Interaction between a cMUT cell and a liquid medium around the parallel resonance frequency

In this paper, we present how a capacitive micromachined ultrasonic transducer (cMUT) couples to the immersion medium, based on an accurate parametric model. We show that the velocity of cMUT membrane can be written as a sum of an average velocity term and a residual term. We demonstrate that this residual term carries non-zero energy at the parallel resonance frequency by investigating the interaction between the cMUT cell and a liquid medium. We develop a model that is also applicable around the parallel resonance frequency. © 2007 IEEE

Stagger tuned cMUT array for wideband airborne applications

In this study, we explore the limits of cMUTs in air-borne applications. First we investigate the ways of increasing the bandwidth of a single cMUT cell in air. The effect of array operation is also considered in order to increase the radiation resistance seen by the transducer. We calculate the bandwidth of a stagger tuned cMUT array. It is shown in this paper that more than 60% bandwidth can be obtained by three staggered frequencies. © 2006 IEEE

High Power CMUTs: Design and experimental verification

Cataloged from PDF version of article.Capacitive micromachined ultrasonic transducers (CMUTs) have great potential to compete with piezoelectric transducers in high-power applications. As the output pressures increase, nonlinearity of CMUT must be reconsidered and optimization is required to reduce harmonic distortions. In this paper, we describe a design approach in which uncollapsed CMUT array elements are sized so as to operate at the maximum radiation impedance and have gap heights such that the generated electrostatic force can sustain a plate displacement with full swing at the given drive amplitude. The proposed design enables high output pressures and low harmonic distortions at the output. An equivalent circuit model of the array is used that accurately simulates the uncollapsed mode of operation. The model facilities the design of CMUT parameters for high-pressure output, without the intensive need for computationally involved FEM tools. The optimized design requires a relatively thick plate compared with a conventional CMUT plate. Thus, we used a silicon wafer as the CMUT plate. The fabrication process involves an anodic bonding process for bonding the silicon plate with the glass substrate. To eliminate the bias voltage, which may cause charging problems, the CMUT array is driven with large continuous wave signals at half of the resonant frequency. The fabricated arrays are tested in an oil tank by applying a 125-V peak 5-cycle burst sinusoidal signal at 1.44 MHz. The applied voltage is increased until the plate is about to touch the bottom electrode to get the maximum peak displacement. The observed pressure is about 1.8 MPa with −28 dBc second harmonic at the surface of the array

Radiation impedance of an array of circular capacitive micromachined ultrasonic transducers in collapsed state

Radiation impedance is one of the important parameters in designing efficient and wideband capacitive micro-machined ultrasonic transducer (CMUT) arrays. It determines how much acoustical power is generated in the surrounding medium given the membrane motion. Recently, considerable effort has been put to characterize the radiation impedance of CMUT arrays in conventional uncollapsed regime. However, the radiation impedance of an array of CMUT cells in collapsed state has not yet been investigated. To calculate the array radiation impedance in collapse mode, we first calculate the radiation impedance of a single cell CMUT. For the array case, the mutual impedances between the neighboring cells must also be taken into account.We consider an array of 7, 19, 37, and 61 cells placed in a hexagonal pattern and try to determine the radiation impedance for different degrees of collapse. We find that in the collapsed case the peak radiation resistance value is reached at higher kd values, where k is the wavenumber and d is the center to center cell spacing, compared to the uncollapsed regime. © 2011 IEEE

Bandwidth improvement in a cMUT array with mixed sized elements

A capacitive micromachined ultrasonic transducer (cMUT) is typically fabricated by concatenation of several cMUT cells with identical physical dimensions. If the membrane thickness is kept fixed, the radius of the cMUT determines the center frequency of operation. A smaller radius implies a greater center frequency. Therefore, it should be possible to put cMUTs with different sizes in parallel to get a larger bandwidth at the expense of gain. In this study, we investigate the optimization of the bandwidth characteristics of a cMUT by using mixed size cells. We designed two mixed size cMUT arrays with a predicted optimized fractional bandwidth value of about 155% at 5.4 MHz, and 146% at 8.8 MHz. These values are about 55% and 58% better than what can be achieved with a uniform size array at the corresponding center frequencies. There is almost no loss in the gain bandwidth product when two different sized cMUTs are used in parallel. There is about 9% increase in gain bandwidth product when three different sized cMUTs are used in parallel. It is shown, in this study, that gain bandwidth product and bandwidth can be enhanced by use of mixed size cMUT cells. © 2005 IEEE

Mass measurements during lymphocytic leukemia cell polyploidization decouple cell cycle- and cell size-dependent growth

Cell size is believed to influence cell growth and metabolism. Consistently, several studies have revealed that large cells have lower mass accumulation rates per unit mass (i.e., growth efficiency) than intermediate-sized cells in the same population. Sizedependent growth is commonly attributed to transport limitations, such as increased diffusion timescales and decreased surface-to-volume ratio. However, separating cell size- and cell cycle-dependent growth is challenging. To address this, we monitored growth efficiency of pseudodiploid mouse lymphocytic leukemia cells during normal proliferation and polyploidization. This was enabled by the development of large-channel suspended microchannel resonators that allow us to monitor buoyant mass of single cells ranging from 40 pg (small pseudodiploid cell) to over 4,000 pg, with a resolution ranging from ∼1% to ∼0.05%. We find that cell growth efficiency increases, plateaus, and then decreases as cell cycle proceeds. This growth behavior repeats with every endomitotic cycle as cells grow into polyploidy. Overall, growth efficiency changes 33% throughout the cell cycle. In contrast, increasing cell mass by over 100-fold during polyploidization did not change growth efficiency, indicating exponential growth. Consistently, growth efficiency remained constant when cell cycle was arrested in G2. Thus, cell cycle is a primary determinant of growth efficiency. As growth remains exponential over large size scales, our work finds no evidence for transport limitations that would decrease growth efficiency