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Precompensated Excitation Waveforms to Suppress Harmonic Generation in MEMS Electrostatic Transducers Shiwei Zhou, Paul Reynolds, Member, IEEE, and John Hossack, Member, IEEE
Abstract—Microelectromechanical systems (MEMS) electrostatic-based transducers inherently produce harmonics as the electrostatic force generated in the transmit mode is approximately proportional to the square of the applied voltage signal. This characteristic precludes them from being effectively used for harmonic imaging (either with or without the addition of microbubble-based contrast agents). The harmonic signal that is nonlinearly generated by tissue (or contrast agent) cannot be distinguished from the inherent transmitted harmonic signal. We investigated two precompensation methods to cancel this inherent harmonic generation in electrostatic transducers. A combination of finite element analysis (FEA) and experimental results are presented. The first approach relies on a calculation, or measurement, of the transducer’s linear transfer function, which is valid for small signal levels. Using this transfer function and a measurement of the undesired harmonic signal, a predistorted transmit signal was calculated to cancel the harmonic inherently generated by the transducer. Due to the lack of perfect linearity, the approach does not work completely in a single iteration. However, with subsequent iterations, the problem becomes more linear and converges toward a very satisfactory result (a 18.6 dB harmonic reduction was achieved in FEA simulations and a 20.7 dB reduction was measured in a prototype experiment). The second approach tested involves defining a desired function [including a direct current (DC) offset], then taking the square root of this function to determine the shape of the required input function. A 5.5 dB reduction of transmitted harmonic was obtained in both FEA simulation and experimental prototypes test.
I. Introduction here has been growing interest in the potential of microelectromechanical systems (MEMS) processed electrostatically operated transducer as a potential replacement for piezoelectric transducer (PZT)-based ultrasound transducers or as an enabling technology for more complex transducer configurations [e.g., two-dimensional (2-D) catheter arrays]. This type of electrostatic transducer has been studied for several decades. However, the application of integrated circuit (IC) semiconductor manufacturing related microlithographic techniques to these devices over the past decade has resulted in significant progress [1]–
T
Manuscript received January 30, 2004; accepted June 23, 2004. This work was funded in part by the Whitaker Foundation and NIH grant EB2349. The authors are with the Department of Biomedical Engineering, University of Virginia, Charlottesville, VA 22908-0759 (e-mail: hossack@ieee.org).
[15]. These devices are frequently referred to as capacitive micromachined ultrasonic transducers (cMUT). The MEMS transducers possess a number of inherent advantages with respect to conventional PZT transducers. These advantages include: The potential to integrate associated transmit/receive electronics adjacent to the element—signal integrity is maintained and an expensive bulky cabling may be avoided. Low cost for high volume— IC processes are capable of very high volumes with modest cost. Transducer cell-to-cell, element-to-element, and transducer array to transducer array consistency due to the inherently high precision, accuracy, and repeatability of microlithographic processes. Well matched to fluids— the membrane possesses a very low acoustic impedance and, hence, is practically nonresonant when in contact with water-like loads (including tissue). One limitation of cMUT is the fact that these devices are inherently nonlinear because the force output is proportional to the square of the applied voltage [3]. In normal practice, a large DC potential in comparison to the applied alternating current (AC) signal is used to bias and thus linearize the response of the device. However, there clearly are practical limits to this approach. In diagnostic ultrasound, there is a need for relatively high acoustic outputs, but there are clear safety, cost, and practical limits to the level of DC voltage that can be used. More specifically, the transducer becomes more efficient as the membrane is drawn down under increasing bias levels [16]. However, once the deflection exceeds more than one third of the gap dimension, the device becomes unstable and the membrane collapses downward onto the base substrate. It is also important to note that, in a recent comparison of cMUT and PZT technology for diagnostic ultrasound, Mills and Smith [17] observed that it was necessary to further improve the efficiency of cMUT technology to make it truly competitive. This underlines the need to operate the transducer as aggressively as possible. Very recently, Bayram et al. [18] described a new approach for operating cMUT in a more linear manner. This involves using them with the center of the membrane collapsed down while the membrane adjacent is free to vibrate. A 10 dB reduction in harmonic was reported. However, these results were based on FEA simulation results rather than relying on experimental confirmation. Another limitation of MEMS transducers, not discussed here, is that, because they are surface machined onto the surfaces
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of low acoustic loss silicon wafers, there is a relatively high level of acoustic crosstalk [19], [20]. At the same time as cMUT are evolving to the point at which they are being considered for diagnostic imaging applications [6], [21], [22], tissue harmonic imaging (THI) [23], wherein the acoustic signal generated nonlinearly by the tissue is isolated, beamformed and scan-converted to form a B-mode image, has displaced fundamental-based, B-mode imaging for a large number of clinical applications. Significant improvements in spatial resolution and image contrast have been widely observed [24]. It is evident that the improvement in image quality outweighs the reduced penetration depth for most clinical applications. Nevertheless, because THI’s penetration is inherently limited and the harmonic signal is a result of nonlinear propagation, there is clearly interest in using relatively high, yet still safe, acoustic intensities in order to maximize its effectiveness. However, the improved resolution of THI is mostly lost if the transducer array emits harmonic energy because it then becomes impossible to distinguish harmonic signals generated via nonlinear effects in tissue from components generated nonlinearly by the transducer and propagated linearly in tissue. The arguments relating to the need to suppress harmonic generation in the transducer also apply to imaging modes optimized for contrast agent imaging. For example, the pulse inversion approaches [25]–[27] in which linear components cancel and nonlinear harmonic components sum, is based on the assumption that the transducer does not itself generate significant nonlinear components. In this paper, we compare two precompensation approaches to achieve a reduction of the inherent harmonic component obtained with cMUT. The approaches were considered using experimental analysis and a simple 1D model for electrostatic force generation. Additionally, finite-element analysis (FEA) was used to simulate the geometry and materials of the actual MEMS transducer that we tested experimentally. The reduction in the transmitted harmonic level that we observed can be used in one of two ways (or in partial combination). For preselected levels of DC bias and AC signal level, it achieves a reduced harmonic signal. Alternatively, for the same absolute amount of acceptable harmonic generation, it enables higher fundamental signal levels to be achieved. II. Theory and Method Fig. 1 illustrates schematically the typical structure of an electrostatic transducer. It consists of a capacitor with a rigid silicon substrate (lower capacitor plate) and a moving silicon nitride membrane (upper capacitor plate). Generally, the silicon nitride membrane has a metal electrode formed on the top surface, and the substrate is inherently conductive due to heavy doping. When a voltage, V, is applied to this capacitor, the silicon membrane will deform and generate an electrostatic force [3]: F =
1 V2 εA 2 , 2 d
(1)
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Fig. 1. Schematic of an electrostatic transducer. 1, Electrode; 2, silicon nitride membrane; 3, silicon wall support; 4, heavily doped silicon substrate; 5, vacuum; 6, DC bias voltage; 7, AC excitation voltage.
where ε is the permittivity of the layer between the two plates (typically a vacuum), A is the capacitor effective electrode surface area, V is the source voltage, and d is the distance between the two electrodes. This electrostatically generated plate force generates membrane displacements that in turn produce the output acoustic pressure. The driving signal generally comprises a DC voltage bias (VDC ) and a desired ultrasonic AC voltage pulse (VAC ). When these are applied together, we obtain: 2 2 V 2 = VDC + 2VDC VAC + VAC .
(2)
Thus, according to (2), we obtain a DC component (which produces no ultrasound output whatsoever), a scaled replica of the desired AC pulse and an undesired transmitted harmonic component in the acoustic result. By inspection, the ratio of the desired AC pulse to the undesired harmonic quantity can be increased by increasing the relative level of the applied DC bias. However, this bias level is limited by practical limits, including, in particular, the threshold beyond which the membrane collapses and ‘sticks’ to the lower plate [3]. Therefore, for a given maximum permitted bias voltage and maximum permissible degree of harmonic generation, there exists a strict limit to the amplitude for VAC —the desired ultrasonic signal. The significance of the need to suppress the transmitted harmonic from MEMS electrostatic transducers, and approaches for achieving this suppression, was apparently realized by several individuals working independently [28]– [30]. Each individual developed slightly different proposed solutions as briefly described below. In this paper, we implemented the iterative linear approach [28] and the square root approach [29] A. Iterative Linear Approach In this approach [28] one attempts to find the approximately linear transfer function valid for frequencies in the vicinity of the unwanted harmonic. The observed harmonic from an initial driving signal is measured. Thereafter, one estimates, using the transfer function, a compensating waveform that, when applied, will largely cancel the
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undesired harmonic. Some degree of iteration is required because the transducer is inherently nonlinear. However, because the harmonic error signal gets smaller with each iteration, the procedure becomes successively more linear and is convergent. B. Square Root Approach Savord and Ossman [29] recognized that the output is approximately determined by the square of the applied input voltage. Therefore, a preferred waveform is defined (with no harmonic content), a DC bias is superimposed, and the square root of this function is taken to determine the required DC and AC quantities that should be applied to obtain the desired waveform. C. Slope Precompensation Approach Fraser [30] identified that, as a result of the nonlinear generation, positive and negative going slopes in the waveform have different absolute rates of change (slope). Therefore, the applied waveform is artificially modified to compensate for this waveform slope distortion. Where the slope is expected to steepen, a shallower slope is applied to the input waveform as a compensatory procedure. 1. Approach I—Iterative Linear Approach: Although the electrostatic transducer operates in a nonlinear manner [28], we can assume approximate linearity when the AC signal level is small compared to the DC bias. In this first approach, a DC bias voltage of 50 V was used. This is about half of the absolute maximum rating of the device we used. (The device we used was a prototype single element device donated by Sensant Corp., San Leandro, CA.) The approach is described via numbered steps in Fig. 2. In Step 1, a 40 V peak, 2.5 MHz, 30% −6 dB fractional bandwidth Gaussian pulse was used as the AC excitation. This AC excitation is relatively large compared with DC bias (about 80%) and was expected to generate significant harmonics around 5 MHz. The corresponding pressure output signal was converted to the frequency domain in Step 2 and filtered in Step 3 to isolate the harmonic signal that was to be suppressed. The transducer’s approximately linear transfer function within the vicinity of the second harmonic then was evaluated using Steps 4 to 6. A 7 MHz, 90% −6 dB fractional bandwidth Gaussian pulse with sufficiently low amplitude so as to obtain an approximately linear operation (5 V, i.e., 10% of DC bias voltage level) was used. This amplitude level was selected experimentally based on it being the lowest level (i.e., the amplitude that would give the most accurate estimate of the transducers linear transfer function) without having excessive electronic noise corrupting the measurement. In Step 6, the transfer function was calculated by dividing the measured output by the input (both of them were converted to the frequency domain). Subsequently, in Step 7, the harmonic signal to be suppressed was divided by the transducer’s transfer function in the frequency domain. The result was converted to the
Fig. 2. Schematic of iterative linear approach.
time domain via an inverse fast Fourier transform (IFFT) and inverted so as to produce a compensation signal antiphase with respect to the existing (undesired) harmonic signal. In Step 8, the required compensation signal was summed with the original large amplitude 2.5 MHz excitation to arrive at the final required excitation. After executing this process through one iteration, the second harmonic component at 5 MHz vicinity will be reduced, but there is a possibility that higher harmonic components will result from the nonlinear response to the cancellation signal we have added in the vicinity of 5 MHz. However, the procedure can be used iteratively, extracting the higher harmonics from new results and dividing by the same transfer function again to obtain new cancellation signals. This procedure can be applied multiple times until a satisfactory result is achieved. Because the required excitation functions to be superimposed become smaller with successive iterations, the approach converges. In this paper, two iterations were found to be sufficient to provide very satisfactory results. 2. Approach II—Square Root Approach: This method is based on the observation that the output is approximately related to the square of the applied input voltage [29]. This approach is described schematically in Fig. 3. In Step 1, a desired ultrasound pulse function is first defined (2.5 MHz, 30% −6 dB fractional bandwidth Gaussian AC signal). In Step 2, a DC quantity is added to it to provide biasing and so that real numbers can be assured when the square root operation is applied. Thereafter, the composite function was scaled (multiplied) by the DC quantity, and the required excitation was determined by taking the square root of it. This substep was used so that the resulting excitation waveforms being used in this approach
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Fig. 4. Slope precompensation approach. The solid line is the original input, the dotted line is the slope-distorted output, and the dashed line illustrates the predistorted waveform, which will revert back to a semblance of the original waveform after nonlinear distortion. Fig. 3. Schematic of square root approach.
and the iterative linear approach are comparable in amplitude. In Step 5, the DC quantity is subtracted so that the new precompensated AC signal (the square root input) can be isolated. The DC level is generated by a suitable high-voltage DC source, and the AC signal is produced by programming the waveform into an arbitrary function generator and amplifying to obtain the correct signal level. 3. Approach III—Slope Precompensation Approach: This approach [30] is based on using the observation that the pressure output waveform of a cMUT is distorted by the nonlinearity of the device so as to evolve from being symmetric (broadly triangular in form) to asymmetric (broadly saw-tooth in form). The positive going portion of the waveform exhibits a steeper slope than that found in the original waveform, and the negative going portion exhibits a shallower slope. Therefore, to compensate for this nonlinear effect, a predistorted waveform is used so that, after the slope distortion induced by the nonlinear effects, it will revert back to a symmetric waveform with reduced harmonic content. Fig. 4 is a schematic illustration of this approach. Where the slope is expected to be steepen, a shallower slope is applied to the input waveform as a compensatory procedure [30]. Because this approach has been described only in a heuristic manner, we have not attempted to implement it systematically in this paper. It is thought to be unlikely that it will yield a result better than Approaches I or II above. III. FEA Simulation Results The PZFlex FEA software (Weidlinger Associates, Inc., Los Altos, CA) with a nonlinear electrostatic solver option [31] was used for the simulation of cMUT transducers taking account of device geometry and material properties. PZFlex is well suited as it uses a time-domain solver that
Fig. 5. Finite-element simulation model (only central region of the model is shown).
is particularly efficient for relatively large-scale transient problems. A time-domain approach also is more amenable to exact nonlinear modeling than is possible in frequency domain solvers because the actual output level on a timeinstant-by-time-instant basis is known and included in the model. Our FEA model is illustrated in Fig. 5 and corresponds to a prototype device donated by Sensant Corp. (San Leandro, CA). It is a single element cMUT device with 1.9mm diameter circular piston shape. There are 1380 cMUT cells in the actual prototype device, but only one cell was simulated in FEA. Therefore, to ensure a match between the electrical loading conditions in the FEA simulation and in the experiment, the series connected source resistance in the simulation was scaled by multiplying the actual impedance (50 Ω) by the number of cells. Parameters
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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 51, no. 11, november 2004 TABLE I Critical Dimensions and Material Properties. Silicon membrane diameter Vacuum gap diameter Silicon density Silicon longitudinal velocity Silicon shear velocity Silicon relative permittivity
50 µm 50 µm 2340 kgm−3 9000 ms−1 5840 ms−1 11.5
Silicon membrane thickness Vacuum gap thickness Silicon nitride (Si3 N4 ) density Si3 N4 longitudinal velocity Si3 N4 shear velocity Si3 N4 relative permittivity
2 µm 0.16 µm 3270 kgm−3 11000 ms−1 6250 ms−1 7.5
Fig. 6. Original AC input signal in time (left) and frequency (right) domains.
Fig. 7. Finite-element simulation of pressure output produced by the original input in time (left) and frequency (right) domains.
for each cell in the Sensant cMUT transducer are described in Table I. PZFlex permits the use of different finite-element mesh sizes in one model. In this simulation, we used a finely sampled mesh with varying element sizes in different regions. There are a total of 6688 elements in the model, and the smallest of them in the vacuum gap is 0.02 µm in each dimension. The simulation was executed on IBM IntelliStation Z Pro PC (IBM, White Plains, NY) with 3 GB RAM. Each simulation run took about 24 hours. We are currently looking into more efficient implementations. A. Iterative Linear Approach We first tested the iterative linear approach in an FEA model. We selected a DC bias of 50 V, and the original AC driving signal was a 2.5 MHz, 30% −6 dB fractional
bandwidth Gaussian pulse as shown in the Fig. 6. The pressure output just above the transducer element in the water is illustrated in Fig. 7. The second harmonic component about 5 MHz is readily evident and is only 8.2 dB below the level of the fundamental. Another simulation was made using a much smaller AC signal (5 V peak, 10% of the DC bias) with 7 MHz central frequency and 90% −6 dB fractional bandwidth. The approximate transfer function was calculated across the entire frequency range, and the harmonic component in the previous simulation was isolated by using a finite impulse response (FIR) band-pass filter with cut-off frequencies at 4 MHz and 10 MHz. Using the calculated transfer function, the required cancellation signal was calculated using the procedure discussed in the previous section. The new AC input signal and its pressure output are illustrated in Figs. 8 and 9. We observed that the second harmonic was
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Fig. 8. Finite-element simulation. The first iteration precompensated AC input signal (left) and resulting pressure output (right).
B. Square Root Approach The same FEA model was used for testing the square root approach. The original AC driving function was the same 2.5 MHz, 30% −6 dB fractional bandwidth Gaussian pulse as illustrated in Fig. 6, left. The DC bias level was 50 V. Fig. 12 illustrates the calculated square-root input function and its associated pressure output. In the frequency domain result in Fig. 13 (in which the square root approach was used), the second harmonic was reduced by 5.5 dB with respect to the level at which no precompensation was used. However, due to the VDC VAC term in (2) and the higher harmonic components in the square-root input function, some second and higher harmonics are still present in the output, even when using this square root approach. Fig. 9. Finite-element simulation of pressure output. Comparison in frequency domain of original output and after using a first iteration step of the iterative linear approach.
reduced from −8.2 dB down to −23.7 dB, but a higher order harmonic component occurred near 7.5 MHz due to the nonlinear operation of the transducer operating on the newly applied 5 MHz signals. This harmonic is significant, (−10 dB magnitude compared to the fundamental component). Therefore, a second iteration of the procedure was used. After performing the second iteration, the second harmonic at 5 MHz was reduced significantly to −26.8 dB, and the higher harmonic generated in the first iteration step was reduced from −10 dB to −30.9 dB (Figs. 10 and 11). The procedure could be repeated to eliminate more of the higher harmonics. However, those high-frequency components are not of interest in most harmonic-imaging situations (which are primarily concerned with the second harmonic). In this paper, we applied the procedure only twice and considered the frequency range below 8 MHz. This frequency range is well within the useful bandwidth of the hydrophone used in our experiments.
IV. Experimental Results Experiments were performed using the donated Sensant single-element transducer. We applied the same AC driving functions and 50 V DC bias that we used in the FEA simulations. The AC signal was generated on a computer and loaded into a Sony-Tektronix 2021 Arbitrary Waveform Generator (AWG) (Tektronix, Beaverton, OR). The AWG outputs were amplified by a radio frequency amplifier (ENI 50 dB, Electronic Navigation Industries, Rochester, NY, 325LA) and connected to the transducer via a series DC blocking capacitor. The DC bias was generated by a DC power supply (HP 6515A, Agilent, Palo Alto, CA). The hydrophone [SEA (Onda Corp, Sunnyvale, CA), GL-0085] was placed 4 mm away from the transducer (in the far-field) and was used to monitor the output acoustic signal. Thereafter, the result was amplified, then recorded on an oscilloscope. Fig. 14 describes the configuration of our experiment. A. Iterative Linear Approach We programmed the original AC signal (2.5 MHz, 30% Gaussian pulse shown in Fig. 6, left) as used in the FEA simulation. The experimentally measured pressure output
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Fig. 10. The second precompensated AC input signal (left) and its pressure output (right) (finite-element simulation).
Fig. 11. Comparison of pressure output in frequency domain after the second iteration of the iterative linear approach (finite-element simulation).
A better understanding and characterization of the device will improve the accuracy of the FEA prediction. The very high level of the harmonic signal for the case in which no precompensation was used is quite striking in this experiment. Clearly, this device could not be used for harmonic imaging without some form of compensation. Conventional practice would be to reduce the level of the AC signal relative to DC but the consequent impact on signalto-noise ratio (SNR) resulting from such an approach is obvious. One additional factor partially explaining the high harmonic level in this case is that we excited the transducer at less than its internal resonant ‘center’ frequency, which we estimate to lie in the range of 7 to 10 MHz. We chose to operate at lower frequencies because experimental measurement of high bandwidth, multiharmonic signals at these lower frequency ranges was considerably simpler, and more accurate, and eliminated any hydrophone bandwidth concerns. B. Square Root Approach
is shown in Fig. 15. The second harmonic was at a −8.3 dB level. Thereafter, we applied a 5 V, 7 MHz, 90% Gaussian pulse (small amplitude—10% of DC bias), and used the experimental measured results to determine the transducer’s approximate transfer function and, hence, to calculate the required compensation input signal. After the first iteration, the second harmonic was reduced from −8.3 dB to −17.6 dB, but there is a −14 dB third harmonic due to the nonlinear operation of the transducer acting on the 4– 5 MHz components in the compensation signals (Fig. 16). Following the same procedure as illustrated in Fig. 2, we repeated the process to complete a second iteration. The final result is illustrated in Fig. 17. It is observed that the second harmonic is further reduced to −28.9 dB, and the higher order harmonic was reduced to −26.8 dB. However, discrepancies can be found between the FEA simulated output waveforms and experimental result. We believe that the explanation for the discrepancy is that it is challenging to accurately characterize the materials properties and device geometry in the actual cMUT transducer.
Using the same experiment apparatus, we tested the square root approach using the same approach as in the simulation above. The square root driving function was the same as that used in the simulation (Fig. 12), and its corresponding pressure output is shown in Fig. 18. Compared with the original output spectrum, we observe that the second harmonic is reduced by 5.5 dB from −8.3 dB to −13.8 dB. Clearly, the iterative linear approach gives a more satisfactory reduction of the harmonic generation. V. Discussion and Conclusions Two precompensation approaches were evaluated in this paper. Both of these methods enable us to use AC driving voltages that are a larger fraction of the amplitude of the DC bias while reducing the level of undesired harmonic signal generation. Using the first, more complex, iterative linear approach, we achieved 18.6 dB suppression in the transmitted second harmonic in FEA simulation, and 20.7 dB in an experiment. It is believed that the fact
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Fig. 12. The square root AC input signal (left) and its pressure output (right) (finite-element simulation).
Fig. 14. Experimental configuration.
Acknowledgment We are grateful to Sensant Corp., San Leandro, CA, for the donation of a prototype single element cMUT. References Fig. 13. Finite-element simulation of output pressure spectra in the frequency domain resulting from the original input and using square root-based compensation approach.
that the experimental result demonstrated a reduction approximately 2 dB better than that obtained in the FEA simulation is coincidental. This may have been caused, for example, by imperfect hydrophone alignment in the experiment resulting in part of the harmonic signal being missed. (The harmonic signal is more directional than the fundamental signal.) Using the square root approach, a 5.5 dB harmonic reduction in generated harmonic was obtained in both FEA simulation and experiment. These methods can be used in practice because the arbitrary function generators that are required for the transmitter circuit are becoming more common among state-ofthe-art premium ultrasound scanners [32], [33]. Ultimately, the approaches will result in improved sensitivity in harmonic imaging modes when cMUT are used for diagnostic THI. Similar improvements will be obtained when the method is used to image contrast agents using nonlinear detection methods.
[1] D. Schindel and D. Hutchins, “Applications of micromachined capacitance transducers in air-coupled ultrasonics and nondestructive evaluation,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 42, pp. 51–58, 1995. [2] A. Bashford, D. Schindel, D. Hutchins, and W. Wright, “Field characterization of an air-coupled micromachined ultrasonic transducer,” J. Acoust. Soc. Amer., vol. 101, pp. 315–322, 1997. [3] I. Ladabaum, X. Jin, H. Soh, A. Atalar, and B. KhuriYakub, “Surface micromachined capacitive ultrasonic transducers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 45, pp. 678–690, 1998. [4] I. Ladabaum, B. Khuri-Yakub, D. Spoliansky, and M. Haller, “Micromachined ultrasonic transducers (MUTs),” in Proc. IEEE Ultrason. Symp., 1995, pp. 501–504. [5] O. Oralkan, X. C. Jin, H. T. Soh, A. Atalar, and B. T. KhuriYakub, “Surface micromachined capacitive ultrasonic transducers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 46, pp. 1337–1340, 1998. [6] O. Oralkan, A. Ergun, J. Johnson, M. Karaman, U. Demirci, K. Kaviani, T. Lee, and B. Khuri-Yakub, “Capacitive micromachined ultrasonic transducers: Next-generation arrays for acoustic imaging?,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 49, pp. 1596–1610, 2002. [7] Y. Roh and B. Khuri-Yakub, “Finite element analysis of underwater capacitor micromachined ultrasonic transducers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 49, pp. 293–298, 2002. [8] X. Jin, O. Oralkan, F. Degertekin, and B. Khuri-Yakub, “Characterization of one-dimensional capacitive micromachined ultrasonic immersion transducer arrays,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 48, pp. 750–760, 2001.
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Fig. 15. Experimental measured pressure output from the original input (2.5 MHz, 30% Gaussian pulse, peak amplitude 80% of DC bias voltage) in time (left) and frequency (right) domains.
Fig. 16. Experimental measured pressure output from the precompensated input signal after the first iteration of the iterative linear approach in time (left) and frequency (right) domains.
Fig. 17. Experimental measured pressure output from the pre-compensated input signal after the second iteration of the ‘Iterative Linear’ approach in time (Left) and frequency (Right) domains
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Fig. 18. Experimentally measured pressure output using the square-root input waveform shown in time (left) and frequency (tight) domains.
[9] A. Bozkurt, I. Ladabaum, A. Atalar, and B. Khuri-Yakub, “Theory and analysis of electrode size optimization for capacitive microfabricated ultrasonic transducers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 46, pp. 1364–1374, 1999. [10] O. Oralkan, X. Jin, F. Degertekin, and B. Khuri-Yakub, “Simulation and experimental characterization of a 2-D capacitive micromachined ultrasonic transducer array element,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 46, pp. 1337–1340, 1999. [11] X. Jin, I. Ladabaum, F. Degertekin, S. Calmes, and B. KhuriYakub, “Fabrication and characterization of surface micromachined capacitive ultrasonic immersion transducers,” J. Microelectromechan. Syst., vol. 8, pp. 100–114, 1999. [12] X. Jin, I. Ladabaum, and B. Khuri-Yakub, “The microfabrication of capacitive ultrasonic transducers,” J. Microelectromechan. Syst., vol. 7, pp. 295–302, 1998. [13] H. Soh, I. Ladabaum, A. Atalar, C. Quate, and B. KhuriYakub, “Silicon micromachined ultrasonic immersion transducers,” Appl. Phys. Lett., vol. 69, pp. 3674–3676, 1996. [14] M. Haller and B. Khuri-Yakub, “Surface micromachined electrostatic ultrasonic air transducer,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 43, pp. 1–6, 1996. [15] J. Knight and F. Degertekin, “Capacitive micromachined ultrasonic transducers for forward-looking intravascular imaging arrays,” in Proc. IEEE Ultrason. Symp., 2002, pp. 1052–1055. [16] G. Yaralioglu, A. Ergun, B. Bayram, E. Haeggstrom, and B. Khuri-Yakub, “Calculation and measurement of electromechanical coupling coefficient of capacitive micromachined ultrasonic transducers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 50, pp. 449–456, 2003. [17] D. M. Mills and L. S. Smith, “Real-time in-vivo imaging with capacitive micromachined ultrasound transducer (cMUT) linear arrays,” in Proc. IEEE Ultrason. Symp., 2003, pp. 568–571. [18] B. Bayram, E. Haeggstrom, A. Ergun, G Yaralioglu, and B. Khuri-Yakub, “Dynamic analysis of cMUTs in different regimes of operation,” in Proc. IEEE Ultrason. Symp., 2003, pp. 481– 484. [19] I. Ladabaum, P. Wagner, C. Zanelli, J. Mould, P. Reynolds, and G. Wojcik, “Silicon substrate ringing in microfabricated ultrasonic transducers,” in Proc. IEEE Ultrason. Symp., 2000, pp. 943–946. [20] G. Wojcik, J. Mould, P. Reynolds, A. Fitzgerald, P. Wagner, and I. Ladabaum, “Time-domain models of MUT array cross-talk in silicon substrates,” in Proc. IEEE Ultrason. Symp., 2000, pp. 909–914. [21] O. Oralkan, A. Ergun, C.-H. Cheng, J. Johnson, M. Karaman, T. H. Lee, and B. Khuri-Yakub, “Volumetric imaging using 2D capacitive micromachined ultrasonic transducer arrays (cMUTs): Initial results,” in Proc. IEEE Ultrason. Symp., 2002, pp. 1083–1086. [22] Sensant, “Silicon UltrasoundTM Images,” http://sensant.com/ diagImag hfla.htm, Sep. 2003. [23] T. Christopher, “Finite amplitude distortion-based inhomogeneous pulse echo ultrasonic imaging,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 44, pp. 125–139, 1997.
[24] K. Spencer, L. Weinert, and R. Lang, “The role of echocardiographic harmonic imaging and contrast enhancement for improvement of endocardial border delineation,” J. Amer. Soc. Echocardiogr., vol. 13, pp. 131–138, 2000. [25] C. Chapman and J. Lazenby, “Ultrasound imaging system employing phase inversion subtraction to enhance the image,” U.S. patent No. 5,632,277, 1997. [26] J. Hwang and D. Simpson, “Two pulse technique for ultrasonic harmonic imaging,” U.S. patent No. 5,951,578, 1999. [27] P. Burns, “Pulse inversion Doppler ultrasonic diagnostic imaging,” U.S. patent No. 6,095,980, 2000. [28] J. Hossack, “Medical diagnostic ultrasound system and method for harmonic imaging with an electrostatic transducer,” U.S. patent No. 6,461,299, 2002. [29] B. Savord and W. Ossman, “Circuit and method for exciting a micro-machined transducer to have low second order harmonic transmit energy,” U.S. patent No. 6,292,435, 2001. [30] J. Fraser, “Capacitive micromachined ultrasonic transducers,” U.S. patent No. 6,443,901, 2002. [31] D. Vaughn and J. Mould, PZFlex Time Domain Finite Element Analysis Package. Los Altos, CA: Weidlinger Associates, Inc., 2003. [32] C. Cole, A. Gee, and T. Lui, “Method and apparatus for transmit beamformer,” U.S. patent No. 5,675,554, 1996. [33] J. A. Hossack, J.-H. Mo, and C. Cole, “Transmit beamformer with frequency dependent focus,” U.S. patent No. 5,608,690, 1997.
Shiwei Zhou was born in Beijing, China in 1974. He received the B.S. and M.S. degrees in optical-electrical engineering from the Beijing Institute of Technology, Beijing, China, in 1996 and 1999, respectively. He is currently working towards the Ph.D. degree in medical ultrasound imaging at the Department of Biomedical Engineering of the University of Virginia, Charlottesville, VA. His research interests are finite element analysis (FEA) modeling for various ultrasound transducers including CMUTs, multi-layer transducers, and 2-D array transducers; applications of digital signal processing techniques in ultrasound; new transducer techniques and optimization.
Paul Reynolds (M’98) was born in Dundee, Scotland in 1972. He earned his B.Eng. in electrical and Mechanical Engineering from the University of Strathclyde in Glasgow, Scotland in 1994. He received his Ph.D. in 1998 from the Electrical Engineering Department at the University of Strathclyde, for research into the finite element modelling of piezoelectric ultrasonic transducers and their applications.
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In 1999 he was a Visiting Professor at the University of Colorado in Boulder, CO, before joining Weidlinger Associates Inc., (WAI) in California as a Senior Research Engineer. At WAI, his primary focus is the development of their finite element modelling package, PZFlex, for use in industry and academia for ultrasound related problems, support of customers in the use of PZFlex, and general engineering consultancy.
John A. Hossack (S’90–M’92–SM’02) was born in Glasgow, Scotland, in 1964. He earned his B.Eng. Hons(I) degree in electrical electronic engineering from Strathclyde University, Glasgow, in 1986 and his Ph.D. degree in the same department in 1990. From 1990 to 1992, Dr. Hossack was a post doctoral researcher in the E. L. Ginzton Laboratory of Stanford University working under B. A. Auld’s guidance. His research was on modeling of 0:3 and 1:3 piezoelectric composite transducers. In 1992, he joined Acuson,
Mountain View, CA, initially working on transducer design. During his time at Acuson his interests diversified into beamforming and 3-D imaging. Dr. Hossack was made a Fellow of Acuson for ‘excellence in technical contribution’ in 1999. In 2000 he joined the Biomedical Engineering Department at the University of Virginia, Charlottesville, VA. His current interests are in improved 3-D ultrasound imaging and high bandwidth transducers/signal processing. Dr. Hossack is a member of the IEEE and serves on both the Administrative Committee and the Technical Program Committee of the Ultrasonics Section. He also is an Associate Editor of the IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.
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