A micromachined efficient parametric array ...

A micromachined efficient parametric array loudspeaker with a wide radiation frequency banda) Yub Je Department of Mechanical Engineering, Pohang University of Science and Technology, San 31, Hyojadong, Namgu, Pohang, Kyungbuk 790-784, South Korea

Haksue Lee Agency for Defense Development, P.O. Box 18, Jinhaegu, Changwon, Kyungnam, South Korea

Kyounghun Been and Wonkyu Moonb) Department of Mechanical Engineering, Pohang University of Science and Technology, San 31, Hyojadong, Namgu, Pohang, Kyungbuk 790-784, South Korea

(Received 19 August 2014; revised 20 February 2015; accepted 12 March 2015) Parametric array (PA) loudspeakers generate directional audible sound via the PA effect, which can make private listening possible. The practical applications of PA loudspeakers include information technology devices that require large power efficiency transducers with a wide frequency bandwidth. Piezoelectric micromachined ultrasonic transducers (PMUTs) are compact and efficient units for PA sources [Je, Lee, and Moon, Ultrasonics 53, 1124–1134 (2013)]. This study investigated the use of an array of PMUTs to make a PA loudspeaker with high power efficiency and wide bandwidth. The achievable maximum radiation bandwidth of the driver was calculated, and an array of PMUTs with two distinct resonance frequencies (f1 ¼ 100 kHz, f2 ¼ 110 kHz) was designed. Out-of-phase driving was used with the dual-resonance transducer array to increase the bandwidth. The fabricated PMUT array exhibited an efficiency of up to 71%, together with a 63-dB bandwidth of 17 kHz for directly radiated primary waves, and 19.5 kHz (500 Hz to 20 kHz) C 2015 Acoustical Society of America. for the difference frequency waves (with equalization). V [http://dx.doi.org/10.1121/1.4916597] [MFH]

Pages: 1732–1743

I. INTRODUCTION

A parametric array (PA) loudspeaker is a highly directional source that exploits second-order nonlinear effects during the propagation of acoustic beams with finite amplitudes.1 It was proposed by Yoneyama et al.1 in 1983 after Bennett and Blackstock2 showed in 1975 that PAs can be observed in air. However, a commercially available PA loudspeaker did not appear until 1998, probably because it is extremely difficult and expensive to build the transducer, the peripheral circuitry, and the signal processors. Since the commercialization of the PA loudspeaker, the extraordinary directivity of the sound has been the focus of attention; however, it has not seen widespread uptake, despite the potential for highly directional applications in information technology (IT) devices such as notebook computers or mobile phones, and scope for providing the user with private listening in public places. Sound generation using PA loudspeakers is the result of nonlinear processes, and therefore requires large amplitudes. For this reason, the power consumption of PA loudspeakers is typically much larger than that of conventional loudspeakers.3,4 Moreover, the radiation efficiency of conventional in-air acoustic radiators is small compared with that of a)

The results of this work were reported in part at the 166th Meeting of the Acoustical Society of America [J. Acoust. Soc. Am. 134(5), 4122 (2013)]. b) Author to whom correspondence should be addressed. Electronic mail: [email protected] 1732

J. Acoust. Soc. Am. 137 (4), April 2015

an in-water acoustic radiator, so PA loudspeakers cannot be used in mobile IT devices despite the many potential applications.5,6 PA loudspeakers typically exhibit a non-uniform frequency response and relatively large harmonic distortion in de-modulated audible sounds. This is largely due to the characteristics of the radiator, as the ultrasonic radiators used for PA loudspeakers typically have a large quality factor and are operated around their resonance frequency, meaning that the frequency response will change markedly within the operating bandwidth. Many trials using signal processing and compensating circuitry have been carried out;7–9 however, the rate of change of the acoustic response with frequency is so large that it is extremely difficult to successfully compensate for these effects. Therefore, development of a PA source with a wide frequency bandwidth will bring about significant improvements to the sound quality. Here we report a PA source transducer with large power efficiency and a wide bandwidth around the resonance frequency. Membrane-type piezoelectric micromachined ultrasonic transducer (PMUT) units10,11 are used to improve the radiation efficiency, and a technique to increase the bandwidth of the array of PMUT sources is described. The large impedance mismatch between a transducer and air typically leads to low radiation efficiency in air; however, this can be overcome by reducing the characteristic mechanical impedance of the transducer.10–12 We have

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previously shown, both theoretically and experimentally,11 that micro-machined ultrasonic transducers that have a small characteristic mechanical impedance with a thin flexible radiating plate can result in high electroacoustic efficiency in air. The electroacoustic efficiency can be increased by up to 80% if the thickness of the membrane in the PMUT unit is reduced to less than 15 lm. The flat region in the frequency response around the operating frequency band can be extended in three ways. One is the use of more efficient PMUTs, with a larger radiation load relative to the internal dissipation, which results in a considerable decrease in the quality factor of the unit radiator.10–12 A radiator with a lower quality factor must have a flatter frequency response around resonance.13 The second is to design the PMUT array with radiator units with two different resonance frequencies to extend the radiation frequency bandwidth, which is an approach that is widely used in array transducer design schemes for PA sources.2,10–12,14 The third is a new operating technique proposed here to make the frequency response function (FRF) flatter in the frequency region from the low to high resonance frequencies of the unit transducers for a PMUT radiator array with two different resonance frequencies. Here, we describe the design and fabrication of PMUT arrays via three technological improvements, and characterize their radiation performance for the primary ultrasonic sounds. The arrays were tested as sources for wideband PA sounds to demonstrate their potential as efficient PA loudspeakers with good sound quality. II. DESIGN OF THE PMUT UNITS

A PMUT can have smaller mechanical characteristic impedance compared with that of a bulk transducer by using a radiating plate of micron-scale thickness. Such a device can be realized only via a micromachining process.10,11 Here, we briefly describe a lumped parameter model of a flexural-mode transducer, as this was used in the design of the PMUTs for the PA loudspeaker to predict their bandwidth and the efficiency. The single-degree-of-freedom lumped parameter model for a flexural-mode PMUT acoustic transducer is shown in Fig. 1(a). The parameters are the equivalent mechanical mass Meq, the equivalent resistance Rm for mechanical damping, and the stiffness of the radiating plate Keq.13 The effects of the medium are incorporated via use of damping with characteristics defined by the acoustic radiation impedance (Zr ¼ Rr þ jXr) of the radiating plate.15 We introduce two quality factors: The unloaded mechanical quality factor (or internal quality factor) Qm and the radiation-loaded quality factor Qr, which are defined as follows: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Meq Keq Meq Keq Qm ¼ ; Qr ¼ : (1) Rm Rr The unloaded mechanical quality factor is the inverse of the loss factor (or loss tangent), i.e., Qm ¼ 1/g,10,11,16 and can be considered to be the material properties of the corresponding J. Acoust. Soc. Am., Vol. 137, No. 4, April 2015

FIG. 1. Flexural mode transducer: (a) Mechanical lumped parameter model with a single degree of freedom and (b) structure and mode shape.

vibration mode, which are independent of the dimensions.10,11,16 The radiation-loaded quality factor is the ratio of the transducer impedance [i.e., the characteristic mechanical impedance (MeqKeq)1/2] to that of air (i.e., the radiation resistance Rr). As described in Ref. 11, the design goal is to reduce the radiation quality factor to decrease the impedance mismatch between the transducer and the air. The mechano-acoustic efficiency gMA of a flexural-mode PMUT unit is determined by the quality factors, and can be expressed in the frequency region around resonance as follows: Rr Qm ¼ ; gMA ¼ Rm þ Rr Qm þ Qr pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Meq Keq 1 ¼ ; Q¼ 1 1 Rm þ Rr þ Qm Qr

(2)

where Q is the quality factor of the PMUT unit, including the acoustic radiation effects. The bandwidth of an acoustic transducer is inversely proportional to the overall quality factor Q;13 therefore, either the unloaded mechanical quality factor or the radiation quality factor should be small to obtain a large bandwidth. To achieve large mechanoacoustic efficiency, the radiation quality factor should be Je et al.: A micromachined parametric transducers

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much smaller than the unloaded mechanical quality factor (i.e., Qr Qm). We have previously shown11 that the condition Qr Qm can be achieved by reducing the size of PMUT to a certain level. Flexural-mode PMUTs can be considered as vibrating circular flexural plates with clamped edges, as shown in Fig. 1(b). The lumped parameters of a circular radiating plate with radius a and thickness t at the first-order resonance frequency are as follows:15,17 192 q ðpa2 tÞ; K2 Et3 ; Keq ¼ 16p ð 1 2 Þa 2 pffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32 3pt2 qE Zc ¼ Meq Keq ¼ ; ð K 1 2Þ Meq ¼

(3)

where K ( ¼ 10.22), a is the frequency constant of the first flexural vibration mode, q is the mass density of the plate material, E is the Young’s modulus of the material comprising the plate, and Zc is the mechanical characteristic impedance of the radiating plate. The radiation impedance, Zr ¼ Rr þ jXr, of a flexural-mode transducer can be numerically calculated by considering the velocity profile of the radiating plate (i.e., the first flexural vibration mode of a plate with clamped edges).15,17 The radiation impedance can in practice be doubled because the backside radiation effects should also be included. Figure 2(a) shows the calculated radiation quality factor of a flexural-mode transducer as a function of the thickness of the radiating plate. The mechanical resonance frequency of the radiating plate was fixed at 100 kHz, which was the chosen nominal operating frequency for primary waves. Since the fixed resonance frequency requires the ratio t/a2 to be constant [from Eq. (3)], the radius of the plate should change as the thickness is varied. The plate was formed of silicon, because of the maturity of the micromachining fabrication process available. The material properties of silicon are listed in Table I. The radiation quality factor decreases as the thickness decreases, and approaches a minimum of about 50 when the thickness is below 15 lm. The characteristic mechanical impedance Zc of a flexural-mode transducer is proportional to the thickness squared [from Eq. (3)]. As the thickness of the plate decreases, the characteristic mechanical impedance is reduced, as is the quality factor. When the radius is sufficiently smaller than the wavelength of the radiated sound, i.e., ka 1, where k ¼ 2p/k is the wave number, the radiation resistance decreases15 with the fourth power of the radius of the plate [Rr (qc)air(ka)2pa2]. This marked drop in radiation resistance leads to saturation of the radiation quality factor because Zc also decreases with the thickness of the plate due to the constraint that the resonance frequency should be held constant (i.e., t/a2 is constant). Hence, in practice, there will be a minimum attainable radiation quality factor for a flexural-mode transducer. Figure 2(b) shows the calculated overall quality factor and mechano-acoustic efficiency of a flexural-mode transducer as a function of the thickness. The overall quality 1734

J. Acoust. Soc. Am., Vol. 137, No. 4, April 2015

FIG. 2. Characteristics of a flexural mode transducer with a fixed resonance frequency of 100 kHz in air: (a) Radiation quality factor with respect to thickness t, and (b) overall quality factor and mechano-acoustic efficiency with respect to thickness t.

factor decreases as the thickness of the plate decreases, and the minimum overall quality factor is approximately 50 when the thickness is less than 15 lm. We may therefore expect a maximum mechano-acoustic efficiency of 90% when the thickness of the radiating plate is less than 15 lm. The existence of a minimum radiation quality factor leads to the optimal design for a flexural-mode transducer for a given nominal operating frequency to achieve maximum efficiency. As described above, the thickness of the radiating plate should be less than 15 lm for a silicon PMUT with a nominal operating frequency of 100 kHz. III. DUAL-RESONANCE TRANSDUCER ARRAY WITH OUT-OF-PHASE DRIVING

A micro-machined unit driver has a small radiating area, and so an array of unit drivers should be used to achieve the required intensity for significant nonlinear effects.10–12 There are a number of design issues related to the TABLE I. Material properties of silicon. Materials Silicon

Properties

Value

Young’s modulus, E Mass density, q Poisson’s ratio, Mechanical quality factor, Qm

130 GPa 2300 kg/m3 0.278 500

Je et al.: A micromachined parametric transducers


arrangement of the drivers to obtain the desired beam patterns, mutual radiation effects, and mixing of primary waves.10,13 Additionally, the radiation bandwidth is a critical characteristic for a PA loudspeaker because the audible bandwidth is about 20 kHz, which is much wider than the nominal radiation bandwidth of a PMUT unit, and is wider than conventional PA loudspeakers on the market today. Compared with conventional PA loudspeakers, the center frequency used in this study for the primary waves was higher than conventional values (100 vs 40 kHz). Although in theory a large bandwidth can be achieved with a flexural-mode transducer using a thin radiating plate, the bandwidth around the resonance frequency of 100 kHz may be at most 4 kHz because the achievable minimum quality factor is approximately 50. PA loudspeakers require extension of the frequency bandwidth relative to that required for audible sounds. Therefore, a dual-resonance transducer array (DRTA) consisting of two types of unit driver with different resonance frequencies was used here to extend the frequency bandwidth. This approach can also be used to generate primary sound with different frequencies for PA sources in water.14 The frequency response of the DRTA is not sufficiently flat for a PA loudspeaker even with a unit transducer with a quality factor of 50. Figure 3 shows the velocity frequency responses of a transducer array with dual-resonance frequencies (f1 ¼ 100 kHz and f2 ¼ 109 kHz), calculated using the lumped parameter model shown in Fig. 1. The frequency is normalized to the lower resonance frequency of 100 kHz, and the amplitudes of the pressure and the velocity are normalized to the maxima plotted in Fig. 3. The quality factor of the unit driver is assumed to be 50. The frequency response of the pressure is calculated by assuming that the DRTA is composed of 60 f1-unit-drivers and 60 f2-unitdrivers, in the far-field approximations. The velocity frequency responses show clear peaks at normalized resonance frequencies of 1 (the resonance frequency of the f1 unit) and 1.09 (the resonance frequency of the f2 unit), as shown in Fig. 3(a). At these frequencies, the velocity phase of each unit driver changes from p/2 to p/2, as shown in Fig. 3(b). It is typical of (electromechanical) resonances that the phase difference between the PMUT surface velocity (mechanical output) and the electrical input changes rapidly from p/2 to p/2 around the resonance frequency. Because of this phase transition at resonance, the two types of unit drivers vibrate almost out-of-phase at frequencies between the two resonances (i.e., when 1 < f < 1.09). This out-of-phase vibration leads to destructive interference in the radiated sound. Therefore, a deep null appears in the pressure–frequency response shown in Fig. 3(c) at f ¼ 1.045. The pressure difference between resonance peaks and the null point is greater than 20 dB when the unit driver has the quality factor of 50. Therefore, we may conclude that a sufficiently flat frequency response cannot be achieved in the frequency range between the two resonances simply by adopting the DRTA scheme. The phase of the driving signal can be adjusted to compensate for the phase differences between the vibration velocities of the two unit drivers at a frequency range J. Acoust. Soc. Am., Vol. 137, No. 4, April 2015

FIG. 3. Calculated frequency response of the double-resonance transducer array (f1 ¼ 100 kHz and f2 ¼ 109 kHz): (a) Normalized amplitude of velocity (Q ¼ 50), (b) phase of velocity (Q ¼ 50), and (c) normalized amplitude of pressure (Q ¼ 20, 50, 70, 90).

between the two resonances. Because the phase difference in the frequency band between two resonances is approximately p, the two transducer groups (f1 and f2 drivers) will be approximately in phase if the f2 units are driven with an out-of-phase signal. We call this operating scheme for a DRTA “out-of-phase driving” (OPD). As shown in Fig. 4(b), the two unit-driver groups vibrate almost in phase at frequencies 1 < f < 1.09 with OPD. Although the two unit drivers vibrate out-of-phase at frequencies below 1 or at frequencies above 1.09, deterioration of sound quality is not expected because the audible sound generated by the PA effects occur only at frequencies in the range f1 < f < f2. The effects of the OPD scheme can be seen in the calculated acoustic pressure response of the DRTA shown in Fig. 4(c). The frequency response in the region f1 < f < f2 exhibits a shallower valley than that shown in Fig. 3(c). This is due to the constructive interference of the sounds from the two groups of drivers with different resonance frequencies. Je et al.: A micromachined parametric transducers

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FIG. 4. Calculated frequency response of the double-resonance transducer array with OPD (f1 ¼ 100 kHz and f2 ¼ 109 kHz): (a) Normalized amplitude of velocity (Q ¼ 50), (b) phase of velocity (Q ¼ 50), (c) normalized amplitude of pressure (Q ¼ 20, 50, 70, 90), and (d) electroacoustic efficiency (Q ¼ 20, 50, 70, 90).

The pressure at the local minimum (around the normalized frequency of 1.045) is 15 dB greater with the OPD scheme. The impact of OPD is also evident from the electroacoustic efficiency of the DRTA shown in Fig. 4(d). The electroacoustic efficiency is relatively flat in the frequency band of interest (i.e., f1 < f < f2). The frequency response of the DRTA with OPD may therefore be considered flat over a range of 10 kHz. Therefore, it is likely that this flat region in the acoustic radiation frequency response can be extended so that there is sufficient bandwidth for PA loudspeaker applications if two sufficiently thin types of film flexure mode vibration PMUTs are used to form the DRTA and if OPD is employed. IV. DESIGN AND FABRICATION OF A PA LOUDSPEAKER UNIT

In this section, we describe the design, fabrication, and characterization of a PA loudspeaker. To evaluate the performance of the radiator array that we developed as a PA loudspeaker, the FRF was measured by setting the desired audio signals as the input and the PA sound generated by the nonlinear effects as the output. An optimized encoding scheme should be used to ensure sufficient precision; that is, an optimized transform from the desired audio signal to the ultrasonic signal should be used to drive the transducer array. No signal-processing scheme is accepted as the standard for this purpose. Our intention here was to examine the ability to generate audible sounds with amplitudes proportional to those of the input signals. Therefore, only the generation of a difference frequency wave (DFW) by the PA was observed for a given input electrical signal driving the transducer array. This wave was a combination of one with amplitude A and frequency fL and another with the same amplitude and frequency fU. If fU changed from f1 to f2 while fL remained fixed at f1, then the frequency of the resulting DFW changed from 0 to the f2 f1. This input–output transfer function is considered here as the nominal FRF of the PA loudspeaker. (Note that there may be other ways to define the FRF, 1736


depending on the signal processing method used to encode the direct input to the PA source.) The first step in designing a PA loudspeaker is to determine the appropriate operating conditions for the primary waves, i.e., the signal that is directly generated by the drivers. This can be calculated based on a nonlinear acoustic model. This process is briefly described below. A. Operating conditions

The sound generated by a PA increases until the primary waves travel a certain distance from the source in the propagation direction. The distance at which the maximum amplitude occurs should be determined by considering the target application of the PA loudspeaker, since this distance is dependent on the center frequency of the primary signal.14 Here, the target applications of the PA loudspeaker are IT devices, such as notebook computers; hence, the distance for the maximum DFW is 0.5 m. From the previous studies of PMUT arrays for generating PA sound, we knew that a DFW reaches its maximum around 0.5 m from the source at 100 kHz,10,11 as shown in Fig. 5. Those results were obtained using an array source with a nominal size of 70 mm and the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Figure 5 shows the calculated normalized sound pressure and half-power beam width (HPBW) of the DFW generated by a PA as a function of the lower primary frequency f1. The size of the source is 2a ⱌ 70 mm, and the separation from the source is d ¼ 0.5 m. A quasi-linear solution of the KZK equation14 is used to calculate the sound field of the DFW, and an ideal Gaussian source distribution with sound pressure of 60 Pa is assumed as the primary source. The quasi-linear approach cannot give precise predictions for the DFW sounds from the target radiator, but may be used for quick confirmation of their level in the design processes. The maximum sound pressure level (SPL) of the DFW is 80 dB at 2 kHz, and the minimum HPBW of the DFW is within 5 –10 . The DFW is generated by primary sounds in the 80–100 kHz frequency range. Note that the optimal primary Je et al.: A micromachined parametric transducers


frequency does not change as a function of the difference frequency. To achieve the maximum SPL and the minimum DFW beam width, the lower driving frequency f1 of the transducer array is 100 kHz. B. Transducer design

FIG. 5. Calculated response of the DFW as a function of a lower primary frequency (source size 2a ⱌ 70 mm, working distance d ¼ 0.5 m, Gaussian source distribution of the primary wave P1 ¼ P2 ¼ 60 Pa): (a) Normalized sound pressure and (b) HPBW.

Two types of unit driver with two different resonance frequencies were designed to construct the DRTA, as discussed in Sec. III. The resonance frequencies of the two types of unit driver were f1 ¼ 100 kHz and f2 ¼ 110 kHz. Flexural-mode circular silicon radiating plates with a lead zirconium titanate (PZT) layer deposited on the top surface were used to form the piezoelectric transducer drivers. The thickness of the silicon radiating plates was 15 lm to achieve the maximum mechano-acoustic efficiency of the unit driver.11 The radii of the circular silicon plates were determined such that the resonance frequencies were f1 ¼ 100 kHz and f2 ¼ 110 kHz. The shapes and dimensions of the PZT layers were determined by considering the electromechanical coupling coefficient and the electro-acoustic efficiency. The radius of the PZT layer was 0.35 times that of the silicon plate. The thickness of the PZT layer was 0.2 times that of the silicon layer (i.e., 3 lm). Note that this was limited by the sol-gel deposition method for the PZT coating process and was not the target thickness for maximum efficiency. Finite element method modeling was used to confirm the calculation results described above for the design of the

FIG. 6. (Color online) PMUT array design: (a) Structure and specific dimensions of two types of unit drivers (f1 ¼ 100 kHz and f2 ¼ 110 kHz), (b) triangular arrangement of the unit drivers, and (c) overall array design which consists of 36 sub-arrays.



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drivers and to obtain the dimensions of the resulting structures shown in Fig. 6(a). The unit drivers were placed in an array to achieve the required radiating area and to mix the two primary waves to achieve a nonlinear interaction. The arrangement of the transducer array was determined by considering the beam patterns and the mutual radiation effect.13,18 Because half-wavelength spacing can eliminate grating lobes, and because of the negligible mutual radiation effect, the spacing between unit drivers was selected to be 1.72 mm, which is half of the wavelength in air (k1 ¼ 3.43 mm) at f1 ¼ 100 kHz. Figure 6(b) shows the arrangement of the unit drivers. A triangular arrangement was used to maximize the number of unit drivers per unit area. The f1-unit drivers and the f2-unit drivers were arranged close together to create a uniform distribution of primary waves to maximize the mixing region of the propagation paths. The sub-array shown in Fig. 6(c) was introduced by considering the yield and the uniformity in the fabrication process, and consisted of 14 f1-unit drivers and 14 f2-unit drivers, with a length of 13 mm and a width of 12 mm. The overall transducer array consisted of 36 sub-arrays to achieve the required source size of 2a ⱌ 70 mm, as shown in Fig. 6(d). C. Fabrication

Figure 7(a) shows an overview of the fabrication process. A 4-in. silicon-on-insulator (SOI) wafer was used to

form the thin-film transducer structure. To inhibit leakage currents through the silicon substrate, a high-resistivity wafer (with substrate resistivity over 10 000 X cm), was employed. The device layer was 15 lm thick, the SiO2 layer was 1 lm thick, and the handle layer was 350 lm thick. A 500-nm-thick SiO2 layer was then grown by thermal oxidation to provide an electrically insulating layer between the Si and PZT (Step I). A bottom-electrode layer (consisting of a 30-nm-thick Ti adhesion layer and a 220-nm-thick Pt layer) was then deposited, followed by sol-gel deposition of the PZT layer (where the atomic ratio of Zr/Ti was 52/48) and then a 100-nm-thick Pt top-electrode layer. The topelectrode layer, the PZT layer, and the bottom-electrode layer were patterned in turn via dry etching (Step II). The air-gap pad connection method6,7 was used to obtain electrical contact between the top electrode and the gold electrode pad, and to isolate the top and bottom electrodes (Steps III and IV). Then, the backside of the SOI wafer was etched using deep reactive ion etching (DRIE) to create a thin-film structure (Step V). The etch rate during the DRIE process was controlled so that the final etch step obtained a uniform membrane size over the entire wafer. The complete transducer was fabricated by releasing the insulating SiO2 layer and the photoresist layer for the air gap (Step VI). Figure 7(b) shows the fabricated transducer array, installed on a base consisting of a baffle and absorbent backing material. V. RESULTS AND DISCUSSION

The fabricated PMUT array was characterized electrically and acoustically. The input electrical admittance was measured in air and in a vacuum to calculate the bandwidth and electroacoustic efficiency of the drivers. The spatial distribution of the primary waves and the DFW from the PMUT array were measured and compared with the results of the calculations. A. Input electrical admittance

FIG. 7. Fabricated PMUT array: (a) Fabrication process and (b) fabricated PMUT array. 1738


Figure 8(a) shows the input electrical admittance curves (conductance and susceptance curves) of the f1-unit driver in air and in vacuum with a direct current (dc) bias voltage of 20 V. The dc bias voltage was applied to polarize the PZT layer. The measured resonance frequency (i.e., the frequency of the conductance peak) of the f1-unit driver was 90.7 kHz in air and 91.3 kHz in vacuum. The fact that these measured resonance frequencies are less than the target of 100 kHz is attributed to the tolerances of the micromachining process such as variances in the material properties and geometry. The mechanical quality factor, evaluated from the measured width of the conductance peak, was 43 in air and 170 in vacuum. Its value in air (43) is close to the theoretical minimum described in Sec. II. The peak conductance in air was 112 lS, which is lower than that in vacuum (444 lS); this was attributed to the radiation load in air. The measured electroacoustic efficiency was evaluated from the peak conductance in air and in vacuum11 to be 70%, which is close to the theoretical maximum. These results show that a micro-machined ultrasonic radiator has favorable bandwidth and efficiency compared with other ultrasonic transducers. Je et al.: A micromachined parametric transducers


FIG. 8. Input electrical admittance curves of the fabricated PMUT (dc bias voltage of 20 V): (a) f1-unit driver in air and in vacuum, (b) the sub-array (14 f1 units and 14 f2 units), and (c) the overall array (34 sub-arrays).

Table II lists the measured bandwidth and efficiency of both the f1- and f2-unit drivers. The input electrical admittance of the sub-array and the overall PMUT array was measured with a dc bias of 15 V applied to maintain the polarization of the PZT. Figure 8(b) shows the measured admittance curves of the fabricated subarray, which consisted of 14 f1 units and 14 f2 units. Two resonance peaks appeared in the conductance curve at the frequencies of f1 ¼ 91.1 kHz and f2 ¼ 99.7 kHz. The peak conductance was 3.24 mS for the f1 units and 3.52 mS for the f2 units. The conductance peaks were more pronounced than those described in Ref. 17; it follows that the variation in the resonance frequencies across the PMUT sub-array was smaller. The conductance of the out-of-peak region was 0.55 mS, which was considerably less than that at resonance. The conductance in the off-resonance region corresponds to leakage via parasitic current pathways.11 Elimination of leakage current leads to small conductance in the off-resonance region.11 The electromechanical efficiency of the sub-array was 83.0% at f1 ¼ 91.1 kHz and 84.4% at f2 ¼ 99.7 kHz, which is similar to that of the unit transducers. Figure 8(c) shows the measured admittance curves of the overall array, which consisted of 34 sub-arrays. Two major peaks appeared in the conductance curve around the resonance frequencies. The conductance peak levels were 76 mS for the f1 units and 58 mS for the f2 units. The total power consumption of the J. Acoust. Soc. Am., Vol. 137, No. 4, April 2015

PMUT array was 38 mW at f1 and 29 mW at f2 when an input signal of 1 Vpk was applied. B. Primary waves

Figure 9 shows the experimental setup for the acoustic measurements. All acoustic measurements were performed in a semi-anechoic chamber with dimensions of 3 m 3 m 2 m. The input signals used to drive each channel (i.e., the f1 and f2 transducers) were generated using a two-channel function generator (Agilent 33522A) and amplified using a two-channel negative feedback amplifier (Apex PA 05) with a maximum output power of 250 W. The radiated sound from the PMUT array was measured using a calibrated highfrequency pressure-field microphone (B&K 1/8-in. microphone, type 4138). The microphone was calibrated using the TABLE II. Measured parameters of the PMUT unit drivers. Performance Resonance frequency, fr (Hz) Q-factor in air, Qm Q-factor in a vacuum, Qm Electromechanical efficiency, gem (%) Mechano-acoustic efficiency, gma (%) Electroacoustic efficiency, gea (%)

f1-unit driver

f2-unit driver

91 300 43.2 170 89.8 74.8 67.2

102 050 42.8 177 93.5 75.9 71.0


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FIG. 9. (Color online) Experimental setup for the acoustic measurements.

frequency response data provided by the manufacturer. The measured data were visualized using a dynamic signal analyzer (SRS, SR785) or an oscilloscope (Tektronix, TDS 2024B). The transducer was installed on a rotation stage, and a microphone was installed on a linear translation stage to measure the spatial distribution of the radiated sound. The primary waves, i.e., the sound directly radiated from the fabricated PMUT array, was measured using two operating schemes: In-phase driving (IPD) and OPD. Figure 10 shows the measured SPLs from the PMUT array as a function of frequency for both driving schemes. The curves in Fig. 10 were plotted after calibrating the raw data from the microphone using the microphone sensitivity calibration chart for the high frequencies (greater than 100 kHz to compensate for the diffraction effects over the cartridge). Using the IPD scheme, two major peaks were measured near the resonance frequencies, and there was a deep null (with an SPL of 102.3 dB) at 97.4 kHz, as predicted by the above calculations. Using the OPD scheme, the null in the frequency response disappeared, and the SPL at the null (around 97 kHz) increased by more than 15 dB. The flat region of the frequency–response function was extended by 17 kHz (from 88 to 105 kHz) by the 63 dB criterion of the bandwidth. This is triple the bandwidth of the PMUT unit driver (4.6 kHz since Qm ¼ 43). Figure 11 shows the measured and calculated far-field beam patterns from the PMUT array (1.5 m from the transducer), with a receiving angle of 690 , a driving signal of 1 Vpk, and a dc bias of 15 V. The HPBW of the measured beam patterns was 3.5 for the 90.5- and 97-kHz signals, and 3 for 102-kHz wave. The beam patterns were calculated using the Rayleigh integral15 of the velocity imposed by the PMUT surfaces while the velocity profile on a unit PMUT driver surface was assumed to be the velocity distribution on a vibrating circular plate with clamped edges [see Fig. 1(b)]. The difference in the SPL between the major lobe and the side lobes in the measured beam patterns was more than 13 dB. No grating lobes were observed in the measured beam 1740


patterns, and the lack thereof is attributed to the halfwavelength spacing of the drivers. The agreement between the measured and calculated beam patterns was satisfactory in the major lobe. There were some differences between the measured and calculated patterns in the minor lobes, which may have been due to unit-to-unit variation in the fabricated PMUT array. Figure 11(d) shows a comparison of the measured beam patterns with OPD and IPD. With IPD, the SPL of the side lobes was much larger than with OPD. This is attributed to unit-to-unit variation in the drivers due to limitations of the fabrication process. The measured data suggest that OPD may yield primary waves with high directionality in a wider frequency band than yielded by IPD. C. Difference frequency wave 1. Models for theoretical references

Precise measurement of the sound field generated by a PA is challenging.2,12,19,20 Bennett and Blackstock2 noted that spurious signals resulting from intermodulation distortion can affect the measured DFW, giving broader near-field or sharper far-field beam patterns, and a steeper gradient of

FIG. 10. Measured SPL (gray line) and corrected SPL (black line) of the PMUT array as a function of frequency (z ¼ 1 m in front of the transducer, input voltage Vin ¼ 1 Vpk, 15 Vdc bias): OPD (solid line) and IPD (dotted line). Je et al.: A micromachined parametric transducers


FIG. 11. Measured and calculated beam patterns of the PMUT array (z ¼ 1.5 m in front of a transducer, input voltage Vin ¼ 1 Vpk, 15 Vdc bias): (a) 91-kHz primary wave, (b) 97-kHz primary wave, (c) 102-kHz primary wave, and (d) 97-kHz primary wave OPD (black solid line) and IPD (gray solid line).

the propagation curve. This distortion makes it difficult to identify the spurious signals in the experimental data. In this study, the measured spatial distribution of the DFW was compared with simulated data. Simulations were carried out using the Texas Code time-domain numerical simulation, which solves the KZK equation.21,22 The KZK equation accounts for the combined effects of diffraction, attenuation, and nonlinearities in the directional sound beams.15 Because it is very challenging to predict the spatial distribution of the DFW field with the complex configuration of the sources, the primary sources were approximated to a piston with the same radiating area and volume velocity as the fabricated PMUT array.

transducer array, with an input dc bias of 15 V and peak-topeak driving signals of 1 V. The frequency response with IPD exhibited a rapid drop at around 7 kHz and the 63-dB frequency bandwidth was 11 kHz (from 9 to 20 kHz). The frequency response with OPD exhibited a wider DFW signal bandwidth, and the 63-dB frequency bandwidth was 14.6 kHz (from 5.4 to 20 kHz). The frequency response with OPD gradually decreased with decreasing frequency below

2. Driving signals

The primary frequency band was 90.5–120.5 kHz; this was used to generate DFWs in the audible frequency range from 100 Hz to 20 kHz. The lower primary frequency was set to f1 ¼ 90.5 kHz, which is the smallest frequency of the primary frequency band, and the higher primary frequency was varied in the range 90.5 < f2 < 110.5 kHz. The IPD and OPD driving signals were as follows: Vc1 ¼ Vdc þ V1 sin ð2pf1 tÞ þ vV2 sin ð2pf2 tÞ; Vc2 ¼ Vdc 6V1 sin ð2pf1 tÞ6vV2 sin ð2pf2 tÞ;

(4)

where Vc1 and Vc2 are the driving signals for the f1- and f2-unit drivers, respectively, and the plus/minus signs in Vc2 correspond to IPD (plus) and OPD (minus). Vdc is the dc bias used to maintain the polarization of the thin PZT layer, and v is the modulation index used to equalize the DFW frequency response. 3. Results

Figure 12(a) shows the measured SPL of the DFW as a function of the difference frequency in the range 100 Hz to 20 kHz. The measurements were carried out 1 m from the J. Acoust. Soc. Am., Vol. 137, No. 4, April 2015

FIG. 12. Measured SPL of the DFW as a function of frequency (z ¼ 1 m in front of the transducer, input voltage V1 ¼ V2 ¼ 1 Vpk, Vdc ¼ 15 V, lower primary frequency f1 ¼ 90.5 kHz) (a) original DFW frequency responses, and (b) DFW frequency responses with equalization. Je et al.: A micromachined parametric transducers

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FIG. 13. Measured (dotted line) and computed (solid line) beam patterns (z ¼ 1 m in front of a transducer, input voltage V1 ¼ V2 ¼ 1 Vpk, Vdc ¼ 15 V, lower primary frequency f1 ¼ 90.5 kHz): (a) Difference frequency fd ¼ 2 kHz, (b) difference frequency fd ¼ 5 kHz, (c) difference frequency fd ¼ 10 kHz, and (d) difference frequency fd ¼ 15 kHz.

about 13 kHz, as the SPL of a DFW is proportional to the square of the difference frequency.14 The frequency response was almost flat at frequencies above 13 kHz, because the decrease in the primary waves outside the frequency band from 90.5 to 103 kHz (as shown in Fig. 10) may alleviate the frequency-squared increase of the DFW generation. The drop in amplitude of the DFW signal at low frequencies can be compensated for via equalization, i.e., by changing the amplitude of the f2 signal. Figure 12(b) shows the frequency response of the SPL of the DFW generated with equalization, where the modulation index was adjusted from 10 dB to þ10 dB to achieve a flat response. By applying this equalization, the frequency response of the DFW was considerably flatter. The 63-dB frequency bandwidth was extended to 19.5 kHz (from 500 Hz to 20 kHz), which covers most of the audible frequency range. This flat response of the fabricated PMUT array demonstrates its potential as a high-fidelity loudspeaker with extraordinarily high directivity in air. Figure 13 shows the measured and calculated beam patterns. The dotted curves show the measured data and the solid curves show the results of the calculations. The beam patterns were measured at a distance of 1 m from the transducer, the driving signal was 1 Vpk, and the dc bias was 15 V. The direction of the acoustic axis of the PMUT array was rotated from 60 through 60 using a rotation stage. The SPL of the DFW was obtained by varying the higher primary frequency in the range 92.5 < f2 < 105.5 kHz, with the lower primary frequency fixed at f1 ¼ 90.5 kHz. The measured HPBW of the DFW was 7 at 2 and 5 kHz, 6.3 at 10 kHz, and 5.2 at 15 kHz. These values are almost identical to the results of the calculations based on the KZK equation. The beam width of the DFW decreased as the frequency of the DFW increased. The difference between the major lobe and the side lobes was 20 dB at 2 kHz. The agreement between the measured and calculated beam patterns confirms the validity of the measured data for the DFW because 1742


spurious signals due to distortion in measuring devices usually have narrower beam patterns in the far field than those predicted by simulations. VI. CONCLUSION

We have described a PMUT array with high electroacoustic efficiency of up to 70% and a wide frequency bandwidth of 15 kHz (63 dB in the range 90–105 kHz). A thinplate PMUT was used to achieve high electroacoustic efficiency due to the size effects of the radiating structures on the radiation impedance. An efficient PMUT unit is helpful in achieving a wide frequency bandwidth; however, the resulting bandwidth is not sufficient to generate DFW signals over the full audio bandwidth. OPD was therefore used to increase the bandwidth of the transducer array with two groups of radiators with different resonance frequencies. The fabricated PMUT array described here has the potential to realize a PA loudspeaker with sufficiently low power consumption and high fidelity for use in a number of devices, such as notebook computers, where private listening in a public space is desirable. ACKNOWLEDGMENTS

This work was supported by Samsung Research Funding Center of Samsung Electronics under Project Number SRFCIT1401-00, and this work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2011-0030075), and this research was financially supported by a grant to MEMS Research Center for National Defense funded by DAPA/ADD. 1

M. Yoneyama, J.-I. Fujimoto, Y. Kawamo, and S. Sasabe, “The audio spotlight: An application of nonlinear interaction of sound waves to a new type of loudspeaker design,” J. Acoust. Soc. Am. 73, 1532–1536 (1983). 2 M. B. Bennett and D. T. Blackstock, “Parametric array in air,” J. Acoust. Soc. Am. 57, 562–568 (1975). Je et al.: A micromachined parametric transducers


3

F. J. Pompei, “Sound from ultrasound: The parametric array as an audible sound source,” Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA, 2002. 4 America Technology Corporation, “Theory, History, and the Advancement of Parametric Loudspeakers,” Rev. E, 3–27 (2003). 5 Technical document from Holosonics, http://www.holosonics.com (Last viewed November 8, 2014). 6 Technical document from Sonicast, http://www.sonicast.co.kr/eng/ index.jsp (Last viewed November 8, 2014). 7 F. J. Pompei, “The use of airborne ultrasonics for generating audible sound beams,” J. Audio Eng. Soc. 47(9), 726–731 (1999). 8 T. D. Kite, J. T. Post, and M. F. Hamilton, “Parametric array in air: Distortion reduction by preprocessing,” in Proceedings of the 16th International Congress on Acoustics, Seattle, WA (1998), pp. 1091–1092. 9 E. L. Tan, P. Ji, and W. S. Gan, “On preprocessing techniques for bandlimited parametric loudspeakers,” Appl. Acoust. 71(5), 486–492 (2010). 10 H. Lee, D. Kang, and W. Moon, “A micro-machined source transducer for a parametric array in air,” J. Acoust. Soc. Am. 125(4), 1879–1893 (2009). 11 Y. Je, H. S. Lee, and W. K. Moon, “The impact of micromachined ultrasonic radiators on the efficiency of transducers in air,” Ultrasonics 53(6), 1124–1134 (2013). 12 I. O. Wygant, M. Kupnik, J. C. Windsor, W. M. Wright, M. S. Wochner, G. G. Yaralioglu, M. F. Hamilton, and B. T. Khuri-Yakub, “50 kHz capacitive micromachined ultrasonic transducers for generation of highly directional sound with parametric arrays,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 56(1), 193–203 (2009).


13

C. H. Sherman and J. L. Butler, Transducers and Arrays for Underwater Sound (Springer, New York, 2007), pp. 58–70, 110–115, 213–261, 320–401, and 505–542. 14 B. K. Novikov, O. V. Rudenko, and V. I. Timoshenko, Nonlinear Underwater Acoustics (AIP, New York, 1987), pp. 1–7, 48–97, and 135–197. 15 L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics (Wiley, New York, 2000), pp. 107–109, 171–209, and 390–422. 16 S. Lee, Y. Lee, H. Lee, and W. Moon, “Improvements in electrical properties of piezoelectric microcantilever sensors by reducing parasitic effects,” J. Micromech. Microeng. 21, 085015 (2010). 17 S. P. Timoshenko, Theory of Plates and Shells, 2nd ed. (McGraw-Hill, New York, 1950), pp. 54–56. 18 R. L. Pritchard, “Mutual acoustic impedance between radiators in an infinite rigid plane,” J. Acoust. Soc. Am. 32, 733–737 (1960). 19 M. Toda, “New type of acoustic filter using periodic polymer layers for measuring audio signal components excited by amplitude-modulated highintensity ultrasonic waves,” J. Audio Eng. Soc. 53(10), 930–941 (2005). 20 V. F. Humphrey, S. P. Robinson, J. D. Smith, M. J. Martin, G. A. Beamiss, G. Hayman, and N. L. Carroll, “Acoustic characterization of panel materials under simulated ocean conditions using a parametric array source,” J. Acoust. Soc. Am. 124(2), 803–814 (2008). 21 Y. S. Lee, “Numerical solution of the KZK equation for pulsed finite amplitude sound beams in thermoviscous fluids,” Ph.D. dissertation, University of Texas at Austin, 1993. 22 Y. S. Lee and M. F. Hamilton, “Time-domain modeling of pulsed finite amplitude sound beams,” J. Acoust. Soc. Am. 97, 906–917 (1995).


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