PAPER Acoustic Field Analysis of Surface Acoustic Wave Dispersive Delay Lines Using Inclined Chirp IDT

Transcription

1 1014 PAPER Acoustic Field Analysis of Surface Acoustic Wave Dispersive Delay Lines Using Inclined Chirp IDT Koichiro MISU a),kojiibata, Shusou WADAKA, Takao CHIBA, and Minoru K. KUROSAWA, Members SUMMARY Acoustic field analysis results of surface acoustic wave dispersive delay lines using inclined chirp IDTs on a Y-Z LiNbO 3 substrate are described. The calculated results are compared with optical measurements. The angular spectrum of the plane wave method is applied to calculation of the acoustic fields considering the anisotropy of the SAW velocity by using the polynomial approximation. Acoustic field propagating along the Z-axis of the substrate, which is the main beam excited by the inclined chirp IDT, shows asymmetric distribution between the +Z and Z directions. Furthermore the SAW beam propagating in a slanted direction with an angle of +18 from the Z axis to the X-axis is observed. It is described that the SAW beam propagating in a slanted direction is the first side lobe excited by the inclined chirp IDT. The acoustic field shows asymmetric distribution along the X-axis because of the asymmetric structure of the inclined chirp IDT. Finally, acoustic field of a two-idt connected structure which consists of the same IDTs electrically connected in series is presented. The acoustic field of the two-idt connected structure is calculated to be superposed onto the calculated result of the acoustic field exited by one IDT on the calculated result shifted along the X-axis. Two SAW beams excited by IDTs are observed. The distributions of the SAW beams are not in parallel. The calculated results show good agreement with the optical measurement results. key words: surface acoustic wave devices, dispersive delay lines, acoustic fields, angular spectrum of plane wave method 1. Introduction A Surface Acoustic Wave (SAW) Dispersive Delay Line (DDL) [1] is one of the SAW devices. The group delay time of the SAW DDL changes depending on operating frequency. SAW DDLs are widely used as pulse expansion and compression devices in signal processing applications [2] [4]. SAW DDLs using inclined chirp IDT [5] are able to apply the same fabrication process of SAW filters, nevertheless the group delay times are over ten micro seconds from micro seconds usually. Apertures of the inclined chirp IDT are arrayed asymmetrically along the SAW propagating direction, furthermore the structure of the inclined chirp IDT is asymmetric about the normal direction of the SAW propagating direction. Because of these asymmetric structure of the inclined chirp IDT, the wave fronts of SAW from the inclined chirp IDTs were distorted [6]. Therefore the acoustic Manuscript received July 27, Manuscript revised December 28, Final manuscript received February 13, The authors are with Mitsubishi Electric Corp., Kamakurashi, Japan. The author is with Meisei University, Hino-shi, Japan. The author is with Tokyo Institute of Technology, Yokohamashi, Japan. a) Misu.Koichiro@cs.MitsubishiElectric.co.jp DOI: /ietfec/e90 a field analysis is important to design the DDLs. Simulated acoustic fields using the parabolic approximation showed good agreement with the optical measurement results in the vicinity of the Z-axis direction [7]. However, error of the SAW velocity on a Y-cut LiNbO 3 substrate becomes large when angle of the propagation direction from the Z-axis is over 10, because the parabolic approximation uses the second order polynomial to approximate the SAW velocity. In this paper, the angular spectrum of plane wave (ASPW) method [8], [9] is applied to calculation of acoustic fields of an inclined chirp IDT. The ASPW method is able to consider the anisotropy of the SAW velocity on Y- cut LiNbO 3. To approximate the SAW velocity, 8th order polynomial is used. Velocity errors of the polynomial are below 1.0 m/sec, so that the 8th order polynomial has sufficient accuracy. As a result of calculation, acoustic field propagating along the Z-axis of the substrate shows asymmetric distribution between the +Z and Z directions as shown in the parabolic approximation [7]. It is described that the SAW beam propagating in a slanted direction with an angle of +18 from the Z-axis to the X-axis is the first side lobe excited by the inclined chirp IDT. Furthermore the acoustic field shows asymmetric distribution along the X-axis because of the asymmetric structure of the inclined chirp IDT. Finally, acoustic field of a two-idt connected structure which consists of the same IDTs electrically connected in series is shown. The acoustic field of the two-idt connected structure is calculated to be superposed onto the calculated result of the acoustic field exited by one IDT on the calculated result shifted along the X-axis. Two SAW beams excited by IDTs are observed. The distributions of the SAW beams are not in parallel. These calculated results show good agreement with the optical measurement results [7]. 2. Calculation of Acoustic Fields by ASPW 2.1 Coordinate System Figure 1 shows a coordinate system to calculate acoustic field of a line wave source using the ASPW method. The wave source is lying along the X-axis on the boundless plane, the length of the wave source is W i which is the i- th aperture of IDT. The center of the wave source is defined as the origin (0,0). k is a wave vector, k 1 is a X axial component of k, andk 3 is a Z axial component of k. It is assumed Copyright c 2007 The Institute of Electronics, Information and Communication Engineers

2 MISU et al.: ACOUSTIC FIELD ANALYSIS OF SURFACE ACOUSTIC WAVE DISPERSIVE DELAY LINES 1015 Fig. 1 source. Coordinate system of the acoustic field analysis from a wave that the diffraction and propagation characteristics are essentially two-dimensional. The amplitude of wave source is defined as one, the function f i (Z,X) at a field point A(Z,X) can be represented by [9] f i (Z, X) = 1 ( ) sin(k1 W i /2) e j[k 1X+k 3 Z] dk 1, (1) π where k 1 k3 2 = k 2 k1 2, (2) k = 2π f /V(θ). (3) In these equations, f is the operating frequency, V(θ) is the SAW velocity propagating along wave vector k, θ is the angle of the wave vector k rotated from the X-axis. The acoustic field from the inclined chirp IDT is calculated to sum the acoustic fields of wave sources, the function f (Z, X) of the inclined chirp IDT at a field point A(Z, X) can be represented by f (Z, X) = N f i (Z z i, X x i ). (4) i=1 Where (z i, x i ) is the coordinate of wave source number i, N is number of wave sources. 2.2 Approximation of SAW Velocity Values of SAW velocity V(θ) must be changed according to the wave vector direction angle θ. For convenience, polynomial approximation of angle θ is used to calculate SAW velocity [10] [12] in this paper. Figure 2 shows the calculated SAW (Rayleigh Wave) velocity of Y-cut LiNbO 3.The calculated result is the velocity on the free surface. Material constants of LiNbO 3 are used as shown by reference [13]. Table 1 shows coefficients of the polynomials to approximate the velocity from θ = 0to90 as shown in Fig. 2. The polynomial is represented by the following function. V(θ) = N A 2n θ 2n. (5) n=0 Fig. 2 Calculated Rayleigh wave velosity on Y-cut LiNbO 3. Table 1 *The unit of angle: θ is degree. Polynomial coefficients. Where θ is the angle from the X-axis, A 2n is the coefficients of the polynomials shown in Table 1. Because of the symmetry of the crystal form about the X-axis, the polynomials use only even component 2n. Table 1 shows maximum errors and standard deviations additionally. Velocity errors of the 8th order polynomial are below 1.0 m/sec, so that the 8th order polynomial has sufficient accuracy. Therefore, the 8th order polynomial shown in Table 1 is used in the following calculations. On the other hand, the parabolic approximation method [14] uses second order polynomial to approximate SAW velocity. The velocity V p (θ) is represented by [ V p (θ) = V γ ] 2 (θ θ 0) 2. (6) Where, γ is an anisotropic coefficient, θ 0 is the angle of the SAW propagation direction, in this case θ 0 is π/2 (rad). Figure 3 shows four SAW velocity lines, the solid line is the same velocity as shown in Fig. 2, the dotted line is the calculated result using the equation (5) with the 8th order polynomial coefficients shown in Table 1. The dotted line and the solid line show good agreement. The dashed lines are calculated results using the equation (6), the one is calculated with γ = which is the anisotropic coefficient shown in Fig. 2, the other is calculated with γ = which is calculated to agree with the velocity shown in Fig. 2 in the range of 80 to 90. The errors between the solid line and the dashed lines become large, when the angle from the X-axis becomes smaller than 80. Therefore, error of the parabolic approximation method becomes large in area be-

3 1016 Fig. 4 Structure of the inclined chirp IDT. Fig. 3 Comparison between SAW velocity calculated by polynomials and the SAW velosity shown in Fig. 2 propagating in the vicinity of the Z-axis on Y-cut LiNbO 3. Table 2 low 80 from the X-axis. Design parameters of the inclined chirp IDT. 2.3 Acoustic Field of the Inclined Chirp IDT Simulation Model Table 2 shows design parameters of the inclined chirp IDT. This IDT is the same as the IDT shown in reference [7]. The center frequency of this IDT is 100 MHz band, the band width is 15 MHz, and dispersion time of the one IDT is 2.5 µsec; dispersion time of DDL is 5 µsec. The IDT is inclined along the X-axis with 5, and the both 20% sides of the IDT are weighted with cosine function to suppress the side lobe of the compressed pulse [15]. Figure 4 shows the structure of the inclined chirp IDT. The left side of the IDT operates at a higher frequency, and the right side of the IDT operates at a lower frequency. In the coordinate system, the Z-coordinate is defined as Z = 0 at the right side of the IDT, the X-coordinate is defined as X = 0atthecenterofthe IDT. It is considered that the SAW velocity depends on the wave vector direction. However the difference of the SAW velocity between the IDT area and the free surface is not considered Calculated Result Figure 5(a) shows the calculated acoustic field of the inclined chirp IDT using the ASPW method. The calculated acoustic field at the center frequency shows the amplitude in the linear scale; black color means minimum amplitude as null, and white color means maximum amplitude as 100. The IDT area is additionally drawn with grey area. The strong beam is excited from the center of the IDT, and propagates along the +Z-axis. Simultaneously, the SAW beam along the Z-axis spreads and shows asymmetric distribution between the +Z and Z directions. This distribution along the Z-axis is similar to the calculated acoustic field using the parabolic approximation [7]. Figure 5(a) shows the other beam which propagates in a slanted direction with an angle of about +20 from the Z-axis to the X-axis. In the calculated acoustic field using the parabolic approximation, the similar beam is excited as the low level [7]. However, the beam shows interference pattern [7], [18]. In Fig. 5(a) the SAW beam which propagates in a slanted direction with an angle of about 20 from the Z-axis is not observed Comparison with the Optical Measurement Figure 5(b) shows the measured acoustic field by the optical heterodyne interferometer [7]. The vertical axis scale and the horizontal axis scale of the measured result shown in Fig. 5(b) are the same as those of the calculated result shown in Fig. 5(a). The values of the amplitudes are relative, so that the values of Fig. 5(b) are not equal to the values of Fig. 5(a). The IDT areas are additionally drawn with grey area. In the calculated result, absorbers which reduces the reflection at the chip ends and a pad area underneath the right of the IDT to compensate the refraction [16] are not considered. Nevertheless the measured acoustic field shown in Fig. 5(b) is almost the same as the calculated acoustic field shown in Fig. 5(a). Especially in Fig. 5(b), the beam propagating in a slanted direction with an angle of about +20 from the Z- axis is observed. On the other hand, the beam propagating in a slanted direction with an angle of about 20 from the Z-axis is not observed same as in Fig. 5(a). Figure 5(c) shows comparison between calculated amplitude profiles and measured amplitude profile along the X-axis at the point of Z = 3 mm. The thin solid line shows the same result as the amplitude shown in Fig. 5(a). The material constants on the free surface are used as shown in reference [13]. The dotted line and the dashed line show amplitude profile using material constants on the free surface as shown in reference [17] and on the metal surface as shown in reference [13]. These three calculated results

4 MISU et al.: ACOUSTIC FIELD ANALYSIS OF SURFACE ACOUSTIC WAVE DISPERSIVE DELAY LINES 1017 calculation is not concerned the refraction Study of the Side Lobe (a) Calculated acoustic field of the inclined chirp IDT. (b) Measured acoustic field of the inclined chirp IDT [7]. (c) Comparison between calculated amplitude profiles and measured amplitude profile shown in (b). (All amplitude profiles along the X-axis at the point of Z = 3 mm) Fig. 5 Acoustic fields of the inclined chirp IDT. are almost same although the different material constants of LiNbO 3 are used. The fat solid line shows the measured amplitude profile along the X-axis at the point of Z = 3mm as shown in Fig. 5(b). The measured amplitude profile is almost same as the calculated profiles. However there is some difference between the calculated results and the measured result. The calculated profiles have sharp peaks in the vicinity of X = 0.1 mm. This is the strong beam excited from the center of the IDT. On the other hand the measured profile shows the maximum amplitude in the range of X = 0 to 0.2 mm. This area seems to be a focused area as shown in Fig. 5(b). This difference of the amplitude profiles along the X-axis is mainly caused by the refraction of the SAW at the boundary between the IDT and the pad, because the The beams propagating in a slanted direction with an angle of about +20 from the Z-axis shown in Fig. 5(a) and Fig. 5(b) seem to be side lobes excited from wave source. The directivity function D(φ) is represented by D(φ) = sin ( kw i 2 kw i 2 sin φ sin φ). (7) Where φ is the angle from the Z-axis, k is wave number, W i is aperture length of wave source. Because the first side lobe point of the function (sin ξ/ξ) isatξ = 4.49, the following equation is satisfied; ξ = kw i sin φ = (8) 2 Using equation (8), the first side lobe direction is solved as φ = 18. In this case, the wave number k depends on the angle φ strictly. The angle φ 1 is defined to be solved the equation (8) assuming that the velocity V is constant and uses as the value of θ = 90 (i.e. φ = 0). The angle φ 2 is defined to be solved the equation (8) assuming that the velocity V is constant and uses as the value of θ = 72 (i.e. φ = 18 ). The difference between the angle φ 1 and the angle φ 2 is about 0.3. Therefore, the wave number k is regarded as constant to solve the equation (8) in this case. To study of the side lobe from IDT, acoustic fields of normal IDTs are calculated because an normal IDT is a fundamental structure. Figure 6(a) shows a calculated acoustic field of an normal IDT. The number of wave sources is 100, the wave sources are arrayed along the Z-axis (non-inclined) with constant pitch. The center frequency of this IDT and the length of the wave sources are the same as those of the inclined chirp IDT shown in Fig. 5(a) and Fig. 5(b). Fig. 6(a) shows acoustic field operating at the center frequency in decibel scale to observe the side lobes. The first side lobes are observed along the dashed lines rotated with 18 from the Z-axis. Figure 6(b) shows calculated amplitude profiles of normal IDTs along the X-axis at the distance with 1.4 mm from the right side of the IDT. The solid line in Fig. 6(b) shows the same result as the amplitude along the line A-A shown in Fig. 6(a). The dotted line is the amplitude of the inclined IDT which has the same pitch as the IDT of solid line. Furthermore the inclined angle φ is the same as that of the inclined chirp IDT shown in Fig. 5(a). The first side lobes are observed in the range of X = 0.5 to 1 mm. The first side lobe level of the inclined IDT decreases compared with the non-inclined IDT in the range of X = 0.5 to 1 mm. On the other hand, the first side lobe level of the inclined IDT increases compared with the non-inclined IDT in the range of X =+0.5 to +1 mm. Figure 6(c) shows calculated amplitude profiles of chirp IDTs. The dispersion slope (i.e. dispersion time divided by band with) of those IDTs is the same

5 1018 Fig. 7 Configuration of the two-idt connected structure. (a) Calculated acoustic field of an normal IDT. (Number of wave sources: N = 100, constant pitch, non-inclined) garded that the beams propagating in a slanted direction with an angle of +18 shown in Fig. 5(a) and Fig. 5(b) are the first side lobe. Furthermore, in Fig. 5(a) and Fig. 5(b) the beam propagating in a slanted direction with an angle of 18 from the Z-axis is not observed. This asymmetric distribution about the Z-axis is caused by the asymmetric structure of the inclined IDT. 2.4 Acoustic Field of a Two-IDT Connected Structure Simulation Model (b) Calculated amplitude profiles of the Normal-IDT. (Constant pitch) Figure 7 shows a configuration of a two-idt connected structure. Two IDTs are the same structure each other. The one IDT is the same as the IDT shown in Table 2 and Fig. 4. The other IDT is shifted with distance X s along the X-axis and is connected electrically to the one in series. The acoustic field of the one inclined chirp IDT is defined as the function f A (Z,X), the acoustic field f B (Z,X) of the other IDT is represented by f B (Z, X) = f A (Z, X X S ). (9) The acoustic field f (Z,X) of the two-idt connected structure is given by the following equation (c) Calculated amplitude profiles of the Chirp-IDT. Fig. 6 Calculated amplitude profiles of the IDTs. (Number of wave sources: N = 100) as that of the inclined chirp IDT shown in Fig. 5(a). The solid line shows the amplitude of a non-inclined chirp IDT. The dotted line shows the amplitude of an inclined chirp IDT. The inclined angle φ is the same as that of the inclined chirp IDT shown in Fig. 5(a) and Fig. 6(b). The number of wave sources, the length of the wave sources, the center frequency and the operating frequency are the same as those of the IDTs shown in Fig. 6(b) respectively. The first side lobes are observed in the range of X = 0.5 to 1 mm. The first side lobe level of the inclined chirp IDT increases compared with the non-inclined chirp IDT in the range of X = +0.5 to +1 mm. The difference of the first side lobe level between the inclined chirp IDT and the non-inclined chirp IDT is almost same as the normal IDTs shown in Fig. 6(b). From the calculation results shown in Fig. 6, it is re- f (Z, X) = f A (Z, X) + f B (Z, X) = f A (Z, X) + f A (Z, X X S ). (10) The equation (10) means that the acoustic field of the two- IDT connected structure is calculated by the superposition onto the acoustic field of the one inclined chirp IDT on the acoustic field of the inclined chirp IDT shifted along the X- axis Calculated Result Figure 8(a) shows a calculated acoustic field of the two-idt connected structure as shown in Fig. 7. The acoustic field shown in Fig. 8(a) is calculated using the equation (10) by the superposition of the acoustic field shown in Fig. 5(a). The distance X s is 150 µm. Figure 8(a) shows in the linear scale; black color means minimum amplitude as null, and white color means maximum amplitude as 100. Additionally, the IDTs are drawn with grey area. Strong beams excited from the IDTs show the different distributions from

6 MISU et al.: ACOUSTIC FIELD ANALYSIS OF SURFACE ACOUSTIC WAVE DISPERSIVE DELAY LINES 1019 Figure 8(b) shows the optical measurement result of the two-idt connected structure [7]. The configuration of the IDTs is the same as the one shown in Fig. 8(a). The vertical axis scale and the horizontal axis scale of the optical measurement result shown in Fig. 8(b) are the same as those of the calculated result shown in Fig. 8(a). The operating frequency is the center frequency. The values of the amplitudes are relative, so that the values are not equal to the values of Fig. 8(a). The IDT areas are drawn with grey area. In Fig. 8(b), the beams excited from the left side IDT are refracted at the boundary and scattered on the right side IDT. However, the refraction and the scatter are not concerned in the calculated result. Nevertheless the calculated acoustic field shown in Fig. 8(a) shows good agreement with the optically measured acoustic field shown in Fig. 8(b). Especially the measured distributions of the strong beams propagating along the +Z direction and the spread beam propagating along the Z direction shown in Fig. 8(b) are almost same as the calculated distributions shown in Fig. 8(a). The validity of the calculation method by use of the superposition is demonstrated. 3. Conclusion Fig. 8 (a) Calculated acoustic field. (b) Optically measured acoustic field [7]. Acoustic fields fo the two-idt connected structure. the single-idt. The strong beams propagate not in parallel each other. Furthermore, the SAW beam shows asymmetric distribution between the +Z and Z directions. In this calculation, only superposition of the acoustic fields of the two IDTs is considered. The effect of SAW propagating over the IDT is not considered. The complicated distribution shown in Fig. 8(a) is caused by the interference of the acoustic fields excited from the two IDTs each other Comparison with the Optical Measurement The acoustic field analysis of the inclined chirp IDT was shown. The calculated results were compared with the optical measurement results. The angular spectrum of plane wave method was applied to the calculation for the acoustic fields considering the anisotropy of SAW velocity on a Y-cut LiNbO 3 substrate. To approximate the SAW velocity depending on the wave vector direction, the 8th order polynomial approximation of the propagation angle was used. The maximum error of the polynomial was below 1.0 m/sec so that the 8th order polynomial approximation had sufficient accuracy. On the other hand, the second order polynomial as used in parabolic approximation showed good agreement within the 10 from the Z-axis, but over the 10 from the Z-axis errors of the second order polynomial became large. The calculated result of the single inclined chirp IDT was shown. The SAW beam propagating along the Z-axis spread and showed asymmetric distribution between the +Z and Z directions similarly as shown in the calculation of the parabolic approximation. Furthermore, the SAW beam propagating in a slanted direction with an angle of +18 from the Z-axis was shown; it was the first side lobe. Because the inclined chirp IDT had the asymmetric structure along the X-axis, the side lobe with an angle of 18 from the Z-axis was not observed. The calculated result showed good agreement with the measured results. The calculated result of the two-idt connected structure was shown. The superposition of the acoustic field of the one inclined chirp IDT was applied to the calculation for the acoustic field of the two-idt connected structure. The calculated result showed the good agreement with the optical measurement result so that the validity of the calculation method was demonstrated. References [1] R.H. Tancrell, M.B. Schulz, H.H. Barrett, L. Davis, Jr., and M.G. Hooland, Dispersive delay lines using ultrasonic surface waves, Proc. IEEE, vol.57, no.6, pp , June [2] J.R. Klauder, A.C. Price, S. Darlington, and W.J. Albersheim, The theory and design of chirp radars, Bell Syst. Tech. J., vol.39, pp , July [3] J.D. Maines and E.G.S. Paige, Surface-acoustic-wave devices for signal processing applications, Proc. IEEE, vol.64, no.5, pp , May [4] M.A. Jack, P.M. Grant, and J.H. Collins, The theory, design, and applications of surface acoustic wave Fourier-transform processors, Proc. IEEE, vol.68, no.4, pp , April [5] R.H. Tancrell and P.C. Meyer, Operation of long surface wave interdigital transducers, IEEE Ultrason. Symp., J7, [6] S. Jen, C.S. Hartmann, and M.A. Domalewski, Propagation of surface acoustic waves generated by slanted transducers: A laser probe study, IEEE Ultrason. Symp., pp , [7] T. Chiba, Optical measurement and numerical analysis of SAW

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