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An oscillator using high order Lamb wave modes
Applied Acoustics 70 (2009) 1446–1448
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Technical Note
An oscillator using high order Lamb wave modes Wei Lin a,*, Li Fan b, Chang-ming Gan b, Zhe-min Zhu b, Xiang-bang Wang c a
Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Institute of Acoustics, Key Laboratory of Modern Acoustics, Nanjing University, Nanjing 210093, China c China Electronics Technology Group Corporation, No. 55 Research Institute, Nanjing, 210016, China b
a r t i c l e
i n f o
Article history: Received 23 May 2008 Received in revised form 25 June 2009 Accepted 29 June 2009 Available online 26 July 2009 Keywords: High order mode Lamb wave Oscillator Interdigital transducer
a b s t r a c t An oscillator using high order Lamb wave modes is presented. Due to the multimode property of Lamb waves, high frequency oscillators using high order mode Lamb waves can be fabricated. To select the operating mode of the Lamb wave oscillator, a high order mode selector is inserted into the feedback loop. An oscillator using the 13th antisymmetric mode (a13) in Lamb wave is achieved in experiments and the oscillating frequency is 5.30 times higher than that of the a0 mode excited by the interdigital transducer. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In recent years there has been a growing interest in using Rayleigh wave devices to fabricate sensors applied to physical, chemical and biological fields [1–4]. Because the sensitivities of the sensors are dependent on the shift of the oscillating frequencies induced by the measured quantities, the sensitivities of the sensors increase with the operating frequencies. Therefore, many researches focused on the increase of the operation frequencies of the sensors, however, the fundamental frequencies of the sensors cannot increase limitlessly due to the technical limitation for fabricating interdigital transducers (IDTs). Several methods for increasing the operation frequencies were presented. Seidel et al. used a new structure of IDT to excite the 48th harmonics of Rayleigh wave, which greatly increased the operating frequency, while at the same time resulted in a large insertion loss about 80 dB [5]. Caliendo et al. used the Rayleigh wave excited in an AlN/Si composite film deposited on a sapphire, in which the wave velocity increases from 2680 m/s in ZnO to 5607 m/s, and consequently improved the operation frequency although the periodicity of the IDT was not changed [6]. On the other hand, the sensors using different acoustic waves have also attracted great attention, in which an important work was the researches of Lamb wave sensors [7,8]. The operating principles of Lamb wave sensors are similar to those of Rayleigh wave sensors, but the sensitivities of the Lamb wave sensors is much
* Corresponding author. Tel./fax: +86 25 83593960. E-mail address: [email protected] (W. Lin). 0003-682X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2009.06.004
higher and the response time is faster than those of the Rayleigh wave sensors if both kinds of sensors have the same frequency [9]. Similarly the increase of operation frequencies can improve the sensitivities of Lamb wave sensors, thus the Lamb wave oscillators with high order modes can be used for obtaining high sensitivities. In this paper, a method to set up a closed loop oscillation by selecting high order Lamb modes is presented, with which one can obtain a higher phase velocity and a higher oscillating frequency, and then the sensitivity is greatly improved. 2. Characterization of high order mode of Lamb wave Fig. 1 shows the theoretical dispersive curves of the Lamb waves excited by IDTs with the periodicity of 0.425 mm in a 127.86° rotated Y-cut, X propagating lithium niobate plate with the thickness 0.4 mm, in which c is phase velocity and fd is the product of the frequency f and thickness d. In the figure, for simplicity, only two high order modes, a13 and a14, are displayed in addition to the a0 and s0 modes. Then, from the dispersive curves of Fig. 1, the relations between the wavelength (k) and frequency (f) can be obtained, which are shown in Fig. 2. Making a line paralleled with the transverse axis via some point k0 on the vertical axis, one can obtain a series of crossing points on the k–f curves in Fig. 2. On the crossing points, the wavelengths of various modes are the same, but the resonance frequencies and phase velocities are different. Therefore, the oscillations in these frequencies can be obtained by a Lamb wave delay line with the wavelength k0 of the IDTs if the amplitude and phase conditions of the oscillations are satisfied at the same time.
W. Lin et al. / Applied Acoustics 70 (2009) 1446–1448
Fig. 1. The theoretical dispersive curve of the Lamb wave excited by an IDT in a 127.86° rotated Y-cut, X propagating lithium niobate plate.
1447
Fig. 3. Insertion loss versus frequency for the Lamb wave delay line fabricated on a 127.86° rotated Y-cut, X propagating lithium niobate plate.
Therefore, for designing the Lamb wave oscillators with different modes, the actual propagation characteristics, such as the phase velocity, insert loss, frequency gap of adjacent modes and phase–frequency response must be considered, especially the phase–frequency response must be monotonic and linear. Based on these factors, the a13 mode is selected as the operation mode in this work, the resonant frequency of which is about 46.24 MHz and the insert loss is about 32 dB. 3. High order Lamb mode oscillator 3.1. Experimental system
Fig. 2. Frequency versus wavelength for different modes of Lamb wave.
The propagation characteristics of the high order Lamb waves excited by IDTs are influenced by the diffraction and reflection between the fingers of IDTs, the reflection of the substrate boundaries, and so on. Therefore the actual dispersive curves are different from the theoretical curves. The propagation characteristics of different modes of the Lamb wave are measured by a frequency domain method [10], by which the amplitude–frequency responses and the phase–frequency responses of the Lamb waves can be obtained. From the measurements, the phase velocities and resonant frequencies of various modes of the Lamb wave are listed in Table 1 and the insertion loss of the Lamb delay line obtained using Agilent8508A Vector voltmeter is shown in Fig. 3.
Fig. 4 shows the block diagram of a high order Lamb mode oscillator, which is composed of the Lamb wave delay line, the lownoise pre-amplifier, the high order mode selector, the large dynamic range amplifier and the direction coupler. In the system, there are two key devises, the Lamb wave delay line and the high order mode selector. As the main and stable unit of the oscillator, the Lamb wave delay line must satisfy the requests as follows: (a) Delay time: For the oscillator, the frequency stability (Q) can be expressed by the equations:
Q ¼p
s T
where s ¼ l=cp is the delay time of the delay line, l is the distance between the input and output IDTs, cp is the phase velocity of the Lamb wave at the operating frequency and T is the periodicity of the IDTs. Therefore, the delay time must be much longer than the periodicity of the IDTs in order to increase the frequency stability of the oscillator.
Table 1 The characteristics of various modes of Lamb wave. Mode
Resonant frequency (MHz)
Phase velocity (m/s)
a0 s0 a13 s14
8.75 9.80 46.24 49.80
3719 4165 19,652 21,165
ð1Þ
Fig. 4. The block diagram of high order Lamb mode oscillator.
1448
W. Lin et al. / Applied Acoustics 70 (2009) 1446–1448
Therefore, the insert loss of the selector must be as low as possible. 3.2. Experimental results Fig. 5 shows the fundamental oscillation spectrum of the oscillator obtained using a spectrum analyzer. The center frequency is about 46.5 MHz, no other modes can be observed in the frequency range below 100 MHz. Therefore, the oscillation frequency is determined by the Lamb wave delay line of a13 mode. By a frequency meter, the oscillation frequency is measured to be 46.48 MHz, whereas the oscillation frequency of the oscillator using the a0 mode of the Lamb wave excited by the same IDT is about 8.75 MHz. Thus, the operation frequency, i.e., the phase velocity, of the high order Lamb mode oscillator is 5.3 times higher than that of the a0 mode. Fig. 5. The oscillation spectrum of the high order Lamb mode oscillator with the center frequency 46.48 MHz (each lattice is 20 kHz in X-axis and 10 dB in Y-axis).
(b) Bandwidth: In order to avoid the multimode oscillation, the bandwidth of the delay line (Df) must satisfy the equation:
Df
1
s
ð2Þ
As one of the key devices, the high order mode selector is a special designed band pass filter constructed by a Rayleigh wave delay line, and the selector must satisfy a series of restricted conditions and requests as follows: (a) Delay time: The delay time of the selector must be much less than that of the Lamb wave delay line in order that the frequency stability of the oscillator is only determined by the Lamb wave delay line. (b) Bandwidth: Since the frequency range of the oscillator must be only determined by the bandwidth of operating mode, such as a13, of the Lamb wave, the bandwidth of the selector must be wider than that of the operating mode. But the pass band of the selector cannot cover the frequencies of other modes, such as the adjacent mode a14, in order to meet the request of the mode selection. (c) Insert loss: The insert loss of the selector increases the loss and reduces the signal to noise ratio of the oscillation circuit, thus reduces the frequency stability of the oscillator.
4. Conclusions The propagation characteristics of the high order modes of Lamb waves are studied. Based on the research, a new Lamb wave oscillator using the high order mode is fabricated, in which the phase velocity of a13 Lamb mode oscillator is 5.3 times higher than that of the a0 mode. Therefore the high frequency oscillator with operating frequency above UHF band can be fabricated more easily by this method, then the sensitivities of the sensors using the new oscillator can be increased greatly. References [1] Wohltjen H. Surface acoustic wave microsensors. In:Proceedings of the international conference on solid-state sensor and actuators; 1987. p. 471–7. [2] Caliendo C, Imperatori P. High-frequency, high-sensitivity acoustic sensor implemented on ALN/Si substrate. Appl Phys Lett 2003;83:1641. [3] Bjurström J, Yantchev V, Katardjiev I. Thin film Lamb wave resonant structure – the first approach. Solid-State Electron 2006:322–6. [4] Duhamel R, Robert L, Hongguang Jia CM, et al. Sensitivity of a Lamb wave sensor with 2 lm AlN membrane. Ultrasonics 2006;44:e893–7. [5] Seidel W, Hesjeda T. Multimode and multifrequency gigahertz surface acoustic wave sensors. Appl Phys Lett 2004;84:1407. [6] Wenzel SW, White RM. A multisensor employing ultrasonic Lamb-wave oscillator. IEEE Trans Electron Dev 1988;35:735–43. [7] Costello BJ, Martin BA, White RM. Ultrasonic plate wave for biochemical measurements. In: Proceedings of IEEE ultrasonic symposiums; 1989. p. 977– 81. [8] Joshi SG, Jin Y. Excitation of ultrasonic Lamb waves in piezoelectric plates. J Appl Phys 1991;69:8018–24. [9] Victorov A. Raleigh and Lamb wave. New York: Plenum; 1967. [10] Lin W, Fan L, Gan CM, et al. Study on measurement of dispersive characteristics of higher order mode Lamb waves. Ultrasonics 2006;44:e911–5.
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Technical Note
An oscillator using high order Lamb wave modes Wei Lin a,*, Li Fan b, Chang-ming Gan b, Zhe-min Zhu b, Xiang-bang Wang c a
Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Institute of Acoustics, Key Laboratory of Modern Acoustics, Nanjing University, Nanjing 210093, China c China Electronics Technology Group Corporation, No. 55 Research Institute, Nanjing, 210016, China b
a r t i c l e
i n f o
Article history: Received 23 May 2008 Received in revised form 25 June 2009 Accepted 29 June 2009 Available online 26 July 2009 Keywords: High order mode Lamb wave Oscillator Interdigital transducer
a b s t r a c t An oscillator using high order Lamb wave modes is presented. Due to the multimode property of Lamb waves, high frequency oscillators using high order mode Lamb waves can be fabricated. To select the operating mode of the Lamb wave oscillator, a high order mode selector is inserted into the feedback loop. An oscillator using the 13th antisymmetric mode (a13) in Lamb wave is achieved in experiments and the oscillating frequency is 5.30 times higher than that of the a0 mode excited by the interdigital transducer. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In recent years there has been a growing interest in using Rayleigh wave devices to fabricate sensors applied to physical, chemical and biological fields [1–4]. Because the sensitivities of the sensors are dependent on the shift of the oscillating frequencies induced by the measured quantities, the sensitivities of the sensors increase with the operating frequencies. Therefore, many researches focused on the increase of the operation frequencies of the sensors, however, the fundamental frequencies of the sensors cannot increase limitlessly due to the technical limitation for fabricating interdigital transducers (IDTs). Several methods for increasing the operation frequencies were presented. Seidel et al. used a new structure of IDT to excite the 48th harmonics of Rayleigh wave, which greatly increased the operating frequency, while at the same time resulted in a large insertion loss about 80 dB [5]. Caliendo et al. used the Rayleigh wave excited in an AlN/Si composite film deposited on a sapphire, in which the wave velocity increases from 2680 m/s in ZnO to 5607 m/s, and consequently improved the operation frequency although the periodicity of the IDT was not changed [6]. On the other hand, the sensors using different acoustic waves have also attracted great attention, in which an important work was the researches of Lamb wave sensors [7,8]. The operating principles of Lamb wave sensors are similar to those of Rayleigh wave sensors, but the sensitivities of the Lamb wave sensors is much
* Corresponding author. Tel./fax: +86 25 83593960. E-mail address: [email protected] (W. Lin). 0003-682X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2009.06.004
higher and the response time is faster than those of the Rayleigh wave sensors if both kinds of sensors have the same frequency [9]. Similarly the increase of operation frequencies can improve the sensitivities of Lamb wave sensors, thus the Lamb wave oscillators with high order modes can be used for obtaining high sensitivities. In this paper, a method to set up a closed loop oscillation by selecting high order Lamb modes is presented, with which one can obtain a higher phase velocity and a higher oscillating frequency, and then the sensitivity is greatly improved. 2. Characterization of high order mode of Lamb wave Fig. 1 shows the theoretical dispersive curves of the Lamb waves excited by IDTs with the periodicity of 0.425 mm in a 127.86° rotated Y-cut, X propagating lithium niobate plate with the thickness 0.4 mm, in which c is phase velocity and fd is the product of the frequency f and thickness d. In the figure, for simplicity, only two high order modes, a13 and a14, are displayed in addition to the a0 and s0 modes. Then, from the dispersive curves of Fig. 1, the relations between the wavelength (k) and frequency (f) can be obtained, which are shown in Fig. 2. Making a line paralleled with the transverse axis via some point k0 on the vertical axis, one can obtain a series of crossing points on the k–f curves in Fig. 2. On the crossing points, the wavelengths of various modes are the same, but the resonance frequencies and phase velocities are different. Therefore, the oscillations in these frequencies can be obtained by a Lamb wave delay line with the wavelength k0 of the IDTs if the amplitude and phase conditions of the oscillations are satisfied at the same time.
W. Lin et al. / Applied Acoustics 70 (2009) 1446–1448
Fig. 1. The theoretical dispersive curve of the Lamb wave excited by an IDT in a 127.86° rotated Y-cut, X propagating lithium niobate plate.
1447
Fig. 3. Insertion loss versus frequency for the Lamb wave delay line fabricated on a 127.86° rotated Y-cut, X propagating lithium niobate plate.
Therefore, for designing the Lamb wave oscillators with different modes, the actual propagation characteristics, such as the phase velocity, insert loss, frequency gap of adjacent modes and phase–frequency response must be considered, especially the phase–frequency response must be monotonic and linear. Based on these factors, the a13 mode is selected as the operation mode in this work, the resonant frequency of which is about 46.24 MHz and the insert loss is about 32 dB. 3. High order Lamb mode oscillator 3.1. Experimental system
Fig. 2. Frequency versus wavelength for different modes of Lamb wave.
The propagation characteristics of the high order Lamb waves excited by IDTs are influenced by the diffraction and reflection between the fingers of IDTs, the reflection of the substrate boundaries, and so on. Therefore the actual dispersive curves are different from the theoretical curves. The propagation characteristics of different modes of the Lamb wave are measured by a frequency domain method [10], by which the amplitude–frequency responses and the phase–frequency responses of the Lamb waves can be obtained. From the measurements, the phase velocities and resonant frequencies of various modes of the Lamb wave are listed in Table 1 and the insertion loss of the Lamb delay line obtained using Agilent8508A Vector voltmeter is shown in Fig. 3.
Fig. 4 shows the block diagram of a high order Lamb mode oscillator, which is composed of the Lamb wave delay line, the lownoise pre-amplifier, the high order mode selector, the large dynamic range amplifier and the direction coupler. In the system, there are two key devises, the Lamb wave delay line and the high order mode selector. As the main and stable unit of the oscillator, the Lamb wave delay line must satisfy the requests as follows: (a) Delay time: For the oscillator, the frequency stability (Q) can be expressed by the equations:
Q ¼p
s T
where s ¼ l=cp is the delay time of the delay line, l is the distance between the input and output IDTs, cp is the phase velocity of the Lamb wave at the operating frequency and T is the periodicity of the IDTs. Therefore, the delay time must be much longer than the periodicity of the IDTs in order to increase the frequency stability of the oscillator.
Table 1 The characteristics of various modes of Lamb wave. Mode
Resonant frequency (MHz)
Phase velocity (m/s)
a0 s0 a13 s14
8.75 9.80 46.24 49.80
3719 4165 19,652 21,165
ð1Þ
Fig. 4. The block diagram of high order Lamb mode oscillator.
1448
W. Lin et al. / Applied Acoustics 70 (2009) 1446–1448
Therefore, the insert loss of the selector must be as low as possible. 3.2. Experimental results Fig. 5 shows the fundamental oscillation spectrum of the oscillator obtained using a spectrum analyzer. The center frequency is about 46.5 MHz, no other modes can be observed in the frequency range below 100 MHz. Therefore, the oscillation frequency is determined by the Lamb wave delay line of a13 mode. By a frequency meter, the oscillation frequency is measured to be 46.48 MHz, whereas the oscillation frequency of the oscillator using the a0 mode of the Lamb wave excited by the same IDT is about 8.75 MHz. Thus, the operation frequency, i.e., the phase velocity, of the high order Lamb mode oscillator is 5.3 times higher than that of the a0 mode. Fig. 5. The oscillation spectrum of the high order Lamb mode oscillator with the center frequency 46.48 MHz (each lattice is 20 kHz in X-axis and 10 dB in Y-axis).
(b) Bandwidth: In order to avoid the multimode oscillation, the bandwidth of the delay line (Df) must satisfy the equation:
Df
1
s
ð2Þ
As one of the key devices, the high order mode selector is a special designed band pass filter constructed by a Rayleigh wave delay line, and the selector must satisfy a series of restricted conditions and requests as follows: (a) Delay time: The delay time of the selector must be much less than that of the Lamb wave delay line in order that the frequency stability of the oscillator is only determined by the Lamb wave delay line. (b) Bandwidth: Since the frequency range of the oscillator must be only determined by the bandwidth of operating mode, such as a13, of the Lamb wave, the bandwidth of the selector must be wider than that of the operating mode. But the pass band of the selector cannot cover the frequencies of other modes, such as the adjacent mode a14, in order to meet the request of the mode selection. (c) Insert loss: The insert loss of the selector increases the loss and reduces the signal to noise ratio of the oscillation circuit, thus reduces the frequency stability of the oscillator.
4. Conclusions The propagation characteristics of the high order modes of Lamb waves are studied. Based on the research, a new Lamb wave oscillator using the high order mode is fabricated, in which the phase velocity of a13 Lamb mode oscillator is 5.3 times higher than that of the a0 mode. Therefore the high frequency oscillator with operating frequency above UHF band can be fabricated more easily by this method, then the sensitivities of the sensors using the new oscillator can be increased greatly. References [1] Wohltjen H. Surface acoustic wave microsensors. In:Proceedings of the international conference on solid-state sensor and actuators; 1987. p. 471–7. [2] Caliendo C, Imperatori P. High-frequency, high-sensitivity acoustic sensor implemented on ALN/Si substrate. Appl Phys Lett 2003;83:1641. [3] Bjurström J, Yantchev V, Katardjiev I. Thin film Lamb wave resonant structure – the first approach. Solid-State Electron 2006:322–6. [4] Duhamel R, Robert L, Hongguang Jia CM, et al. Sensitivity of a Lamb wave sensor with 2 lm AlN membrane. Ultrasonics 2006;44:e893–7. [5] Seidel W, Hesjeda T. Multimode and multifrequency gigahertz surface acoustic wave sensors. Appl Phys Lett 2004;84:1407. [6] Wenzel SW, White RM. A multisensor employing ultrasonic Lamb-wave oscillator. IEEE Trans Electron Dev 1988;35:735–43. [7] Costello BJ, Martin BA, White RM. Ultrasonic plate wave for biochemical measurements. In: Proceedings of IEEE ultrasonic symposiums; 1989. p. 977– 81. [8] Joshi SG, Jin Y. Excitation of ultrasonic Lamb waves in piezoelectric plates. J Appl Phys 1991;69:8018–24. [9] Victorov A. Raleigh and Lamb wave. New York: Plenum; 1967. [10] Lin W, Fan L, Gan CM, et al. Study on measurement of dispersive characteristics of higher order mode Lamb waves. Ultrasonics 2006;44:e911–5.