Surface transverse wave asynchronous multimode resonator on quartz
grating, respectively, f is the frequency, and v is the STW velocity. It is assumed that v is the same in all areas of the resonator. Without the reflectors (G ¼ 0) the following expression for the transfer function A120 is obtained from (1):
W. Soluch A surface transverse wave asynchronous multimode resonator on quartz was designed, fabricated and measured. Grating phase shifters were placed between interdigital transducers and reflectors to obtain the incident and reflected waves in phase, and the centre frequency of the resonator was located near the centre frequency of the reflectors. At a frequency of about 509.6 MHz, insertion loss, and loaded and unloaded quality factors of about 6 dB, 9 000 and 18 000, respectively, were obtained.
Introduction: A surface transverse wave (STW) propagates in the area of periodical electrodes on Y rotated cuts in the direction perpendicular to the X-axis of quartz [1, 2]. Until now, STW resonators were designed in a synchronous configuration [3]. In this case, an interdigital transducer (IDT) is a part of a reflector, the resonance frequency is located near the low frequency edge of the reflection band of the reflector, and the spurious signal level below this frequency is high. Some improvement was achieved by using different numbers of electrodes in the reflectors [4]. It was also shown recently that the reflection coefficient and losses are approximately the same both below and above the centre frequency of the reflector [5]. Therefore, it was interesting to determine whether an asynchronous resonator could be designed with the resonance frequency located near the centre frequency of the reflector. The purpose of this Letter is to present results of calculations and measurements of such a resonator.
Resonator structure and transfer function: In a surface acoustic wave (SAW) asynchronous resonator, incident and reflected (forward and backward) waves are in phase if proper distance between the IDT centre and the reflector is chosen [6]. This can be done also in the case of STW by using a grating phase shifter. The structure of the STW symmetrical asynchronous resonator is shown in Fig. 1. To eliminate reflections from the gratings and the IDTs located between the reflectors, three different periods, p1, p2 and p3, of the reflector, the grating phase shifter and the centre grating, and the IDT, respectively, are used in the structure.
A120 ¼
tS 213 1 t 2 S 211
ð2Þ
This is the transfer function of a delay line without reflections from the periodical electrodes of the IDTs. The second term in the denominator represents the triple transit signal. The insertion losses IL and IL0 for the resonator and the delay line, respectively, can be calculated from the following expressions: IL ¼ 20 log jA12 j IL0 ¼ 20 log jA120 j
ð3Þ ð4Þ
Measurement and calculation results: The resonator was designed on the 36 YX90 cut quartz and the same data for the STW parameters were used as presented in [4]. For the aluminium layer thickness h ¼ 0.1 mm at a frequency of about 509 MHz (h=l ¼ 1%), the following data of the resonator were obtained: W ¼ 1 mm, p1 ¼ 5 mm, p2 ¼ 4.9 mm, p3 ¼ 4.98 mm, Nr ¼ 800, Np ¼ 45, Nt ¼ 121, Nc ¼ 770, where W is the aperture, p1, p2 and p3 are the periods of electrodes (Fig. 1), Nr, Np, Nt and Nc are the numbers of electrodes of the reflector, the phase shifter, the IDT and the centre grating, respectively. The resonators were fabricated by the lift-off method, mounted in metal packages, and measured in a 50 O system (Agilent Technologies network analyser type 8753ET). The measured insertion loss IL of the resonator is presented in Fig. 2a. It can be seen that there are three main longitudinal modes. The lowest IL ffi 7.4 dB at a frequency of about 509.6 MHz was obtained for the second longitudinal mode (marker 2). It was estimated that the internal loss of the measuring system was about 1.6 dB, and a net IL ffi 5.8 dB, QL ffi 9 000 and QU ffi 18 000 were obtained, where QL and QU are the loaded and unloaded quality factors, respectively. The two traps (markers 4 and 5), located symmetrically around the centre frequency of the reflector, are caused by a phase difference of 180 between the incident and reflected waves [6]. Then the centre frequency fc of the reflector can be determined from the expression: f c ffi ð f 5 þ f 4 Þ=2
ð5Þ
It can be seen that fc ffi f2 (Fig. 2a). To determine the STW parameters, the measured (Fig. 2a) and calculated (Fig. 2b) amplitude responses were matched. As a result of this matching, g ffi 4.26 103, v ffi 5097.4 m=s, K2 ffi 9 104 and Ti ffi 0.891 have been obtained (for h=l ¼ 0.01), and the following approximate expressions can be written: g ffi 42:6 ðh=lÞ2
ð6Þ
v ffi vS ½1 14:8 ðh=lÞ2 ; and
ð7Þ
K2 ffi 0:09 ðh=lÞ Fig. 1 Structure of STW asynchronous resonator
The transfer function A12 of a symmetrical resonator can be written as [4, 6]: A12 ¼
t½1 þ rðS 12 S 11 Þ2 S 213 ð1 rS 11 Þ2 t 2 ½S 11 þ rðS 212 S 211 Þ2
ð1Þ
where r ¼ G expð2jbd 1 Þ; t ¼ Ti expðjbd 2 Þ d 1 ¼ ðNp þ 1Þp2 þ ðNt 1Þp3 =2 p1 =4 d 2 ¼ ðNc þ 1Þp2 þ ðNt 1Þp3 ; and b ¼ 2pf =v Sij are the scattering coefficients of the IDT, G is the reflection coefficient of the reflector, Ti is the loss coefficient, d1 is the distance between the centre of the IDT and the edge of the reflector electrode, d2 is the distance between the centres of the IDTs, Np, Nt and Nc are the numbers of electrodes of the phase shifter, the IDT and the centre
ð8Þ
where vS ffi 5105 m=s is the surface skimming bulk wave velocity for the 36 YX90 cut quartz [7]. If we compare the above expressions with that obtained earlier [4], we see that g is about two times larger, and K2 is about two times smaller. This can be explained by a frequency dependence of these parameters. In the case of the synchronous resonator, both g and K2 were determined at the frequencies below the low frequency edge of the reflection band, while in the case of the asynchronous resonator, it was done near the centre frequency of this band. For equal electrode and gap widths, the measured and calculated K2 [8] are in good agreement.
Conclusions: The asynchronous STW resonator was designed by the scattering matrix method using grating phase shifters placed between the IDTs and the reflectors. In this resonator, compared to the synchronous one, the spurious signals’ level at the frequencies below the reflection band of the reflector is significantly reduced. For a properly designed and sufficiently long resonator, three resonance modes are present, and one of them is located near the centre frequency of the reflector. This mode exhibits the lowest insertion loss and the highest unloaded quality factor. The scattering matrix
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method and the experimentally determined STW parameters can be used for the design of low insertion loss and high quality factor asynchronous resonators on quartz.
Acknowledgment: This research work was financed by a state budget for science under Grant No. 3 T10C 013 28. # IEE 2005 Electronics Letters online no: 20051997 doi: 10.1049/el:20051997
1 June 2005
W. Soluch (Institute of Electronic Material Technology, 133 Wolczynska Str., 01-919 Warsaw, Poland) E-mail:
[email protected] References 1 2 3 4 5 6 7 8
Thompson, D.F., and Auld, B.A.: ‘Surface transverse wave propagation under metal strip gratings’. Proc. IEEE Ultrasonics Symp., Williamsburg, USA, 1986, pp. 261–266 Auld, B.A., and Thompson, D.F.: ‘Temperature compensation of surface transverse waves for oscillator applications’. Proc. IEEE Ultrasonics Symp., Denver, USA, 1987, pp. 305–312 Bagwell, T.L., and Bray, R.C.: ‘Novel surface transverse wave resonators with low loss and high Q’. Proc. IEEE Ultrasonics Symp., Denver, USA, 1987, pp. 319–324 Soluch, W.: ‘Scattering matrix approach to STW resonators’, IEEE Trans. Ultrason. Ferroelectr., Freq. Contr., 2002, 49, (3), pp. 327–330 Soluch, W.: ‘Scattering matrix approach to STW multimode resonators’, Electron. Lett., 2005, 41, (1), pp. 49–50 Soluch, W.: ‘Scattering analysis of two-port SAW resonators’, IEEE Trans. Ultrason. Ferroelectr., Freq. Contr., 2001, 48, (3), pp. 769–772 Soluch, W.: ‘STW filter with long interdigital transducers on quartz’, Electron. Lett., 2003, 39, (17), pp. 1292–1293 Strashilov, V.L., Djordjev, K.D., and Yantchev, V.M.: ‘The coupling-ofmodes approach to the analysis of STW devices: Part II’, IEEE Trans. Ultrason. Ferroelectr., Freq. Contr., 1999, 46, (6), pp. 1512–1517
Fig. 2 Measured and calculated amplitude responses of resonator a Measured b Calculated IL: insertion loss of resonator; RL: reflection loss of reflector; IL0: insertion loss of delay line (G ¼ 0)
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