声表面波器件的快速精确模拟研究
摘要
随着现代通信产业的飞速发展,声表面波(SAW)器件作为移动通信系统的核心部件已经得到了广泛的应用。在激烈的市场竞争中,人们对高频率、高性能、低损耗SAW器件的需求日益迫切,因此迫切需要发展快速、精确的理论模拟模型。有限长FEM/BEM(有限元／边界元法)是模拟SAW器件最精确的理论模型,但由于计算时间太长,无法在器件结构的优化设计中得到实际应用。耦合模式(COM)模型和P矩阵模型因其模拟速度很快,已经广泛应用于低损耗SAW滤波器的设计中。这两种模型都是唯象模型,所用参量的数值必须由精确理论或实验来确定,参量的准确度决定了分析SAW器件的精确程度,因此,直到现在人们还在不断努力得到更为准确的COM参量。
传统的COM参量被视作是与频率无关的常数,在模拟瑞利波器件时没有明显的误差。然而,对于36°～42°YX-LiTa03基片上的漏波,在通带上边缘附近及更高的频率范围,因其不断向体内辐射体声波而导致色散很强,因此使用传统的COM参量会带来相当大的误差。近年来,许多研究人员致力于对COM模型进行改进。Plessky提出了二参量模型,表征了表面横波(STW)的色散关系；在此基础上,Abbott和Hashimoto把Plessky模型写成COM方程的形式,建立了STW-COM模型,并提取了分析STW器件所需要的参量。Plessky、Abbott和Hashimoto的工作使LiTaO3基片上漏波器件的模拟有了很大的改进,但由于漏波毕竟不是纯切变波,且他们提取参量的方法是通过无限周期栅格下的精确理论模拟,因此预期与实验结果依然存在一定的差异。为了获得更进一步的改进结果,近十年人们又致力于研究色散的COM参量。按照他们提取色散COM参量的理论方法,四个COM参量中只能独立得到三个参量的色散关系,问题的关键在于无法独立获得色散的反射系数和中心频率(或传播速度)。他们的努力尽管获得了明显的改进,但结果仍然有待提高。
本文基于有限长FEM/BEM,提出两种新方法来实现SAW器件的快速、精确模拟。
其一是使用经典的COM方程,将所有COM参量都作为频率的函数来提取。用有限长FEM/BEM计算每一个频率下有限长周期栅格内部左、右向SAW场分布(包括位移和电势分布),利用源再生理论将入射SAW贡献的场分布从总的场分布中分离出来,获得足够精确的场分布信息。选取有限长周期栅格的中间部分作为无限周期栅格中的一部分进行研究,能够很好地满足COM模型的周期性前提假设。利用每一个频率下SAW场分布的特征量,可以拟合出该频率下所有的COM参量,特别是能够分别独立地提取出反射系数和中心频率(或传播速度)的色散关系。用得到的色散COM参量对128°YX-LiNbO3基片上的同步单端对谐振器进行了模拟,得到的导纳曲线与直接使用有限长FEM/BEM计算的结果吻合良好。
其二是使用STW-COM方程的形式来表示栅格下STW的色散行为,精确提取作为常数的STW-COM参量。用有限长FEM/BEM计算SAW同步单端对谐振器的导纳曲线,找出导纳曲线的特征量,通过它们与STW-COM参量之间的关系提取出全部STW-COM参量。最后,利用所得到的参量对42°YX-LiTaO3基片上的一种基于五换能器多模结构的单端输入平衡输出滤波器进行了模拟,与直接使用有限长FEM/BEM模拟的结果比较,符合得相当好,验证了该方法的良好效果,说明该方法有很好的实际应用价值。
本文基于有限长FEM/BEM精确提取色散COM参量或STW-COM参量也许非常耗时,但是一旦所需要的COM参量已经提取出来,其模拟过程是非常迅速的。因此,本文的方法能够实现对SAW器件的快速、精确模拟,并可以应用于射频低损耗SAW滤波器的优化设计中。
With the rapid development of modern communication industry, surface acoustic wave (SAW) devices have been widely applied as the core components of mobile communication systems. With increased competition in the market, the requirement of high-performance, low-loss SAW devices with higher operating frequency is becoming increasingly expected by consumers. As a result, it is of some urgency to develop rapid and precise simulation models. The finite FEM/BEM (finite element method/boundary element method) is a precise theoretical tool for the simulation of SAW devices, but it requires too long calculation time so that it is not suitable to practical devices structure optimization. The coupling-of-modes (COM) model and P-matrix model have been used in the design of low-loss SAW filters because of their high simulation speed. Both models are phenomenological, and the values of the parameters must be determined by other approaches, either precise theoretical ones or experimental ones. The precision of analyzing SAW devices depends on the accuracy of the parameters, thus people tried to get more accurate COM parameters.
Traditional COM parameters are considered as frequency independent constants, and the error is not significant when Rayleigh wave devices are simulated. However, the practical dispersion of leaky SAW on36°～42°YX-LiTaO3is strong close to the higher edge of the passband and higher frequency range because of strong bulk wave interaction. Therefore, using traditional COM parameters will introduce considerable error. Much research has been devoted to improve COM model in the past years. Plessky suggested a two-parameter model for the surface transverse wave (STW) dispersion relation. Abbott and Hashimoto developed a new COM formalism based on Plessky's model, which had been called the STW-COM model and extracted the parameters for the analysis of STW devices. The works by Plessky, Abbott and Hashimoto had greatly improved the simulation of leaky SAW devices on the substrate of LiTaO3. However, because of the leaky SAW is not pure SH-type SAW in fact, and their methods used to extract parameters are based on the precise theoretical simulation of infinite periodic gratings, there are still some discrepancies between the experimental results and expectations. In order to have further improvements, the dispersive COM parameters have been studied during the last decade. According to their theoretical methods used to extract the dispersive COM parameters, only three of four COM parameters were independently obtainable. The critical issue is that the dispersive reflection coefficient and central frequency (or propagation velocity) cannot be obtained independently. Although there have been some obvious advancements through their efforts, the results are still to be improved.
In this thesis, two kinds of new approach are proposed to realize the rapid and precise simulation of SAW devices based on utilization of the finite FEM/BEM.
One is to extract all the COM parameters as functions of frequency while using the classic COM equations. The field distributions (including mechanical displacement and electric potential distributions) of forward and backward SAW within a periodic grating of finite length are calculated by finite FEM/BEM at each frequency. Then, the source regeneration method is used to separate the SAW field contributed by incident wave from the total field, so that the information of field distributions of enough accuracy is obtained. The cells in the middle part of the periodic grating of finite length regarded as within an infinite periodic structure are investigated, which could well satisfy the periodicity presupposition of the COM model. From the characteristics of SAW field distributions at each frequency, all the COM parameters are able to be evaluated at the corresponding frequency. In particular, the dispersion of reflection coefficient and central frequency (or propagation velocity) can be extracted independently, respectively. As an example, a synchronous one-port resonator on the substrate of128°YX-LiNbO3is simulated by using the resultant dispersive COM parameters, and the admittance curve shows good agreement with the result directly computed by using finite FEM/BEM.
Another one is to use the STW-COM formalism, which characterizes the dispersive behaviors of STW under the gratings by some exact constant STW-COM parameters. The admittance curve of a synchronous one-port SAW resonator is calculated using finite FEM/BEM, from which the characteristic quantities are found out, and then the relationships between them and the STW-COM parameters are utilized to extract all the STW-COM parameters. Finally, using the obtained parameters, a single ended-balanced (Se-Bal) filter based on a5-IDT multi-mode structure on the substrate of42°YX-LiTaO3is simulated, and the responses are in good agreement with the results directly calculated by finite FEM/BEM. The results validate this method is effective, which indicates it is of great value in practical applications.
The computation for getting rigorous dispersive COM parameters or STW-COM parameters based on finite FEM/BEM may be time-consumed using the approaches in the thesis, but once all the needed COM parameters have been extracted, the simulating process is very rapid. Therefore, it will be able to realize the rapid and precise simulation of SAW devices using the methods in this thesis, which is available to the optimal design of low-loss RF SAW filters.
传统的COM参量被视作是与频率无关的常数,在模拟瑞利波器件时没有明显的误差。然而,对于36°～42°YX-LiTa03基片上的漏波,在通带上边缘附近及更高的频率范围,因其不断向体内辐射体声波而导致色散很强,因此使用传统的COM参量会带来相当大的误差。近年来,许多研究人员致力于对COM模型进行改进。Plessky提出了二参量模型,表征了表面横波(STW)的色散关系；在此基础上,Abbott和Hashimoto把Plessky模型写成COM方程的形式,建立了STW-COM模型,并提取了分析STW器件所需要的参量。Plessky、Abbott和Hashimoto的工作使LiTaO3基片上漏波器件的模拟有了很大的改进,但由于漏波毕竟不是纯切变波,且他们提取参量的方法是通过无限周期栅格下的精确理论模拟,因此预期与实验结果依然存在一定的差异。为了获得更进一步的改进结果,近十年人们又致力于研究色散的COM参量。按照他们提取色散COM参量的理论方法,四个COM参量中只能独立得到三个参量的色散关系,问题的关键在于无法独立获得色散的反射系数和中心频率(或传播速度)。他们的努力尽管获得了明显的改进,但结果仍然有待提高。
本文基于有限长FEM/BEM,提出两种新方法来实现SAW器件的快速、精确模拟。
其一是使用经典的COM方程,将所有COM参量都作为频率的函数来提取。用有限长FEM/BEM计算每一个频率下有限长周期栅格内部左、右向SAW场分布(包括位移和电势分布),利用源再生理论将入射SAW贡献的场分布从总的场分布中分离出来,获得足够精确的场分布信息。选取有限长周期栅格的中间部分作为无限周期栅格中的一部分进行研究,能够很好地满足COM模型的周期性前提假设。利用每一个频率下SAW场分布的特征量,可以拟合出该频率下所有的COM参量,特别是能够分别独立地提取出反射系数和中心频率(或传播速度)的色散关系。用得到的色散COM参量对128°YX-LiNbO3基片上的同步单端对谐振器进行了模拟,得到的导纳曲线与直接使用有限长FEM/BEM计算的结果吻合良好。
其二是使用STW-COM方程的形式来表示栅格下STW的色散行为,精确提取作为常数的STW-COM参量。用有限长FEM/BEM计算SAW同步单端对谐振器的导纳曲线,找出导纳曲线的特征量,通过它们与STW-COM参量之间的关系提取出全部STW-COM参量。最后,利用所得到的参量对42°YX-LiTaO3基片上的一种基于五换能器多模结构的单端输入平衡输出滤波器进行了模拟,与直接使用有限长FEM/BEM模拟的结果比较,符合得相当好,验证了该方法的良好效果,说明该方法有很好的实际应用价值。
本文基于有限长FEM/BEM精确提取色散COM参量或STW-COM参量也许非常耗时,但是一旦所需要的COM参量已经提取出来,其模拟过程是非常迅速的。因此,本文的方法能够实现对SAW器件的快速、精确模拟,并可以应用于射频低损耗SAW滤波器的优化设计中。
With the rapid development of modern communication industry, surface acoustic wave (SAW) devices have been widely applied as the core components of mobile communication systems. With increased competition in the market, the requirement of high-performance, low-loss SAW devices with higher operating frequency is becoming increasingly expected by consumers. As a result, it is of some urgency to develop rapid and precise simulation models. The finite FEM/BEM (finite element method/boundary element method) is a precise theoretical tool for the simulation of SAW devices, but it requires too long calculation time so that it is not suitable to practical devices structure optimization. The coupling-of-modes (COM) model and P-matrix model have been used in the design of low-loss SAW filters because of their high simulation speed. Both models are phenomenological, and the values of the parameters must be determined by other approaches, either precise theoretical ones or experimental ones. The precision of analyzing SAW devices depends on the accuracy of the parameters, thus people tried to get more accurate COM parameters.
Traditional COM parameters are considered as frequency independent constants, and the error is not significant when Rayleigh wave devices are simulated. However, the practical dispersion of leaky SAW on36°～42°YX-LiTaO3is strong close to the higher edge of the passband and higher frequency range because of strong bulk wave interaction. Therefore, using traditional COM parameters will introduce considerable error. Much research has been devoted to improve COM model in the past years. Plessky suggested a two-parameter model for the surface transverse wave (STW) dispersion relation. Abbott and Hashimoto developed a new COM formalism based on Plessky's model, which had been called the STW-COM model and extracted the parameters for the analysis of STW devices. The works by Plessky, Abbott and Hashimoto had greatly improved the simulation of leaky SAW devices on the substrate of LiTaO3. However, because of the leaky SAW is not pure SH-type SAW in fact, and their methods used to extract parameters are based on the precise theoretical simulation of infinite periodic gratings, there are still some discrepancies between the experimental results and expectations. In order to have further improvements, the dispersive COM parameters have been studied during the last decade. According to their theoretical methods used to extract the dispersive COM parameters, only three of four COM parameters were independently obtainable. The critical issue is that the dispersive reflection coefficient and central frequency (or propagation velocity) cannot be obtained independently. Although there have been some obvious advancements through their efforts, the results are still to be improved.
In this thesis, two kinds of new approach are proposed to realize the rapid and precise simulation of SAW devices based on utilization of the finite FEM/BEM.
One is to extract all the COM parameters as functions of frequency while using the classic COM equations. The field distributions (including mechanical displacement and electric potential distributions) of forward and backward SAW within a periodic grating of finite length are calculated by finite FEM/BEM at each frequency. Then, the source regeneration method is used to separate the SAW field contributed by incident wave from the total field, so that the information of field distributions of enough accuracy is obtained. The cells in the middle part of the periodic grating of finite length regarded as within an infinite periodic structure are investigated, which could well satisfy the periodicity presupposition of the COM model. From the characteristics of SAW field distributions at each frequency, all the COM parameters are able to be evaluated at the corresponding frequency. In particular, the dispersion of reflection coefficient and central frequency (or propagation velocity) can be extracted independently, respectively. As an example, a synchronous one-port resonator on the substrate of128°YX-LiNbO3is simulated by using the resultant dispersive COM parameters, and the admittance curve shows good agreement with the result directly computed by using finite FEM/BEM.
Another one is to use the STW-COM formalism, which characterizes the dispersive behaviors of STW under the gratings by some exact constant STW-COM parameters. The admittance curve of a synchronous one-port SAW resonator is calculated using finite FEM/BEM, from which the characteristic quantities are found out, and then the relationships between them and the STW-COM parameters are utilized to extract all the STW-COM parameters. Finally, using the obtained parameters, a single ended-balanced (Se-Bal) filter based on a5-IDT multi-mode structure on the substrate of42°YX-LiTaO3is simulated, and the responses are in good agreement with the results directly calculated by finite FEM/BEM. The results validate this method is effective, which indicates it is of great value in practical applications.
The computation for getting rigorous dispersive COM parameters or STW-COM parameters based on finite FEM/BEM may be time-consumed using the approaches in the thesis, but once all the needed COM parameters have been extracted, the simulating process is very rapid. Therefore, it will be able to realize the rapid and precise simulation of SAW devices using the methods in this thesis, which is available to the optimal design of low-loss RF SAW filters.
引文
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