## 1 Introduction  
Surface acoustic wave (SAW) devices have expanded into diverse application fields such as filters, sensors and radio frequency identification (RFID) tags [1; 2; 3; 4]. Accurate and efficient simulation methods are crucial for designing high-performance SAW devices. Several methods have been proposed for modeling and analyzing the characteristics of SAW devices [5; 6; 7; 8], including the earlier \(\delta\)-function models, equivalent circuit models and the later coupling-of-modes (COM) equations, finite element method/boundary element method (FEM/BEM), etc. However, the first two methods cannot take into account the interdigital transducer (IDT)'s internal reflections. Though the FEM/BEM model is considered to be the most accurate simulation method, it is time-consuming [7]. Therefore, the COM method is widely used for analyzing and designing SAW devices for the reason that it is extremely fast and holds enough accuracy. Regardless of the accuracy of the model itself, the accuracy of this method entirely depends on the accuracy of the COM parameters (SAW velocity \(v\), reflectivity \(\kappa\), transduction coefficient \(\alpha\), static capacitance C and propagation attenuation \(\gamma\)). Thus, obtaining accurate COM parameters is crucial for designing SAW devices. To obtain these key parameters, perturbation theory [9] and measurement harmonic admittance [10] have been proposed, but they are either costly or lack of accuracy. FEM-based methods FEM/spectral domain analysis (FEM/SDA) [11] and FEM/BEM [12] have also been employed in COM parameters extraction, but they are invalid for the multilayer structures. Recently, the pure FEMs, especially in combination with the existing commercial software such as ANSYS and COMSOL Multiphysics, have been attractively studied to extract these parameters [13; 14; 15]. They can conquer the problems mentioned above and several methods have been proposed, which can be divided into two branches:one is by calculating the dispersion characteristics [16,17]. The SAW velocity at different frequencies (dispersive curves) is calculated, which is realized by applying the Floquet boundary conditions, under short-circuit (SC) and open-circuit (OC) conditions. Then, SAW velocity \(\
u\), reflectivity \(\kappa\), transduction coefficient \(\alpha\) and static capacitance \(C\) are obtained by finding the stopband edges and fitting the dispersive curves, respectively. Such methods are sophisticated and time-consuming for the reason that velocity at each frequency must be calculated. The other is by calculating the Harmonic Admittance (HA) [18]. The COM parameters are obtained from the HA in the same way as the former. The harmonic analysis is time-consuming because the computation time is proportional to the number of frequency points. Moreover, the accuracy totally depends on the step length of frequency, which makes the extracted parameters not exactly accuracy.  
Thus, in this paper, we propose a simple and fast method, performed by COMSOL Multiphysics, to extract accurate COM parameters of SAW devices. It is based on the FEM and combines the stationary analysis with modal analysis. Firstly, we describe in detail the basic principles and procedures of the proposed method. Then, we make a comprehensive comparison between the proposed method and the other two existing methods which are both based on the harmonic analysis. Finally, we examine the proposed method by extracting COM parameters of some common SAW substrates (ST quartz, ST-25\({}^{\circ}\)X quartz and Y-51.25\({}^{\circ}\)Z LiTaO\({}_{3}\)), and compare our extracted results with those reported in the other literatures.