Title : 
Doubly rotated resonators for sensing the properties of liquids
         
        
            Author : 
Kim, Yoonkee ; Vig, John R. ; Ballato, Arthur
         
        
            Author_Institution : 
Res. Dev. & Eng. Center, US Army Commun.-Electron., Fort Monmouth, NJ, USA
         
        
        
        
        
        
        
            Abstract : 
When a doubly rotated resonator is operated in a liquid, the displacement of the surface is partly out of the plane of the plate of the resonator. The out-of-plane component of the displacement propagates a damped compressional wave into the liquid, and the in-plane component propagates a damped shear wave. In this paper, we report the measurements of the series resonant frequency and the motional arm resistance of doubly rotated quartz resonators (/spl theta//spl ap/35/spl deg/ and /spl phi/=7/spl deg/) in liquids to compare with singly rotated AT-cut resonators (/spl theta//spl ap/35/spl deg/ and /spl phi/=0/spl deg/). A modified Butterworth-Van Dyke (BVD) equivalent circuit model is suggested to analyze doubly rotated cut resonators under liquid loading.
         
        
            Keywords : 
chemical sensors; crystal resonators; elastic waves; frequency measurement; AT-cut resonators; Butterworth-Van Dyke equivalent circuit model; damped compressional wave; damped shear wave; doubly rotated cut resonators; doubly rotated quartz resonators; liquid properties; motional arm resistance; resonant frequency; resonator plate; surface displacement; Coupling circuits; Equivalent circuits; Frequency measurement; Liquids; Resonant frequency; Rotation measurement; Rough surfaces; Surface acoustic waves; Surface roughness; Surface treatment;
         
        
        
            Journal_Title : 
Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on
         
        
        
        
        
            DOI : 
10.1109/TUFFC.2004.1367477