This paper presents an analysis of an elastically coupled piezoelectric resonator system consisting of a linear array of two or more counter electrode pairs placed on the major surfaces of a quartz crystal plate. Each pair of counter electrodes establishes resonator having a transverse thickness mode of motion. The equations describing this system are derived and applied to an array of n coupled resonators and specific numerical computations are made for the cases where n is equal to 2, 3, and 6. These results are plotted and show the dependence of the effective interresonator coupling on the dimensions of the electrode configuration.

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e r m i t s a n i m p r o v e d c h a r a c t e r i s t i c r e s i s t a n c e o v e r t h e t r a n s m i s s i o n b a n d .No a d d i t i o n a l compon e n t s a r e r e q u i r e d t o p r o v i d e e s s e n t i a l l y f l a t t r a n s m i s s i o n bands From a u s e r ' s p o i n t o f v i e w , the p e r f o r m a n c e c h a r a c t e r i st i c s o f m o n o l i t h i c c r y s t a l f i l t e r s a r e v e r y s i m p l y s t a t e d i n t h e form ' B -' A ---2 x Ro; t h a t i s , t h e f r a c t i o n a l b a n d w i d t h i n ' m Hz/MHz i s a d i r e c t m u l t i p l e o f t h e t e r m i n a t i o n ' r e s i s t a n c e . A s p e c i f i c c a s e i s shown where a s i n g l e c r y s t a l p l a t e may be used t o form a m o n o l i t h i c f i l t e r t h a t may b e t e r m i n a t e d i n 100-ohm c i r c u i t s w i t h a r e s u l t i n g b a n d w i d t h o f .005$ o f t h e 'mean ' f r equency. T h i s m a y ' b e u s e d f o r a s i n g l e f r e q u e n c y s e l e c t o r s u c h a s c a r r i e r and p i l o t f i l t e r s i n t h e -r a n g e f r o m 6 t o 25 MHz o v e r n o r m a l c e n t r a l o f f i c e t e m p e r a t u r e r a n g e s . B a n d w i d t h s a s h i g h a s -07% may e a s i l y be r e a l i z e d w h i c h c a n a l l o w t h e u s e of s i n g l e s i d e band channel f i l t e r s a t c a r r i e r f r e q u e n c i e s a s low a s 6 MHz. Some e x a m p l e s o f t r a n s m i s s i o n c h a r a c t e r i s t i c s f o r m o n o l i t h i c c r y s t a l f i l t e r s a r e shown for narrow band and wide band cases a t a p p r o x i m a t e l y 10 MHz. O t h e r c o n v e n t i o n a l c r y s t a l f i l t e r s may be r e a l i z e d by t h e a d d i t i o n o f i n d u c t o r s a n d / o r c a p a c i t o r s w i t h i n t h e limits t h a t t h e e q u i v a l e n t l a t t i c e o f c r y s t a l u n i t s i m p o s e s . F i n a l l y , i t i s shown t h a t t h e g e n e r a l c a s e , f o r m o n o l i t h i c f i l t e r s o f t h i s t y p e , may b e c o n s i d e r e d a s a m e c h a n i c a l f i l t e r formed by e i a s t i c a l l y c o u p l e d r e s o n a t o r s and may be d e a l t w i t h b y c o n v e n t i o n a l t r a n s m i s s i o n m e t h o d s .200

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