Surface acoustic wave resonator

Claim 2

A surface acoustic wave resonator of the type having a pair of surface acoustic wave reflectors which are spaced apart from each other by a suitable distance on a piezoelectric substrate and each of which comprises a grating electrode structure and a periodic array of grooves and a surface acoustic wave transducer which is interposed between the pair of surface acoustic wave reflectors and which comprises an interdigital electrode structure and a periodic array of grooves, characterized in that the electrode period L T of said surface acoustic wave transducer and the electrode period L R of said surface acoustic wave reflectors are so selected as to satisfy the following equation: ##EQU12## where C 1T : the acoustic mismatching term at the boundary between the electroded portion and the non-electroded portion of the surface acoustic wave transducer and is given by C.sub.1T =|1-Z.sub.2 /Z.sub.1 |/π where Z 2 : the acoustic impedance of the electroded portion, and Z 1 : the acoustic impedance of the non-electroded portion; C 2T : the relative frequency decrease due to the periodic structure of the surface acoustic wave transducer; C 2R : the relative frequency decrease due to the periodic structure of the surface acoustic wave reflector; and q T =πC 1T N where N: the number of electrode finger pairs in the surface acoustic wave transducer.

Claim 3

A surface acoustic wave resonator as set forth in claim 1 further characterized in that said piezoelectric substrate comprises an ST-cut quartz; the electrodes in said surface acoustic wave reflectors and transducer are made of aluminum; and C 2R , C 2T and C 1T are given by the following equations, respectively: C.sub.2R ≃4.33×10.sup.-4 +4.23×10.sup.-2 (h.sub.mR /L.sub.R)+7.9(h.sub.mR /L.sub.R).sup.2 +10.8(h.sub.gR /L.sub.R).sup.2 +18.5(h.sub.mR /L.sub.R)(h.sub.gR /L.sub.R) C.sub.2T ≃4.33×10.sup.-4 +4.23×10.sup.-2 (h.sub.mT /L.sub.T)+7.9(h.sub.mT /L.sub.T).sup.2 +10.8(h.sub.gT /L.sub.T).sup.2 +18.5(h.sub.mT /L.sub.T)(h.sub.gT /L.sub.T) C.sub.1T =6.25×10.sup.-4 +0.12(h.sub.mT /L.sub.T)+0.172(h.sub.gT /L.sub.T) where h mR : the thickness of the electrodes in the surface acoustic wave reflectors; h gR : the depth of the grooves in the surface acoustic wave reflectors; h mT : the thickness of the electrodes in the surface acoustic wave transducer; and h gT : the depth of the grooves in the surface acoustic wave transducer.

Claim 4

A surface acoustic wave resonator as set forth in claim 2 further characterized in that both or either of the depth h gR of the surface acoustic wave reflector grooves and/or the depth h gT of the surface acoustic wave transducer grooves are/is zero.

Claim 5

A surface acoustic wave resonator as set forth in claim 1, 2 or 3 further characterized in that the spacing l 1 between said surface acoustic wave transducer and one of said two surface acoustic wave reflectors and the spacing l 2 between said surface acoustic wave transducer and the other surface acoustic wave reflector are determined by the following equation: ##EQU13## where n i : a positive integer; and i=1 and 2.

Claim 6

A two-port surface acoustic wave resonator of the type having a pair of surface acoustic wave reflectors which are spaced apart from each other by a suitable distance on a piezoelectric substrate and each of which comprises a grating electrode structure and a periodic array of grooves and two surface acoustic wave transducers which are interposed between said two surface acoustic wave reflectors and each of which comprises an interdigital electrode structure and a periodic array of grooves, characterized in that the electrode periodic L T of the surface acoustic wave transducers and the electrode period L R of the surface acoustic wave reflectors are so selected as to satisfy the following equation: ##EQU14## where C 1T : the acoustic mismatching term at the boundary between the electroded portion and the non-electroded portion of the surface acoustic wave transducer and is given by C.sub.1T =|1-Z.sub.2 /Z.sub.1 |/π where Z 2 : the acoustic impedance of the electroded portion, and Z 1 : the acoustic impedance of the non-electroded portion; C 2T : the relative frequency decrease due to the periodic structure of the surface acoustic wave transducer; C 2R : the relative frequency decrease due to the periodic structure of the surface acoustic wave reflector; and q T =πC 1T N where N: the number of electrode finger pairs in each of the surface acoustic wave transducers.

Claim 7

A two-port surface acoustic wave resonator of the type having a pair of surface acoustic wave reflectors which are spaced apart from each other by a suitable distance on a piezoelectric substrate and each of which comprises a grating electrode structure and a periodic array of grooves and two surface acoustic wave transducers which are interposed between said two surface acoustic wave reflectors and each of which comprises an interdigital electrode structure and a periodic array of grooves, characterized in that the electrode periodic L T of the surface acoustic wave transducers and the electrode period L R of the surface acoustic wave reflectors are so selected as to satisfy the following equation: ##EQU14## where C 1T : the acoustic mismatching term at the boundary between the electroded portion and the non-electroded portion of the surface acoustic wave transducer and is given by C.sub.1T =|1-Z.sub.2 /Z.sub.1 |/π where Z 2 : the acoustic impedance of the electroded portion, and Z 1 : the acoustic impedance of the non-electroded portion; C 2T : the relative frequency decrease due to the periodic structure of the surface acoustic wave transducer; C 2R : the relative frequency decrease due to the periodic structure of the surface acoustic wave reflector; and q T =πC 1T N where N: the number of electrode finger pairs in each of the surface acoustic wave transducers.

Claim 8

A two-port surface acoustic wave resonator as set forth in claim 5 further characterized in that said piezoelectric substrate comprises an ST-cut quartz; the electrodes in said surface acoustic wave reflectors and transducers are made of aluminum; and C 2R , C 2T and C 1T are given by the following relations, respectively: C.sub.2R ≃4.33×10.sup.-4 +4.23×10.sup.-2 (h.sub.mR /L.sub.R)+7.9(h.sub.mR /L.sub.R).sup.2 +10.8(h.sub.gR /L.sub.R).sup.2 +18.5(h.sub.mR /L.sub.R)(h.sub.gR /L.sub.R) C.sub.2T ≃4.33×10.sup.-4 +4.23×10.sup.-2 (h.sub.mT /L.sub.T)+7.9(h.sub.mT /L.sub.T).sup.2 +10.8(h.sub.gT /L.sub.T).sup.2 +18.5(h.sub.mT /L.sub.T)(h.sub.gT /L.sub.T) C.sub.1T =6.25×10.sup.-4 +0.12(h.sub.mT /L.sub.T)+0.172(h.sub.gT /L.sub.T) where h mR : the thickness of the electrodes in the surface acoustic wave reflectors; h gR : the depth of the grooves in the surface acoustic wave reflectors; h mT : the thickness of the electrodes in the surface acoustic wave transducers; and h gT : the depth of the grooves in the surface acoustic wave transducers.

Claim 9

A two-port surface acoustic wave resonator as set forth in claims 5 or 6 further characterized in that the spacing l 1 between one of the two surface acoustic wave reflectors and one of the two surface acoustic wave transducers, the spacing l 2 between the other surface acoustic wave reflector and the other surface acoustic wave transducer and the spacing l 3 between the two surface acoustic wave transducers are determined so as to satisfy the following relation: ##EQU15## where n: a positive integer.

Claim 10

A surface acoustic wave resonator characterized in that the electrode period L T of a surface acoustic wave transducer and the electrode period L R of a surface acoustic wave reflector or surface acoustic wave reflectors are so selected as to satisfy the following equation: ##EQU16## where C 1T : the acoustic mismatching term at the boundary between the electroded portion and the non-electroded portion of the surface acoustic wave transducer and is given by C.sub.1T =|1-Z.sub.2 /Z.sub.1 |/π where Z 2 : the acoustic impedance of the electroded portion, and Z 1 : the acoustic impedance of the non-electroded portion; C 2T : the relative frequency decrease due to the periodic structure of the surface acoustic wave transducer; C 2R : the relative frequency decrease due to the periodic structure of the surface acoustic wave reflector; and q T =πC 1T N where N: the number of electrode finger pairs in the surface acoustic wave transducer; a pair of terminals are attached substantially at the midpoints of the longer sides, respectively, of a piezoelectric substrate upon which said surface acoustic wave reflectors and transducer are formed and are electrically connected to said surface acoustic wave transducer; lead wires extended from a base are electrically joined to said pair of terminals, respectively, whereby said piezoelectric substrate is supported at two points by said lead wires; and said piezeoelectric substrate and said pair of lead wires are encapsulated in a case which in turn is sealed air-tightly with said base.

Claim 11

A surface acoustic wave resonator characterized in that the electrode period L T of a surface acoustic wave transducer and the electrode period L R of a surface acoustic wave reflector or surface acoustic wave reflectors are so selected as to satisfy the following equation: ##EQU16## where C 1T : the acoustic mismatching term at the boundary between the electroded portion and the non-electroded portion of the surface acoustic wave transducer and is given by C.sub.1T =|1-Z.sub.2 /Z.sub.1 |/π where Z 2 : the acoustic impedance of the electroded portion, and Z 1 : the acoustic impedance of the non-electroded portion; C 2T : the relative frequency decrease due to the periodic structure of the surface acoustic wave transducer; C 2R : the relative frequency decrease due to the periodic structure of the surface acoustic wave reflector; and q T =πC 1T N where N: the number of electrode finger pairs in the surface acoustic wave transducer; a pair of terminals are attached substantially at the midpoints of the longer sides, respectively, of a piezoelectric substrate upon which said surface acoustic wave reflectors and transducer are formed and are electrically connected to said surface acoustic wave transducer; lead wires extended from a base are electrically joined to said pair of terminals, respectively, whereby said piezoelectric substrate is supported at two points by said lead wires; and said piezeoelectric substrate and said pair of lead wires are encapsulated in a case which in turn is sealed air-tightly with said base.