Cut angles for tuning fork type quartz resonators

Claim 2

A piezoelectric resonator of the tuning fork type having two tines, said resonator comprising a quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal by means of first rotation through an angle φ about the axis Y, and a second rotation through an angle θ about the axis Z', said resonator vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the tines of the tuning fork being parallel to the axis X' of the quartz plate and the angles of cut φ and θ being such that: 50°<φ<70° and 40°<θ<65°.

Claim 3

The resonator of claim 1, wherein said angles of cut φ and θ are: φ=59° and θ=49°.

Claim 4

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal by means of a first rotation through an angle φ about the axis Y, and a second rotation through an angle θ about the axis Z', said resonator vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the geometrical dimensions of the resonator being selected so that the fundamental torsional mode is coupled to a flexural vibration mode, whereby the second-order temperature coefficient is substantially zero, the tines of the tuning fork being parallel to the axis X' of the quartz plate and the angles of cut φ and θ being such that: 50°<φ<70 ° and 40°<θ<65°.

Claim 5

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal by means of a first rotation through an angle φ about the axis Y, and a second rotation through an angle θ about the axis Z', said resonator vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the geometrical dimensions of the resonator being selected so that the fundamental torsional mode is coupled to a flexural vibration mode, whereby the second-order temperature coefficient is substantially zero, the tines of the tuning fork being parallel to the axis X' of the quartz plate and the angles of cut φ and θ being such that: 50°<φ<70 ° and 40°<θ<65°.

Claim 6

The resonator of claim 3, wherein said angles of cut φ and θ are: φ=59° and θ=49°.

Claim 7

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanicl axis Y and the optical axis Z of the quartz crystal by means of a first rotation through an angle φ about the axis Y, and a second rotation through an angle θ about the axis Z', said resonator vibrator vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the tines of the tuning fork being parallel to the axis Y' of the quartz plate and the angles of cut φ and θ being such that: 50°<φ<70° and 40°<θ<70°.

Claim 8

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanicl axis Y and the optical axis Z of the quartz crystal by means of a first rotation through an angle φ about the axis Y, and a second rotation through an angle θ about the axis Z', said resonator vibrator vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the tines of the tuning fork being parallel to the axis Y' of the quartz plate and the angles of cut φ and θ being such that: 50°<φ<70° and 40°<θ<70°.

Claim 9

The resonator of claim 5, wherein the angles of cut φ and θ are: φ=60° and θ=50.5°.

Claim 10

The resonator of claim 5, wherein the angles of cut φ and θ are: φ=61° and θ=57.5°.

Claim 11

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the elecrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal by means of a first rotation through an angle φ about the axis Y, and a second rotation through an angle θ about the axis Z', said resonator vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the geometrical dimensions of the resonator being selected so that the fundamental torsional mode is coupled to a flexural vibration mode, whereby the second-order temprature coefficient is substantially zero, the tines of the tuning fork being parallel to the axis X' of the quartz plate and the angles of cut φ and θ being such that: 50°<φ<70° and 40°<θ<70°.

Claim 12

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the elecrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal by means of a first rotation through an angle φ about the axis Y, and a second rotation through an angle θ about the axis Z', said resonator vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the geometrical dimensions of the resonator being selected so that the fundamental torsional mode is coupled to a flexural vibration mode, whereby the second-order temprature coefficient is substantially zero, the tines of the tuning fork being parallel to the axis X' of the quartz plate and the angles of cut φ and θ being such that: 50°<φ<70° and 40°<θ<70°.

Claim 13

The resonator of claim 8, wherein the angles of cut φ and θ are: φ=60° and θ=50.5°.

Claim 14

The resonator of claim 8, wherein the angles of cut φ and θ are: φ=61° and θ=57.5°.

Claim 15

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal, by means of a first rotation through an angle φ about the axis X, and a second rotation through an angle θ about the axis Z', said tines of the tuning fork being parallel to the axis X' of the plate, the tuning fork vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, and the angles of cut φ and θ being such that: -50°<φ<-32° and θ=±45°.

Claim 16

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal, by means of a first rotation through an angle φ about the axis X, and a second rotation through an angle θ about the axis Z', said tines of the tuning fork being parallel to the axis X' of the plate, the tuning fork vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, and the angles of cut φ and θ being such that: -50°<φ<-32° and θ=±45°.

Claim 17

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal by means of a first rotation through an angle φ about the axis X, and a second rotaion through an angle θ about the axis Z', said tines of the tuning fork being parallel to the axis X'of the plate, the tuning fork vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the geometrical dimensions of the resonator being selected so that the fundamental torsional mode is coupled to a flexural vibration mode, whereby the first-order and second-order temperature coefficients are substantially zero, and the angles of cut φ and θ being such that: -50°<φ<-32° and θ=±45°.

Claim 18

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising quartz crystal plate having axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal by means of a first rotation through an angle φ about the axis X, and a second rotaion through an angle θ about the axis Z', said tines of the tuning fork being parallel to the axis X'of the plate, the tuning fork vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the geometrical dimensions of the resonator being selected so that the fundamental torsional mode is coupled to a flexural vibration mode, whereby the first-order and second-order temperature coefficients are substantially zero, and the angles of cut φ and θ being such that: -50°<φ<-32° and θ=±45°.

Claim 19

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate hving axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal by means of a first rotation through an angle φ about the axis X, and a second rotation through an angle θ about the axis Z', said tines of the tuning fork being parallel to the axis X' of the plate, the tuning fork vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, and the angles of cut φ and θ being such that: 40°<φ<80° and θ=±45°.

Claim 20

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate hving axes X', Y' and Z' and angles of cut φ and θ such that the axes X', Y' and Z' are established from the electrical axis X, the mechanical axis Y and the optical axis Z of the quartz crystal by means of a first rotation through an angle φ about the axis X, and a second rotation through an angle θ about the axis Z', said tines of the tuning fork being parallel to the axis X' of the plate, the tuning fork vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, and the angles of cut φ and θ being such that: 40°<φ<80° and θ=±45°.

Claim 21

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate having axes X', Y' and Z' such that the axes X', Y' and Z' are established from the electrical axis X, the mechanicl axis Y and the optical axis Z of the quartz crystal by means of a first rotaion through an angle φ about the axis X, and a second rotation through an angle θ about the axis Z', said tines of the tuning fork being parallel to the axis X' of the plate, the tuning fork vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the geometrical dimensions of the resonator being selected so that the fundamental torsional mode is coupled to a flexural vibration mode, whereby the first-order and second-order temperature coefficients are substantially zero, and the angles of cut φ and θ being such that: 40°<φ<80° and θ=±45°.

Claim 22

A piezoelectric resonator of the tuning fork type having two tines, the resonator comprising a quartz crystal plate having axes X', Y' and Z' such that the axes X', Y' and Z' are established from the electrical axis X, the mechanicl axis Y and the optical axis Z of the quartz crystal by means of a first rotaion through an angle φ about the axis X, and a second rotation through an angle θ about the axis Z', said tines of the tuning fork being parallel to the axis X' of the plate, the tuning fork vibrating in accordance with the fundamental torsional mode, the angles of cut φ and θ being selected so that the first-order temperature coefficient is substantially zero, the geometrical dimensions of the resonator being selected so that the fundamental torsional mode is coupled to a flexural vibration mode, whereby the first-order and second-order temperature coefficients are substantially zero, and the angles of cut φ and θ being such that: 40°<φ<80° and θ=±45°.