Resonator and resonance device

1. A resonator comprising:

a base;

at least one vibration arm extending from a front end of the base and including an upper electrode, a lower electrode and piezoelectric film disposed therebetween;

a frame that holds the base; and

a holding arm that connects the base to the frame,

wherein the at least one vibration arm is configured to vibrate in a main mode at a frequency Fm,

wherein the holding arm is configured to operate in a spurious mode at a frequency Fs, and

wherein the resonator is constructed such that Fs/Fm<1.9 or Fs/Fm>2.1.

2. The resonator according to claim 1 , wherein the at least one vibration arm has a fixed end connected to the front end of the base and an open end located away from the front end.

3. The resonator according to claim 1 , wherein the resonator is constructed such that Fs/Fm<1.8 or Fs/Fm>2.2.

4. The resonator according to claim 1 , wherein the holding arm includes a rear arm connected to a rear end of the base that is opposite the front end of the base and that extends along the rear end, and a side arm that is connected to the rear arm and extends along the at least one vibration arm.

5. The resonator according to claim 4 ,

wherein Lc is a distance between an edge that is farther than any other edge of the rear arm from the side arm and an edge that farther than any other edge of the side arm from the rear arm,

wherein L 5 is a length of an imaginary vibration arm having a constant width, with the imaginary vibration arm being obtained by transforming the at least one vibration arm into a form for the imaginary vibration arm that has a moment of inertia that is equal to a moment of inertia of the at least one vibration arm, and

wherein the resonator is constructed such that Lc/L 5 <0.520 or Lc/L 5 >0.550.

6. The resonator according to claim 5 , wherein the resonator is constructed such that Lc/L 5 <0.506 or Lc/L 5 >0.566.

7. The resonator according to claim 1 , wherein the frame includes a left frame and a right frame that extend along the at least one vibration arm and are disposed on opposite sides with the at least one vibration arm being disposed between the left frame and the right frame.

8. The resonator according to claim 7 , wherein the holding arm includes a side arm that extends along the at least one vibration arm, and the side arm is connected to the left frame or the right frame of the frame.

9. The resonator according to claim 8 , wherein the at least one vibration arm includes an arm portion that extends from the front end of the base, and a mass addition portion that is connected to a tip of the arm portion and is heavier in weight per unit length than the arm portion.

10. The resonator according to claim 9 , wherein the side arm is connected to the left frame or the right frame such that a junction between the side arm and the left or right frame faces the arm portion.

11. A resonance device comprising:

the resonator according to claim 1 ;

a lower cover coupled to the resonator;

an upper cover coupled to the lower cover with the resonator therebetween; and

a vibration space defined between the lower and upper cover in which the at least one vibration arm vibrate therein.

12. A resonator comprising:

a base;

at least one vibration arm that extends from a front end of the base and that includes an upper electrode, a lower electrode, and a piezoelectric film disposed therebetween;

a frame that holds the base; and

a holding arm that connects the base section to the frame,

wherein the holding arm includes:

a rear arm connected to a rear end of the base that is opposite the front end of the base and extends along the rear end, and

a side arm connected to the rear arm and that extends along the at least one vibration arm, and

wherein Lc is a distance between an edge that is farther than any other edge of the rear arm from the side arm and an edge that farther than any other edge of the side arm from the rear arm,

wherein L 5 is a length of an imaginary vibration arm having a constant width, with the imaginary vibration arm being obtained by transforming the at least one vibration arm into a form for the imaginary vibration arm that has a moment of inertia that is equal to a moment of inertia of the at least one vibration arm, and

wherein the resonator is constructed such that Lc/L 5 <0.520 or Lc/L 5 >0.550.

13. The resonator according to claim 12 , wherein the at least one vibration arm has a fixed end connected to the front end of the base and an open end disposed away from the front end.

14. The resonator according to claim 12 , wherein the resonator is constructed such that Lc/L 5 <0.506 or Lc/L 5 >0.566.

15. A resonator comprising:

a base;

at least one vibration arm extending from the base and including an upper electrode, a lower electrode and piezoelectric film disposed therebetween;

a frame that surrounds the base; and

a holding arm that connects the base to the frame,

wherein the at least one vibration arm vibrates in a main mode at a frequency Fm and the holding arm operates in a spurious mode at a frequency Fs, and

wherein the at least one vibration arm and the holding arm are configured such that Fs/Fm<1.9 or Fs/Fm>2.1.

16. The resonator according to claim 15 , wherein the at least one vibration arm and the holding arm are configured such that Fs/Fm<1.8 or Fs/Fm>2.2.

17. The resonator according to claim 15 ,

wherein the holding arm includes a rear arm connected to the base on a side opposite the at least one vibration arm and that extends along the base, and a side arm that is connected to the rear arm and extends along the at least one vibration arm, and

wherein Lc is a distance between an edge that is farther than any other edge of the rear arm from the side arm and an edge that farther than any other edge of the side arm from the rear arm,

wherein L 5 is a length of an imaginary vibration arm having a constant width, with the imaginary vibration arm being obtained by transforming the at least one vibration arm into a form for the imaginary vibration arm that has a moment of inertia that is equal to a moment of inertia of the at least one vibration arm, and

wherein the at least one vibration arm and the holding arm is constructed such that Lc/L 5 <0.520 or Lc/L 5 >0.550.

18. The resonator according to claim 17 , wherein the at least one vibration arm and the holding arm is constructed such that Lc/L 5 <0.506 or Lc/L 5 >0.566.

19. The resonator according to claim 15 ,

wherein the frame includes a left frame and a right frame that extend along the at least one vibration arm and are disposed on opposite sides with the at least one vibration arm being disposed between the left frame and the right frame, and

wherein the holding arm includes a side arm that extends along the at least one vibration arm, and the side arm is connected to the left frame or the right frame of the frame.

20. The resonator according to claim 19 , wherein the at least one vibration arm includes an arm portion that extends from the base, and a mass addition portion that is connected to a tip of the arm portion and is heavier in weight per unit length than the arm portion.