Resonator and oversampling A/D converter

1. A resonator comprising:

an operational amplifier coupled to a common node at a non-inverting input terminal;

a first resistive element coupled between a first node and an inverting input terminal of the operational amplifier;

a second resistive element coupled between the first node and an output terminal of the operational amplifier;

a first capacitive element coupled between a second node and the inverting input terminal of the operational amplifier;

a second capacitive element coupled between the second node and the output terminal of the operational amplifier;

a third capacitive element coupled between the first node and the common node;

a third resistive element coupled between the second node and the common node;

a fourth resistive element coupled between the first node and a signal input terminal;

a fourth capacitive element coupled between the second node and the signal input terminal;

a fifth capacitive element coupled between the first node and the signal input terminal; and

a sixth capacitive element coupled between the second node and the common node.

2. The resonator of claim 1 , wherein

a sum of inverse numbers of resistance values of the first, second and fourth resistive elements is equal to an inverse number of a resistance value of the third resistive element, and

a sum of capacitance values of the third and fifth capacitive elements is equal to a sum of capacitance values of the first, second, fourth and sixth capacitive elements.

3. The resonator of claim 1 , wherein

resistance values of the second and fourth resistive elements, and capacitance values of the fourth and fifth capacitive elements are variable.

4. The resonator of claim 3 , wherein

the second and fourth resistive elements include a plurality of resistive elements coupled in parallel, each of which coupled to the first node at a first end, and selectively coupled to either one of a signal path or the common node at a second end,

the fourth capacitive element includes a plurality of capacitive elements coupled in parallel, each of which coupled to the second node at a first end, and selectively coupled to either one of a signal path or the common node at a second end, and

the fifth capacitive element includes a plurality of capacitive elements coupled in parallel, each of which coupled to the first node at a first end, and selectively coupled to either one of a signal path or the common node at a second end.

5. The resonator of claim 1 , further comprising:

a fifth resistive element coupled between the first node and a second signal input terminal, and having a resistance value of 1/α of that of the second resistive element; and

a seventh capacitive element coupled between the second node and the second signal input terminal, and having a capacitance value α times of that of the second capacitive element.

6. The resonator of claim 5 , wherein

resistance values of the second, fourth, and fifth resistive elements, and capacitance values of the fourth and fifth capacitive elements are variable.

7. The resonator of claim 6 , wherein

the second, fourth, and fifth resistive elements include a plurality of resistive elements coupled in parallel, each of which coupled to the first node at a first end, and selectively coupled to either one of a signal path or the common node at a second end,

the fourth capacitive element includes a plurality of capacitive elements coupled in parallel, each of which coupled to the second node at a first end, and selectively coupled to either one of a signal path or the common node at a second end, and

the fifth capacitive element includes a plurality of capacitive elements coupled in parallel, each of which coupled to the first node at a first end, and selectively coupled to either one of a signal path or the common node at a second end.

8. A resonator comprising:

an operational amplifier coupled to a common node at a non-inverting input terminal;

a first resistive element coupled between a first node and an inverting input terminal of the operational amplifier;

a second resistive element coupled between the first node and an output terminal of the operational amplifier;

a first capacitive element coupled between a second node and the inverting input terminal of the operational amplifier;

a second capacitive element coupled between the second node and the output terminal of the operational amplifier;

a third capacitive element coupled between the first node and the common node;

a third resistive element coupled between the second node and the common node;

a fourth resistive element coupled between the first node and a signal input terminal;

a fourth capacitive element coupled between the second node and the signal input terminal;

a fifth resistive element coupled between the second node and the signal input terminal; and

a sixth resistive element coupled between the first node and the common node.

9. The resonator of claim 8 , wherein

a sum of inverse numbers of resistance values of the first, second, fourth, and sixth resistive elements is equal to a sum of inverse numbers of resistance values of the third and fifth resistive elements, and

a capacitance value of the third capacitive element is equal to a sum of capacitance values of the first, second and fourth capacitive elements.

10. The resonator of claim 8 , wherein

resistance values of the second, fourth, and fifth resistive elements, and a capacitance value of the fourth capacitive element are variable.

11. The resonator of claim 10 , wherein

the second and fourth resistive elements include a plurality of resistive elements coupled in parallel, each of which coupled to the first node at a first end, and selectively coupled to either one of a signal path or the common node at a second end,

the fifth resistive element includes a plurality of resistive elements coupled in parallel, each of which coupled to the second node at a first end, and selectively coupled to either one of a signal path or the common node at a second end, and

the fourth capacitive element includes a plurality of capacitive elements coupled in parallel, each of which coupled to the second node at a first end, and selectively coupled to either one of a signal path or the common node at a second end.

12. The resonator of claim 8 , further comprising:

a seventh resistive element coupled between the first node and a second signal input terminal, and having a resistance value of 1/α of that of the second resistive element; and

a fifth capacitive element coupled between the second node and the second signal input terminal, and having a capacitance value α times of that of the second capacitive element.

13. The resonator of claim 12 , wherein

resistance values of the second, fourth, fifth and seventh resistive elements, and a capacitance value of the fourth capacitive element are variable.

14. The resonator of claim 13 , wherein

the second, fourth, and seventh resistive elements include a plurality of resistive elements coupled in parallel, each of which coupled to the first node at a first end, and selectively coupled to either one of a signal path or the common node at a second end,

the fifth resistive element includes a plurality of resistive elements coupled in parallel, each of which coupled to the second node at a first end, and selectively coupled to either one of a signal path or the common node at a second end, and

the fourth capacitive element includes a plurality of capacitive elements coupled in parallel, each of which coupled to the second node at a first end, and selectively coupled to either one of a signal path or the common node at a second end.

15. An oversampling A/D converter comprising the resonator of claim 1 .

16. An oversampling A/D converter comprising the resonator of claim 8 .