Active RC resonators with enhanced Q factor

An active RC resonator, comprising:

• a first differential integrator;
• a second differential integrator, wherein first and second inputs of the first differential integrator are respectively coupled to second and first outputs of the second differential integrator via first and second signal paths, and first and second outputs of the first differential integrator are respectively coupled to first and second inputs of the second differential integrator via third and fourth signal paths;
• and
• at least one of:
• 1) a first capacitor coupled from the first output of the second differential integrator to the first input of the first differential integrator, and a second capacitor coupled from the second output of the second differential integrator to the second input of the first differential integrator,
• 2) a third capacitor coupled from the first output of the first differential integrator to the second input of the second differential integrator, and a fourth capacitor coupled from the second output of the first differential integrator to the first input of the second differential integrator,
• wherein capacitances of the first and second capacitors are set to a level such that the set capacitances of the first and the second capacitors equal or substantially equal the parasitic capacitance in the first and second signal paths, wherein capacitances of the third and fourth capacitors are set to a level such that the set capacitances of the third and fourth capacitors equal or substantially equal the parasitic capacitances in the fourth and third signal paths.

An active RC resonator, comprising:

• a first differential integrator;
• a second differential integrator, wherein first and second inputs of the first differential integrator are respectively coupled to second and first outputs of the second differential integrator via first and second signal paths, and first and second outputs of the first differential integrator are respectively coupled to first and second inputs of the second differential integrator via third and fourth signal paths;
• and
• at least one of:
• 1) a first capacitor coupled from the first output of the second differential integrator to the first input of the first differential integrator, and a second capacitor coupled from the second output of the second differential integrator to the second input of the first differential integrator,
• 2) a third capacitor coupled from the first output of the first differential integrator to the second input of the second differential integrator, and a fourth capacitor coupled from the second output of the first differential integrator to the first input of the second differential integrator,
• wherein capacitances of the first and second capacitors are set to a level such that the set capacitances of the first and the second capacitors are larger than the parasitic capacitance in the first and second signal paths, wherein capacitances of the third and fourth capacitors are set to a level such that the set capacitances of the third and fourth capacitors are larger than the parasitic capacitances in the fourth and third signal paths.

An active RC resonator, comprising:

• a first operational amplifier having first and second inputs and first and second outputs;
• a second operational amplifier having first and second inputs and first and second outputs;
• a first resistor coupled between the first input of the first operational amplifier and the second output of the second operational amplifier;
• a second resistor coupled between the second input of the first operational amplifier and the first output of the second operational amplifier;
• a third resistor coupled between the first output of the first operational amplifier and the first input of the second input of the second operational amplifier;
• a fourth resistor coupled between the second output of the first operational amplifier and the second input of the second operational amplifier;
• and
• at least one of:
• 1) a first capacitor coupled between the first input of the first operational amplifier and the first output of the second operational amplifier, and a second capacitor coupled between the second input of the first operational amplifier and the second output of the second operational amplifier,
• 2) a third capacitor coupled between the second output of the first operational amplifier and the first input of the second operational amplifier, and a fourth capacitor coupled between the first output of the first operational amplifier and the second input of the second operational amplifier.

A loop filter, comprising:

• an active RC resonator that includes:
• a first differential integrator;
• a second differential integrator, wherein first and second inputs of the first differential integrator are respectively coupled to second and first outputs of the second differential integrator via first and second signal paths, and first and second outputs of the first differential integrator are respectively coupled to first and second inputs of the second differential integrator via third and fourth signal paths, each of the first, second, third, and fourth signal paths including a respective resistor;
• and
• at least one of:
• 1) a first capacitor coupled from the first output of the second differential integrator to the first input of the first differential integrator, and a second capacitor coupled from the second output of the second differential integrator to the second input of the first differential integrator,
• 2) a third capacitor coupled from the first output of the first differential integrator to the second input of the second differential integrator, and a fourth capacitor coupled from the second output of the first differential integrator to the first input of the second differential.

A loop filter, comprising:

• an active RC resonator that includes:
• a first operational amplifier having first and second inputs and first and second outputs;
• a second operational amplifier having first and second inputs and first and second outputs;
• a first resistor coupled between the first input of the first operational amplifier and the second output of the second operational amplifier;
• a second resistor coupled between the second input of the first operational amplifier and the first output of the second operational amplifier;
• a third resistor coupled between the first output of the first operational amplifier and the first input of the second input of the second operational amplifier;
• a fourth resistor coupled between the second output of the first operational amplifier and the second input of the second operational amplifier;
• and
• at least one of:
• 1) a first capacitor coupled between the first input of the first operational amplifier and the first output of the second operational amplifier, and a second capacitor coupled between the second input of the first operational amplifier and the second output of the second operational amplifier,
• 2) a third capacitor coupled between the second output of the first operational amplifier and the first input of the second operational amplifier, and a fourth capacitor coupled between the first output of the first operational amplifier and the second input of the second operational amplifier.

An analog-to-digital converter, comprising:

• at least one loop filter, wherein the at least one loop filter includes:
• an active RC resonator that includes:
• a first differential integrator;
• a second differential integrator, wherein first and second inputs of the first differential integrator are respectively coupled to second and first outputs of the second differential integrator via first and second signal paths, and first and second outputs of the first differential integrator are respectively coupled to first and second inputs of the second differential integrator via third and fourth signal paths, each of the first, second, third, and fourth signal paths including a respective resistor;
• and
• at least one of:
• 1) a first capacitor coupled from the first output of the second differential integrator to the first input of the first differential integrator, and a second capacitor coupled from the second output of the second differential integrator to the second input of the first differential integrator,
• 2) a third capacitor coupled from the first output of the first differential integrator to the second input of the second differential integrator, and a fourth capacitor coupled from the second output of the first differential integrator to the first input of the second differential integrator.

An analog-to-digital converter, comprising:

• at least one loop filter, wherein the at least one loop filter includes:
• an active RC resonator that includes:
• a first operational amplifier having first and second inputs and first and second outputs;
• a second operational amplifier having first and second inputs and first and second outputs;
• a first resistor coupled between the first input of the first operational amplifier and the second output of the second operational amplifier;
• a second resistor coupled between the second input of the first operational amplifier and the first output of the second operational amplifier;
• a third resistor coupled between the first output of the first operational amplifier and the first input of the second input of the second operational amplifier;
• a fourth resistor coupled between the second output of the first operational amplifier and the second input of the second operational amplifier;
• and
• at least one of:
• 1) a first capacitor coupled between the first input of the first operational amplifier and the first output of the second operational amplifier, and a second capacitor coupled between the second input of the second operational amplifier and the first output of the second operational amplifier,
• 2) a third capacitor coupled between the second output of the first operational amplifier and the first input of the second operational amplifier, and a fourth capacitor coupled between the first output of the first operational amplifier and the second input of the second operational amplifier.