Metastability shaping technique for continuous-time sigma-delta analog-to-digital converters

An apparatus, comprising:

• a first feedback loop having a first digital-to-analog-converter (DAC) coupled to a first quantizer, a first DAC output provided by the first DAC of the first feedback loop is configured to compensate for a first quantizer delay;
• a second feedback loop having a second DAC coupled to a second quantizer, a second DAC output provided by the second DAC is configured to compensate for a second quantizer delay, wherein the first DAC is coupled to the first quantizer to compensate for a first excess loop delay (ELD) associated with the first quantizer, the second DAC is coupled to the second quantizer to compensate for a second excess loop delay (ELD) associated with the second quantizer, and the second quantizer reduces a metastability error associated with an output of the first quantizer;
• and
• a third feedback loop, wherein the output of the second quantizer is fed through a third DAC of the third feedback loop, the third feedback loop having a total quantization gain.

A method, comprising:

• generating a first quantization noise of a first quantizer associated with a first feedback loop;
• generating, based on the first quantization noise of the first quantizer, a second quantization noise of a second quantizer associated with a second feedback loop;
• and
• using the second quantization noise of the second quantizer to shape a first metastability error associated with an output of the first quantizer, the using the second quantization noise comprising subtracting the second quantization noise of the second quantizer from the first metastability error to generate a second metastability error.

A method, comprising:

• using a first feedback loop to compensate for a first excess loop delay (ELD) associated with a first quantizer;
• providing a first quantizer output of the first quantizer to a second feedback loop, the second feedback loop compensating for a second ELD associated with a second quantizer, the second quantizer reducing a metastability error associated with the first quantizer output;
• converting the first quantizer output of the first quantizer to an analog signal using the first DAC;
• converting a second quantizer output of the second quantizer to a second analog signal using the second DAC;
• and
• converting the second quantizer output of the second quantizer to a third analog signal using a third DAC.

A method, comprising:

• using a first feedback loop to compensate for a first excess loop delay (ELD) associated with a first quantizer;
• providing a first quantizer output of the first quantizer to a second feedback loop, the second feedback loop compensating for a second ELD associated with a second quantizer, the second quantizer reducing a metastability error associated with the first quantizer output;
• subtracting a first DAC output from a second feedback loop adder output using a first feedback loop adder;
• and
• subtracting a second DAC output from a loop filter output to generate the second feedback loop adder output.