Digital correction of digital-to-analog converter errors in continuous-time analog-to-digital converters
Continuous-time (CT) analog-to-digital converters (ADCs) implementing digital correction of digital-to-analog converter (DAC) errors are disclosed. In a CT pipeline stage of a CT ADC, a CT analog input signal is sent to two different paths. A first path (a “feedforward” path) includes a cascade of a sub-ADC and a sub-DAC. A second path (a “forward” path) includes an analog delay circuit to align the delays of the input signal in the feedforward and forward paths. A combiner subtracts the output of the analog delay of the forward path from the output of the sub-DAC in the feedforward path to generate a residue signal. Devices and methods disclosed herein are based on recognition that, if the errors introduced by the sub-DAC are known, they can be corrected in the digital domain during reconstruction, achieving superior NSD and distortion performance compared to conventional approaches.
1. A continuous-time (CT) analog-to-digital converter (ADC), comprising:
a delay circuit, configured to generate a delay circuit output signal by applying a delay to an analog input signal;
a sub-ADC, configured to generate a sub-ADC output signal based on the analog input signal;
an error correction circuit, configured to generate a digital error-corrected signal based on the sub-ADC output signal; and
a digital reconstruction filter (DRF) combiner, configured to generate an ADC output signal based on the digital error-corrected signal.
2. The CT ADC according to claim 1 , wherein:
the error correction circuit includes an error correction unit and at least one adder,
the error correction unit includes a plurality of error correction blocks configured to generate a plurality of digital corrections based on one or more error estimates, and
the at least one adder is configured to add the plurality of digital corrections to the sub-ADC output signal to generate the digital error-corrected signal.
3. The CT ADC according to claim 2 , wherein:
the at least one adder includes a first adder and a second adder,
the first adder is configured to, for an individual bit of a plurality of bits of the sub-ADC output signal, add the individual bit and a corresponding one of the plurality of digital corrections to generate an individual error-corrected bit of a plurality of error-corrected bits of an error-corrected sub-ADC output signal, and
the second adder is configured to add the plurality of error-corrected bits to generate the digital error-corrected signal.
4. The CT ADC according to claim 2 , wherein:
the at least one adder includes a first adder, a second adder, and a third adder,
the first adder is configured to add individual digital corrections of the plurality of digital corrections to generate a digital correction sum,
the second adder is configured to add individual bits of a plurality of bits of the sub-ADC output signal to generate a sub-ADC output sum, and
the third adder is configured to add the digital correction sum and the sub-ADC output sum.
5. The CT ADC according to claim 2 , wherein the one or more error estimates include one or more of an estimate of a static error, an estimate of a timing error, and an estimate of a switching error.
6. The CT ADC according to claim 5 , wherein the static error is an error based on device mismatch.
7. The CT ADC according to claim 5 , wherein the timing error is an error based on one or more of driver mismatch or switch mismatch.
8. The CT ADC according to claim 5 , wherein the switching error is an error based on a pulse-width error.
9. The CT ADC according to claim 2 , wherein:
the sub-ADC output signal includes M bits,
M is an integer greater than or equal to 1,
the plurality of error correction blocks includes M error correction blocks, and
each of the M error correction blocks corresponds to a respective one of the M bits of the sub-ADC output signal.
10. The CT ADC according to claim 9 , further comprising a sub-digital-to-analog converter (sub-DAC), wherein:
the sub-DAC is to generate a sub-DAC output signal, and
the sub-DAC includes M sub-DAC units.
11. The CT ADC according to claim 2 , further comprising:
an error extraction arrangement to generate the one or more error estimates.
12. The CT ADC according to claim 11 , wherein:
the CT ADC further includes a backend-ADC, a sub-digital-to-analog converter (sub-DAC) that includes M sub-DAC units, a first cross-correlator, and a second cross-correlator, and
wherein the error extraction arrangement is configured to generate the one or more error estimates by:
disabling provision of the analog input signal to the CT ADC,
selecting one sub-DAC unit of the M sub-DAC units as a reference sub-DAC unit,
selecting another sub-DAC unit of the M sub-DAC units as a measurement sub-DAC unit,
applying a first pseudo-random bit sequence (PRBS) to the reference sub-DAC unit,
applying a second PRBS to the measurement sub-DAC unit,
using the first cross-correlator to cross-correlate the first PRBS with an output of the backend-ADC generated when the first PRBS is applied to the reference sub-DAC and the second PRBS is applied to the measurement sub-DAC,
using the second cross-correlator to cross-correlate a product of the first PRBS and a delayed first PRBS with the output of the backend-ADC generated when the first PRBS is applied to the reference sub-DAC and the second PRBS is applied to the measurement sub-DAC, and
generating the one or more error estimates based on outputs of the first and second cross-correlators.
13. The CT ADC according to claim 12 , wherein the error extraction arrangement is configured to generate the one or more error estimates further by:
applying the second PRBS to the reference sub-DAC unit,
applying the first PRBS to the measurement sub-DAC unit,
using the first cross-correlator to cross-correlate the first PRBS with an output of the backend-ADC generated when the second PRBS is applied to the reference sub-DAC and the first PRBS is applied to the measurement sub-DAC,
using the second cross-correlator to cross-correlate a product of the first PRBS and a delayed first PRBS with the output of the backend-ADC generated when the second PRBS is applied to the reference sub-DAC and the first PRBS is applied to the measurement sub-DAC, and
generating the one or more error estimates based on outputs of the first and second cross-correlators.
14. The CT ADC according to claim 12 , wherein the second PRBS is a negative version of the first PRBS.
15. The CT ADC according to claim 11 , wherein:
the CT ADC further includes a backend-ADC, a sub-digital-to-analog converter (sub-DAC) that includes M+2 sub-DAC units, a first cross-correlator, and a second cross-correlator,
the sub-ADC output signal includes M bits, and
wherein the error extraction arrangement is configured to generate the one or more error estimates by:
selecting one sub-DAC unit of the M+2 sub-DAC units as a reference sub-DAC unit,
selecting another sub-DAC unit of the M+2 sub-DAC units as a measurement sub-DAC unit,
applying a first pseudo-random bit sequence (PRBS) to the reference sub-DAC unit,
applying a second PRBS to the measurement sub-DAC unit,
using the first cross-correlator to cross-correlate the first PRBS with an output of the backend-ADC generated when the first PRBS is applied to the reference sub-DAC and the second PRBS is applied to the measurement sub-DAC,
using the second cross-correlator to cross-correlate a product of the first PRBS and a delayed first PRBS with the output of the backend-ADC generated when the first PRBS is applied to the reference sub-DAC and the second PRBS is applied to the measurement sub-DAC, and
generating the one or more error estimates based on outputs of the first and second cross-correlators.
16. The CT ADC according to claim 15 , wherein the second PRBS is a negative version of the first PRBS.
17. A device for assisting error correction in a continuous-time (CT) analog-to-digital converter (ADC), the device comprising:
means for disabling provision of an analog input signal to the CT ADC;
means for selecting one sub-digital-to-analog converter (sub-DAC) unit of M sub-DAC units of the CT ADC as a reference sub-DAC unit;
means for selecting another sub-DAC unit of the M sub-DAC units as a measurement sub-DAC unit;
means for applying a first pseudo-random bit sequence (PRBS) to the reference sub-DAC unit;
means for applying a second PRBS to the measurement sub-DAC unit;
a first cross-correlator to cross-correlate the first PRBS with an output of a backend-ADC of the CT ADC, wherein the output of the backend-ADC is generated when the first PRBS is applied to the reference sub-DAC and the second PRBS is applied to the measurement sub-DAC;
a second cross-correlator to cross-correlate a product of the first PRBS and a delayed first PRBS with the output of the backend-ADC generated when the first PRBS is applied to the reference sub-DAC and the second PRBS is applied to the measurement sub-DAC; and
means for generating one or more error estimates based on outputs of the first and second cross-correlators.
18. The device according to claim 17 , further comprising:
an error correction unit to use the one or more error estimates to apply error correction to an output of a sub-ADC to generate an output of the error correction unit,
wherein the output of the error correction unit is a digital signal.
19. A device for assisting error correction in a continuous-time (CT) analog-to-digital converter (ADC), the device comprising:
the CT ADC further includes a backend-ADC, a sub-digital-to-analog converter (sub-DAC) that includes M+2 sub-DAC units, a first cross-correlator, and a second cross-correlator,
the sub-ADC output signal includes M bits, and
means for selecting one sub-digital-to-analog converter (sub-DAC) unit of the M+2 sub-DAC units of the CT ADC as a reference sub-DAC unit;
means for selecting another sub-DAC unit of the M+2 sub-DAC units as a measurement sub-DAC unit;
means for applying a first pseudo-random bit sequence (PRBS) to the reference sub-DAC unit;
means for applying a second PRBS to the measurement sub-DAC unit;
a first cross-correlator to cross-correlate the first PRBS with an output of a backend-ADC of the CT ADC, wherein the output of the backend-ADC is generated when the first PRBS is applied to the reference sub-DAC and the second PRBS is applied to the measurement sub-DAC;
a second cross-correlator to cross-correlate a product of the first PRBS and a delayed first PRBS with the output of the backend-ADC generated when the first PRBS is applied to the reference sub-DAC and the second PRBS is applied to the measurement sub-DAC; and
means for generating the one or more error estimates based on outputs of the first and second cross-correlators.
20. The device according to claim 19 , further comprising:
an error correction unit to use the one or more error estimates to apply error correction to an output of a sub-ADC to generate an output of the error correction unit,
wherein the output of the error correction unit is a digital signal.