Sigma-delta analog-to-digital converter

1. A sigma-delta analog-to-digital converter (ADC), comprising:

a first forward path connected to an input of the sigma-delta ADC comprising a filtering stage and a quantization stage, the first forward path having a transfer function H ff ;

a first feedback path from an output of the first forward path to the input of the sigma-delta ADC, said first feedback path comprising a digital-to-analog converter (DAC) and a digital filter for converting the output of the first forward path, said first feedback path having a transfer function H fb ;

wherein the sigma-delta ADC has a stable noise transfer function NTF given by:

NTF

=

1

1

+

H

ff

⁢

H

fb

=

1

1

+

H

wherein H is the loop transfer function, said NTF having at least one damped zero;

wherein, if H comprises undamped poles, H ff comprising all the undamped poles of H, and wherein H fb comprises at least one damped pole associated with one of said at least one damped zero;

wherein the first feedback path comprises a finite impulse response (FIR) digital filter that has an impulse response that approximates the impulse response associated with H fb , wherein the first N coefficients of the impulse response are implemented as said FIR filter, wherein N is at least equal to the time constant of the most low frequent pole of H fb ;

wherein the FIR digital filter is combined with the DAC for forming a finite impulse response digital-to-analog converter FIRDAC.

2. The sigma-delta ADC of claim 1 , wherein H fb comprises a plurality of undamped poles.

3. The sigma-delta ADC of claim 1 , further comprising a correction filter connected to the output of the first forward path.

4. The sigma-delta ADC of claim 3 , said correction filter having a transfer function H cor substantially given by:

H

cor

=

1

+

H

H

ff

.

5. The sigma-delta ADC of claim 1 , wherein a signal band of interest is contained within the pass-band of both H ff and H fb .

6. The sigma-delta ADC of claim 1 , wherein both H ff and H fb have low-pass characteristics.

7. The sigma-delta ADC of claim 1 , wherein the filtering stage comprises a passive filter.

8. The sigma-delta ADC of claim 1 , wherein the filtering stage comprises a plurality of passive filters and/or a plurality of integrators.

9. The sigma-delta ADC of claim 1 , comprising only a single integrator in the filtering stage.

10. A digital control loop, comprising:

a second forward path connected to an input of the digital control loop comprising an amplifier for amplifying a difference between a digital input signal and a second digital signal and for converting the amplified signal into an analog output signal; and

a second feedback path from an output of said second forward path to the input of the digital control loop, said second feedback path comprising the sigma-delta ADC as defined in claim 1 for converting the analog output signal into said second digital signal.

11. A digital audio amplifier comprising the digital control loop as defined in claim 10 for driving a speaker, when connected to the digital audio amplifier, in accordance with the digital input signal.

12. A method for designing a sigma-delta analog-to-digital converter (ADC) comprising a forward path connected to an input of the sigma-delta ADC comprising a filtering stage and a quantization stage, the forward path having a transfer function F ff , a feedback path from an output of the forward path to the input of the sigma-delta ADC, said feedback path comprising a digital-to-analog converter (DAC) and a digital filter for converting the output of the forward path, said feedback path having a transfer function H fb , wherein the sigma-delta ADC has a stable noise transfer function NTF given by:

NTF

=

1

1

+

H

ff

⁢

H

fb

=

1

1

+

H

wherein H is the loop transfer function, said NTF having at least one damped zero, wherein, if H comprises undamped poles, H ff comprising all the undamped poles of H, and wherein H fb comprises at least one damped pole associated with one of said at least one damped zero, wherein the feedback path comprises a finite impulse response (FIR) digital filter that has an impulse response that approximates the impulse response associated with H fb , wherein the first N coefficients of the impulse response are implemented as said FIR filter, wherein N is at least equal to the time constant of the most low frequent pole of H fb , wherein the FIR digital filter is combined with the DAC for forming a finite impulse response digital-to-analog converter FIRDAC, the method comprising:

defining a desired stable noise transfer function NTF of the sigma-delta ADC that comprises at least one damped zero;

translating NTF into a loop transfer function H of the sigma-delta ADC according to:

H

=

1

NTF

-

1

=

H

ff

⁢

H

fb

extracting poles and zeros of H;

splitting H into H ff and H fb , wherein, if H comprises undamped poles, H ff comprising all said undamped poles of H, and wherein H fb comprises at least one damped pole associated with one of said at least one damped zero;

approximating an impulse response associated with H fb with a finite impulse response, and implementing said finite impulse response with a finite impulse response (FIR) filter;

wherein the first N coefficients of the impulse response are implemented as said FIR filter, wherein N is at least equal to the time constant of the most low frequent pole of H fb ;

wherein the FIR digital filter is combined with the DAC or forming a finite impulse response digital-to-analog converter FIRDAC.

13. The method according to claim 12 , further comprising correcting an output of the forward path using a correction filter connected to the output of the forward path.

14. The method according to claim 13 , wherein the correction filter has a transfer function H cor substantially given by:

H

cor

=

1

+

H

H

ff

.

15. A method for manufacturing a sigma-delta analog-to-digital converter (ADC), comprising:

designing the ADC according to claim 12 ; and

manufacturing the ADC according to the design of the ADC.