Method and apparatus for A/D conversion
A method and an apparatus for converting an analog input signal into a digital output signal using a sigma-delta modulator architecture with a digital tracking filter. The digital tracking filter may have and order greater than one, and the signal and noise transfer functions of the sigma-delta modulator architecture are chosen to provide a sigma-delta modulator architecture with a high dynamic range even if a relatively low oversampling ratio is used.
1. A method for converting an analog input signal to a digital output signal, the method comprising:
forming a difference signal between the analog input signal and an analog estimate signal of the analog input signal;
filtering with a first filter function and quantizing the difference signal to obtain a quantized difference signal;
filtering the quantized difference signal with a second filter function having an order greater than one to obtain a digital estimate signal of the analog input signal, wherein the second filter function is a second order or third order filter function; and
converting the digital estimate signal to the analog estimate signal.
2. The method according to claim 1 , wherein the digital estimate signal is quantized by a further quantizer before converting it into the analog estimate signal.
3. The method according to claim 1 , wherein the analog input signal is oversampled with an oversampling ratio less than or equal to twenty.
4. The method of claim 1 , wherein the difference signal is quantized using a quantizer having a resolution of up to six bits to obtain the quantized different signal.
5. A method for converting an analog input signal to a digital output signal, the method comprising:
scaling the analog input signal with a scaling factor K;
forming a difference signal between the scaled analog input signal and an analog estimate signal of the analog input signal;
filtering with a first filter function and quantizing the difference signal to obtain a quantized difference signal;
filtering the quantized difference signal with a second filter function to obtain a digital estimate signal of the analog input signal; and
converting the digital estimate signal to the analog estimate signal,
wherein the scaling factor is
K
=
1
STF
1
(
ⅇ
jω
0
)
,
wherein STF 1 is a signal transfer function defined between the quantized difference signal and the analog input signal and ω 0 is a frequency at which STF 1 has a maximum gain within a given signal band of interest of the analog input signal.
6. The method according to claim 5 , wherein the digital estimate signal is converted to the analog estimate signal using a digital-to-analog converter having a resolution of log 2 (K) plus a resolution of a quantizer used for quantizing the different signal.
7. The method according to claim 5 , wherein the second filter function is a second order filter function or a third order filter function.
8. The method according to claim 5 , wherein the signal transfer function STF 1 has a high pass behavior.
9. The method according to claim 5 , wherein a noise transfer function, which is defined between the quantized difference signal and a quantization noise introduced during the quantizing of the difference signal, and the signal transfer function STF 1 have common zeros.
10. A method for converting an analog input signal to a digital output signal, the method comprising:
forming a difference signal between the analog input signal and an analog estimate signal of the analog input signal;
filtering with a first filter function and quantizing the difference signal to obtain a quantized difference signal;
filtering the quantized difference signal with a second filter function to obtain a digital estimate signal of the analog input signal; and
converting the digital estimate signal to the analog estimate signal;
wherein a signal transfer function defined between the quantized difference signal and the analog input signal and a noise transfer function defined between the quantized difference signal and quantization noise introduced during the quantizing of the difference signal have common zeros.
11. The method according to claim 10 , wherein the signal transfer function and the noise transfer function have common complex conjugate zeros.
12. The method according to claim 10 , wherein the signal transfer function has a high pass behavior.
13. The method according to claim 10 , wherein a further signal transfer function defined between the digital estimate signal and the analog input signal has an approximately uniform gain in a given signal band of interest of the analog input signal.
14. The method according to claim 10 , wherein a further noise transfer function defined between the digital estimate signal and quantization noise introduced during the quantizing of the difference signal has a high pass behavior.
15. The method according to claim 10 , wherein the first filter function has an order greater than one.
16. The method according to claim 10 , wherein the analog input signal is oversampled with an oversampling ratio less than or equal to twenty.
17. The method according to claim 10 , wherein the difference signal is quantized using a quantizer having a resolution of up to six bits.
18. The method according to claim 10 , wherein the analog input signal is scaled using a scaling factor K before forming the difference signal with
K
=
1
STF
1
(
ⅇ
jω
0
)
,
whereby STF 1 is the signal transfer function and ω 0 is a frequency at which STF 1 has a maximum gain within a given signal band of interest of the analog input signal.
19. The method according to claim 18 , wherein the digital estimate signal is converted to the analog estimate signal using a digital-to-analog converter having a resolution of log 2 (K) plus a resolution of a quantizer used for quantizing the difference signal.
20. The method according to claim 10 , wherein the digital estimate signal is quantized before converting it to the analog estimate signal.
21. An apparatus configured to convert an analog input signal to a digital output signal, the apparatus comprising:
a first filter configured to filter a difference signal between the analog input signal and an analog estimate signal of the analog input signal;
a quantizer configured to quantize the difference signal filtered by the first filter to obtain a quantized different signal;
a second filer having an order greater than one, the second filter configured to obtain a digital estimate signal of the analog input signal, and wherein the second filter is a second order or third order filter; and
a digital/analog converter configured to convert the digital estimate signal into the analog estimate signal.
22. The apparatus according to claim 21 , wherein a further quantizer is provided between the second filter and an adder which is configured to form the difference signal.
23. The apparatus according to claim 21 , wherein the quantizer has a resolution of up to six bits.
24. An apparatus configured to convert an analog input signal to a digital output signal, the apparatus comprising:
an amplifier configured to scale the analog input signal with a scaling factor K;
a first filter configured to filter a difference signal between the scaled analog input signal and an analog estimate signal of the analog input signal;
a quantizer configured to quantize the filtered difference signal to obtain a quantized difference signal;
a digital second filter configured to filter the quantized difference signal to obtain a digital estimate signal of the analog input signal; and
a digital/analog converter configured to convert the digital estimate signal to the analog estimate signal,
wherein the scaling factor is
K
=
1
STF
1
(
ⅇ
jω
0
)
,
wherein STF 1 is a signal transfer function defined between the quantized difference signal and the analog input signal and ω 0 is a frequency at which STF 1 has a maximum gain within a given signal band of interest of the analog input signal.
25. The apparatus according to claim 24 , wherein the digital second filter has an order greater than one.
26. The apparatus according to claim 24 , wherein the digital/analog converter has a resolution of log 2 (K) plus a resolution of the quantizer.
27. The apparatus according to claim 24 , wherein the signal transfer function STF 1 exhibits a high pass behavior.
28. The apparatus according to claim 24 , wherein the signal transfer function STF 1 and a noise transfer function, which is defined between the quantized difference signal and quantization noise introduced by the quantizer, have common zeros.
29. An apparatus configured to convert an analog input signal to a digital output signal, the apparatus comprising:
a first filter configured to filter a difference signal between the analog input signal and an analog estimate signal of the analog input signal;
a quantizer configured to quantize the filtered difference signal to obtain a quantized difference signal;
a second filter configured to filter the quantized difference signal to obtain a digital estimate signal of the analog input signal; and
a digital/analog converter configured to convert the digital estimate signal to the analog estimate signal,
wherein a signal transfer function, which is defined between the quantized digital signal and the analog input signal, and a noise transfer function, which is defined between the quantized digital signal and quantization noise introduced by the quantizer, have common zeros.
30. The apparatus according to claim 29 , wherein the signal transfer function and the noise transfer function have common complex conjugate zeros.
31. The apparatus according to claim 29 , wherein the signal transfer function has a high pass behavior.
32. The apparatus according to claim 29 , wherein a further signal transfer function, which is defined between the digital estimate signal and the analog input signal, has an approximately uniform gain in a given signal band of interest of the analog input signal.
33. The apparatus according to claim 29 , wherein a further noise transfer function, which is defined between the digital estimate signal and the quantization noise introduced by the quantizer, has a high pass behavior.
34. The apparatus according to claim 29 , wherein the second filter has an order greater than one.
35. The apparatus according to claim 29 , wherein the quantizer is a quantizer having a resolution of up to six bits.
36. The apparatus according to claim 29 , wherein an amplifier is configured to amplifying the analog input signal by a scaling factor K before forming the difference signal with
K
=
1
STF
1
(
ⅇ
jω
0
)
,
wherein STF 1 is the signal transfer function defined between the quantized difference signal and the analog input signal and ω 0 is a frequency at which the signal transfer function STF 1 has a maximum gain within a given signal band of interest of the analog input signal.
37. The apparatus according to claim 36 , wherein the digital/analog converter has a resolution of log 2 (K) plus a resolution of the quantizer.
38. The apparatus according to claim 29 , wherein a further quantizer is provided between the digital second filter and the digital/analog converter.