Bandpass delta-sigma modulator
A bandpass delta-sigma modulator is formed to include a bandpass filtering circuit that bandpass filters an input signal. An analog-to-digital converter (ADC) receives output of the bandpass filtering circuit and generates an output quantization code. A digital filter receives the output quantization code. A digital-to-analog converter (DAC) receives output of the digital filter and scales the value of the output quantization code by DAC coefficients to the bandpass filtering circuit.
1. A bandpass delta-sigma modulator, comprising:
a bandpass filtering circuit configured to bandpass filter an input signal;
an analog-to-digital converter (ADC) coupled to receive output of the bandpass filtering circuit and generate an output quantization code;
a digital filter coupled to receive the output quantization code; and
a digital-to-analog converter (DAC) coupled to receive an output of the digital filter and scale a value of the output quantization code by DAC coefficients to the bandpass filtering circuit, wherein the digital filter comprises a transfer function H(z) in z-domain according to
H
(
z
)
=
1
1
-
k
d
z
-
1
with k d being a predefined constant.
2. The modulator of claim 1 , wherein the ADC comprises a quantizer.
3. The modulator of claim 1 , wherein the digital filter comprises a digital lowpass filter (LPF).
4. The modulator of claim 3 , wherein the digital LPF has a transfer function H DLP in z-domain expressed as
H
DLP
(
z
)
=
1
1
-
k
d
z
-
1
where k d is a predefined constant.
5. The modulator of claim 4 , wherein the predefined constant k d has a value less than 1.
6. The modulator of claim 3 , wherein a time-domain representation of the digital LPF is expressed as y[n]=Q{x[n]+k d *y[n−1]} where Q{ } represents a quantize-like behavior, y[n−1] is a previous output of the digital LPF, y[n] is a present output of the digital LPF, and x[n] is a present output of the ADC.
7. The modulator of claim 1 , wherein the DAC comprises a non-return-to-zero (NRZ) DAC.
8. The modulator of claim 7 , wherein the NRZ DAC has a transfer function H NRZ in s-domain expressed as
H
NRZ
(
s
)
=
1
-
ⅇ
-
s
T
s
where T is a period.
9. The modulator of claim 1 , wherein each of the bandpass filters comprises an LC resonator.
10. A bandpass delta-sigma modulator, comprising:
a bandpass filtering circuit configured to bandpass filter an input signal;
an analog-to-digital converter (ADC) coupled to receive an output of the bandpass filtering circuit and generate an output quantization code;
a digital lowpass filter (LPF) configured to lowpass the output quantization code; and
a non-return-to-zero (NRZ) digital-to-analog converter (DAC) coupled to receive an output of the digital LPF and scale a value of the output quantization code by DAC coefficients to the bandpass filtering circuit;
wherein the digital LPF has a transfer function H DLP in z-domain expressed as
H
DLP
(
z
)
=
1
1
-
k
d
z
-
1
with k d being a predefined constant.
11. The modulator of claim 10 , wherein the ADC comprises a quantizer.
12. The modulator of claim 10 , wherein the predefined constant k d has a value less than 1.
13. The modulator of claim 10 , wherein a time-domain representation of the digital LPF is expressed as
y[n]=Q{x[n]+k d *y[n− 1]}
where Q{ } represents a quantize-like behavior, y[n−1] is a previous output of the digital LET, y[n] is a present output of the digital LPF, and x[n] is a present output of the ADC.
14. The modulator of claim 10 , wherein the NRZ DAC has a transfer function H NRZ in s-domain expressed as
H
NRZ
(
s
)
=
1
-
ⅇ
-
s
T
s
where T is a period.
15. The modulator of claim 10 , wherein the bandpass filtering circuit comprises:
a plurality of series-connected bandpass filters; and
a plurality of adders, wherein every two neighboring bandpass filters is inserted with one of the adders, with each of the bandpass filters being preceded by one of the adders;
wherein the adder adds output of the preceding bandpass filter or adds the input signal if the adder is the first one, the adder further subtracts output of the NRZ DAC, and the adder then outputs a difference to the succeeding bandpass filter.
16. The modulator of claim 15 , wherein each of the bandpass filters comprises an LC resonator.