Dithering method for sigma-delta analog-to-digital converters

Details Dithering method for sigma-delta analog-to-digital converters Dithering method for sigma-delta analog-to-digital converters

2004-02-18

2004-11-30

Young, Brian (Department: 2819)

Coded data generation or conversion

Analog to or from digital conversion

Increasing converter resolution

C341S155000

Reexamination Certificate

active

06825784

ABSTRACT:

FIELD OF THE INVENTION
The present invention relates to sigma-delta Analog-to-Digital Converters (ADCs), and, more particularly, to a sigma-delta ADC having efficient dithering.
BACKGROUND OF THE INVENTION
Most sigma-delta modulators include periodic idle channel noise. Even after lowpass filtering, the peak amplitudes of the periodic idle channel noise can be relatively high, even though the RMS power level of the noise is low. Accordingly, this noise gives rise to an annoying sound for the human ear in any audio application; yet, this same idle channel noise may not interfere with a data acquisition system using the same modulator.
An example of a second-order sigma-delta modulator architecture susceptible to having idle channel noise is shown in FIG.
1
. As shown, modulator
10
includes two integrators,
16
and
22
, and two negative feedback loops, wherein the first feedback loop includes a digital-to-analog converter (DAC)
26
. Summers,
12
and
20
, couple these two negative feedback loops to the feed forward portion of modulator
10
. Coefficients k
1
and k
2
supplied by respective multipliers,
14
and
18
, represent forwarding coefficients, while coefficients k
f1
and k
f2
supplied by respective multipliers,
28
and
30
, represent feedback coefficients. Quantizer
24
can be a two-level quantizer having one bit or a multi-level quantizer having three or more bits. When the input x(n) is a small DC signal or some small DC offset and the channel is idle, the output y(n) of the sigma-delta modulator will exhibit a series of digital codes having a low frequency pattern proportional to the DC offset and the sampling clock. As explained previously, in audio applications where there is a DC offset in addition to a small frequency signal, the idle channel tones could lead to an unpleasant sound.
Conventional dithering methods to whiten or decorrelate the idle channel tones include but are not limited to, (1) adding an out-of-band sine or square wave; (2) adding a DC offset to the input of the modulator; (3) adding a small amount of white noise to the input; (4) adding a small-amplitude periodic pulse train; and (5) starting the integrators with irrational values. These techniques are either too complicated to implement or are not effective.
An effective dithering method is to add dither in such a way that the dither transfer function is the same as the quantization noise transfer function. This generalized dither is shown in
FIG. 2
a
. As shown, input x(n) represents the input signal that is fed to a feed forward Z transfer function G(z)
104
. Through summer
106
, a dither input d(n) is added to the resultant signal of the feed forward Z transfer function G(z)
104
. Quantizer
108
receives the result to provide an output y(n). Output y(n) is fed back through a feedback transfer function H(z)
112
and the output of transfer function H(z)
112
is added to the input using summer
102
. An error function e(n) is provided through the subtraction of the signal after summer
106
from the output signal y(n).
In the alternative, as shown in
FIG. 2
b
, the dither input d(n) can be added to the input of quantizer
120
directly or added to the input of modulator
120
after a pre-filter
122
. As shown, the input x(n) is summed with the output of the pre-filter
122
using adder
124
. The feed forward Z transfer function G(z) couples to receive sum and provides its result to quantizer
128
. The output y(n) is fed back to feedback transfer function H(z)
132
. Adder
124
sums the result to feed forward portion of modulator
120
. Adding dither to the input of the quantizer is not simple. An equivalent representation is to shift the decision thresholds of the quantizer.
Conventionally a uniformly distributed signal is added in front of the quantizer so that the x and y signals maintain the same transfer function. Given the hypothetical when an input signal is fixed having a small DC offset, the idle channel tone can repeat itself for several cycles; thereby creating a periodic idle channel tone. When, however, a dithering sequence is added, the periodic idle channel tone is destroyed. Thus, the resultant signal will look more like a random signal where the power is reduced and spread over the frequencies.
In general, an idle channel tone is proportional to the input DC offset. Thus, if there is a fixed DC offset there is a fixed frequency. Once, however, dithering is introduced, the output will a decreased power for that fixed frequency and the other frequencies may increase in power.
FIG. 3
illustrates a known method and apparatus for adding a dither signal to a 3-level quantizer. Specifically,
FIG. 3
gives the details of how the dithering signal may couple into the quantizer
108
as shown in
FIG. 2
a
. The input signal V
in
comes from the feed forward Z transfer function G(z) as is shown in
FIG. 2
a
. Conventionally, the first threshold voltage V
th0
is the negative value of the second threshold voltage V
th1
where V
th0
=−-V
th
, V
th1
=V
th
. The first and second threshold voltages, V
th0
and V
th1
, are received by the inverted input of each comparator,
136
and
134
, respectively. Signals B
0
and B
1
, represent the output signal y(n) of
FIG. 2
a
. As shown, adder
132
adds a pseudo-random series dither d(n) to the quantizer input represented by V
in
, wherein the quantizer is implemented using adder
132
and comparators,
134
and
136
. When the inputs (V
in
+d(n)) of comparators,
134
and
136
, are larger than threshold voltage V
th
, the output nodes B
1
B
0
are both high or “11”. As shown in
FIG. 2
, when the digital signal y(n) is fed back to the transfer function H(z), it is converted to an analog signal proportional to a reference voltage V
ref
. This reference voltage V
ref
is fed back to the integrators coupled as shown in
FIGS. 1 and 2
. When the inputs (V
in
+d(n)) of comparators,
134
and
136
, are less than or equal to threshold voltage V
th
and greater than the negative value of threshold voltage −V
th
, the output nodes B
1
B
0
are both low or “00”. Thereby a value of “0” is fed back to the integrators. When the input (V
in
+d(n)) of the comparators,
134
and
136
, are less than the negative value of threshold voltage −V
th
the output nodes B
1
B
0
are both high or “11”. As a result, the negative value of reference voltage −V
ref
is fed back to the integrators. The 0 dBFS input to the converter, in this case is the transfer function H(z), is either a positive or negative value of the reference voltage +/−V
ref
.
Without a dither signal where d(n)=0 for all n, the decision threshold window for the quantizer is (−V
th
, V
th
). With the dither signal d(n), the window is shifted to (−V
th
−d(n), V
th
−d(n)). When the dither signal d(n) is a pseudorandom series, the window shifts randomly and, thereby, generates a decorrelated output sequence. Thus, the periodicity of the output series y(n) is destroyed and the idle channel tones are removed.
The dithering d(n) amplitude, however, must be large enough to remove the idle channel tones. For example, for a 1-bit quantizer, the ratio of the peak-to-peak range of the dither to the quantizer interval &dgr;/&Dgr; must be greater than 0.5, where &dgr; is the peak-to-peak range of the dither and &Dgr; is the quantizer interval. The dynamic range is degraded by 5 dB when dither peak-to-peak range &dgr; is equal to quantizer interval &Dgr;.
For a high input signal range, however, there still exists penalties wherein the signal to noise ratio decreases when there is a high input signal. Thus, a need exists for a more efficient dithering method that removes idle channel noise from a sigma-delta modulator.
SUMMARY OF THE INVENTION
To address the above-discussed deficiencies of sigma-delta modulators, the present invention teaches a sigma-delta modulator having a more efficient dithering method that removes idle channel noise. This sigma-delta modulator and novel dithering method for rem

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