Coded data generation or conversion – Analog to or from digital conversion – Differential encoder and/or decoder
Reexamination Certificate
2001-09-04
2003-01-14
Williams, Howard L. (Department: 2819)
Coded data generation or conversion
Analog to or from digital conversion
Differential encoder and/or decoder
Reexamination Certificate
active
06507302
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to an analog-to-digital converter, and more specifically to a &Dgr;&Sgr; A/D converter constituted of a combination of an oversampling and a noise shaping.
An oversampling A/D converter not only can minimize a quantization noise in a signal band but also can realize a highly precise conversion by making a sampling frequency greatly higher than a Nyquist frequency which is a double of signal band frequency. Namely, a ratio of a signal power to a noise power (called a “SN ratio” hereinafter) is increased. The reason for this is as follows:
The quantization noise generated in a quantizer for converting an analog signal into a digital signal, is a white noise which generates irregularly and distributes over the whole of a frequency region. Assuming that the sampling frequency of the oversampling A/D converter is fs, the noise power distributes from DC to fs/2. If the sampling frequency is remarkably larger than the signal band, the noise power in the signal band correspondingly becomes small. The noise power distributing out of the signal band can be removed by a decimation filter which is located at a later stage in an ordinary practice.
Therefore, the larger the ratio of the sampling frequency fs to the Nyquist frequency fn (called an “oversampling ratio” hereinafter) is, the SN ratio becomes larger.
A &Dgr;&Sgr; A/D converter, which is one kind of the oversampling A/D converter, is a technology having a frequency characteristics of a high pass filter for a noise power distributed from DC to fs/2, so as to further decrease the noise power in a low frequency region. Accordingly, the noise power in the signal band is further reduced. In general, a technology of expelling the noise power in the signal band to the outside of the signal band is known as a noise shaping.
FIG. 10
illustrates a basic structure of a conventional &Dgr;&Sgr; A/D converter. This comprises an analog adder
1
for obtaining a difference between an analog input signal X(z) and an output of a one-bit D/A converter provided in a feedback part, an analog integrator
2
for integrating an output of the analog adder
1
, an one-bit quantizer
3
for converting an output of the analog integrator
2
into a digital value, a delay
8
for holding an output of the one-bit quantizer
3
until a next sampling time, and the one-bit D/A converter
6
for converting a one-bit data of the delay
8
into an binary analog signal. A digital output of the one-bit quantizer
3
constitutes an output Y(z) of this &Dgr;&Sgr; A/D converter. Incidentally, the analog integrator
2
has a characteristics of a low pass filter for allowing to only a low frequency component to pass and for cutting off a high frequency component. Seeking a transfer function of this structure, it becomes the following expression (1):
Y
(
z
)=
X
(
z
)+(1−
z
−1
)
Q
(
Z
) (1)
In this case, since only one analog integrator is provided in a closed loop, the shaping noise of a first-order can be realized. For example, in a &Dgr;&Sgr; A/D converter having two analog integrators in a closed loop, the noise shaping of a second-order is realized, thereby to increase a noise suppression in the signal band.
In a Nyquist sampling A/D converter performing a sampling at a Nyquist frequency, the precision of conversion is determined by precision in the circuit in a voltage axis. In the oversampling &Dgr;&Sgr; A/D converter, however, it is possible to increase the SN ratio by increasing the oversampling ratio or increasing the order of the noise shaping. In other words, since the oversampling &Dgr;&Sgr; A/D converter is a technology for increasing the precision of conversion in a time axis, the precision in the circuit in a voltage axis can be relaxed. Therefore, the precision of conversion is bounded by 12 bits in the Nyquist sampling A/D converter, but the oversampling &Dgr;&Sgr; A/D converter can obtain a further high precision of conversion. For example, in an audio band having a signal band of about 20 kHz, if the oversampling ratio is 64 times with the noise shaping of a third-order, the sampling frequency becomes about 2.5 MHz. In this case, the precision of conversion of 16 bits can be sufficiently realized.
However, considering to what degree a convertible signal band can be enlarged while the precision of conversion, a several 100 kHz is an upper limit. For example, if it is attempted to obtain the precision of conversion compatible to the above example in the signal band of 1 MHz, the sampling frequency becomes 128 MHz with the noise shaping of the third-order. In this case, an unity gain frequency of an operational amplifier used in the integrator is required to be on the order of 500 MHz. However, it is very difficult to design such an operational amplifier, and although it possible, a consumed electric power remarkably increases. If the order of the noise shaping is increased to a fourth-order or A fifth order, the oversampling ratio can be lowered. However, if the order of the noise shaping exceeds the third-order, the closed loop becomes unstable.
In order to realize a stable structure, it is necessary to give an attenuation coefficient (0<a
i
<1) to the integrator, so that an output amplitude of the integrator never becomes large. For example,
FIG. 11
illustrate a basic structure of a stability-considered &Dgr;&Sgr; A/D converter realizing the noise shaping of the third-order. Three analog integrators are provided, and an analog multiplier
9
a
,
9
b
and
9
c
is located behind each analog integrator. The transfer function is expressed by the following expression (2):
Y
(
z
)={
a
1
a
2
a
3
X
(
z
)+(1−
z
−1
)
Q
(
z
)}/
f
(
z
) (2)
where
f
(
z
)=1+(
a
1
a
2
a
3
+
a
2
a
3
+
a
3
−3)
z
−1
+(3−
a
2
a
3
+2
a
3
)
z
−2
+(
a
3
−1)
z
−3
Namely, the signal component is attenuated by the product “a
1
a
2
a
3
” of attenuation coefficients of the respective integrators. Therefore, even if the order is increased, it is not possible to estimate an increase of the SN ratio as expected.
Now, a multi-bit &Dgr;&Sgr; A/D converter is known, which comprises, as shown in
FIG. 12
, an n-bit quantizer
4
for converting an analog signal into a digital signal of a multi value, and an n-bit D/A converter
7
for converting the multi-bit digital signal of the multi value into an analog signal of a multi value, in place of the one-bit quantizer
3
and the one-bit D/A converter
6
. In this A/D converter, by increasing the resolution of the quantizer, the quantization noise Q′(z) becomes small and the noise power distributed over the whole frequency region is decreased. In general, by increasing the resolution of the n-bit quantizer
4
by each one bit, the SN ratio is elevated by each 6 dB. However, the n-bit D/A converter
7
has a non-linear error E(z). The transfer function of the multi-bit &Dgr;&Sgr; A/D converter shown in
FIG. 12
becomes as the following equation (3):
Y
(
z
)=
X
(
z
)+
E
(
z
)+(1−
z
−1
)
Q
′(
z
) (3)
The non-linear error E(z) of the n-bit D/A converter
7
is added to the analog signal X(z) with no modification, and the noise shaping is not made. Namely, the SN ratio is remarkably deteriorated by this non-linearity. Therefore, the n-bit D/A converter
7
is required to have the precision comparable to the precision of conversion in the A/D converter. However, it is very difficult to realize the n-bit D/A converter
7
mentioned above, and the circuit scale greatly becomes large. For example, in the case that the n-bit D/A converter
7
is realized in an integrated circuit, many capacitors are required. If a 16-bit D/A converter is constituted using 2
16
unitary capacitors of 5 &mgr;m square, a size variation to be controlled in a fabricating process is 4.9 nm, which is a value difficult to realize. In addition, even if such very small capacitors are used, the total area of the capa
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