Digital Signal Processing Reference
In-Depth Information
Fig. 8
Block diagram of a
first-order sigma-delta
modulator
X(z)
Y(z)
+
+
Integrator
Q
-
DAC
3.2.2
First-Order Sigma-Delta Modulator
Oversampled converters usually take advantage of noise shaping, that can be accom-
plished using sigma-delta (also called delta-sigma) modulators. Various modulator
topologies exist. The block diagram of a first-order sigma-delta modulator for an
and taken as input to the integrating filter. The integrator output is quantized by the
quantizer Q. One-bit quantizers are most common but also multi-bit quantizers are
used. The quantized output is the oversampled digital output from the modulator.
It is also converted back to digital using a DAC and subtracted from the input in
the addition node. In practice, a modulator is often implemented using switched-
comparator, and the one-bit DAC is simply a switch choosing one of two reference
voltages.
The sigma-delta modulator can be analyzed using a linearized model, where the
quantizer is modeled as an additive noise source. Denoting the input by
X
(
z
)
,the
noise by
N
(
z
)
and the integrator transfer function by
H
(
z
)
, the output
Y
(
z
)
can be
expressed as
Y
(
z
)=
ST F
(
z
)
X
(
z
)+
NTF
(
z
)
N
(
z
)
(17)
where the signal transfer function
ST F
(
z
)
and the noise transfer function
NTF
(
z
)
are respectively given by
(
)
H
z
ST F
(
z
)=
(18)
1
+
H
(
z
)
1
NTF
(
z
)=
)
.
(19)
1
+
H
(
z
When the integrator has a transfer function
z
−
1
H
(
z
)=
(20)
1
−
z
−
1
z
−
1
X
z
−
1
Y
(
z
)=
(
z
)+(
1
−
)
N
(
z
)
.
(21)
