Relationship to .CE.94-modulation Delta-sigma modulation
fig. 2: derivation of ΔΣ- Δ-modulation
ΔΣ modulation (sdm) inspired Δ modulation (dm), shown in fig. 2. if quantization homogeneous (e.g., if linear), following sufficient derivation of equivalence of dm , sdm:
however, quantizer not homogeneous, , explanation flawed. s true ΔΣ inspired Δ-modulation, 2 distinct in operation. first block diagram in fig. 2, integrator in feedback path can removed if feedback taken directly input of low-pass filter. hence, delta modulation of input signal
u
{\displaystyle \scriptstyle u}
, low-pass filter sees signal
y
dm
=
∫
quantize
(
u
−
y
dm
)
.
{\displaystyle y_{\text{dm}}=\int \operatorname {quantize} \left(u-y_{\text{dm}}\right).\,}
however, sigma-delta modulation of same input signal places @ low-pass filter
y
sdm
=
quantize
(
∫
(
u
−
y
sdm
)
)
.
{\displaystyle y_{\text{sdm}}=\operatorname {quantize} \left(\int \left(u-y_{\text{sdm}}\right)\right).\,}
in other words, sdm , dm swap position of integrator , quantizer. net effect simpler implementation has added benefit of shaping quantization noise away signals of interest (i.e., signals of interest low-pass filtered while quantization noise high-pass filtered). effect becomes more dramatic increased oversampling, allows quantization noise programmable. on other hand, Δ-modulation shapes both noise , signal equally.
additionally, quantizer (e.g., comparator) used in dm has small output representing small step , down quantized approximation of input while quantizer used in sdm must take values outside of range of input signal, shown in fig. 3.
fig. 3: example of sdm of 100 samples of 1 period sine wave. 1-bit samples (e.g., comparator output) overlaid sine wave logic high (e.g.,
+
v
c
c
{\displaystyle \scriptstyle +v_{cc}}
) represented blue , logic low (e.g.,
−
v
c
c
{\displaystyle \scriptstyle -v_{cc}}
) represented white.
in general, ΔΣ has advantages versus Δ modulation:
the whole structure simpler:
only 1 integrator needed
the demodulator can simple linear filter (e.g., rc or lc filter) reconstruct signal
the quantizer (e.g., comparator) can have full-scale outputs
the quantized value integral of difference signal, makes less sensitive rate of change of signal.
Comments
Post a Comment