MT-022 Datasheet, PDF (5/12 Pages) Analog Devices – ADC Architectures III: Sigma-Delta ADC Basics

MT-022
especially in consumer audio applications where the cost of a sharp cutoff linear phase filter can
be significant.
A
f_s
ADC
Nyquist
Operation
Oversampling
B
+ Digital Filter
Kf_{s + Decimation} f_s
ADC
DIGITAL
FILTER
DEC
QUANTIZATION
NOISE = q / 12
q = 1 LSB
f_s
2
f_s
DIGITAL FILTER
REMOVED NOISE
Oversampling
+ Noise Shaping
+ Digital Filter
C
Kf_s ^{+ Decimation} f_s
ΣΔ
MOD
DIGITAL
FILTER
DEC
f_s
Kf_s
Kf_s
2
2
REMOVED NOISE
f_s
Kf_s
Kf_s
2
2
Figure 3: Oversampling, Digital Filtering, Noise Shaping, and Decimation
Since the bandwidth is reduced by the digital output filter, the output data rate may be lower than
the original sampling rate (Kf_s) and still satisfy the Nyquist criterion. This may be achieved by
passing every Mth result to the output and discarding the remainder. The process is known as
"decimation" by a factor of M. Despite the origins of the term (decem is Latin for ten), M can
have any integer value, provided that the output data rate is more than twice the signal
bandwidth. Decimation does not cause any loss of information (see Figure 3B).
If we simply use oversampling to improve resolution, we must oversample by a factor of 2^2N to
obtain an N-bit increase in resolution. The Σ-Δ converter does not need such a high oversampling
ratio because it not only limits the signal passband, but also shapes the quantization noise so that
most of it falls outside this passband as shown in Figure 3C.
If we take a 1-bit ADC (a comparator), drive it with the output of an integrator, and feed the
integrator with an input signal summed with the output of a 1-bit DAC fed from the ADC output,
we have a first-order Σ-Δ modulator as shown in Figure 4. Add a digital low pass filter (LPF)
and decimator at the digital output, and we have a Σ-Δ ADC—the Σ-Δ modulator shapes the
quantization noise so that it lies above the passband of the digital output filter, and the ENOB is
therefore much larger than would otherwise be expected from the oversampling ratio.
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