MT-022 Datasheet, PDF (4/12 Pages) Analog Devices – ADC Architectures III: Sigma-Delta ADC Basics

MT-022
stream of process and design improvements in the fundamental architecture proposed in the early
works cited above.
Modern CMOS Σ-Δ ADCs (and DACs, for that matter) are the converters of choice for
voiceband and audio applications. The highly digital architectures lend themselves nicely to fine-
line CMOS. In addition, high resolution (up to 24 bits) low frequency Σ-Δ ADCs have virtually
replaced the older integrating converters in precision industrial measurement applications.
BASICS OF Σ-Δ ADCS
There have been innumerable descriptions of the architecture and theory of Σ-Δ ADCs, but most
commence with a maze of integrals and deteriorate from there. Some engineers who do not
understand the theory of operation of Σ-Δ ADCs are convinced, from study of a typical published
article, that it is too complex to comprehend easily.
There is nothing particularly difficult to understand about Σ-Δ ADCs, as long as you avoid the
detailed mathematics, and this section has been written in an attempt to clarify the subject. A Σ-
Δ ADC contains very simple analog electronics (a comparator, voltage reference, a switch, and
one or more integrators and analog summing circuits), and quite complex digital computational
circuitry. This digital circuitry consists of a digital signal processor (DSP) which acts as a filter
(generally, but not invariably, a low pass filter). It is not necessary to know precisely how the
filter works to appreciate what it does. To understand how a Σ-Δ ADC works, familiarity with
the concepts of oversampling, quantization noise shaping, digital filtering, and decimation is
required.
Let us consider the technique of oversampling with an analysis in the frequency domain. Where
a dc conversion has a quantization error of up to ½ LSB, a sampled data system has quantization
noise. A perfect classical N-bit sampling ADC has an rms quantization noise of q/√12 uniformly
distributed within the Nyquist band of dc to f_s/2 (where q is the value of an LSB and f_s is the
sampling rate) as shown in Figure 3A. Therefore, its SNR with a full-scale sinewave input will
be (6.02N + 1.76) dB. (Refer to Tutorial MT-001 for the derivation). If the ADC is less than
perfect, and its noise is greater than its theoretical minimum quantization noise, then its effective
resolution will be less than N-bits. Its actual resolution (often known as its Effective Number of Bits
or ENOB) will be defined by
ENOB = ^{SNR − 1.76dB} .
6.02dB
Eq. 1
If we choose a much higher sampling rate, Kf_s (see Figure 3B), the rms quantization noise
remains q/√12, but the noise is now distributed over a wider bandwidth dc to Kf_s/2. If we then
apply a digital low pass filter (LPF) to the output, we remove much of the quantization noise, but
do not affect the wanted signal—so the ENOB is improved. We have accomplished a high
resolution A/D conversion with a low resolution ADC. The factor K is generally referred to as
the oversampling ratio. It should be noted at this point that oversampling has an added benefit in
that it relaxes the requirements on the analog antialiasing filter. This is a big advantage of Σ-Δ,
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