The differentiating aspects of delta-sigma ADCs are the use of oversampling in conjunction with decimation filtering, and quantization noise shaping.
Delta-sigma ADCs use sample rates that are a large multiple, for instance, 128 times the sample rate sufficient for a given signal. For example, to sample a 25 kHz signal, a sample rate greater than the Nyquist rate (that is, > 50 KHz) would be sufficient. However, a delta-sigma ADC using an oversample factor of 128 samples the signal at 6 MHz. This approach has several benefits, such as better antialiasing and higher resolution.
In the frequency domain, sampling a signal effectively modulates the input signal spectrum with carrier frequencies that are multiples of the sample rate Fs (that is, 0, Fs, 2Fs, 3 Fs, and so on). To ensure that these modulated versions of the input signal spectrum do not overlap, thus causing aliasing, the sample rate has to be greater than twice the maximum frequency component of the signal (that is, 2Fmax), the Nyquist rate. Conversely, if the input signal has frequency components above Fs /2, also called the Nyquist frequency, these components may alias into the sub-Nyquist frequency range, making it hard to detect signals of interest from among the aliases. This aliasing effect manifests as noise and signal distortion.
To prevent aliasing, the analog frontend of a data acquisition device often uses an analog lowpass filter that attenuates frequency components greater than the Nyquist frequency, prior to sampling by the ADC. There are stringent requirements on such filters as they are expected to have brick wall-like characteristics, which include sharp roll-off, flat passband, and so on. With such tight constraints and the fact that they have to be implemented as analog circuitry, these filters are complex to design and expensive to manufacture.
Figure 2. Oversampling relaxes the requirements on an analog antialiasing filter.
Delta-sigma ADCs relax the requirements on analog antialiasing filters by oversampling the input signal, as shown in Figure 2. Through oversampling, the modulated versions of the input signal spectrum are further separated in the frequency domain allowing for gradual roll-off filter characteristics, which make the analog antialiasing filter construction much simpler. Delta-sigma ADCs are composed mainly of digital components, making them even more attractive. With a primarily digital construction, they can be implemented in silicon and thus take advantage of advancements in very-large-scale integration VLSI technology.
Digital Decimation Filtering
The bit stream from the delta-sigma modulator is output to a digital decimation filter that averages and downsamples, thus producing an n-bit sample at the desired sample rate, Fs. This process of averaging has the effect of lowpass filtering the signal in the frequency domain, which attenuates the quantization noise and removes aliases from the band of interest. This decimation filter is usually built for an extremely flat frequency response in the passband and no phase error, a sharp roll-off near the cutoff frequency (about 0.49 times the sample rate Fs) and excellent rejection in the stop band, making it very effective at antialiasing. A digital decimation filter is typically implemented as a Finite Impulse Response (FIR) filter, such as a comb filter, which is a cost-effective way of implementing decimation.
Quantization Noise Shaping
The conversion of an analog signal into a digital signal introduces noise in the signal, which is called quantization noise. For a single digital sample, the noise is simply ± 1/2 LSB. The smaller the LSB, the higher the resolution of the ADC will be. A higher resolution implies lower quantization noise or a higher signal-to-noise ratio (SNR). The classical equation that captures the relation between ADC resolution and SNR is seen in Equation 1, where N is the effective number of bits of resolution of the ADC.
SNR = 6.02N + 1.76 dB (Equation 1)
However, that is not the end of the story. A delta-sigma modulator behaves as a lowpass filter for the signal and a highpass filter for the quantization noise, thus pushing the noise to higher frequency regions, as shown in Figure 3. This phenomenon is called quantization noise shaping, and is taken advantage of by employing digital decimation that effectively lowpass filters the modulator output and removes the quantization noise. The reduction of noise power in the frequency band of interest means a higher SNR or a greater dynamic range, as the noise floor has been significantly lowered.
This improvement in SNR due to oversampling can be seen in Equation 2, where Fs is the sample rate, K is the oversample factor, and BW is the bandwidth of the input signal. This increase in SNR results in a larger effective number of bits of ADC resolution.
SNR = 6.02N + 1.76 + 10log (KFs /2BW) dB (Equation 2)
Figure 3 illustrates quantization noise shaping, which is one of the key advantages of delta-sigma ADCs.
Figure 3. Oversampling results in quantization noise shaping.