Deltasigma ADCs in a nutshell, part 2: the modulator
A deltasigma converter uses many samples from the modulator to produce a stream of 1bit codes. The deltasigma ADC accomplishes this task by using an inputsignal quantizer running at a high sample rate. Like all quantizers, the deltasigma modulator takes an input and produces a stream of digital values that represents the voltage of the input. You can look at the deltasigma modulator in the time or in the frequency domain. If you look at a timedomain representation, you can see the mechanics of a firstorder modulator (Figure 1).
The modulator measures the difference between the analoginput signal and the analog output of a feedback DAC. An integrator then measures the analogvoltage output of the summing junction and presents a sloping signal to the 1bit ADC. The 1bit ADC converts the integrator’s output signal to a digital one or zero. Using the system clock, the ADC sends the 1bit digital signal to the modulator’s output, as well as back through the feedback loop, where a 1bit DAC is waiting.

The 1bit ADC digitizes the signal to a coarse output code that has the quantization noise (e_{i}) of the converter. The modulator output is equal to the input plus the quantization noise, (e_{i}–e_{i–1}). As this formula shows, the quantization noise is the difference of the current error (e_{i}) minus the previous error (e_{i–1}) of the modulator. The timedomain output signal is a pulsewave representation of the input signal at the sampling frequency, f_{S}. If you average the outputpulse train, it equals the value of the input signal.
The frequencydomain diagram tells a different story (Figure 2). The timedomain output pulses in the frequency domain appear as the input signal (or spur) and shaped noise. The noise characteristic in Figure 2 is the key to the modulator’s frequency operation.
Unlike most quantizers, the deltasigma modulator includes an integrator that shapes the quantization noise. The noise spectrum at the modulator output is not flat. More important, in a frequency analysis, you can see how the modulator shapes the noise to higher frequencies, facilitating the production of a higher resolution result.
The modulator output in Figure 2 shows that the quantization noise of the modulator starts low at 0 Hz, rises rapidly, and then levels off at a maximum value at the modulator sampling frequency.
Integrating twice with a secondorder modulator, instead of just once, is a great way to minimize lowfrequency quantization noise. Most deltasigma modulators are of a higher order. For instance, the designs of the more popular deltasigma converters include second, third, fourth, fifth, or sixthorder modulators. Multiorder modulators shape the quantization noise even harder to higher frequencies.
References 

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