If we simply use over-sampling to improve resolution, we must over-sample by a factor of 2 2N to obtain an N-bit increase in resolution. The Sigma-Delta converte does not need such a high over-sampling ratio because it not only limits the signal passband, but also shapes the quantization noise so that most of it falls outside this passband If we take a l-bit adc (generally known as 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 Sigma-Delta modulator as shown in Figure 3.9. Add a digital low pass filter (LPF)and decimator at the digital output, and we have a Sigma-Delta ADC: the Sigma-Delta 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 over-sampling ratio FIRST ORDER SIGMA-DELTA ADC 当∑ VREF Figure 3.9 B than one integration and summing stas Delta modulator, we can achieve higher orders of quantization noise shaping and even better ENOB for a given over-sampling ratio as is shown in figure 3. 10 for both a first and second-order Sigma-Delta modulator The block diagram for the second order Sigma-Delta modulator is shown in Figure 3. 11. Third, and higher, order Sigma- Delta ADCs were once thought to be potentially unstable at some values of input- recent analyses using finite rather than infinite gains in the comparator have shown that this is not necessarily so, but even if instability does start to occur, it is not important, since the DSP in the digital filter and decimator can be made to recognize incipient instability and react to prevent it.8 If we simply use over-sampling to improve resolution, we must over-sample by a factor of 2^2N to obtain an N-bit increase in resolution. The Sigma-Delta converter does not need such a high over-sampling ratio because it not only limits the signal passband, but also shapes the quantization noise so that most of it falls outside this passband. If we take a 1-bit ADC (generally known as 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 Sigma-Delta modulator as shown in Figure 3.9. Add a digital low pass filter (LPF) and decimator at the digital output, and we have a Sigma-Delta ADC: the Sigma-Delta 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 over-sampling ratio. FIRST ORDER SIGMA-DELTA ADC Figure 3.9 By using more than one integration and summing stage in the Sigma-Delta modulator, we can achieve higher orders of quantization noise shaping and even better ENOB for a given over-sampling ratio as is shown in Figure 3.10 for both a first and second-order Sigma-Delta modulator. The block diagram for the second￾order Sigma-Delta modulator is shown in Figure 3.11. Third, and higher, order Sigma-Delta ADCs were once thought to be potentially unstable at some values of input - recent analyses using finite rather than infinite gains in the comparator have shown that this is not necessarily so, but even if instability does start to occur, it is not important, since the DSP in the digital filter and decimator can be made to recognize incipient instability and react to prevent it