*2.3. First-Order Delta–Sigma (*ΔΣ*) Modulator (*ΔΣ*M) ADC*

The ΔΣM topology emerged to avoid the shortcomings of the ΔM by moving the integrator from the feedback to the forward path. As illustrated in Figure 3a, in which the local quantizer (ADC) can again simply be a single comparator, the integrator operates over the error difference instead of the signal estimation, as in the ΔM case.

**Figure 3.** First-order ΔΣM ADC: (**a**) block diagram and (**b**) illustrative magnitude of STF, NTF and *Smax*.

This architecture relies essentially on an analog filter (integrator), a quantizer, and a DAC [4,11]. Using the linear additive white-noise model for the quantizer, this system can be represented in the Z domain, resulting in the following STF and NTF:

$$STF(z) = \frac{H(z)}{1 + H(z)}\tag{1}$$

$$NTF(z) = \frac{1}{1 + H(z)}\tag{2}$$

where *H*(*z*) is the integrator transfer function. The NS effect is more effective for higher *H*(*z*) filter orders, promoting higher-resolution converters; however, extra complexity is added to the system. These functions are represented in Figure 3b.
