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Incremental data converters (IDCs) are useful in instrumentation and measurement applications, where low-frequency analog signals need to be converted into digital form with high accuracy and low power dissipation. They are particularly well suited for applications where a single analog-digital converter is multiplexed between many channels. This paper proposes an exact design methodology for IDCs, which optimizes the signal-to-noise ratio of the converter under practical design constraints. The process also allows the designer to apportion the noise budget in an arbitrary manner between thermal and quantization noise. The design process is illustrated by an example which describes the optimization of a third-order multiplexed IDC. Index Terms--Analog-digital (A/D) conversion, data conversion, decimation filters, incremental data converters (IDCs).

Thermal noise represents a major limitation on the performance of most electronic circuits. It is particularly important in switched circuits, such as the switched-capacitor (SC) filters widely used in mixed-mode CMOS integrated circuits. In these circuits, switching introduces a boost in the power spectral density of the thermal noise due to aliasing. Unfortunately, even though the theory of noise in SC circuits is discussed in the literature, it is very intricate. The numerical calculation of noise in switched circuits is very tedious, and requires highly sophisticated and not widely available software. The purpose of this paper is twofold. It provides a tutorial description of the physical phenomena taking place in an SC circuit while it processes noise (Sections II--III). It also proposes some specialized but highly efficient algorithms for estimating the resulting sampled noise in SC circuits, which need only simple calculations (Sections IV--VI). A practical design procedure, which follows directly from the estimate, is also described. The accuracy of the proposed estimation algorithms is verified by simulation using SpectreRF. As an example, it is applied to the estimation of the total thermal noise in a second-order low-distortion delta-sigma converter. Index Terms--Delta-sigma ([DELTA] [SIGMA]) modulator, switched-capacitor (SC) circuit, thermal noise.