Design of COR Σ-Δ A/D converters amenable to capacitor scaling in switched-capacitor hardware implementations

It is well known that the cascade-of-resonators (COR) Σ-Δ A/D converters achieve high signal-to-quantization-noise ratio (SQNR) levels in virtue of the fact that the constituent noise transfer function zeros are located at real frequencies. The existing techniques for the design of COR Σ-Δ A/D converters fail to take into account the capacitance spread and the total capacitance in a corresponding switched-capacitor hardware implementation. This paper presents a novel approach to the design of COR Σ-Δ A/D converters yielding small capacitance spread as well as small total capacitance. This is achieved by making the constituent feedforward capacitors mirror images of the corresponding feedback capacitors. These conditions are themselves satisfied by ensuring that the signal transfer function is made complementary to the noise transfer function. The application of the proposed approach to the design of a hitherto benchmark COR A/D converter results in a 450% reduction in the capacitance spread, and a 340% reduction in the total capacitance, while yielding the same achievable SQNR and dynamic range.