Sigmadelta

Sigmadelta, or sigma-delta (ΣΔ), refers to a class of analog-to-digital and digital-to-analog conversion techniques that use oversampling and noise shaping to achieve high resolution with relatively simple circuitry. The basic idea is to sample the input signal at a rate well above the signal bandwidth and to quantize it with a coarse, typically one-bit or few-bit, quantizer. The quantization error is fed back through a filter, shaping its spectrum so that most of the noise energy is pushed to higher frequencies outside the band of interest. A digital decimation filter then reduces the sample rate and reconstructs a high-resolution digital output.

In operation, a sigmadelta modulator converts the input into a high-rate stream of low-resolution bits. The accompanying digital decimation filter removes out-of-band noise and produces a lower-rate, high-resolution representation of the signal. There are continuous-time and discrete-time variants, and the order of the loop (first order, second order, and higher) determines the amount of noise shaping and the achievable resolution. The multi-stage noise shaping (MASH) architecture is one approach used to implement higher-order systems while managing stability.

Applications and characteristics: Sigmadelta converters are widely used in audio ADCs and DACs, precision measurement instruments, sensor front ends, and communications receivers. They offer high dynamic range and good linearity with relatively simple analog components, making them well suited for integration in CMOS processes. Disadvantages include the need for high oversampling ratios, complex digital filtering, potential stability issues in high-order loops, and limitations in bandwidth. Overall, sigmadelta is valued for achieving high resolution with robust performance in low- to medium-bandwidth applications.