Model a Sigma-Delta DAC Plus RC Filter

Neil Robertson

Still RelevantIntermediate

Sigma-delta digital-to-analog converters (SD DAC’s) are often used for discrete-time signals with sample rate much higher than their bandwidth. For the simplest case, the DAC output is a single bit, so the only interface hardware required is a standard digital output buffer. Because of the high sample rate relative to signal bandwidth, a very simple DAC reconstruction filter suffices, often just a one-pole RC lowpass. In this article, I present a simple Matlab function that models the combination of a basic SD DAC and one-pole RC filter. This model allows easy evaluation of the overall performance for a given input signal and choice of sample rate, R, and C.

Summary

This blog presents a compact Matlab function that models a 1-bit sigma-delta (SD) DAC followed by a one-pole RC reconstruction filter, letting the reader simulate time- and frequency-domain behavior for arbitrary input signals. It shows how sample rate, R, and the RC time constant affect in-band noise shaping, spectral content, and overall analog output fidelity.

Key Takeaways

Use the provided Matlab model to simulate a 1-bit SD DAC driving a one-pole RC filter for arbitrary input waveforms.
Evaluate the effect of oversampling ratio and modulator switching on in-band noise and overall SNR using time- and frequency-domain plots.
Choose R and C values to meet desired bandwidth and attenuation trade-offs by inspecting the filter's frequency response and transient output.
Compute and interpret FFT-based spectra to quantify quantization-noise shaping, harmonic content, and residual tones at the analog output.

Who Should Read This

DSP engineers or graduate students with basic Matlab experience who need to model and evaluate 1-bit sigma-delta DACs and simple RC reconstruction filters for audio, communications, or mixed-signal projects.

Still RelevantIntermediate

Topics

Filter Design FFT/Spectral Analysis MATLAB/Simulink Multirate Systems