Simulink Model Implementation of First- and Second-Order Sigma-Delta ADCs

This document presents a detailed implementation of Simulink models for first- and second-order sigma-delta analog-to-digital converters (ADCs). Sigma-delta ADCs, also known as oversampling ADCs, represent a widely adopted methodology for achieving high-resolution analog-to-digital conversion through noise shaping and oversampling techniques. These converters find extensive applications in audio processing systems, communication equipment, and precision sensor interface circuits. The implementation leverages MATLAB's integrator blocks, quantizers, and feedback loops to construct the sigma-delta modulator core. The Simulink environment provides a robust platform for simulating and analyzing sigma-delta ADC behavior through block diagram implementations. Key parameters including modulator order selection (first vs. second-order), oversampling ratio (OSR) configuration, and noise transfer function (NTF) characteristics can be systematically optimized using Simulink's built-in DSP blocksets. The modeling approach incorporates digital filter components (typically CIC or FIR filters) and decimation stages to achieve targeted signal-to-noise ratio performance. Model development follows a structured workflow: initial system specification definition using MATLAB script-based parameter initialization, followed by modulator design employing Simulink's library components (summers, delays, quantizers). The implementation includes crucial algorithm considerations such as stability analysis for second-order modulators and optimal coefficient selection using MATLAB's delta-sigma toolbox functions. Digital post-processing stages implement decimation filters through Simulink's Digital Filter Design block with configurable passband ripple and stopband attenuation parameters. Post-implementation analysis capabilities include SNR evaluation using Simulink's Spectrum Analyzer tool, THD measurement through FFT analysis, and dynamic performance validation via test signal injection. The model supports Monte Carlo simulations for robustness testing and parameter sweep functionalities for design optimization. This comprehensive modeling framework enables deep understanding of sigma-delta ADC operational principles while providing practical tools for performance optimization meeting specific application requirements.