Optimization of fourth order noise transfer function using PSO algorithm for delta sigma modulator

• Published in: Integration (Amsterdam) Vol. 106; p. 102539
• Main Authors: J, Arockia Twinkle, R, Srinivasan, Chandramani, Premanand V.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2026
• Subjects: Analog to digital converter; Delta sigma modulator-synthesis; Linear model; Noise transfer function; Particle swarm optimization algorithm; Signal to quantization noise ratio; Signal to quantization noise ratio; Analog to digital converter; Noise transfer function; Linear model; Particle swarm optimization algorithm; Delta sigma modulator-synthesis
• ISSN: 0167-9260
• DOI: 10.1016/j.vlsi.2025.102539

Delta Sigma Modulator (ΔΣM) has in-built noise shaping feature, which is defined by Noise Transfer Function (NTF). Optimization of NTF directly improves the noise shaping property of the ΔΣM and its overall performance. The proposed method employs PSO algorithm for optimizing the NTF. By utilizing its robust global optimization abilities, the PSO algorithm efficiently navigates the design space, converging on optimal NTF that yields Signal to Quantization Noise (SQNR) of 62.7244 dB. Additionally, Cascade of Resonators with Feed-Forward (CRFF) ΔΣM synthesized with the proposed NTF achieves peak-to-peak SNR (SNRp2p)/peak signal-to-noise ratio (Peak SNR)/average SNR (Peak SNR) of 92.5 dB/82.9594 dB/82.1 dB with reduced computational complexity. The proposed method achieves higher SQNR × Over load level for different Oversampling Ratio (OSR) values when compared to the existing methods. •The primary goal of this work is to optimize the noise transfer function for delta sigma modulator using PSO algorithm for OSR of 32 and bandwidth of 22.05 kHz.•The optimized noise transfer function achieves SQNR of 62.7244 dB. It also satisfies all the realizability and stability criteria required for the delta sigma modulator.•A fourth order CRFF delta sigma modulator is synthesized with the optimized noise transfer function and achieves peak-to-peak SNR/peak signal-to-noise ratio/average SNR of 92.5dB/82.9594dB/82.1 dB.•The efficiency of the proposed method is validated using the metric, SQNR × Over load level. The proposed method achieves highest SQNR × Over load level compared to the existing methods.•The computational complexity of the proposed method is significantly low compared to the existing methods.