Design of high order stable delta sigma modulator with state space approach

A new design far high-order oversampled delta sigma (ΔΣ) modulators that are robust to any initial state offsets by using state space approach and optimizing the spectral norm of system transfer matrix is presented. The modulator is designed by state space model to have the stable quantization noise transfer function (NTF) and signal transfer function (STF) as high signal-to-noise ratio (SNR) as the conventional high-order modulator. Moreover the parameters of the structure are designed and optimized by decreasing a spectral norm of system transfer matrix. Since the transfer matrix reduces the vector norm of node signals in the modulator every clock process, the quantization overload frequency from any initial offset can be decreased and can be recovered from the unstable status with zero input condition. Simulation results of the designed modulator are compared with the conventional ones to show a remarkable performance and to confirm the advantage of the proposed method.