Derivation of the transfer functions of 1-bit Multi-Step Look-Ahead ΣΔ modulators using system identification methods

A method to calculate the transfer functions of Multi-Step Look-Ahead (MSLA) ΣΔ modulators is presented. MSLA ΣΔ modulators exhibit better noise shaping characteristics and stability than conventional ones. They are comprised of a number of conventional ΣΔ modulators in parallel, sharing a multi-input 1-bit output quantizer. MSLA modulators are highly nonlinear systems due to the multi-input quantizer. Modeling of the quantizer using conventional linearization methods does not give satisfactory results. Therefore, this work applies system identification methods to derive the linearized MSLA modulator system transfer functions. More specifically the Vector Fitting algorithm is used for the linearization of a number of MSLA modulators. The obtained transfer functions are in very good agreement with simulation results, showcasing the effectiveness of the applied methods.