Design of Noise Transfer Function for Delta Sigma Modulator based on Modified Jacobi Polynomial Approximations

Abstract

This paper presents the design of Noise Transfer Function (NTF) for Delta Sigma Modulator (DSM) based on continuous time high pass filter approximated by modified Jacobi polynomial. $\boldsymbol{\upalpha}, \boldsymbol{\upbeta}$ are the orders of the Jacobian polynomial. Different combination of $\boldsymbol{\upalpha}, \boldsymbol{\upbeta}$ results in different NTFs. The objective of this work is to determine the $\upalpha, \upbeta$ values for which the optimum attenuation characteristic is achieved in the stopband of the NTF while satisfying the realizability condition of the DSM. For the $\boldsymbol{5}^{\mathbf{th}}$ order DSM with an Oversampling Ratio (OSR) of 32 and $\gamma$ of 1.5 an SQNR of 69.9 dB is achieved which is an improvement of 5.15 dB compared to the Delta Sigma Toolbox (DST) method.