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. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\upalpha}, \boldsymbol{\upbeta}$</tex> are the orders of the Jacobian polynomial. Different combination of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\upalpha}, \boldsymbol{\upbeta}$</tex> results in different NTFs. The objective of this work is to determine the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\upalpha, \upbeta$</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{5}^{\mathbf{th}}$</tex> order DSM with an Oversampling Ratio (OSR) of 32 and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\gamma$</tex> 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.
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