On the design and analysis of the 4^th-order leapfrog sigma-delta modulator

In this paper, a novel methodology for designing and analyzing high performance sigma-delta leapfrog modulators for ultra-high resolution analog-to-digital (A/D) converters is presented. The less sensitive topology, the leapfrog topology, in component variations is analyzed by considering the noise transfer function (NTF). By using theoretical analysis, the loop coefficients are constrained to a small, clear and definite range called the stable region. With the output voltage limited within + 2V, an absolutely stable region (ASR) is obtained. A program that analyzes and generates the required coefficients is constructed for easily designing this topology. For a 256 over-sampling ratio (OSR) and the coefficients from ASR, the signal to noise ratio (SNR) and dynamic range (DR) are 105 dB and 100 dB, respectively. In accordance with the behavior simulation results, the system is not only stable and efficient but also suitable for high-resolution applications.