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 (SR). With the output voltage limited within 2 V, 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.

An organization may suffer large losses if its computer service is interrupted. For protection, it can purchase computer backup service from the outside market which temporarily provides service replacement from a central facility. A dynamic probabilistic model is developed which describes such a computer backup service system. The parties involved have conflicting motivations. The supplier is interested in optimizing his expected profits subject to a given set of parameters while the subscriber will evaluate the service contract to his own best interest. This paper analyzes how the economic interests of the supplier and subscribers interact based on a dynamic reliability analysis of their respective computer systems. Assuming all physical parameters fixed, the supplier's optimal value in terms of economic parameters is determined. An algorithmic procedure is developed for computing such values. Some numerical examples are presented in order to gain insights into the system.