Design and Implementation of an 8-Bit 1-kS/s Successive-Approximation ADC

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2021, Tutora: Anna Maria Vilà ArbonèsSuccessive-approximation (SAR) analog-to-digital converters (ADCs) are among the most common and widely used general-purpose ADC architectures for their moderate resolutions and sampling rates. This paper aims to study and understand the conventional SAR ADC by proposing an N-bit architecture with a split capacitor digital-to-analog converter (DAC), and design, simulate, and finally implement a functional 8-bit 1-kS/s 0-5V SAR ADC prototype on a breadboard. The simulations and the tested prototype allow us to analyze the results and notice some of the most relevant advantages and disadvantages of the SAR ADC besides its limitation

Ideal multipartite secret sharing schemes

Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. In this work, the characterization of ideal multipartite access structures is studied with all generality. Our results are based on the well-known connections between ideal secret sharing schemes and matroids and on the introduction of a new combinatorial tool in secret sharing, integer polymatroids . Our results can be summarized as follows. First, we present a characterization of multipartite matroid ports in terms of integer polymatroids. As a consequence of this characterization, a necessary condition for a multipartite access structure to be ideal is obtained. Second, we use representations of integer polymatroids by collections of vector subspaces to characterize the representable multipartite matroids. In this way we obtain a sufficient condition for a multipartite access structure to be ideal, and also a unified framework to study the open problems about the efficiency of the constructions of ideal multipartite secret sharing schemes. Finally, we apply our general results to obtain a complete characterization of ideal tripartite access structures, which was until now an open problem

On the Information Ratio of Non-perfect Secret Sharing Schemes

A secret sharing scheme is non-perfect if some subsets of players that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes and the construction of efficient linear non-perfect secret sharing schemes. To this end, we extend the known connections between matroids, polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information on the secret value that is obtained by each subset of players. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, access functions whose values depend only on the number of players, generalize the threshold access structures. The optimal information ratio of the uniform access functions with rational values has been determined by Yoshida, Fujiwara and Fossorier. By using the tools that are described in our work, we provide a much simpler proof of that result and we extend it to access functions with real values