Square-Wave-Based Systems: Theory, Application and Implementation

Abstract

The properties of square-waves, such as reproducibility and frequency control make them appealing to be exploited in signal processing systems. This dissertation shows the relevance of these properties and their convergence with ideas from different fields, such as math, signal processing, and integrated circuit design techniques. Consequently, the objective of this dissertation is to propose and develop new on-silicon square-wave-based signal processing topologies.

This dissertation presents two parts. The first one introduces a single-tone generator for built-in self-test systems. This application aims to reduce the expensive testing process within the production flow of a given integrated circuit. The proposed single-tone generator is based on a harmonic-canceling filter the basic principle of which is to reject the odd harmonics of a given square-wave in order to generate a highly-pure tone. The use of this topology imposes two main challenges: the implementation of equally-spaced square-waves and irrational tap coefficients on silicon. In this dissertation, the latter is addressed by proposing a new irrational coefficient generator which exploits the properties of the skew circulant matrices. A proof-of-concept version and a subsequent version which has been improved are presented. It considers the process variations that affect the precision of the irrational weights, and applies calibration techniques to alleviate their effects. The system is fabricated in 180nm complementary metal-oxide semiconductor technology and occupies 0.149mm². Measurement results show that the proposed single-tone generator can achieve an spurious-free dynamic range of 71.2dB while consuming a maximum of 16.7mW and operating from 0.5MHz to 110MHz. This shows that the performance of the proposed solution is competitive when compared with previous similar works.

The second part of this dissertation presents a multi-tone generator for brain stimulation. This answers the need for a drug-free alternative to treat brain diseases such as sleep disorders that affect millions of people worldwide. The goal of brain stimulation is to modify the brain physiology by applying different types of signals. In particular, this second part of the dissertation focuses on the transcranial electrical stimulation, since it is non-intrusive and produces minimal side effects. This type of stimulation is based on the application of low currents in the order of mAs directly to the skull via electrodes. Several stimulation waveforms have been studied, such as direct current, alternating current and random noise current. Furthermore, other solutions offer a patient-customized system that combines the ability to obtain brain signals, make a decision based on this information and apply a control signal to the brain in a closed-loop fashion. In this dissertation, a new approach to implement the analyze rand synthesizer blocks of a potential closed-loop brain stimulation system is proposed. The main goal is to be able to stimulate the brain with signals that resemble those the brain generates during the sleep only using square-waves. These blocks exploit the properties of a mathematical tool called square-wave analysis which provides a way to process any continuous-time signal in real time by using square-waves as carriers. The square-wave analysis theory is studied and a square-wave-based signal processing system is implemented at circuit-level in 130nm complementary metal-oxide semiconductor technology. It occupies 0.187mm², consumes 105µW and is able to reproduce brain signals during sleep from an open database with a percentage root-mean-square difference of 12%. These simulation results show the functionality of the proposed solution.