This master's thesis deals with modeling of linear electrical circuits through the differential algebraical equation systems. It describes methods of numerical solving, discusses the need of algebraical conversions and possibility of minimalization through the use of parasitic components. In addition, it involves the design and implementation of extension of available simulation tool.

<p>The last few decades have witnessed unprecedented growth in multiple areas of electronics spanning low-power sensing, intelligent computing and high-speed wireless connectivity. In the foreseeable future, there would be hundreds of billions of computing devices, sensors, things and people, wherein the technology will become intertwined with our lives through continuous interaction and collaboration between humans and machines. Such human-centric ideas give rise to the concept of internet of bodies (IoB), which calls for novel and energy-efficient techniques for sensing, processing and secure communication for resource-constrained IoB nodes.As we have painfully learnt during the pandemic, point-of-care diagnostics along with continuous sensing and long-term connectivity has become one of the major requirements in the healthcare industry, further emphasizing the need for energy-efficiency and security in the resource-constrained devices around us.</p> <p>  </p> <p>  With this vision in mind, I’ll divide this dissertation into the following chapters. The first part (Chapter 2) will cover time-domain sensing techniques which allow inherent energy-resolution scalability, and will show the fundamental limits of achievable resolution. Implementations will include 1) a radiation sensing system for occupational dosimetry in healthcare and mining applications, which can achieve 12-18 bit resolution with 0.01-1 µJ energy dissipation, and 2) an ADC-less neural signal acquisition system with direct Analog to Time Conversion at 13pJ/Sample. The second part (Chapters 3 and 4) of this dissertation will involve the fundamentals of developing secure energy-efficient electro-quasistatic (EQS) communication techniques for IoB wearables as well as implants, and will demonstrate  2 examples: 1) Adiabatic Switching for breaking the αCV^2f limit of power consumption in capacitive voltage mode human-body communication (HBC), and 2) Bi-Phasic Quasistatic Brain Communication (BP-QBC) for fully wireless data transfer from a sub-6mm^3, 2 µW brain implant. A custom modulation scheme, along with adiabatic communication enables wireline-like energy efficiencies (<5pJ/b) in HBC-based wireless systems, while the BP-QBC node, being fully electrical in nature, demonstrates sub-50pJ/b efficiencies by eliminating DC power consumption, and by avoiding the transduction losses observed in competing technologies, involving optical, ultrasound and magneto-electric modalities. Next in Chapter 5, we will show an implementation of a reconfigurable system that would include 1) a human-body communication transceiver and 2) a traditional wireless (MedRadio) transceiver on the same integrated circuit (IC), and would demonstrate methods to switch between the two modes by detecting the placement of the transmitter and receiver devices (on-body/away from the body). Finally, in Chapter 6, we shall show a technique of augmenting security in resource-constrained devices through authentication using the Analog/RF properties of the transmitter, which are usually discarded as non-idealities in a digital transceiver chain. This method does not require any additional hardware in the transmitter, making it an extremely promising technique to augment security in highly resource-constrained scenarios. Such energy-efficient intelligent sensing and secure communication techniques, when combined with intelligent in-sensor-analytics at the resource-constrained nodes, can potentially pave the way for perpetual, and even batteryless systems for next-generation IoT, IoB and healthcare applications.</p>

<p dir="ltr">In today’s age of information, we are constantly informed about our surroundings by the network of distributed sensors to decide the next action. One major class of distributed sensors is wearable, implantable, and environmental (WIE) electrochemical sensors, widely used for analyte concentration measurement in personalized healthcare, environmental monitoring, smart agriculture, food, and chemical industries. Although WIE sensors offer an opportunity for prompt and prudent decisions, reliable sensing with such sensors is a big challenge. Among them, one is uncontrolled outside environment. Rapidly varying temperature, humidity, and target concentration increase noise and decrease the data reliability of the sensors. Second, because they are closely coupled to the physical world, they are subject to biofouling, radiation exposure, and water ingress which causes physical degradation. Moreover, to correct the drift due to degradation, frequent calibration is not possible once the sensor is deployed in the field. Another challenge is the energy supply needed to support the autonomous WIE sensors. If the sensor is wireless, it must be powered by a battery or an energy harvester. Unfortunately, batteries have limited lifetime and energy harvesters cannot supply power on-demand limiting their overall operation.</p><p dir="ltr">The objective of this thesis is to achieve reliable sensing with WIE sensors by overcoming the challenges of uncontrolled environment, drift or degradation, and calibration subject to limited power supplies. First, we have developed a concept of “Nernst thermometry” for potentiometric ion-selective electrodes (ISE) with which we have self-corrected concentration fluctuation due to uncontrolled temperature. Next, by using “Nernst thermometry,” we have developed a physics-guided data analysis method for drift detection and self-calibration of WIE ISE. For WIE sensor, wireless data transmission is an energy-intensive operation. To reduce unreliable data transmission, we have developed a statistical approach to monitor the credibility of the sensor continuously and transmit only credible sensor data. To understand and monitor the cause of ISE degradation, we have proposed a novel on-the-fly equivalent circuit extraction method that does not require any external power supply or complex measurements. To ensure an on-demand power supply, we have presented the concept of “signal as a source of energy.” By circuit simulation and long-term experimental analysis, we have shown that ISE can indefinitely sense and harvest energy from the analyte. We have theoretically calculated the maximum achievable power with such systems and presented ways to achieve it practically. Overall, the thesis presents a holistic approach to developing a self-sustainable WIE sensor with environmental variation correction, self-calibration, reliable data transmission, and lifelong self-powering capabilities, bringing smart agriculture and environmental sensing one step closer to reality.</p>

The thesis deals with qualitative properties of solutions of singular initial value problems for ordinary differential and integrodifferential equations which occur in the theory of linear and nonlinear electrical circuits and the theory of therminionic currents. The research is concentrated especially on questions of existence and uniqueness of solutions, asymptotic estimates of solutions and modications of Adomian decomposition method for singular initial problems. Solution algoritms are derived for scalar differential equations of Lane-Emden type using Taylor series and modication of the Adomian decomposition method. For certain classes of nonlinear of integrodifferential equations asymptotic expansions of solutions are constructed in a neighbourhood of a singular point. By means of the combination of Wazewski's topological method and Schauder xed-point theorem there are proved asymptotic estimates of solutions in a region which is homeomorphic to a cone having vertex coinciding with the initial point. Using Banach xed-point theorem the uniqueness of a solution of the singular initial value problem is proved for systems of integrodifferential equations of Volterra and Fredholm type including implicit systems. Moreover, conditions of continuous dependence of a solution on a parameter are determined. Obtained results are presented in illustrative examples.

<p dir="ltr">This project aimed to develop an instrumentation and control system for a micro-drilling robot based on Industrial Internet of Things (IIoT) technologies. The automation system integrated IIoT technological tools to create a robust automation system capable of being used in drilling operations. The system incorporated industrial-grade sensors, which carried out direct measurements of the critical variables of the process. The indirect variables relevant to the control of the robot were calculated from the measured parameters. The system also considered the telemetry architecture necessary to reliably transmit data from the down-the-hole (DTH) robot to a receiver on the surface. Telemetry was based on wireless communication through long-range radio frequency (LoRa). The system developed had models based on Artificial Intelligence (AI) and Machine Learning (ML) for determining the mode of operation, detecting changes in the process, and changes in drilling variables in critical hydraulic components for the drilling process. Algorithms based on AI and ML models also allowed the user to make better decisions based on the variables' correlation to optimize the drilling process (e.g., dynamic change of flow, pressure, and RPMs based on automatic rock identification). A user interface (UI) was developed, and digital tools to perform data analysis were implemented. Safety assessment in all robot systems (e.g., electrical, hardware, software) was contemplated as a critical design component. The result of this research project provides innovative micro-drilling robots with the necessary technological tools to optimize the drilling process. The system made drilling more efficient, reliable, and safe, providing diagnostic and prognostic tools that allowed planning maintenance based on the actual health of the devices. The system that was developed was tested in a test bench under controlled conditions within a laboratory to characterize the system and collect data that allowed ML models' development, training, validation, and testing. The prototype of a micro-drilling robot installed on the test bench served as a case study to assess the implemented models' reliability and the proposed telemetry.</p>

Die Hauptthemen dieser Arbeit sind einerseits eine tiefgehende Analyse von nichtlinearen differential-algebraischen Gleichungen (DAEs) vom Index 2, die aus der modifizierten Knotenanalyse (MNA) von elektrischen Schaltkreisen hervorgehen, und andererseits die Entwicklung von Konvergenzkriterien für Waveform Relaxationsmethoden zum Lösen gekoppelter Probleme. Ein Schwerpunkt in beiden genannten Themen ist die Beziehung zwischen der Topologie eines Schaltkreises und mathematischen Eigenschaften der zugehörigen DAE. Der Analyse-Teil umfasst eine detaillierte Beschreibung einer Normalform für Schaltkreis DAEs vom Index 2 und Abschätzungen, die für die Sensitivität des Schaltkreises bezüglich seiner Input-Quellen folgen. Es wird gezeigt, wie diese Abschätzungen wesentlich von der topologischen Position der Input-Quellen im Schaltkreis abhängen. Die zunehmend komplexen Schaltkreise in technologischen Geräten erfordern oftmals eine Modellierung als gekoppeltes System. Waveform relaxation (WR) empfiehlt sich zur Lösung solch gekoppelter Probleme, da sie auf die Subprobleme angepasste Lösungsmethoden und Schrittweiten ermöglicht. Es ist bekannt, dass WR zwar bei Anwendung auf gewöhnliche Differentialgleichungen konvergiert, falls diese eine Lipschitz-Bedingung erfüllen, selbiges jedoch bei DAEs nicht ohne Hinzunahme eines Kontraktivitätskriteriums sichergestellt werden kann. Wir beschreiben allgemeine Konvergenzkriterien für WR auf DAEs vom Index 2. Für den Fall von Schaltkreisen, die entweder mit anderen Schaltkreisen oder mit elektromagnetischen Feldern verkoppelt sind, leiten wir außerdem hinreichende topologische Konvergenzkriterien her, die anhand von Beispielen veranschaulicht werden. Weiterhin werden die Konvergenzraten des Jacobi WR Verfahrens und des Gauss-Seidel WR Verfahrens verglichen. Simulationen von einfachen Beispielsystemen zeigen drastische Unterschiede des WR-Konvergenzverhaltens, abhängig davon, ob die Konvergenzbedingungen erfüllt sind oder nicht. / The main topics of this thesis are firstly a thorough analysis of nonlinear differential-algebraic equations (DAEs) of index 2 which arise from the modified nodal analysis (MNA) for electrical circuits and secondly the derivation of convergence criteria for waveform relaxation (WR) methods on coupled problems. In both topics, a particular focus is put on the relations between a circuit's topology and the mathematical properties of the corresponding DAE. The analysis encompasses a detailed description of a normal form for circuit DAEs of index 2 and consequences for the sensitivity of the circuit with respect to its input source terms. More precisely, we provide bounds which describe how strongly changes in the input sources of the circuit affect its behaviour. Crucial constants in these bounds are determined in terms of the topological position of the input sources in the circuit. The increasingly complex electrical circuits in technological devices often call for coupled systems modelling. Allowing for each subsystem to be solved by dedicated numerical solvers and time scales, WR is an adequate method in this setting. It is well-known that while WR converges on ordinary differential equations if a Lipschitz condition is satisfied, an additional convergence criterion is required to guarantee convergence on DAEs. We present general convergence criteria for WR on higher index DAEs. Furthermore, based on our results of the analysis part, we derive topological convergence criteria for coupled circuit/circuit problems and field/circuit problems. Examples illustrate how to practically check if the criteria are satisfied. If a sufficient convergence criterion holds, we specify at which rate of convergence the Jacobi and Gauss-Seidel WR methods converge. Simulations of simple benchmark systems illustrate the drastically different convergence behaviour of WR depending on whether or not the circuit topological convergence conditions are satisfied.

<p dir="ltr">Decades of semiconductor technology scaling and breakthroughs in communication technology have miniaturized computing, embedding it everywhere, enabling the development of smart things connected to the internet, forming the Internet of Things. Further miniaturization of devices has led to an exponential increase in the number of devices in and around the body in the last decade, forming a subset of IoT which is increasingly becoming popular as the Internet of Bodies (IoB). The gradual shift from the current form of human-electronics coexistence to human-electronics cooperation, is the vision of Internet of Bodies (IoB). This vision of a connected future with devices in and around our body talking to each other to assist their day-to-day functions demands energy efficient means of communication. Electro-Quasistatic Human Body Communication (EQS-HBC) has been proposed as an exciting alternative to traditional Radio Frequency based methodologies for communicating data around the body. In this dissertation, we expand the boundaries of wearable and implantable IoB nodes using Electro-Quasistatic Human Body Communication and Powering by developing advanced channel models and demonstrating novel applications.</p><p dir="ltr">Leveraging the advanced channel models developed for wearable EQS-HBC, we demonstrate wearable applications like ToSCom which extend the use cases of touchscreens to beyond touch detection and location to enable high-speed communication strictly through touch. We further demonstrate an application of EQS Resonant Human Body Powering to demonstrate Step-to-Charge, allowing mW-scale wireless power transfer to wearable devices. With increasing connected implanted healthcare devices becoming a part of the IoB space, we benchmark RF-based technologies for In-Body to Out-of-Body (IBOB) communication using novel in-vivo experiments. We then explore EQS-HBC in the realm of IBOB communication using advanced channel modeling, revealing its potential for low-power and physically secure data transfer from implantable devices to wearable nodes on the body, demonstrating its potential in extending the battery life span of implantable nodes. Finally, an overview of the potential of IoB devices is analyzed with the use of EQS-HBC where we propose a human-inspired distributed network of IoB nodes which brings us a step closer to the potential for perpetually operable devices in and around the body.</p>

<p dir="ltr">The short lifespan of capacitors in power electronics converters is a significant challenge. These capacitors, often electrolytic, are vital for voltage smoothing and frequency filtering. However, their susceptibility to heat, ripple current, and aging can lead to premature faults. This can cause issues like output voltage instability and short circuits, ultimately resulting in catastrophic failure and system shutdown. Capacitors are responsible for 30% of power electronics failures.</p><p dir="ltr">To tackle this challenge, scientists, researchers, and engineers are exploring various approaches detailed in technical literature. These include exploring alternative capacitor technologies, implementing active and passive cooling solutions, and developing advanced monitoring techniques to predict and prevent failures. However, these solutions often come with drawbacks such as increased complexity, reduced efficiency, or higher upfront costs. Additionally, research in material science is ongoing to develop corrosion-resistant capacitors, but such devices are not readily available.</p><p dir="ltr">This dissertation presents a capacitorless solution for dc-dc and dc-ac converters. The proposed solution involves harnessing parasitic elements and integrating them as intrinsic components in power converter technology. This approach holds the promise of enhancing power electronics reliability ratings, thereby facilitating breakthroughs in electric vehicles, compact power processing units, and renewable energy systems. The central scientific premise of this proposal is that the capacitance requirement in a power converter can be met by deliberately augmenting parasitic components.</p><p dir="ltr">Our research hypothesis that incorporating high dielectric material-based thin-films, fabricated using nanotechnology, into planar magnetics will enable the development of a family of capacitorless electronic converters that do not rely on discrete capacitors. This innovative approach represents a departure from the traditional power converter schemes employed in industry.</p><p dir="ltr">The first family of converters introduces a novel capacitorless solid-state power filter (SSPF) for single-phase dc-ac converters. The proposed configuration, comprising a planar transformer and an H-bridge converter operating at high frequency, generates sinusoidal ac voltage without relying on capacitors. Another innovative dc-ac inverter design is the twelve step six-level inverter, which does not incorporate capacitors in its structure.</p><p dir="ltr">The second family of capacitorless topologies consists of non-isolated dc-dc converters, namely the buck converter and the buck-boost converter. These converters utilize alternative materials with high dielectric constants, such as calcium copper titanate (CCTO), to intentionally enhance specific parasitic components, notably inter capacitance. This innovative approach reduces reliance on external discrete capacitors and facilitates the development of highly reliable converters.</p><p dir="ltr">The study also includes detailed discussions on the necessary design specifications for these parasitic capacitors. Furthermore, comprehensive finite element analysis solutions and detailed circuit models are provided. A design example is presented to demonstrate the practical application of the proposed concept in electric vehicle (EV) low voltage side dc-dc power converters used to supply EVs low voltage loads.</p>