This dissertation is concerned with the responses of nonlinear systems to both deterministic and stochastic excitations. For a single-degree-of-freedom system, the response of a simply-supported buckled beam to parametric excitations is investigated. Two types of excitations are examined: deterministic and random. For the nonlinear response to a harmonic axial load, the method of multiple scales is used to determine to second order the amplitude-and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using simulations on a digital computer and are compared with results obtained using an analog computer. For the stochastic response to a wide-band random excitation, the Gaussian and non-Gaussian closure schemes are used to determine the response statistics. The results are compared with those obtained from real-time analysis (analog-computer simulation). The normality assumption is examined. A comparison between the responses to deterministic and random excitations is presented. / Ph. D.

The piezoelectric energy harvester has become a new powering option for some low-power electronic devices such as MEMS (Micro Electrical Mechanical System) sensors. Piezoelectric materials can collect the ambient vibrations energy and convert it to electrical energy. This thesis is intended to demonstrate the behavior of a piezoelectric energy harvester system at elevated temperature from room temperature up to 82°C, and compares the system’s performance using different piezoelectric materials. The systems are structured with a Lead Magnesium Niobate-Lead Titanate (PMN-PT) single crystal patch bonded to an aluminum cantilever beam, Lead Indium Niobate-Lead Magnesium Niobate-Lead Titanate (PIN-PMN-PT) single crystal patch bonded to an aluminum cantilever beam and a bimorph cantilever beam which is made of Lead Zirconate Titanate (PZT). The results of this experimental study show the effects of the temperature on the operation frequency and output power of the piezoelectric energy harvesting system. The harvested electrical energy has been stored in storage circuits including a battery. Then, the stored energy has been used to power up the other part of the system, a wireless resonator force sensor, which uses frequency conversion techniques to convert the sensor’s ultrasonic signal to a microwave signal in order to transmit the signal wirelessly.

Cesium lead halide perovskite quantum dots (PQDs) provide an extraordinary solution-based method to fabricate high-performance solar cells, luminescent lightemitting devices, highly coherent single-photon quantum sources, and studying quantum mechanisms for quantum computing technologies. In these applications, characterizing heterogeneity and observing coupling between dots is critical. In this thesis, we use double-nanohole (DNH) optical tweezers to realize single trapping for PQDs in solution. We can estimate the size of an individual dot by studying thermal fluctuations and correlate it to emission energy shifts from quantum confinement. Based on single trapping experiment, we also use the same setup to capture a second dot by using the DNH tweezer and observe a systematic red-shift of 1.1 ± 0.6 meV in the emission wavelength upon multiple repeated measurements. Theoretical analysis shows that the experiment results are consistent with Förster resonant energy transfer (FRET), which has been proposed to obtain entanglement between colloidal quantum dots for quantum information applications. The value of the FRET is quite large when compared with the confined quantum dots and it is exciting for FRET to generate entanglement for quantum information processing applications (e.g. quantum logic gates). In the thesis, we have proved that our method allows for in-situ sizing of individual PQDs for the first time, which is relevant for improving the growth process and does not require expensive techniques. It also enables future work to search and select two dots that are nominally identical. Optical trapping with DNHs fabricated using colloidal lithography can be used to control PQD growth in-situ and enables further studies of the coupling of quantum dots at a small distance with quantum information applications. / Graduate

Two new power conversion techniques, the constant-frequency zero-voltage-switching multiresonant-converter (CF ZVS-MRC) technique and the zero-voltage-switching technique that uses the magnetizing inductance of the power transformer as a resonant element {ZVS {L_M)) are proposed. analyzed, and evaluated for high-frequency applications. In addition, a novel design optimization approach for resonant type converters is introduced. Complete dc analysis of CF forward and half-bridge {HB) ZVS-MRCs are given, and the dc voltage-conversion-ratio characteristics for each of these two converters are derived. Graphic design procedures that maximize the efficiency and minimize current and voltage stresses are established. The design guidelines are verified on a 50 W CF forward ZVS-MRC operating with a switching frequency above 2 MHz, and on a 100 W HB ZVS-MRc operating with a switching frequency of 750 kHz. The ZVS (LM) technique is developed to eliminate the need for a large, inefficient external resonant inductor in ZVS resonant converters. This new family of isolated converters can operate with zero-voltage-switching of the primary active switches only (quasi-resonant (QR) operation) or with soft-switching of all semiconductor devices (multi-resonant (MR) operation). Furthermore, variable and constant frequency operation of all topologies in this new family of dc/dc converters are possible. A complete dc analysis of the HB ZVS-MRC (L_M) is given, and the dc voltage-conversion-ratio characteristics are derived. Design guidelines are defined using the same graphic method employed in the design of CF ZVS-MRCs. Constant frequency implementation of the HB ZVS-MRC (L_M) using controllable saturable inductors is also proposed. Finally, a novel approach to evaluate and design resonant converters based on the minimization of reactive power is developed. / Ph. D.

Over the past several years, energy efficiency and power density have become the top concerns for power conversion. Rising energy intensity leads to a higher cost of delivering power. Meanwhile, the demand for compact power supplies grows significantly. It requires power supplies with high efficiency, low profile and high power density. Dc-dc power conversion has been widely applied for industry, medial, military and airspace applications. Conventional PWM dc-dc converters have relatively low power transfer efficiency and low power density. In contrast, resonant dc-dc converters have numerous advantages for dc-dc power conversions. In this work, topologies and system optimization of resonant converters are investigated to meet challenges of high efficiency, high power density, low EMI, easy startup and over current protection. LLC resonant converters can achieve zero-voltage-switching (ZVS) for primary side devices and zero-current-switching (ZCS) for the secondary side rectifiers. The switching loss is minimized. LLC is very attractive to overcome the issues of conventional circuits. However, challenges still remain. First of all, for low-voltage high-current applications, the synchronous rectifier (SR) with lower conduction loss is a must for high efficiency. To solve the driving issues of SRs, a novel synchronous driving scheme is proposed. Experimental results demonstrate the considerable loss reduction with utilization of the proposed driving scheme. Secondly, dc-dc converters are required to meet EMI standard. This work proposes an EMI mode. Based on the proposed model, EMI analysis and noise attenuation techniques are proposed and verified by experiments. Thirdly, startup and over-load protection are another issues of LLC resonant converters. With proposed multi-element resonant converters, the current limit issues can be resolved. In addition, the proposed multi-element resonant converters can utilize higher-order harmonics to enhance power transfer. Fourthly, for high-current applications, the secondary side structure becomes very critical. An improved secondary side construction is proposed to alleviate ac termination losses and SR paralleling issues. Novel winding structures are proposed to reduce the winding loss. The magnetic integration technique is proposed and analyzed, and an optimal integrated transformer design is proposed, which has low loss and compact size. / Ph. D.

Two constant-frequency resonant power processors are discussed. The parallel resonant converter(PRC) with a controlled output rectifier can provide both forward and reverse power flow. A new control parameter — "θ-angle" is proposed for achieving output regulation and bidirectional power flow of the PRC. The θ-angle, measured as the displacement angle between the firing of the inverter switches and the firing of their corresponding output rectifier switches, provides a control-to-output characteristic independent of load variations and is very easy to implement. Unified closed-form expressions for the steady-state operating conditions are derived. Circuit performances are analyzed through closed-form solutions. Similar analyses are performed for a phase-controlled dual-inverter resonant converter. The feasibility of generating a regulated high-frequency AC bus employing this circuit is investigated. A controlled rectifier and LC filter type of load is used for the circuit to demonstrate the complex interactions between the inverters and the load and the effect of load power factor on the quality of the ac bus voltage. Desired operating regions for input, output, and various control parameters are analytically defined through closed-form solutions such that good quality ac bus voltage can be achieved. / M.S.

LLC resonant converters have been a popular choice for DC-DC converters due to their high efficiency, high power density, and hold-up capability in power supplies for communication systems, datacenters, consumer electronics, and automobiles. With the rapid development of wide-bandgap devices and novel magnetic materials, the push for higher switching frequencies to achieve higher power densities at lower costs is gaining traction. To demonstrate high efficiency and high power density, the Center for Power Electronics Systems (CPES) at Virginia Tech designed an 800W, 1MHz 400V/12V LLC converter for future datacenters, which could achieve a peak efficiency of 97.6% and a power density of 900 W/in3. However, with the ever-increasing demand for online services, the performance of power delivery must also be simultaneously improved to keep pace with the demand. The focus of this thesis is improving the performance of CPES’ previous 400V/12V LLC converter by investigating different aspects of its design and operation. Ultimately, design guidelines are proposed, and improvements are demonstrated to effectively achieve higher efficiency and higher power density than the previous CPES converter. Multiple aspects of the LLC converter’s design and structure are investigated to further improve its performance, and three main areas are the focus of this thesis. The output-side termination design of the planar transformer is investigated and modeled, and design guidelines for filter capacitor selection are provided for optimal efficiency. Next, the existing shielding technique for matrix transformers, which helps reduce common-mode (CM) noise without compromising on efficiency, is investigated for asymmetry and current-sharing issues, and modifications have been proposed to improve its efficiency. Thirdly, the LLC converter’s switching frequency is optimized to improve its performance over the previous CPES converter. Finally, the hardware results with the proposed improvements are demonstrated, and the converter’s performance is compared with the previous CPES converter as well as other recent proposed solutions. / M.S. / The electricity demand by datacenters has been growing exponentially over the past few decades, especially due to the boom of artificial intelligence in addition to other internet services. This has resulted in a requirement to continually improve the efficiencies of the power delivery from the grid, through the datacenter power architecture, and finally to the loads on the server racks. The overall datacenter power architecture has been improved over time to improve the total efficiency. However, the performance of each stage along the power architecture must be improved to keep in pace with the energy demand. The focus of this thesis is to improve the performance of the 400V/12V DC-DC stage for future datacenters. Previously, the Center for Power Electronics Systems (CPES) at Virginia Tech developed a 1MHz 800W 400V/12V LLC converter with 97.6% peak efficiency and 900W/in3 power density. However, the performance of the converter must be further improved to stay ahead of the competition and keep in pace with the increasing energy demand. Multiple aspects of the LLC converter’s design and structure are investigated to further improve its performance, and three main areas are the focus of this thesis. Firstly, the high-frequency termination design, or how different components are interconnected and arranged, is studied, and a capacitance selection guideline is proposed to maximize the efficiency. Next, the existing shielding technique for matrix transformers, which helps reduce common-mode (CM) noise without compromising on efficiency, is investigated for asymmetry and current-sharing issues, and modifications have been proposed to improve its efficiency. Thirdly, the LLC converter’s switching frequency is optimized to improve its performance over the previous CPES converter. Finally, the hardware results with the proposed improvements are demonstrated, and the converter’s performance is compared with the previous CPES converter as well as other recent proposed solutions.