In this thesis we investigate some properties of market making and statistical arbitrage applied to High Frequency Trading (HFT). Using the Hamilton-Jacobi-Bellman(HJB) model developed by Guilbaud, Fabien and Pham, Huyen in 2012, we studied how market making works to obtain optimal strategy during limit order and market order. Also we develop the best investment strategy through Moving Average, Exponential Moving Average, Relative Strength Index, Sharpe Ratio.

The increasing market demand for wideband gap (WBG) power switches has led to heightened competition to increase converter power density, switching frequencies, and reduce form factor, among other factors. However, this technology has also brought about an increase in encounters with electromagnetic interference (EMI), posing significant challenges. Nevertheless, the maturation of power switches has been accompanied by an improvement in gate drive technology aimed at resolving EMI challenges, albeit at a higher component and cost expense. This thesis aims to design, analyze, and implement a recent innovative differential gate driver for a 1.2 kV SiC MOSFET full bridge module. The purpose of this design is to mitigate EMI, improve performance, and reduce the number of filtering elements that are typically required. The investigation into the impact of EMI on electrical systems involves exploring factors such as testing equipment, power supplies, and gate drive layout. Based on these considerations, system and sub-system level analyses are conducted to derive practical design recommendations for implementing the differential gate driver. Three gate drive PCBs are designed and evaluated through extensive double pulse tests (DPTs). Furthermore, continuous switching of the driver presents its own set of challenges that are not apparent during the DPTs, requiring further exploration of low-cost solutions. Finally, a comparison between custom and discrete module solutions employing 1.2 kV SiC MOSFETs is conducted, highlighting the advantages and disadvantages of each approach. The solutions proposed in this work are intended to be extended to other gate drive ICs, with the goal of providing valuable insights and guidelines for EMI suppression and gate driver performance enhancement. / Master of Science / The increasing demand for powerful and efficient electronic devices has led to competition to develop better converters with wideband gap (WBG) power switches. These switches can make electronics work faster and take up less space, but they can also cause electromagnetic interference (EMI) that can be problematic. Despite these challenges, advances in power switch technology have led to improvements in gate drive technology, which can help reduce EMI, albeit, sometimes, at a higher cost. This research aims to design and analyze an innovative differential gate driver for a 1.2 kV SiC MOSFET full bridge module that can help mitigate EMI, improve performance, and reduce the number of required filtering elements. A system-level analysis is conducted to identify critical noise paths and potential solutions in response to poor gate driver performance. Practical design recommendations are provided for implementing a differential gate driver, and three PCB designs are tested and evaluated to showcase the effectiveness of the proposed solutions. The work also includes a comparison between a custom module and discrete module solutions employing 1.2 kV SiC MOSFETs, highlighting the advantages and disadvantages of each approach. The findings are extended to other gate drivers that share similar performance specifications, demonstrating the potential and improvements that can be achieved with the suggested techniques. Overall, the study provides valuable insights and guidelines for EMI suppression and performance enhancement in power electronics systems utilizing differential gate drivers.

Icing on aircraft wings is one of the leading causes of aircraft crashes. It is mainly caused due to accumulation of ice or snow on the wing surface due to impact with supercooled droplets when passing through clouds at high altitudes, causing loss of lift obtained by the wings. It was found that droplet impact characteristics are dependent on droplet size, surface roughness, surface material hydrophobicity, and droplet impact velocity. As a continuation of the study of droplet impact contact characteristics by varying surface roughness and impact velocity, this study focuses on droplets impacting the vibrating surface at frequencies between 2-7 kHz. Atomization (water drop splitting into smaller droplets and ejecting from the surface) has been observed at different rates for all frequencies. The first set of data is collected by keeping roughness constant and increasing the amplitude of the vibration to observe the critical amplitude at which atomization is initiated. The surface roughness is varied for the second set of experiments. The data is quantified using image processing of the high-speed videos to obtain the rate of ejection for each case. / Master of Science / Icing on aircraft wings is among the leading causes of crashes, which involves small freezing water drops sticking to the wing surface thus reducing the lift. This study is an investigation to experimentally observe how small water droplets interact with surfaces vibrating at high frequencies when impacted. Surface roughness, materials, droplet velocities, and frequency of vibration have been varied and the droplet was captured using high-speed photography to study their effect on the aforementioned interaction. Glass, PET-G. and aluminum having specific roughness were fabricated using laser and chemical etching. Atomization (water drop splitting into smaller droplets and ejecting from the surface) has been observed at different rates for all frequencies. A relation between the amplitude of the vibration and the rate of atomization was found. The effect of varying frequencies and surface roughness has also been documented.

<p> There is a great need for sensors that can infer the properties of polymer latices. Measuring ultrasonic wave travel parameters through a latex and calibrating these against polymer properties is one potential technique for measuring the polymer properties of a latex without separating the polymer particles from water. Ultrasonic longitudinal waves can be characterized by three travel parameters: the velocity, the attenuation and the frequency. For colloidal systems the attenuation will depend on molecular properties of the system inside a frequency window where diffraction and scattering are negligible.</p> <p> In this thesis the equipment for measuring ultrasonic waves is discussed and a measurement cell for measuring waves in liquids is designed and built. This equipment is used to measure the velocity and attenuation as functions of frequency for two sets of copolymer latices. These latices were measured separately using a combination of standard quality control analyses and polymer characterization techniques. It was discovered that the velocity of sound through latices does not differ significantly from the velocity for pure water while the ultrasonic attenuation of latices at solids concentrations of greater than 10 percent is much greater than the value for pure water.</p> <p> For the copolymer latices produced from styrene and methyl-methacrylate the attenuation measurements were all too similar to distinguish between changes in the properties of the latex. For the copolymer latices produced from styrene and butadiene, the attenuation and composition were related by an approximately linear relationship between 30 and 80 mole percent styrene. In this region, the attenuation spectra were regressed onto the property space using a linear multivariate algorithm called projection to latent structures. It was found that the attenuation is only useful for predicting latex properties that are related to composition in this range. Future work should focus on the use of a non-linear regression technique to model the behaviour of attenuation over the entire composition range and the use of independent analyses to better characterize some of the polymer properties such as crosslinking.</p> / Thesis / Master of Engineering (MEngr)

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Future microprocessor poses many challenges to its dedicated power supplies, the voltage regulators (VRs), such as the low voltage, high current, fast load transient, etc. For the VR designs using multiphase buck converters, one of the results from these stringent challenges is a large amount of output capacitors, which is undesired from both a cost and a motherboard real estate perspective. In order to save the output capacitors, the control-loop bandwidth must be increased. However, the bandwidth is limited in the practical design. The influence from the switching frequency on the control-loop bandwidth has not been identified, and the influence from multiphase is not clear, either. Since the widely-used average model eliminates the inherent switching functions, it is not able to predict the converter's high-frequency performance. In this dissertation, the primary objectives are to develop the methodology of high-frequency modeling for the buck and multiphase buck converters, and to analyze their high-frequency characteristics. First, the nonlinearity of the pulse-width modulator (PWM) scheme is identified. Because of the sampling characteristic, the sideband components are generated at the output of the PWM comparator. Using the assumption that the sideband components are well attenuated by the low-pass filters in the converter, the conventional average model only includes the perturbation-frequency components. When studying the high-frequency performance, the sideband frequency is not sufficiently high as compared with the perturbation one; therefore, the assumption for the average model is not good any more. Under this condition, the converter response cannot be reflected by the average model. Furthermore, with a closed loop, the generated sideband components at the output voltage appear at the input of the PWM comparator, and then generate the perturbation-frequency components at the output. This causes the sideband effect to happen. The perturbation-frequency components and the sideband components are then coupled through the comparator. To be able to predict the converter's high-frequency performance, it is necessary to have a model that reflects the sampling characteristic of the PWM comparator. As the basis of further research, the existing high-frequency modeling approaches are reviewed. Among them, the harmonic balance approach predicts the high-frequency performance but it is too complicated to utilize. However, it is promising when simplified in the applications with buck and multiphase buck converters. Once the nonlinearity of the PWM comparator is identified, a simple model can be obtained because the rest of the converter system is a linear function. With the Fourier analysis, the relationship between the perturbation-frequency components and the sideband components are derived for the trailing-edge PWM comparator. The concept of multi-frequency modeling is developed based on a single-phase voltage-mode-controlled buck converter. The system stability and transient performance depend on the loop gain that is affected by the sideband component. Based on the multi-frequency model, it is mathematically indicated that the result from the sideband effect is the reduction of magnitude and phase characteristics of the loop gain. With a higher bandwidth, there are more magnitude and phase reductions, which, therefore, cause the sideband effect to pose limitations when pushing the bandwidth. The proposed model is then applied to the multiphase buck converter. For voltage-mode control, the multiphase technique has the potential to cancel the sideband effect around the switching frequency. Therefore, theoretically the control-loop bandwidth can be pushed higher than the single-phase design. However, in practical designs, there is still magnitude and phase reductions around the switching frequency in the measured loop gain. Using the multi-frequency model, it is clearly pointed out that the sideband effect cannot be fully cancelled with unsymmetrical phases, which results in additional reduction of the phase margin, especially for the high-bandwidth design. Therefore, one should be extremely careful to push the bandwidth when depending on the interleaving to cancel the sideband effect. The multiphase buck converter with peak-current control is also investigated. Because of the current loop in each individual phase, there is the sideband effect that cannot be canceled with the interleaving technique. For higher bandwidths and better transient performances, two schemes are presented to reduce the influence from the current loop: the external ramps are inserted in the modulators, and the inductor currents are coupled, either through feedback control or by the coupled-inductor structure. A bandwidth around one-third of the switching frequency is achieved with the coupled-inductor buck converter, which makes it a promising circuit for the VR applications. As a conclusion, the feedback loop results in the sideband effect, which limits the bandwidth and is not included in the average model. With the proposed multi-frequency model, the high-frequency performance for the buck and multiphase buck converters can be accurately predicted. / Ph. D.