In comparison with PWM converters, resonant converters are gaining increasing popularity for cases in which efficiency and power density are at a premium. However, the lack of an accurate small-signal model has become an impediment to performance optimization. Many modeling attempts have been made to date. Besides the discrete time-domain modeling, most continuous-time modeling approaches are based on fundamental approximation, and are thus unable to provide sufficient accuracy for practical use. An equivalent circuit model was proposed by Yang, which works well for series resonant converters (SRCs) with high Q (quality factor), but which is inadequate for LLC resonant converters. Furthermore, the model is rather complicated, with system orders that are as high as five and seven for the SRC and LLC converter, respectively. The crux of the modeling difficulty is due to the underlying assumption based on the use of a band-pass filter for the resonant tank in conjunction with a low-pass output filter, which is not the case for most practical applications. The matter is further complicated by the presence of a rectifier, which is a nonlinearity that mixes and matches the original modulation frequency. Thus, the modulation signal becomes intractable when using a frequency-domain modeling approach. This dissertation proposes an extended describing function modeling that is based on a Fourier analysis on the continuous-time-domain waveforms. Therefore, all important contributions from harmonics are taken into account. This modeling approach is demonstrated on the frequency-controlled SRC and LLC converters. The modeling is further extended to, with great accuracy, a charge-controlled LLC converter. In the case of frequency control, a simple third-order equivalent circuit model is provided with high accuracy up to half of the switching frequency. The simplified low-frequency model consists of a double pole and a pair of right-half-plane (RHP) zeros. The double pole, when operated at a high switching frequency, manifests the property of a well-known beat frequency between the switching frequency and the resonant frequency. As the switching frequency approaches the resonant frequency of the tank, a new pair of poles is formed, representing the interaction of the resonant tank and the output filter. The pair of RHP zeros, which contributes to additional phase delay, was not recognized in earlier modeling attempts. In the case of charge control, a simple second-order equivalent circuit model is provided. With capacitor voltage feedback, the order of the system is reduced. Consequently, the resonant tank behaves as an equivalent current source and the tank property is characterized by a single pole. The other low-frequency pole represents the output capacitor and the load. However, the capacitor voltage feedback cannot eliminate the high-frequency poles and the RHP zeros. These RHP zeros may be an impediment for high-bandwidth design if not properly treated. Based on the proposed model, these unwanted RHP zeros can be mitigated by either changing the resonant tank design or by proper feedback compensation. The accurate model is essential for a high-performance high-bandwidth LLC converter. / Doctor of Philosophy / For high-frequency power conversion, resonant converters are increasingly popular. However, the lack of an accurate small-signal model has become an impediment to performance optimization. The existing equivalent circuit model and its simplified circuit were based on fundamental approximation, where the resonant tank was deemed a good band-pass filter. These models work well for series resonant converters (SRCs) with high Q (quality factor), but are inadequate for LLC resonant converters. The crux of the modeling difficulty is due to the fact that the operation of this type of resonant converter is based on the use of a band-pass filter in conjunction with a low-pass filter. The matter is further complicated by the presence of a rectifier, which is a nonlinearity that mixes and matches the original modulation frequency. Thus, the modulation signal becomes intractable when using a frequency-domain modeling approach. This dissertation proposes an extended describing function modeling that is based on a Fourier analysis on the continuous-time-domain waveforms. Therefore, all important contributions from harmonics are taken into account. This modeling approach is demonstrated on the frequency-controlled SRC, frequency-controlled LLC converter, and charge-controlled LLC converter, and the resulting models are proven to be accurate at all frequencies. A simple equivalent circuit model is provided that targets the frequency range below the switching frequency. This simple, accurate model is able to predict the small-signal behaviors of the LLC converter with high accuracy at half of the switching frequency. At high modulation frequencies, the resonant converter behaves like a non-minimum phase system, which was neither recognized nor characterized before. This property can be represented by RHP zeros, and these RHP zeros may be an impediment for high-bandwidth design if not properly treated. Based on the proposed model, these unwanted RHP zeros can be mitigated by either changing the resonant tank design or by proper feedback compensation. Accurate modeling is essential for a high-performance high-bandwidth LLC converter.

As traditional control schemes, open-loop Hysteresis and closed-loop pulse-width-modulation (PWM) have been used for the switched reluctance motor (SRM) current controller. The Hysteresis controller induces large unpleasant audible noises because it needs to vary the switching frequency to maintain constant Hysteresis current band. In contract, the PWM controller is very quiet but difficult to design proper gains and control bandwidth due to the nonlinear nature of the SRM. In this thesis, the ac small signal modeling technique is proposed for linearization of the SRM model such that a conventional PI controller can be designed accordingly for the PWM current controller. With the linearized SRM model, the duty-cycle to output transfer function can be derived, and the controller can be designed with sufficient stability margins. The proposed PWM controller has been simulated to compare the performance against the conventional Hysteresis controller based system. It was found that through the frequency spectrum analysis, the noise spectra in audible range disappeared with the fixed switching frequency PWM controller, but was pronounced with the conventional Hysteresis controller. A hardware prototype is then implemented with digital signal processor to verify the quiet nature of the PWM controller when running at 20 kHz switching frequency. The experimental results also indicate a stable current loop operation. / Master of Science

It can be expected that digital controllers will be increasingly used in low voltage, high-current and high frequency voltage regulator modules (VRMs) where conventional analog controllers are currently preferred because of the cost and performace reasons. However, there are still remaining two significant challenges for the spread of the digital control techniques: quantization effects and the delay effects. Quantization effects might introduce the limit cycle oscillations (LCOs) to the converter, which will generate the stability issues. Actually, LCOs can not be totally eliminated theoretically. One way to reduce the possibilities of LCOs is to employ a high resolution Digital Pulse-Width-Modulator (DPWM). However, designing such a DPWM which can meet the requirements of VRMs application requires ultra-high system clock frequency, up to several GHz. Such high frequency is impractical due to huge power consumption. Hybrid DPWM might be an alternative solution but will occupy large silicon area. Single phase digital constant on-time modulation method is another good candidate to improve the DPWM resolution without adding too much cost. However, directly extending this method to multi-phase application, which is the prevalent structure in VRMs application, will introduce some issues. With more phases in parallel, the duty cycle resolution will drop more. To solove the mentioned issue, this work proposed a multi-phase digital constant on-time modulation method. The proposed method will control the control voltage to alternate between two adjacent values, or dither, within one switching period. The outcome is that the phase duty cycle's resolution is improved and independent on phase number. Compared with conventional constant frequency modulation method, the proposed method can achieve about 10 times higher duty cycle resolution for the VRM application. The effectiveness of the proposed method is verified by the simulation as well as the experiment results. Delay effect is another concern for the digital controlled VRMs. There exist several types of delays in the digital feedback loop, including the ADC conversion delay, digital compensator calculation delay, DPWM delay as well as some propagation delays. Usually these delays are inside the digital controller and it is hard to know the exact values. There are several papers talking about the small signal models of the digital voltage mode control. These models are valid only if all the delay terms are known exactly since each delay is considered separately. Actually, this process is not easy. Moreover, there is no literature talking about the complete small signal model of the digital VRMs. But in reallity, different implementations of the sampling process will give different impacts to the loop. This work proposed the small signal signal models of digital VRMs. The analysis is based on the assumptions that DPWM is a double-edge modulation and the sampling instants are aligned with the middle of one phase's off time. At first, the conversion and calculation delay is neglected. The focus of the modeling is on the small signal model of the current sampling methods and the DPWM delay. This model is valid for those digital controllers which have fast ADC and fast calculation capabilities. It is shown that even with a "fast" controller, the current sampling and DPWM might introduce some delay to the loop. After that, the conversion and calculation delay are considered into the modeling. Two time periods, T1ff and T1rr, are employed to describe the total delay effects in the control loop. It is observed that the total delay in the loop is integral times of sampling periods, which is never reported by any other literatures. Therefore, the proposed model only includes one delay term and the value of this delay can be found through a pre-determined lookup table. Finally, the complete small signal model of the digital VRMs considering the conversion and calculation delay is proposed. This model is helpful for the researchers to find the delay effects in their control loop based on the range of the total physical delay in the controller. With the derived small signal mondels of digital VRMs, the design guildeline for AVP control are presented. The digital active-droop control is employed and it borrows the concept of constant output impedance control from the analog world. Two design examples are provided for the verification. / Master of Science

In this thesis, a detailed study of the electrical and optical characterisations of Heterojuction Bipolar Transistors (HBTs) for optical detection is presented. By comparing both DC and optical characterisations between In0.49Ga0.51P/GaAs Single Heterojuction Bipolar Transistors (SHBTs) and Double Heterojuction Bipolar Transistors (DHBTs), the advantages of using the DHBT as a short wavelength detector are shown. Phenomena related to the base region energy band bending in the DHBT caused by a self-induced effective electric field is discussed and its effects on the performance of the device are elaborated. The use of an eye diagram has been employed to provide requisite information for performance qualification of SHBT/DHBT devices. These give a more detailed understanding compared to conventional S-parameters method. A detailed comparison of In0.49Ga0.51P/GaAs SHBT and DHBT performance using an eye diagram as a functional tool by adopting a modified T-shaped small signal equivalent circuit are given. By adopting this modified T-shaped small signal equivalent circuit, the use of In0.49Ga0.51P/GaAs Double Heterojuction Phototransistors (DHPT) as a short wavelength photodetector is analysed. It is therefore shown that an eye diagram can act as a powerful tool in HBTs/HPTs design optimisations, for the first time in this work. In order to predict the spectral response (SR) and optical characterisations of GaAs-based HPTs, a detailed theoretical absorption model is also presented. The layer dependence of an optical flux absorption profile, along with doping dependent absorption coefficients are taken into account for the optical characterisation prediction. With the aim of eliminating the limitation of current gain as a prerequisite, analytical modelling of SR has been developed by resolving the continuity equation and applying realistic boundary conditions. Then, related physical parameters and a layer structure profile are used to implement simulations. A good agreement with the measured results of the Al0.3Ga0.7As/GaAs HPT is shown validating the proposed theoretical model.

No description available.

Motivated by the recent commercialization of gallium-nitride (GaN) switches, an effort was initiated to determine whether it was feasible to switch the flyback converter at 5 MHz in order to improve the power density of this versatile isolated topology. Soft switching techniques have to be utilized to eliminate the switching loss to maintain high efficiency at multi-megahertz. Compared to the traditional modeling of zero-voltage-switching quasi-square-wave converters, a numerical methodology of parameters design is proposed based on the steady-state model of zero-voltage switching quasi-square-wave flyback converter. The magnetizing inductance is selected to guarantee zero-voltage switching for the entire input and load range with the trade-off design for conduction loss and turn-off loss. A design methodology is introduced to select a minimum core volume for an inductor or coupled inductors experiencing appreciable core loss. The geometric constant Kgac = MLT/(Ac2WA) is shown to be a power function of the core volume Ve, where Ac is the effective core area, WA is the area of the winding window, and MLT is the mean length per turn for commercial toroidal, ER, and PQ cores, permitting the total loss to be expressed as a direct function of the core volume. The inductor is designed to meet specific loss or thermal constraints. An iterative procedure is described in which two- or three-dimensional proximity effects are first neglected and then subsequently incorporated via finite-element simulation. Interleaved and non-interleaved planar PCB winding structures were also evaluated to minimize leakage inductance, self-capacitance and winding loss. The analysis on the trade-off between magnetic size, frequency, loss and temperature indicated the potential for a higher density flyback converter. A small-signal equivalent circuit of QSW converter was proposed to design the control loop and to understand the small-signal behavior. By adding a simple damping resistor on the traditional small-signal CCM model, it can predict the pole splitting phenomenon observed in QSW converter. With the analytical expressions of the transfer functions of QSW converters, the impact of key parameters including magnetizing inductance, dead time, input voltage and output power on the small-signal behavior can be analyzed. The closed-loop bandwidth can be pushed much higher with this modified model, and the transient performance is significantly improved. With the traditional fix dead-time control, a large amount of loss during dead time occurred, especially for the eGaN FETs with high reverse voltage drop. An adaptive dead time control scheme was implemented with simple combinational logic circuitries to adjust the turn on time of the power switches. A variable deadtime control was proposed to further improve the performance of adaptive dead-time control with simplified sensing circuit, and the extra conduction loss caused by propagation delay in adaptive dead-time control can be minimized at multi-megahertz frequency. / Ph. D.

Ma thèse porte sur la relation entre la microstructure des tissus et le signal macroscopique d'imagerie par résonance magnétique de diffusion (IRMd). Les estimations des paramètres de tissus provenant de signaux mesurées expérimentalement est très important dans l'IRMd. En dépit d'une histoire de la recherche intensive dans ce domaine depuis longtemps, de nombreux aspects de ce problème inverse restent mal compris. Nous avons proposé et testé une solution approchée à ce problème, dans lequel le signal d'IRMd est d'abord approché par un modèle macroscopique appropriée, puis le paramètres effectifs de ce modèle sont estimés.Nous avons étudié deux modèles macroscopiques du signal d'IRMd. Le premier est le modèle Karger qui suppose une certaine forme de (macroscopique) diffusion de compartiments multiples et les échanges inter-compartiment, mais est soumis à la restriction d'impulsion étroite sur les impulsions de gradient de champ magnétique diffusion codant. Le deuxième est un modèle ODE de plusieurs aimantations compartiment obtenus à partir de l'homogénéisation mathématique de l'équation de Bloch-Torrey, qui n'est pas soumis à la restriction d'impulsion étroite.Tout d'abord, nous avons étudié la validité de ces modèles macroscopiques en comparant le signal d'IRMd proposée par le modèle Karger et le modèle ODE avec le signal d'IRMd de diffusion simulé sur certaines geometries de tissu relativement complexes en résolvant l'équation de Bloch-Torrey en cas de membranes semi-perméables cellule biologique. Nous avons conclu que la validité de ces deux modèles macroscopiques est limitée au cas où la diffusion dans chaque compartiment est effectivement gaussien et où l'échange inter-compartimentale peut être représenté par des termes cinétiques de premier ordre standard.Deuxièmement, en supposant que les conditions ci-dessus sur la diffusion compartimentale et l'échange inter-compartiment sont satisfaits, nous avons résolu le problème des moindres carrés associée à monter les paramètres du modèle Karger et du modèle ODE au signal simulé d'IRMd obtenu en résolvant l'équation de Bloch-Torrey microscopique. Parmi divers paramètres efficaces, nous avons examiné les fractions volumiques des compartiments intra-cellulaires et extra-cellulaires, la perméabilité de la membrane, la taille moyenne des cellules, la distance inter-cellulaire, ainsi que des coefficients de diffusion apparents. Nous avons commencé par étudier la faisabilité de la méthod des moindres carrés pour les deux groupes de geometries de tissu relativement simples. Pour le premier groupe, dans lequel les domaines sont constitués de cellules identiques ou sphériques de taille variable noyées dans l'espace extra-cellulaire, nous avons conclu que problème d'estimation de paramètres peut être résolu robuste, même en présence de bruit. Dans le second groupe, on a considéré les cellules cylindriques parallèles, qui peuvent être couverts par une couche de membrane d'épaisseur, et noyés dans l'espace extra-cellulaire. Dans ce cas, la qualité de l'estimation des paramètres dépendant fortement de la quantité de la structure cellulaire est allongée dans la direction du gradient. Dans la pratique, l'orientation des cellules allongées n'est pas de priori connue, de plus, les tissus biologiques peuvent contenir des structures allongées orientées de manière aléatoire et également en mélange avec d'autres éléments compacts (par exemple, les axones et les cellules gliales). Cette situation a été étudiée numériquement sur notre domaine le plus complexe dans lequel les couches de cellules cylindriques dans différentes directions sont mélangés avec des couches de cellules sphériques. Nous avons vérifié que certains paramètres peuvent encore être estimés assez fidèlement tandis que l'autre reste inaccessible. Dans tous les cas considérés, le modèle ODE a fourni des estimations plus précises que le modèle Karger. / My thesis focused on the relationship between the tissue microstructure and the macroscopic dMRI signal. Inferring tissue parameters from experimentally measured signals is very important in diffusion MRI. In spite of a long standing history of intensive research in this field, many aspects of this inverse problem remain poorly understood. We proposed and tested an approximate solution to this problem, in which the dMRI signal is first approximated by an appropriate macrosopic model and then the effective parameters of this model are estimated.We investigated two macroscopic models of the dMRI signal. The first is the Kärger model that assumes a certain form of (macroscopic) multiple compartmental diffusion and intercompartment exchange, but is subject to the narrow pulse restriction on the diffusion-encoding magnetic field gradient pulses. The second is an ODE model of the multiple compartment magnetizations obtained from mathematical homogenization of the Bloch-Torrey equation, that is not subject to the narrow pulse restriction.First, we investigated the validity of these macroscopic models by comparing the dMRI signal given by the Kärger and the ODE models with the dMRI signal simulated on some relatively complex tissue geometries by solving the Bloch-Torrey equation in case of semi-permeable biological cell membranes. We concluded that the validity of both macroscopic models is limited to the case where diffusion in each compartment is effectively Gaussian and where the inter-compartmental exchange can be accounted for by standard first-order kinetic terms.Second, assuming that the above conditions on the compartmental diffusion and intercompartment exchange are satisfied, we solved the least squares problem associated with fitting the Kärger and the ODE model parameters to the simulated dMRI signal obtained by solving the microscopic Bloch-Torrey equation. Among various effective parameters, we considered the volume fractions of the intra-cellular and extra-cellular compartments, membrane permeability, average size of cells, inter-cellular distance, as well as apparent diffusion coefficients. We started by studying the feasibility of the least squares solution for two groups of relatively simple tissue geometries. For the first group, in which domains consist of identical or variably-sized spherical cells embedded in the extra-cellular space, we concluded that parameters estimation problem can be robustly solved, even in the presence of noise. In the second group, we considered parallel cylindrical cells, which may be covered by a thick membrane layer, and embedded in the extra-cellular space. In this case, the quality of parameter estimation strongly depends on how much the cellular structure is elongated in the gradient direction. In practice, the orientation of elongated cells is not known a priori; moreover, biological tissues may contain elongated structures randomly oriented and also mixed with other compact elements (e.g., axons and glial cells). This situation has been numerically investigated on our most complicated domain in which layers of cylindrical cells in various directions are mixed with layers of spherical cells. We checked that certain parameters can still be estimated rather accurately while the other remains inaccessible. In all considered cases, the ODE model provided more accurate estimates than the Kärger model.

This dissertation presents a novel large signal modeling approach which can be used to accurately model CMOS transistors used in millimeter-wave CMOS power amplifiers. The large signal model presented in this work is classified as an empirical compact device model which incorporates temperature-dependency and device periphery scaling. These added features allow for efficient design of multi-stage CMOS power amplifiers by virtue of the process-scalability. Prior to the presentation of the details of the model development, background is given regarding the 90nm CMOS process, device test structures, de-embedding methods and device measurements, all of which are necessary preliminary steps for any device modeling methodology. Following discussion of model development, the design of multi-stage 60GHz Class AB CMOS power amplifiers using the developed model is shown, providing further model validation. The body of research concludes with an investigation into designing a CMOS power amplifier operating at frequencies close to the millimeter-wave range with a potentially higher-efficiency class of power amplifier operation. Specifically, a 24GHz 130nm CMOS Inverse Class F power amplifier is simulated using a modified version of the device model, fabricated and compared with simulations. This further demonstrates the robustness of this device modeling method.

No description available.

The unconventional improvements in the power electronics field have been the primary reason for massive deployment of renewable energy sources in the electrical power grid over the past several decades. This needed trend, together with the increasing penetration of micro-, and nano- grids, is bringing significant improvements in system controllability, performance, and energy availability, but is fundamentally changing the nature of electronically-interfaced sources and loads, altering their conventionally mild aggregate dynamics, and inflicting low- and high- frequency dynamic interactions that never before existed at this magnitude. This problem is not restricted only to the grid; modern electronic power distribution systems built for airplanes, ships, electric vehicles, data-centers, and homes, comprise dozens, even hundreds of power electronics converters, produced by different manufacturers, who provide very limited details on converters' dynamic behavior - distinctiveness that has the highest impact on how two converters, or converter and a system interact. Consequently, substantial dispersion of power electronics into the future grid will significantly depend on engineers' capability to understand how to model and dynamically control power flow and subsystem interactions. It is therefore essential to continue developing innovative methods that allow easier system-level modeling, continuous monitoring of dynamic interactions, and advanced control concepts of power electronics converters and systems. The dissertation will start with a "black box" approach to modeling of three-phase power electronics converters, introducing a method to remove source and load dynamics from in-situ measured terminated frequency responses. It will be then shown how converter, itself, can perform an online stability assessment knowing its own unterminated dynamics, and being able to measure all terminal immittances. The dissertation will further advance into an approach to control power electronics converters based on the electro-mechanical duality with synchronous machines, and end with selected examples of system-level operation, where small-signal instability in multi-source power systems can be mitigated using this concept. / Ph. D. / The modern technological advancements and ever-increasing needs for a sustainable future silently demand a serious revision of the conventional practice in electricity production, distribution, and utilization. These technologies are already challenging the limits of the biggest and most complex system ever built by humankind - the electrical grid. One practical solution to this problem is much higher dispersion of electronic power conversion systems capable of decoupling dynamics between system sources, distribution, and loads, while improving system controllability, reliability, and efficiency. Such a trend is already happening, and there has been an increased immersion of power electronics converters in electric cars, ships, airplanes, and the grid, in an effort to replace their traditional thermal, mechanical, hydraulic, and pneumatic systems. The goals have been to reduce the size, weight, and operational costs while increasing efficiency and reliability. In all these applications, a majority of energy sources and loads are interfaced to the power system through power electronics converters ranging in power from few watts to hundreds of megawatts. However, massive dispersion of power electronics into the future grid will significantly depend on engineers’ capability to understand how to model and dynamically control power flow and subsystem interactions. It is important to continue researching innovative methods that allow easier system-level modeling, continuous monitoring of interactions, and advanced control concepts of power electronics converters and systems. This dissertation hence addresses modeling of power electronics converters using their behavioral models, and shows how these models can assist the stability assessment of the system converters operate in. Additionally, dissertation presents an alternative way to control power electronics converters to behave as synchronous machines, and how this concept can be used to mitigate some stability problems.