Current-mode control architectures have been an indispensable technique in many applications, such as Voltage Regulator, Point-of-load converters, power factor correction, battery charger and LED driver. Since the inductor current ramp is used in the modulator in current-mode control without any low pass filter, high order harmonics play important role in the feedback control. This is the reason for the difficulty in obtaining the small-signal model for current-mode control in the frequency domain. A continuous time domain model was recently proposed as a successful model for current-mode control architectures. However, the model was derived by describing function method, which is very arithmetically complicated, not to mention time consuming. For the analysis and design of non-linear system, equivalent circuit model, which is user friendly and intuitive, is an effective tool. In this dissertation, the primary objective is to develop a unified three-terminal switch model for current-mode controls using the results of describing function derivation, which characterizes the small signal property of the common subcircuit of current mode controlled PWM converters. Its application is extended to average current mode control, V2 control and other proposed novel current mode control schemes. First, the existing model for current mode control is reviewed. The limitations of existing model for current-mode control are identified. Based on the universal small signal relationship between terminal currents and the results of describing function derivation, a unified three-terminal switch model for current mode control is proposed. A three-terminal equivalent circuit is developed to represent the small signal behavior of this common sub-circuit. The proposed model is applicable in both constant frequency and variable frequency modulation. After that, the modeling of digital predictive current mode control is presented. Predictive current mode control is one of the promising digital current mode control method featuring fast dynamic response and low sample rate requirement. Many implementations were presented in past ten years. To understand the benefit and the limitation of each implementation, help the engineer to choose the modulation scheme and design the control loop, a small signal Laplace-domain model for digital predictive current mode controls is proposed. The model is extended to the multi-sampled implementation. The modeling result is summarize as the small signal equivalent circuit mode, whose form is consistent with that of analog current mode controls. Based on S-domain model, digital predictive current mode controls are compared with analog implementation to demonstrate the advantages and limitation. Implementation selection guideline and compensation is discussed based on the modeling results. Then, using the proposed unified model is used in the analysis of average current mode control. Under proper design, the inductor current ripple passes through the current compensator and appears in PWM comparator. It significantly influence the high frequency small signal property of the converter. In chapter 3, the proportional feedback is separated from integral feedback so that the sideband frequency feedback effect can be taken into consideration. It extends the results obtained in peak-current model control to average current mode control. The proposed small signal model is accurate up to half switching frequency, predicting the sub-harmonic instability. Based on the proposed model, a new feedback design guideline is proposed. By designing the external ramp following the proposed design guideline, quality factor of the double poles at half of switching frequency in control-to-output transfer function can be precisely controlled. This helps the feedback design to achieve widest control bandwidth and proper damping. V2 control is a popular control scheme in Point-of-load converters due to the unique fast transient response. As the output voltage ripple is used as PWM modulation ramp, V2 control has close relationship with current mode control but this relationship was not addressed in the existing model. Chapter 4 utilizes the three-terminal switch model to build the equivalent circuit model for V2 control, which clearly shows that V2 control is a particular implementation of current mode control, with proportional capacitor voltage feedback and load current feedback embedded. The analysis presented in Chapter 3 provides a clear physical understanding of average current mode control. With constant frequency modulation, the control bandwidth is usually limited by the double pole at half of swithcing frequency, especially in the converters with wide duty cycle range. Chapter 5 proposed a novel I2 current mode control to improve the dynamic performance of average current mode control. In particular, constant on-time I2 control eliminates the need of external ramp while the current loop is inherently stable. Moreover, constant on-time modulation improves the light load efficiency. As a conclusion, this dissertation proposed a unified three-terminal switch model for current mode controls. The application of this equivalent circuit model is extended to average current mode control, V2 control and the novel I2 current mode control. The Laplace-domain model of predictive current mode control is also presented. All the modeling results are verified through simulation and experiments. / Ph. D.

Current-mode control architectures with different implementation approaches have been an indispensable technique in many applications, such as voltage regulator, power factor correction, battery charger and LED driver. Since the inductor current ramp, one of state variables influenced by the input voltage and the output voltage, is used in the modulator in current-mode control without any low pass filter, high order harmonics play important role in the feedback control. This is the reason for the difficulty in obtaining the small-signal model for current-mode control in the frequency domain. A continuous time domain model was recently proposed as a successful model for current-mode control architectures with different implementation. However, the model was derived by describing function method, which is very arithmatically complicated, not to mention time consuming. Although an equivalent circuit for a current mode control Buck converter was proposed to help designers to use the model without involving complicated math, the equivalent circuit is not a complete model. Moreover, no equivalent circuit for other topologies is available for designers. In this thesis, the primary objective is to develop a unified three-terminal switch model for current-mode control with different implementation methods, which are applicable in all the current mode control power converters. First, the existing model for current mode control is reviewed. The limitation of average models and the discrete time model for current-mode control is identified. The continuous time model and its equivalent circuit of Buck converter is introduced. The deficiency of the equivalent circuit is discussed. After that, a unified three-terminal switch model for current mode control is presented. Based on the observation, the PWM switch and the closed current loop is taken as an invariant sub-circuit which is common to different DC/DC converter topologies. A basic small signal relationship between terminal currents is studied and the result shows that the PWM switch with current feedback preserves the property of the PWM switch in power stage. A three-terminal equivalent circuit is developed to represent the small signal behavior of this common sub-circuit. The proposed model is a unified model, which is applicable in both constant frequency modulation and variable frequency modulation. The physical meaning of the three-terminal equivalent circuit model is discussed. The model is verified by SIMPLIS simulation in commonly used converters for both constant frequency modulation and variable frequency modulation. Then, based on the proposed unified model, a comparison between different current mode control implementations is presented. In different applications, different implementations have their unique benefit on extending control bandwidth. The properties of audio susceptibility and output impedance are discussed. It is found that, for adaptive voltage positioning design, constant on-time current mode control can simplifies the outer loop design. Next, since multiphase interleaving structure is widely used in PFC, voltage regulator and other high current applications, the model is extended to multiphase current mode control. Some design concerns are discussed based on the model. As a conclusion, a unified three-terminal switch model for current mode controls is investigated. The proposed model is quite general and not limited by implementation methods and topologies. All the modeling results are verified through simulation and experiments. / Master of Science

This theis deals with the general overview of the piezoelectric theory, focused both on the mathematical description and on the attributes of piezoelectric materials. It further focuses on the description of piezoelectric resonators with a more detailed explantation of their equivalent scheme and measurement methods of its single elements. The practical part of the thesis rests on the proposal of a measurement apparatus which will serve to measuring the equivalent circuit piezoelectric resonator elements. The realization of the apparatus and its functionality testing are described. In the experimental part of the thesis, the measured rates are processed and levels of the electric equivalent circuit elements of the used piesoelectric resonator for the basic and the two higher closest resonance frequency are set. The measured results are compiled into a standard measurement protocol. This thesis should place basics to the growing laboratory. It should also be a source of necessary theoretical and practical information for this lab.

This thesis investigates simulation of synchronous machines using a novel Magnetic Equivalent Circuit (MEC) model. The proposed model offers sufficient detail richness for design calculations, while still keeping the simulation time acceptably short. Different modeling methods and circuit alternatives are considered. The selected approach is a combination of several previous methods added with some new features. A detailed description of the new model is given. The flux derivative is chosen as the magnetic flow variable which enables a description with standard circuit elements. The model is implemented in dq-coordinates to reduce complexity and simulation time. A new method to reflect winding harmonics is introduced. Extensive measurements have been made to estimate the traditional dq-model parameters. These in combination with analytical calculations are used to determine the parameters for the new MEC model. The model is implemented using the Dymola simulation program. The results are evaluated by comparison with measurements and FEM simulations. Three different operation cases are investigated; synchronous operation, asynchronous start and inverter fed operation. The agreement with measurements and FEM simulations varies, but it is believed that it can be improved by more work on the parameter determination. The overall conclusion is that the MEC method is a useful approach for detailed simulation of synchronous machines. It enables proper modeling of magnetic saturation, and promises sufficiently detailed results to enable accurate loss calculations. However, the experience is that the complexity of the circuits should be kept at a reasonable low level. It is believed that the practical problems with model structure, parameter determination and the simulation itself will otherwise be difficult to master.

Batteries have imparted momentum to the process of transition towards a green future. However, mass application of batteries is obstructed due to their explosive nature, a trait specific to Li-Ion batteries. To cater to an efficient battery utilization, an introduction of a battery management system would provide an ultimate solution. This thesis deals with different aspects crucial in designing a battery management system for high energy as well as high power applications. To build a battery management system capable of predicting battery behavior, it is necessary to analyze the dynamic processes happening inside the battery. Hence, a battery equivalent circuit model is proposed in this thesis as well as proper analysis is done in MATLAB to project a generic structure applicable to all Li-Ion chemistries. The model accounts for all dynamic characteristics of a battery including non-linear open circuit voltage, discharge current and capacity. Effect of temperature is also modeled using a cooling system. The model is validated with test current profiles. Less than 0.1% error between measured and simulated voltage profiles indicates the effectiveness of the proposed model to predict the runtime behavior of the battery. Furthermore, the model is implemented with the energy as well as the power battery pack. State of charge calculations are performed using the proposed model and the coulomb counting method and the results indicate only a 4% variance. Therefore, the proposed model can be applied to develop a real-time battery management system for accurate battery states estimation.

This Ph.D. thesis focuses on the high-frequency electrical capabilities of the carbon-nanotube, field-effect transistor (CNFET). The thesis can be categorized into three stages, leading up to an assessment of the RF capabilities of realistic array-based CNFETs. In the first stage, the high-frequency and time-dependent behavior of ballistic CNFETs is examined by numerically solving the time-dependent Boltzmann transport equation (BTE) self-consistently with the Poisson equation. The RF admittance matrix, which contains the transistor’s y-parameters, is extracted. At frequencies below the transistor’s unity-current-gain frequency fT, the y-parameters are shown to agree with those predicted from a quasi-static equivalent circuit, provided that the partitioning factor for the device charge is properly extracted. It is also shown that a resonance behavior exists in the transistor’s y-parameters. In the second stage, non-quasi-static effects in ballistic CNFETs are examined by analytically developing a transmission-line model from the BTE and Poisson equation. This model includes nonclassical transistor elements, such as the "quantum capacitance" and "kinetic inductance," and it is shown to represent the intrinsic (contact-independent) transistor’s behavior at high frequencies, including a correct prediction of the resonances in the y-parameters. Moreover, it is shown that the kinetic inductance can be represented using lumped elements in the transistor’s small-signal equivalent circuit, and it is demonstrated that the resulting circuit is capable of modeling intrinsic CNFET behavior to frequencies beyond fT. In the last stage, by building upon the first two stages, a comprehensive study is performed to assess the RF performance potential of array-based CNFETs. First, phonon scattering is incorporated into the time-dependent BTE to study the impacts of collisions on different aspects of intrinsic CNFET operation, including the intrinsic fT and the small-signal equivalent circuit. These results are then further extended by adding the effects of extrinsic (contact-dependent) parasitics and then examining the behavior of key RF figures of merit, such as the extrinsic fT, the attainable power gain, and the unity-power-gain frequency. The results are compared to those of state-of-the-art high-frequency transistors and to the next generation of RF CMOS, and they provide an indication of the potential advantages of array-based CNFETs for RF applications. / Micro-Electro-Mechanical Systems (MEMS) and Nanosystems

This dissertation aims to design and implement wireless passive components using domestic integrated passive device (IPD) technology. The research focuses on exploiting novel 3-D structures for various kinds of IPD-based wireless passive components including high-quality and high-efficiency planar transformers, baluns, filters, and combiners to achieve miniature size and high performance. A physical model has been developed for modeling the planar transformers. In this dissertation, a scalable transformer model in integrated passive device technology is further used to correlate with the coupled-line sections of a conventional Marchand balun. This improves the efficiency of the design of planar transformers with equivalent coupled-line parameters such as the coupling factor, and even- and odd-mode characteristic impedances and quality factors. Additionally, the proposed model-based design approach provides effective optimization techniques that incorporate geometrical and material parameters. In addition, a compact transformer-based coupled balun bandpass filter design is proposed based on integrated circuit technology and the equivalent circuit is established. Using a planar transformer with high-density fully symmetrical wiring not only greatly reduces the component size but also provides a superior stopband rejection and selectivity. Finally, by using the spiral-shaped resonators, the dual-band third-order bandpass filter has been implemented on organic substrates. The proposed BPF design is verified to overcome the elements¡¦ parasitic effects, and thus can be miniaturized and optimized with high degree of freedom. The simulation and measurement results have good agreement for the proposed design in this dissertation.

The objective of this thesis is to provide a reliable and effective iron loss estimation scheme for the electromagnetic steel products in the design and on-line operation stages. To investigate the possible performance of electromagnetic steel products, proper iron loss information of the products that are constructed by different steels is one of the key concerns. Along with the various power electronic device applications and iron core structures, the magnetic fluxes flowing through the machine cores will be non-uniform and include harmonic terms. Unless excessive computation efforts in expensive software tools are performed, large discrepancies will be exhibited the estimated and actual values of machine iron losses. To overcome these drawbacks, a rational machine iron loss estimation scheme is proposed. By adopting the iterative magnetic equivalent circuits and the nonlinear magnetic characteristics of the electromagnetic steels, the preliminary operational flux information in the machine is first obtained, and then a numerical Epstein Frame test circuit with magnetizing inductance modeled by Preisach model is applied. With appropriate circuit input voltages devised from preliminary information, the detailed hysteresis inner-loop characteristics resulting from product structures and magnetization harmonics can be properly modeled. Based on the circuit results, the iron losses of electric machines with any operation can be rationally evaluated, and a valuable reference in machine designing can be provided.

This thesis provides a detailed field analysis of a specially designed axial-flow radial-flux permanent magnet motor for cooling fan applications. By implementing an iron strip segment at the stator base, this motor can provide a stable guidance force in its axial direction, such that the operational vibration effects can be minimized and the undesired forces applied onto associated bearing system can be alleviated. Supported by adaptive magnetic equivalent circuit and three-dimensional finite element analyses, the motor operational fluxes and forces can be analyzed. Results show that excellent performance and enhanced reliability objectives can all be achieved.

High voltage power transformers are designed to withstand a variety of overvoltages and short circuit forces. Occurrence of these events in a power system is natural, inevitable, and one of the main causes of transformer failure. Therefore, an early and reliable detection of an incipient fault is paramount. To this end, diagnostic testing and condition monitoring, not only enables power utilities in early detection of incipient fault-like conditions, but also is a practical way of optimizing existing assets, lowering operating costs, scheduling maintenance, preventing unplanned outages, etc. and consequently improve efficiency. Over the years, many monitoring and diagnostic methods have evolved. In par- ticular, low voltage impulse and frequency response analysis or transfer function approaches have emerged as useful tools in detecting winding deformations. Literature study reveals that although much has been acclaimed about these methods, advancement in interpretation of acquired data must be rigorously pursued, to facilitate a more meaningful assessment. As a matter of fact, diagnosis (which means interpretation of monitored data) has at-the-most been confined to a mere comparison of two subsequently acquired data sets. This philosophy certainly needs to be improved, to realize the true potential of monitoring/diagnostic tools. Achieving this goal calls for newer impetus. It is natural that there will arise many problems while achieving this goal and they will have to be resolved. Keeping these aspects in mind, the objective of this thesis was aimed at developing Solutions to two specific topics that are closely related to and concern the transformer winding, namely, * An efficient solution to the generalized model of a transformer winding, with no particular limitation on the size of network and number of windings, no restriction on circuit topology and terminal condition, etc. * Propose a method to locate the position, quantum and type of change (i.e. deformation) a model winding undergoes, based on terminal measurements. Details of these approaches are presented in this thesis, which is divided into two parts. 1. A comprehensive analysis of the behaviour of a transformer winding under impulse excitation and its interaction with adjacent windings was until now severely limited, due to the simplifying assumptions imposed (by the existing approaches), like neglecting interaction with neighbouring windings, Ignoring loss, considering only a few sections, etc. thereby rendering the computed results less accurate. A solution considering all these aspects often times results in a very large-sized circuit that needs to be solved. Although circuit simulation software afford iterative solutions, a direct estimation of poles and zeros of any desired network function is not possible. In the first part of the thesis, a novel and closed-form (i.e. analytical) solution based on state space analysis is proposed. It is shown, how the renders the entire computation to be purely numeric. Thus, time-consuming symbolic manipulations are avoided. With this feature, there is practically no limit on the size of network and no restriction on circuit topologies that can be considered. So, virtually any number of windings of a transformer can be considered, permitting a comprehensive analysis of winding behaviour and its interactions. Further, the formulation also permits computation of poles and zeros of any desired network function (e.g. transfer admittance), response to any excitation (e.g. neutral current, transferred surge), estimation of voltage distribution, etc. with little extra effort. Hence, it would be apppropriate to term the proposed method as a \Generalized" solution. For the sole purpose of demonstration, a large-sized network (representing a two-winding transformer with 250 sections/winding) was solved and required only 700 seconds. This shows the time-efficiency achieved, and also that it is free from issues like numerical instability, convergence problems, etc. encountered in some of the existing methods. 2. Detection of mechanical deformation in transformer windings can be achieved with a fair degree of sensitivity using frequency response methods. However, a major challenge that has remained elusive is ascertaining the \extent of damage" and likewise \its location along the winding". It is needless to say that finding these answers is crucial. Ideally, a diagnosis tool is expected to be endowed with powers to answer these questions. Therefore, it is desirable to explore alternative ways of harnessing these embedded features, if any. This was the next motivation. Obviously, a direct solution to this problem on an actual transformer winding is far too complex. Hence, in this preliminary effort a solution was attempted considering a model winding. However, care was taken to incorporate other winding-related nuances as far as practicable. The method was formulated based on quantities measured at the terminals. In the second part of the thesis, a novel algorithm is proposed for determining the location, extent and type of changes intrroduced in a model winding, based on terminal measurements. It employs the well-known properties of driving-point functions and adopts an iterative circuit synthesis approach. From knowledge of the measured short-circuit and open-circuit natural frequencies, and some relevant winding design data, an equivalent circuit was synthesized (called reference circuit). Next, changes were introduced at different locations in the model winding and natural frequencies measured again. Corresponding to every new set of measured natural frequencies, a fresh circuit was synthesized (with topology remaining unchanged). A comparison of these circuits with the reference circuit revealed that a mapping could be established between changes introduced in the model winding and those predicted by the synthesized circuits. Initially, the underlying principle is discussed, and thereafter, the experimental results are presented for both continuous-disc and interleaved winding representations. The case studies involved examples wherein changes in the model winding were made to elements connected to a single tap, two physically different tap positions, multiple changes to different elements, and so on. In all cases, the positions of all the `changes' were reasonably well locatable, and so was the `type of change'. The results were very encouraging. In summary, localization of changes based on terminal measurements, is shown to be a possibility. Lastly, it is conjectured that these findings could be of some assistance in addressing the ultimate task of locating mechanical deformations in actual transformer windings.