Lead-lag dampers are present in most rotors to provide the required level of damping in all flight conditions. These dampers are a critical component of the rotor system, but they also represent a major source of maintenance cost. In present rotor systems, both hydraulic and elastomeric lead-lag dampers have been used. Hydraulic dampers are complex mechanical components that require hydraulic fluids and have high associated maintenance costs. Elastomeric dampers are conceptually simpler and provide a ``dry" rotor, but are rather costly. Furthermore, their damping characteristics can degrade with time without showing external signs of failure. Hence, the dampers must be replaced on a regular basis. A semi-active friction based lead-lag damper is proposed as a replacement for hydraulic and elastomeric dampers. Damping is provided by optimized energy dissipation due to frictional forces in semi-active joints. An actuator in the joint modulates the normal force that controls energy dissipation at the frictional interfaces, resulting in large hysteretic loops. Various selective damping strategies are developed and tested for a simple system containing two different frequency modes in its response, one of which needs to be damped out. The system reflects the situation encountered in rotor response where 1P excitation is present along with the potentially unstable regressive lag motion. Simulation of the system response is obtained to compare their effectiveness. Next, a control law governing the actuation in the lag damper is designed to generate the desired level of damping for performing adaptive selective damping of individual blade lag motion. Further, conceptual design of a piezoelectric friction based lag damper for a full-scale rotor is presented and various factors affecting size, design and maintenance cost, damping capacity, and power requirements of the damper are discussed. The selective semi-active damping strategy is then studied in the context of classical ground resonance problem. In view of the inherent nonlinearity in the system due to friction phenomena, multiblade transformation from rotating frame to nonrotating frame is not useful. Stability analysis of the system is performed in the rotating frame to gain an understanding of the dynamic characteristics of rotor system with attached semi-active friction based lag dampers. This investigation is extended to the ground resonance stability analysis of a comprehensive UH-60 model within the framework of finite element based multibody dynamics formulations. Simulations are conducted to study the performance of several integrated lag dampers ranging from passive to semi-active ones with varying levels of selectivity. Stability analysis is performed for a nominal range of rotor speeds using Prony's method.

Liquid sloshing with unrestrained free surface in a moving container is associated with various engineering problems, such as tankers on highways, liquid oscillations in large storage tanks caused by earthquakes, sloshing of liquid cargo in ocean-going vessels, and the motion of liquid fuel in aircraft and spacecraft. The purpose of this study is to develop a three-dimensional (3D) numerical wave tank with or without internal structures to investigate the mechanism of liquid sloshing and the interaction between the fluid and internal structures. The developed 3D time-independent finite difference method is applied on solving liquid sloshing in tanks with or without the influence of baffles under the ground motion of six-degrees of freedom. The 3D Navier-Stokes equations were solved and transformed to a tank-fixed coordinate system, and the fully nonlinear kinematic and dynamic free surface boundary conditions for fluid sloshing in a rectangular tank with a square base were considered. The fluid is assumed incompressible in this study. The complicated interaction in the vicinity of the fluid-structure interface was solved by implementing one dimensional ghost cell approach and the stretching grid technique near the fluid-structure boundaries were used to catch the detailed evolution of local flow field. A PC-cluster was established by linking several single computers to reduce the computational times due to the implementation of the 3D numerical model. The Message Passing Interface (MPI) parallel language and MPICH2 software were utilized to code the computer codes and to carry out the circumstance of parallel computation, respectively. The developed numerical scheme was verified by rigorous benchmark tests. Not only the reported analytical, numerical and experimental studies were compared with the present numerical results, the experimental investigation was also involved in the present work to further validate the accuracy of the numerical scheme. All the benchmark tests of this study showed excellent accuracy of the developed numerical scheme. For a tank without internal structures, the coupled motions of surge and sway are simulated with various excitation angles, excitation frequencies and water depths. The characteristics of sloshing waves are dissected in terms of the classification of sloshing wave types, sloshing amplitude, beating phenomenon, sloshing-induced forces and energy transfer of sloshing waves. Six types of sloshing waves, named single-directional, diagonal, square-like, swirling-like, swirling and irregular waves, were found and classified in the present study and the occurrence of these waves are tightly in connection with the excitation frequency of the tank. The effect of excitation angle on the characteristics of sloshing waves is explored and discussed, especially for swirling waves. The spectral analyses of sloshing displacement of various sloshing waves are examined and a clear evidence of the correlation between sloshing wave patterns and resonant modes of sloshing waves are demonstrated. The mechanism of switching direction of swirling waves is discussed by investigating the situation of circulatory flow, the instantaneous free surface, the gravitational effect and the instantaneous direction of external forcing. The coupling effects of heave, surge and sway motions were also included in this study and the result showed an unstable influence of heave motion on the kinematic and dynamic characteristics of sloshing waves when the vertical excitation frequency of the tank is twice as large as the fundamental natural frequency. Except irregular waves, the other types of sloshing waves are converted into swirling waves due to the effect of heave motion. The study related to tuned liquid damper (TLD) in 2D and 3D tanks were considered. A comprehensive investigation for a 2D tank with vertically tank bottom-mounted baffles (baffled tank) are demonstrated and discussed with respect to the influence of baffle height on the natural mode of the tank, the evolution of vortices and vortex shedding phenomenon, the relationship between the vortex shedding frequency and the excitation frequency of the tank, the vortex size generated in the vicinity of the baffle tip, the interaction of vortices inside the tank. The baffle height shows a significant influence on the shift of the first natural frequency of the baffled tank and the liquid depth also plays an important part in determining this influence. In other words, the shift of the first natural mode due to various baffle height is varied with water depths. The design of two baffles separated by 0.2 times the tank breadth is an efficient tool to not only reduce the sloshing amplitude but switch the first natural frequency of the tank. The sloshing displacement is affected distinctly by different numbers of baffles mounted vertically on the tank bottom. The more baffles mounted onto the tank bottom, the smaller the sloshing displacement is presented in both the transient and steady-state periods. The processes of the evolution of vortices near the baffle tip are categorized into four phases: the formation of separated shear layer and generation of vortices, the formation of a vertical jet and shedding of vortices, the interaction between shedding vortices and sloshing flow (the generation of snaky flow) and the interaction between snaky flow and sloshing waves. Vortex shedding phenomenon due to stronger vertical jets occurs when the excitation frequency is close to the first natural mode of the baffled tank. The size of the vortex generated near the baffle tip is discussed and the vortex size is closely correlated with the baffle height. Two types of 3D tuned liquid dampers, a vertically tank bottom-mounted baffle and a vertical plate, are discussed for a tank under coupled surge-sway motions. The wave types of diagonal and single-directional waves switch to the swirling type due to the influence of the baffle. The phenomenon of square-like waves or irregular waves coexisting with swirling waves is found in the baffled tank under diagonal excitation. The baffle and the vertical plate mounted parallel to the east (west) wall of the tank can effectively reduce the sloshing amplitude when the excitation angle is between 0 degree and 10 degree and the corresponding sloshing displacement in the sway (z) direction becomes more dominant with the increase of the excitation angle. The shift of the first natural mode of the baffled tank due to various baffle heights in the x direction is dominated in this design of baffled tank. The length of the plate can cause a significant influence on not only the variation of the natural frequencies but the type of the sloshing waves. The influence of the vertical plate on the irregular waves is insignificant and several peaks appear in the spectral analysis of the sloshing displacement for the irregular waves and the numbers of peaks are more than that of the baffled tank.

The main motivation of this study is the design of a control strategy for semi-active vehicle suspension systems to improve ride comfort for road vehicles. In order to achieve this objective, firstly the damping characteristics of Magnetorheological dampers will be reviewed. Then an appropriate semi-active control strategy manipulating the inputs of the dampers to create suitable damping forces will be designed. Linear Quadratic Regulator (LQR) control strategy is the primary focus area on semi-active control throughout this study. Further, skyhook controllers are examined and compared with optimal LQR controllers. The semi-active controller is tuned using a linearized full (4 wheel) vehicle ride model with seven degrees of freedom. Some selected simulations are carried out by using a nonlinear model to tune LQR controller in an effort to optimize bounce, pitch, and roll motion of the vehicle. Time domain simulations and frequency response analysis are used to justify the effectiveness of the proposed LQR control strategy.

In this study, the efficiency of linear and rotational tuned mass dampers (TMD) and lever type vibration isolators (LVI) in improving ride comfort is investigated based on a vehicle quarter-car model. TMDs reduce vibration levels by absorbing the energy of the system, especially at their natural frequencies. Both types of TMDs are investigated in the first part of this study. Although linear TMDs can be implemented more easily on suspension systems, rotational TMDs show better performance in reducing vibration levels / since, the inertia effect of rotational TMDs is higher than the linear TMDs. In order to obtain better results with TMDs, configurations with chain of linear TMDs are obtained in the second part of the study without changing the original suspension stiffness and damping coefficient. In addition to these, the effect of increasing the number of TMDs used in the chain configuration is investigated. Results show that performance deterioration at lower frequencies than wheel hop is reduced by using chain of TMDs. In the third part of this study, various configurations of LVIs with different masses are considered and significant attenuation of vibration amplitudes at both body bounce and wheel hop frequencies is achieved. Results show that TMDs improve ride comfort around wheel hop frequency while LVIs are quite efficient around body bounce frequency. Finally, parameter uncertainty due to aging of components and manufacturing defects are investigated.

As Civil Engineering structures, e.g., tall buildings, long span bridges, deep water offshore platforms, nuclear power plants, etc., have become more costly, complex and serve more critical functions, the consequences of their failure are catastrophic. Therefore, the protection of these structures against damage induced by large environmental loads, e.g., earthquakes, strong wind gusts and waves, etc., is without doubt, a worldwide priority. However, structures cannot be designed to withstand all possible external loads and some extraordinary loading episodes do occur, leading to damage or even failure of the structure. Protection of a structure against hazards can be achieved by various means such as modifying structural rigidities, increasing structural damping, and by attaching external devices, known as control devices. Control devices can be deployed either to isolate the structure from external excitation or to absorb input seismic energy to the structure (absorber) so as to mitigate vibration in the primary structure. Seismic base isolation is one such mechanism which isolates a structure from harmful ground excitations. Seismic base isolation is a widely accepted and implemented structural control mechanism due to its robustness and ease in deployment. Following the Northridge earthquake (1994), and Kobe earthquake (1995), the interest of structural engineers in understanding near-source ground motions has enhanced. Documents published after these earthquakes emphasized the issue of large base displacements because of the use of none or little isolation damping (of viscous type only) prior to these events. More recent studies have investigated analytically and experimentally, the efficiency of various dissipative mechanisms to protect seismic isolated structures from recorded near-source long period, pulse-type, high velocity ground motions. Consequently, hybrid isolation systems, seismic base isolation supplemented with damping mechanisms, have become the focus of current research trend in structural vibration control. Hybrid base isolation system incorporating passive supplemental damping devices like, viscous fluid dampers, etc., performs satisfactorily in minimizing isolator displacement but at the same time increases superstructure acceleration response. Furthermore, the passive system can be tuned to a particular frequency range and its performance decreases for frequencies of excitation outside the tunning bandwidth. In such a scenario, active control devices in addition to base isolation mechanism provide better performance in reducing base displacement and superstructure acceleration for a broad range of excitation frequencies. Tremendous power requirement and the possibility of power failure during seismic hazards restrict the usage of active systems as a supplemental device. Semi-active devices provide the robustness of passive devices and adaptive nature of active devices. These characteristics make them better suited for structural control applications. The recent focus is on the development of magnetorheological (MR) dampers as semi-active device for structural vibration control applications. MR dampers provide hysteretic damping and can operate with battery power. The thrust of this thesis is on developing a hybrid base isolation mechanism using MR dampers as a supplemental damping device. The use of MR damper as a semi-active device involves two steps; development of a model to describe the MR damper hysteretic behaviour; development of a proper nonlinear control algorithm to monitor MR damper current / voltage supply. Existing parametric models of MR damper hysteretic behaviour, e.g., Bouc-Wen model, fail to consider the effect of amplitude and frequency of excitation on the device. Recently reported literature has demonstrated the necessity of incorporating amplitude and frequency dependence of MR damper models. The current/voltage supply as the input variable to the MR damper restricts the direct use of any control algorithms developed for active control of structures. The force predicted by the available control algorithms should be mapped to equivalent current/voltage and then to be fed into the damper. Available semi-active algorithms in the literature used ‘on-off’ or ‘bang-bang’ strategy for MR applications due to nonlinear current/voltage-force relation of MR damper. The ‘on-off’ nature of these algorithms neither provides smooth change in MR damper current/voltage input nor considers all possible current/ voltage values within its minimum to maximum range. Secondly, these algorithms fail to consider the effect of the MR damper applied and commanded current/voltage dynamics. The thrust of this dissertation is to develop semi-active control algorithms to monitor MR damper supply current/voltage. The study develops a Bouc-Wen based model to characterize the MR damper hysteretic phenomenon. Experimental results and modeling details have been documented. A fuzzy based intelligent control and two model-based nonlinear control algorithms based on optimal dynamic inversion and integral backstepping have been developed. Performance of the fuzzy logic based intelligent control has been explored using experimental investigation on a three storey base isolated building. Further the application of the proposed controllers on a benchmark building; a benchmark highway bridge and a stay cable vibration reduction have been discussed. Experimental study has revealed that the performance of optimal FLC is better than manually designed FLC in terms of reducing base displacement and storey accelerations. The performance of both the FLCs (simple FLC and genetic algorithm based optimal FLC) is better than ‘passive-off’ (zero ampere current supply) and ‘passive-on’ (one ampere current supply) condition of MR damper applications. The ‘passive-off’ results have shown higher base displacements with lower storey accelerations, whereas, the ‘passive-on’ results have reduced base displacement to the least but at the same time increased the storey acceleration too much. The FLC monitored MR damper show a compromise between the two passive conditions. Analytical results confirm these observations. Numerical simulations of the base isolated building with the two model based MR damper control algorithms developed have shown a better performance over FLC and widely used clipped optimal algorithms. The applications of the proposed semi-active control algorithms (FLC, dynamic inversion and integral backstepping) have shown better performance in comparison to that of control algorithms provided with the benchmark studies.

The dynamic behaviour of high-rise buildings has become a critical design consideration as buildings are built taller and more slender. Large wind vibrations cause an increase in the lateral wind loads, but more importantly, they can be perceived by building occupants creating levels of discomfort ranging from minor annoyance to severe motion sickness. The current techniques to address these issues include stiffening the lateral load resisting system, reducing the number of stories, or incorporating a vibration absorber at the top of the building. All of which have consequences on the overall project cost. The dynamic response of high-rise buildings is highly dependent on damping. Full-scale measurements of high-rise buildings have shown that the inherent damping decreases with height and recent in-situ measurements have shown that the majority of buildings over 250 meters have levels of damping less than 1% of critical. Studies have shown that small increases in the inherent damping can lead to vast improvement in dynamic response. A new damping system, the viscoelastic (VE) Fork Configuration Damper (FCD), has been developed at the University of Toronto to address these design challenges. The proposed FCDs are introduced in lieu of coupling beams in reinforced concrete (RC) coupled wall buildings and take advantage of the large shear deformations at these locations when the building is subjected to lateral loads. An experimental study was conducted on 5 small-scale VE dampers to characterize the VE material behaviour and 6 full-scale FCD samples in an RC coupled wall configuration (one designed for areas where low to moderate ductility is required and one with built-in ductile structural “fuse” for areas where high ductility is required). The VE material tests exhibited stable hysteretic behaviour under expected high-rise loading conditions and the full-scale tests validated the overall system performance based on the kinematic behaviour of coupled walls, wall anchorage and VE material behaviour. Analytical models were developed that capture the VE material behaviour and the FCD system performance well. An 85-storey high-rise building was studied analytically to validate the design approach and to highlight the improvements in building response resulting from the addition of FCDs.

The dynamic behaviour of high-rise buildings has become a critical design consideration as buildings are built taller and more slender. Large wind vibrations cause an increase in the lateral wind loads, but more importantly, they can be perceived by building occupants creating levels of discomfort ranging from minor annoyance to severe motion sickness. The current techniques to address these issues include stiffening the lateral load resisting system, reducing the number of stories, or incorporating a vibration absorber at the top of the building. All of which have consequences on the overall project cost. The dynamic response of high-rise buildings is highly dependent on damping. Full-scale measurements of high-rise buildings have shown that the inherent damping decreases with height and recent in-situ measurements have shown that the majority of buildings over 250 meters have levels of damping less than 1% of critical. Studies have shown that small increases in the inherent damping can lead to vast improvement in dynamic response. A new damping system, the viscoelastic (VE) Fork Configuration Damper (FCD), has been developed at the University of Toronto to address these design challenges. The proposed FCDs are introduced in lieu of coupling beams in reinforced concrete (RC) coupled wall buildings and take advantage of the large shear deformations at these locations when the building is subjected to lateral loads. An experimental study was conducted on 5 small-scale VE dampers to characterize the VE material behaviour and 6 full-scale FCD samples in an RC coupled wall configuration (one designed for areas where low to moderate ductility is required and one with built-in ductile structural “fuse” for areas where high ductility is required). The VE material tests exhibited stable hysteretic behaviour under expected high-rise loading conditions and the full-scale tests validated the overall system performance based on the kinematic behaviour of coupled walls, wall anchorage and VE material behaviour. Analytical models were developed that capture the VE material behaviour and the FCD system performance well. An 85-storey high-rise building was studied analytically to validate the design approach and to highlight the improvements in building response resulting from the addition of FCDs.

Los sistemas tales como edificios y veh¨ªculos est¨¢n sujetos a vibraciones que pueden causar mal funcionamiento, incomodidad o colapso. Para mitigar estas vibraciones, se suelen instalar amortiguadores. Estas estructuras se convierten en sistemas adaptr¨®nicos cuando los amortiguadores son controlables. Esta tesis se enfoca en la soluci¨®n del problema de vibraciones en edificios y veh¨ªculos usando amortiguadores magnetoreol¨®gicos (MR). Estos son unos amortiguadores controlables caracterizados por una din¨¢mica altamente no lineal. Adem¨¢s, los sistemas donde se instalan se caracterizan por la incertidumbre param¨¦trica, la limitaci¨®n de medidas y las perturbaciones desconocidas, lo que obliga al uso de t¨¦cnicas complejas de control. En esta tesis se usan Backstepping, QFT y H2/H¡Þ mixto para resolver el problema. Las leyes de control se verifican mediante simulaci¨®n y experimentaci¨®n. / Buildings and vehicle systems are subject to vibrations that may cause malfunctioning, discomfort or collapse. It is an extended practice to install damping devices in order to mitigate such vibrations. With controllable dampers, structures act as adaptronic systems. This dissertation focuses on solving the vibration mitigation problem in buildings and vehicles making use of magnetorheological (MR) dampers which are controllable devices characterized by a highly nonlinear dynamics. Additionally, the systems where they are installed, are characterized by parametric uncertainties, limited measurement availability and unknown disturbances. This implies the use of complex control techniques in order to get a reliable performance of the control system. This research makes use of Backstepping, QFT and Mixed H2/H¡Þ control techniques for achieving the proposed goal. These are verified thorugh simulations and experimentation.

[pt] A redução de deslocamentos e acelerações em edifícios é um aspecto de vital importância no projeto de estruturas sob a ação de sismos. Assim, o controle de vibrações de estruturas em regiões sujeitas a eventos sísmicos tem se tornado um importante tema de pesquisa em engenharia. Dentre os mecanismos propostos para a redução de vibrações em estruturas, encontram-se os amortecedores magnetoreológicos (MR). Amortecedores magnetoreológicos são dispositivos passivos ou semiativos que controlam as vibrações com um consumo mínimo de energia. Estes mecanismos são caracterizados por um comportamento histerético não linear que leva em geral a uma grande dissipação de energia. Neste trabalho estuda-se o efeito de um amortecedor MR e de seus parâmetros característicos na redução das vibrações de edifícios e torres esbeltas. Para isto, utiliza-se o modelo de Bouc-Wen. O edifício é descrito como um sistema discreto massa-mola-amortecedor do tipo shear-building e a torre como um pêndulo múltiplo, onde se leva em conta a possibilidade de grandes rotações e deslocamentos. Considera-se o amortecedor localizado na estrutura (primeiro andar) e como um sistema de isolamento de base, com o propósito de verificar a influência da localização do amortecedor na redução das respostas dinâmicas. Quando o dispositivo é usado como isolamento de base, ambos os modelos mostraram uma grande diminuição da resposta dinâmica, em comparação aos resultados com o dispositivo no primeiro andar. Estuda-se também a influência da relação entre as frequências da estrutura e o conteúdo de frequências da excitação na eficiência do amortecedor MR. Os resultados mostram que esta relação tem uma grande influência no grau de redução das vibrações da estrutura controlada. Em todos os casos analisados, observa-se que o amortecedor MR leva a uma redução das vibrações, em particular dos deslocamentos da estrutura. / [en] The reduction of displacements and accelerations in buildings is a vital aspect in the design of structures under an earthquake excitation. Thus, the vibration control of structures in areas subject to seismic events has become an important research topic in engineering. Among the proposed mechanisms to reduce vibrations in structures, are the magneto rheological dampers (MR). Magneto rheological dampers are passive or semi-active devices for vibration control characterized by small energy consumption. These mechanisms are characterized by a nonlinear hysteretic behavior that usually leads to large energy dissipation. In this paper the effect of an MR damper and its characteristic parameters in reducing the vibrations of buildings and slender towers is studied. For this, the Bouc-Wen model is adopted. The building is described as a discrete mass-spring-damper-type shear-building and the tower as a multiple pendulum, which takes into account large displacements and rotations. It is considered that the damper is located in the structure (first floor) or as a base isolation system, in order to verify the influence of the location of the damper in the reduction of dynamic responses. When the device is used as a base isolation, both models show a large decrease of the dynamic response as compared to the results with the device on the first floor. The influence of the relationship between the frequencies of the structure and frequency content of the excitation on the efficiency of MR damper is also investigated. The results show that this relation has a great influence on the degree of reduction of vibrations of the controlled structure. In all cases here analyzed, it is observed that the MR damper leads to a reduction of the vibration response, in particular the displacement of the structure.

Power distribution network (PDN) design was a non-existent entity during the early days of microprocessors due to the low frequency of operation. Once the switching frequencies of the microprocessors started moving towards and beyond MHz regions, the parasitic inductance of the PCB tracks and planes started playing an important role in determining the maximum voltage on a PDN. Voltage regulator module (VRM) sup-plies only the DC power for microprocessors. When the MOSFETs inside a processor switches, it consumes currents during transition time. If this current is not provided, the voltage on the supply rails can go below the specifications of the processor. For lower MHz processors few ceramic-capacitors known as ‘decoupling capacitors’ were connected between power and ground to provide this transient current demand. When the processor frequency increased beyond MHz, the number of capacitors also increased from few numbers to hundreds of them. Nowadays, the PDN is said to be comprising all components from VRM till the die location. It includes VRM, bulk capacitors, PCB power planes, capacitor mounting pads and vias, mount for the electronic package, package capacitors, die mount and internal die capacitance. So, the PDN has evolved into a very complex system over the years. A PDN should provide three distinct roles; 1) provide transient current required by the processor 2) act as a stable reference voltage for processor 3) filter out the noise currents injected by the processor. The first two are required for the correct operation of the processor. Third one is a requirement from analog or other sensitive circuits connected to the same PDN. If the noise exits the printed circuit board (PCB), it can result in conducted and radiated EMI, which can in turn result in failure of a product in EMC testing. Every PDN design starts with the calculation of a target impedance which is given as the ratio of maximum allowed ripple voltage to the maximum transient current required by the processor. The transient current is usually taken as half the average input current. The definition of target impedance assumes that the PDN is flat over the entire frequency of operation, which is true only for a resistive network. This is seldom true for a practical PDN, since it contains inductances and capacitances. Because of this, a practical PDN has an uneven impedance versus frequency envelope. Whenever two capacitors with different self resonant frequencies are connected in parallel, their equivalent impedance produces a pole between the self resonant frequencies known as antiresonance peaks. Because of this, a PDN will have phase angles associated with them. Also, these antiresonance peaks are energy reservoirs which will be excited during the normal operation of a processor by the varying currents. The transient current of a microprocessor is modeled as a gamma function, but for practical cases it can be approximated as triangular waveforms during the transition time which is normally 10% of the time period. Depending upon the micro-operations running inside the processor, the peak value of this waveform varies. This is filtered by the on-chip capacitors, package inductance and package capacitors. Due to power gating, clock gating, IO operations, matrix multiplications and magnetic memory readings the waveforms at the board will be like pulse type, and their widths are determined by these operations. In literatures, these two types of waveforms are used for PDN analysis, depending upon at which point the study is conducted. Chapter 1 introduces the need for PDN design and the main roles of a PDN. The issue of antiresonance is introduced from a PDN perspective. Different types of capacitors used on a PDN are discussed with their strengths and limitations. The general nature of the switching noise injected by a microprocessor is also discussed. This chapter discusses the thesis contributions, and the existing work related to the field. Chapter 2 introduces a new method to calculate the target impedance (Zt ) by including the phase angles of a PDN which is based on a maximum voltage calculation. This new Zt equals to conventional Zt for symmetrical triangular switching current waveforms. The value of new Zt is less than the conventional Zt for trapezoidal excitation patterns. By adding the resonance effects into this, a maximum voltage value is obtained in this chapter. The new method includes the maximum voltage produced on a PDN when multiple antiresonance peaks are present. Example simulations are provided for triangular and pulse type excitations. A measured input current wave-form for PIC16F677 microcontroller driving eight IO ports is provided to prove the assumption of pulse type waveforms. For triangular excitation waveform, the maximum voltage predicted based on the expression was ¡0.6153 V, and the simulated maximum voltage was found to be at ¡0.5412 V which is less than the predicted value. But the predicted value based on Zt method was 1.9845 V. This shows that the conventional as well as the new target impedance method leads to over estimating the maximum voltage in certain cases. This is because most of the harmonics are falling on the minimum impedance values on a PDN. If the PDN envelope is changed by temperature and component tolerances, the maximum voltage can vary. So the best option is to design with the target impedance method. When pulse current excitation was studied for a particular PDN, the maximum voltage produced was -139.39 mV. The target impedance method produced a value of -100.24 mV. The maximum voltage predicted by the equation was -237 mV. So this shows that some times the conventional target impedance method leads to under estimating the PDN voltage. From the studies, it is shown that the time domain analysis is as important as frequency domain analysis. Another important observation is that the antiresonance peaks on a PDN should be damped both in number and peak value. Chapter 3 studies the antiresonance peak suppression methods for general cases. As discussed earlier, the antiresonance peaks are produced when two capacitors with different self resonant frequencies are connected in parallel. This chapter studies the effect of magnetic coupling between the mounting loops of two capacitors in parallel. The mounting loop area contribute to the parasitic inductance of a capacitor, and it is the major contributing factor to it. Other contributing factors are equivalent series inductance (ESL) and plane spreading inductance. The ESL depends on the size and on how the internal plates of the capacitors are formed. The spreading inductance is the inductance contributed by the parts of the planes connecting the capacitor connector vias to the die connections or to other capacitor vias. If the power and ground planes are closer, the spreading inductance is lower. On one/two layer boards dedicated power/ground planes are absent. So the spreading inductance is replaced by PCB track inductances. The inductance contributed by the mounted area of the capacitor is known as mounting inductance. On one/two layer boards dedicated power/ground planes are absent. So the spreading inductance is replaced by PCB track inductances. The dependencies of various circuit parameters on antiresonance peak are studied using circuit theory. A general condition for damping the antiresonance is formulated. The antiresonance peak reduces with Q factor. The conventional critical condition for antiresonance peak damping needs modification when magnetic coupling is present between the mounting loops of two parallel unequal value capacitors. By varying the connection geometry it is possible to obtain negative and positive coupling coefficients. The connection geometries to obtain these two are shown. An example is shown for positive and negative coupling coefficient cases with simulation and experimental results. For the example discussed, RC Æ 32 - for k Æ Å0.6 and RC Æ 64 - for k Æ ¡0.6, where RC is the critical damping value and k is the magnetic coupling coefficient between the two mounting loops. The reason for this is that, the antiresonance peak impedance value is higher for negative coupling coefficient case than that for positive coupling coefficient case. Above the self resonant frequencies of both the capacitors, the equivalent impedance of the parallel capacitors become inductive. This case is studied with two equal value capacitors in parallel. It is shown that the equivalent inductance is lower for negative coupling coefficient case as compared to positive coupling coefficient case. An example is provided with simulation and experimental results. In the experimental results, parasitic inductance is observed to be 2.6 times lower for negative coupling coefficient case than that for positive coupling coefficient case. When equal value capacitors are connected in parallel, it is advantageous to use a negative coupling geometry due to this. Chapter 4 introduces a new method to damp the antiresonance peak using a magnet-ically coupled resistive loop. Reducing the Q factor is an option to suppress the peak. In this new method, the Q factor reduction is achieved by introducing losses by mag-netically coupling a resistive loop. The proposed circuit is analyzed with circuit-theory, and governing equations are obtained. The optimum value of resistance for achieving maximum damping is obtained through analysis. Simulation and experimental results are shown to validate the theory. From the experimental results approximately 247 times reduction in antiresonance peak is observed with the proposed method. Effectiveness of the new method is limited by the magnetic coupling coefficient between the two mounting loops of capacitors. The method can be further improved if the coupling coefficient can be increased at the antiresonance frequency. Chapter 5 focuses on the third objective of a PDN, that is to reduce the noise injected by the microprocessor. A new method is proposed to reduce the conducted noise from a microprocessor with switched super capacitors. The conventional switched capacitor filters are based on the concept that the flying capacitor switching at high frequency looks like a resistor at low frequency. So for using at audio frequencies the flying capacitors were switching at MHz frequencies. In this chapter the opposite of this scenario is studied; the flying capacitors are the energy storage elements of a switched capacitor converter and they switch at lower frequencies as compared to the noise frequencies. Two basic circuits (1:1 voltage conversion ratio) providing noise isolation were discussed. They have distinct steady state input current waveforms and are explained with PSPICE simulations. The inrush current through switches are capable of destroying them in a practical implementation. A practical solution was proposed using PMOS-PNP pair. The self introduced switching noise of the converter is lower when switching frequency is low and turn ON-OFF time is higher. If power metal oxide semiconductor field effect transistor (MOSFET)s are used, the turn ON and turn OFF are slow. The switching frequency can be lowered based on the voltage drop power loss. The governing equations were formulated and simulated. It is found that the switching frequency can be lowered by increasing the capacitance value without affecting the voltage drop and power loss. From the equations, it is found that the design parameters have a cyclic dependency. Noise can short through the parasitic capacitance of the switches. Two circuits were proposed to improve the noise isolation: 1) T switch 2) ¦ switch. Of these, the ¦ switch has the higher measured transfer impedance. Experimental results showed a noise reduction of (40-20) dB for the conducted frequency range of 150 kHz - 30 MHz with the proposed 1:1 switched capacitor converter. One possible improvement of this method is to combine the noise isolation with an existing switched capacitor converter (SCC) topology. The discussed example had a switching frequency of 700 Hz, and it is shown that this can isolate the switching noise in kHz and MHz regions. In a PDN there are antiresonance peaks in kHz regions. If the proposed circuit is kept close to a microprocessor, it can reduce the excitation currents of these low frequency antiresonance peaks. Chapter 6 concludes the thesis by stating the major contributions and applications of the concepts introduced in the thesis. This chapter also discusses the future scope of these concepts.