Efficient and Robust Simulation, Modeling and Characterization of IC Power Delivery Circuits

As the Moore’s Law continues to drive IC technology, power delivery has become one of the most difficult design challenges. Two of the major components in power delivery are DC-DC converters and power distribution networks, both of which are time-consuming to simulate and characterize using traditional approaches. In this dissertation, we propose a complete set of solutions to efficiently analyze DC-DC converters and power distribution networks by finding a perfect balance between efficiency and accuracy. To tackle the problem, we first present a novel envelope following method based on a numerically robust time-delayed phase condition to track the envelopes of circuit states under a varying switching frequency. By adopting three fast simulation techniques, our proposed method achieves higher speedup without comprising the accuracy of the results. The robustness and efficiency of the proposed method are demonstrated using several DCDC converter and oscillator circuits modeled using the industrial standard BSIM4 transistor models. A significant runtime speedup of up to 30X with respect to the conventional transient analysis is achieved for several DC-DC converters with strong nonlinear switching characteristics. We then take another approach, average modeling, to enhance the efficiency of analyzing DC-DC converters. We proposed a multi-harmonic model that not only predicts the DC response but also captures the harmonics of arbitrary degrees. The proposed full-order model retains the inductor current as a state variable and accurately captures the circuit dynamics even in the transient state. Furthermore, by continuously monitoring state variables, our model seamlessly transitions between continuous conduction mode and discontinuous conduction mode. The proposed model, when tested with a system decoupling technique, obtains up to 10X runtime speedups over transistor-level simulations with a maximum output voltage error that never exceeds 4%. Based on the multi-harmonic averaged model, we further developed the small-signal model that provides a complete characterization of both DC averages and higher-order harmonic responses. The proposed model captures important high-frequency overshoots and undershoots of the converter response, which are otherwise unaccounted for by the existing techniques. In two converter examples, the proposed model corrects the misleading results of the existing models by providing the truthful characterization of the overall converter AC response and offers important guidance for converter design and closed-loop control. To address the problem of time-consuming simulation of power distribution networks, we present a partition-based iterative method by integrating block-Jacobi method with support graph method. The former enjoys the ease of parallelization, however, lacks a direct control of the numerical properties of the produced partitions. In contrast, the latter operates on the maximum spanning tree of the circuit graph, which is optimized for fast numerical convergence, but is bottlenecked by its difficulty of parallelization. In our proposed method, the circuit partitioning is guided by the maximum spanning tree of the underlying circuit graph, offering essential guidance for achieving fast convergence. The resulting block-Jacobi-like preconditioner maximizes the numerical benefit inherited from support graph theory while lending itself to straightforward parallelization as a partitionbased method. The experimental results on IBM power grid suite and synthetic power grid benchmarks show that our proposed method speeds up the DC simulation by up to 11.5X over a state-of-the-art direct solver

Efficient and Robust Simulation, Modeling and Characterization of IC Power Delivery Circuits

As the Moore’s Law continues to drive IC technology, power delivery has become one of the most difficult design challenges. Two of the major components in power delivery are DC-DC converters and power distribution networks, both of which are time-consuming to simulate and characterize using traditional approaches. In this dissertation, we propose a complete set of solutions to efficiently analyze DC-DC converters and power distribution networks by finding a perfect balance between efficiency and accuracy. To tackle the problem, we first present a novel envelope following method based on a numerically robust time-delayed phase condition to track the envelopes of circuit states under a varying switching frequency. By adopting three fast simulation techniques, our proposed method achieves higher speedup without comprising the accuracy of the results. The robustness and efficiency of the proposed method are demonstrated using several DCDC converter and oscillator circuits modeled using the industrial standard BSIM4 transistor models. A significant runtime speedup of up to 30X with respect to the conventional transient analysis is achieved for several DC-DC converters with strong nonlinear switching characteristics. We then take another approach, average modeling, to enhance the efficiency of analyzing DC-DC converters. We proposed a multi-harmonic model that not only predicts the DC response but also captures the harmonics of arbitrary degrees. The proposed full-order model retains the inductor current as a state variable and accurately captures the circuit dynamics even in the transient state. Furthermore, by continuously monitoring state variables, our model seamlessly transitions between continuous conduction mode and discontinuous conduction mode. The proposed model, when tested with a system decoupling technique, obtains up to 10X runtime speedups over transistor-level simulations with a maximum output voltage error that never exceeds 4%. Based on the multi-harmonic averaged model, we further developed the small-signal model that provides a complete characterization of both DC averages and higher-order harmonic responses. The proposed model captures important high-frequency overshoots and undershoots of the converter response, which are otherwise unaccounted for by the existing techniques. In two converter examples, the proposed model corrects the misleading results of the existing models by providing the truthful characterization of the overall converter AC response and offers important guidance for converter design and closed-loop control. To address the problem of time-consuming simulation of power distribution networks, we present a partition-based iterative method by integrating block-Jacobi method with support graph method. The former enjoys the ease of parallelization, however, lacks a direct control of the numerical properties of the produced partitions. In contrast, the latter operates on the maximum spanning tree of the circuit graph, which is optimized for fast numerical convergence, but is bottlenecked by its difficulty of parallelization. In our proposed method, the circuit partitioning is guided by the maximum spanning tree of the underlying circuit graph, offering essential guidance for achieving fast convergence. The resulting block-Jacobi-like preconditioner maximizes the numerical benefit inherited from support graph theory while lending itself to straightforward parallelization as a partitionbased method. The experimental results on IBM power grid suite and synthetic power grid benchmarks show that our proposed method speeds up the DC simulation by up to 11.5X over a state-of-the-art direct solver

Pulse Train™, a Novel Digital Control Method, Applied to a Discontinuous Conduction Mode Flyback Converter

Pulse TrainTM, a new digital control technique for DC-DC converters is introduced and applied to a Flyback converter operating in discontinuous conduction mode (DCM). In contrast to the conventional analog control methods, the principal idea of this new algorithm is to use real time analysis. The proposed technique is appropriate for any converter operating in DCM. However, this work mainly focuses on Flyback converter. In this paper, the main mathematical concept of the new control algorithm is introduced and simulations as well as experimental results are presented

Accurate modeling techniques for power delivery

“Power delivery is essential in electronic systems to provide reliable power from voltage sources to load devices. Driven by the ambitious user demands and technology evolutions, the power delivery design is posed serious challenges. In this work, we focus on modeling two types of power delivery paths: the power distribution network (PDN) and the wireless power transfer (WPT) system. For the modeling of PDN, a novel pattern-based analytical method is proposed for PCB-level PDN impedance calculations, which constructs an equivalent circuit with one-to-one correspondences to the PCB’s physical structure. A practical modeling methodology is also introduced to optimize the PDN design. In addition, a topology-based behavior model is developed for the current-mode voltage regulator module (VRM). This model includes all the critical components in the power stage, the voltage control loop, and the current control loop of a VRM device. A novel method is also proposed to unify the modeling of the continuous and discontinuous conduction modes for transient load responses. Cascading the proposed VRM model with the PCB-level PDN model enables a combined PDN analysis, which is much needed for modern PDN designs. For the modeling of WPT system, a system-level model is developed for both efficiency and power loss of all the blocks in WPT systems. A rectifier characterization method is also proposed to obtain the accurate load impedance. This model is capable of deriving the power capabilities for both the fundamental and higher order harmonics. Based on the system model, a practical design methodology is introduced to simultaneously optimize multiple system parameters, which greatly accelerates the design process”--Abstract, page iv

Control of a Satellite Based Photovoltaic Array for Optimum Power Draw

This thesis analyzes the general performance and design requirements of photovoltaic(PV) systems, and specifically how they relate to the design of a system intended to supply power to a rotating satellite. The PV array geometry was discussed, different DC-DC converter topologies were analyzed, and optimum array geometry and converter topologies were determined. The potential reference quantities for use in control of the system are examined. Due to its comparably greater linearity with respect to changes in apparent load and its relative insensitivity to insolation changes, voltage was determined to be the best reference quantity for use in stable tracking of the maximum power operating point of photovoltaic modules. The preceding work is used to design and model a photovoltaic system for a rotating satellite ensuring the supply of the maximum available power as well as stable operation. Simulations of the system are performed at rotational velocities up to 300 rev/min and its behavior is analyzed to demonstrate the validity of the preceding work. It was concluded that: ● parallel connected photovoltaic panels provide greater efficiency than series connected panels. ● Buck, Boost, and Cuk Converter architectures are best suited to PV applications ● PV Voltage is the best reference quantity for use in stable control of PV systems

A Novel Mathematical Analysis for Electrical Specifications of Step-up Converter

This study presents a unique comprehensive mathematical model for both transient and steady states of the step-up power converter in order to structure physical aspects evaluations. The main disadvantage of different existence mathematical models such as impedance, small signal analysis and steady space average models is that they use numerical analysis methods or simplification solutions that lead to approximate analysis. Therefore, the physical behaviours of the system such as inductor current, output voltage and physical effects of components will not be accurately predictable. This study presents very accurate equations and all aspects of the structure are predictable. In our research, this issue is investigated in Laplace and Z domains using the output-to-input transfer function calculations, and the effect of converter circuit elements is assessed using equations obtained. For extracting the transfer function, initial values are calculated in the Z domain and based on the final value theorem, converter output voltage and input current have been calculated. Effects of converter components on capacitor voltage and input current ripples have been analysed and reported. In the final step, results of the theoretical analysis were confirmed by simulation results obtained in MATLAB/SIMULINK environment and implementation on a prototype in laboratory scales

H-GA-PSO Method for Tuning of a PID Controller for a Buck-Boost Converter Modeled with a New Method of Signal Flow Graph Technique

In this paper, a new method of signal flow graph technique and Mason's gain formula are applied for extracting the model and transfer functions from control to output and from input to output of a buck-boost converter. In order to investigate necessity of a controller for the converter with assumed parameters, the frequency and time domain analysis is done and the open loop system characteristics are verified. In addition, the needed closed loop controlled system specifications are determined. Moreover, designing a controller for the mentioned converter system based on the extracted model is discussed. For this purpose, a proportional-integral-derivative (PID) controller is designed and the hybrid of genetic algorithm (GA) and particle swarm optimization (PSO), called H-GA-PSO method is used for tuning of the PID controller. Finally, the simulation results are used to show the performance of the proposed modeling and regulation methods

Mixed-source charger-supply CMOS IC

The proposed research objective is to develop, test, and evaluate a mixer and charger-supply CMOS IC that derives and mixes energy and power from mixed sources to accurately supply a miniaturized system. Since the energy-dense source stores more energy than the power-dense source while the latter supplies more power than the former, the proposed research aims to develop an IC that automatically selects how much and from which source to draw power to maximize lifetime per unit volume. Today, the state of the art lacks the intelligence and capability to select the most appropriate source from which to extract power to supply the time-varying needs of a small system. As such, the underlying objective and benefit of this research is to reduce the size of a complete electronic system so that wireless sensors and biomedical implants, for example, as a whole, perform well, operate for extended periods, and integrate into tiny spaces.Ph.D