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

Analysis of the structure of time-frequency information in electromagnetic brain signals

This thesis encompasses methodological developments and experimental work aimed at revealing information contained in time, frequency, and time–frequency representations of electromagnetic, specifically magnetoencephalographic, brain signals. The work can be divided into six endeavors. First, it was shown that sound slopes increasing in intensity from undetectable to audible elicit event-related responses (ERRs) that predict behavioral sound detection. This provides an opportunity to use non-invasive brain measures in hearing assessment. Second, the actively debated generation mechanism of ERRs was examined using novel analysis techniques, which showed that auditory stimulation did not result in phase reorganization of ongoing neural oscillations, and that processes additive to the oscillations accounted for the generation of ERRs. Third, the prerequisites for the use of continuous wavelet transform in the interrogation of event-related brain processes were established. Subsequently, it was found that auditory stimulation resulted in an intermittent dampening of ongoing oscillations. Fourth, information on the time–frequency structure of ERRs was used to reveal that, depending on measurement condition, amplitude differences in averaged ERRs were due to changes in temporal alignment or in amplitudes of the single-trial ERRs. Fifth, a method that exploits mutual information of spectral estimates obtained with several window lengths was introduced. It allows the removal of frequency-dependent noise slopes and the accentuation of spectral peaks. Finally, a two-dimensional statistical data representation was developed, wherein all frequency components of a signal are made directly comparable according to spectral distribution of their envelope modulations by using the fractal property of the wavelet transform. This representation reveals noise buried processes and describes their envelope behavior. These examinations provide for two general conjectures. The stability of structures, or the level of stationarity, in a signal determines the appropriate analysis method and can be used as a measure to reveal processes that may not be observable with other available analysis approaches. The results also indicate that transient neural activity, reflected in ERRs, is a viable means of representing information in the human brain.reviewe

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

A Signal Processing Analysis of Purkinje Cells in vitro

Cerebellar Purkinje cells in vitro fire recurrent sequences of Sodium and Calcium spikes. Here, we analyze the Purkinje cell using harmonic analysis, and our experiments reveal that its output signal is comprised of three distinct frequency bands, which are combined using Amplitude and Frequency Modulation (AM/FM). We find that the three characteristic frequencies – Sodium, Calcium and Switching – occur in various combinations in all waveforms observed using whole-cell current clamp recordings. We found that the Calcium frequency can display a frequency doubling of its frequency mode, and the Switching frequency can act as a possible generator of pauses that are typically seen in Purkinje output recordings. Using a reversibly photo-switchable kainate receptor agonist, we demonstrate the external modulation of the Calcium and Switching frequencies. These experiments and Fourier analysis suggest that the Purkinje cell can be understood as a harmonic signal oscillator, enabling a higher level of interpretation of Purkinje signaling based on modern signal processing techniques