Analysis and simulation methods for free-running, injection-locked and super-regenerative oscillators

RESUMEN: En los últimos años, muchos esfuerzos han sido dedicados al desarrollo de técnicas complementarias para el análisis de circuitos autónomos de microondas. Estas técnicas están pensadas para su uso en combinación con balance armónico, ampliamente usado para el análisis a frecuencias de microondas. De hecho, balance armónico sufre de restricciones cuando se utiliza para el análisis de circuitos autónomos, en su mayoría debidos a su falta de sensibilidad a las propiedades de estabilidad de la solución que se genera o se extingue mediante bifurcaciones. En esta tesis doctoral se presentan nuevos métodos de simulación y análisis para la caracterización y modelado de osciladores libres, sincronizados y superregenerativos. Todos los resultados obtenidos mediante los nuevos métodos de simulación y análisis han sido comparados satisfactoriamente con otras técnicas de simulación y con medidas.ABSTRACT: In the last years, numerous efforts have been devoted to the development of complementary analysis tools for autonomous microwave circuits. They are intended to be applied in combination with the harmonic-balance (HB) method, widely used at microwave frequencies. In fact, HB suffers from a number of shortcomings when dealing with autonomous circuits, mostly due the fact that it is insensitive to the stability properties of the solution, generated and extinguished through bifurcation phenomena. Here, new simulation and analysis methodologies for the characterization and modeling of free-running, injection-locked and super-regenerative oscillators have been proposed to overcome these problems when using commercial software. Results from the different new analysis methodologies have been successfully compared with independent simulations and with measurements

Analysis of superregenerative oscillators in nonlinear mode

Superregenerative oscillators in a nonlinear mode are investigated in detail using methodologies based on envelope transient, complemented with additional algorithms. A maximum-detection technique is applied to obtain the input-power threshold for nonlinear operation under different implementations of the quench signal. A mapping procedure enables the prediction of hangover and self-oscillation effects. It is based on the detection of the sequence of local maxima in the envelope amplitude after the application of a single input pulse. Using a contour-intersection method, and depending on the analysis time interval, it is possible to quantify the hangover effects and obtain the oscillation boundary, in terms of any two significant parameters. Then, a compact time-variant behavioral model is derived, valid in the absence of hangover and self-oscillation effects. It consists of a single time-variant Volterra kernel and is applicable provided that the amplitude transitions occur outside the sensitivity interval. Various methodologies are tested in a practical FET-based oscillator at 2.7 GHz. The prototype has been manufactured and measured, obtaining good agreement with the analysis results.This work was supported by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under the research project TEC2017-88242-C3-1-R

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

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

A Robust and Tunable Mitotic Oscillator in Artificial Cells

This dissertation aims to develop a droplet-based artificial cell system using cell-free extracts of Xenopus laevis eggs and understand mitotic oscillations with the proposed system. Single-cell analysis is pivotal to deciphering complex phenomena such as cellular heterogeneity, bistable switches, and oscillations, where a population ensemble cannot represent the individual behaviors. Despite having unique advantages of manipulation and characterization of biochemical networks, bulk cell-free systems lack the essential single-cell information to understand out-of-steady-state dynamics including cell cycles. In this dissertation, we present a novel artificial single-cell system for the study of mitotic dynamics by encapsulating Xenopus egg extracts in water-in-oil micro-emulsions. The artificial cells are different from real cells, i.e., their surface is formed by surfactant oil instead of the cell membrane. These “cells”, adjustable in sizes and periods, encapsulate cycling cytoplasmic extracts that can sustain mitotic oscillations for over 30 cycles. The artificial cells function in forms from the simplest cytoplasmic-only oscillators to the more complicated ones involving demembranated sperm chromatin that can reconstitute downstream mitotic events. The dynamic activities of cell cycle clock can be detected by fluorescent reporters such as cyclin B1-YFP and securin-mCherry. This innate flexibility makes it key to studying cell cycle clock tunability and stochasticity. Our experimental results indicate that the mitotic oscillators generated by our system are effectively tunable in frequency with cyclin B1 mRNAs and the dynamic behavior of single droplet oscillators is size-dependent. We also establish a stochastic model that highlights energy supply as an essential regulator of cell cycles. Moreover, the model explains experimental observations including the increase of baseline and amplitude of cyclin B1 time course. This dissertation study demonstrates a simple, powerful, and likely generalizable strategy of integrating single-cell approaches into conventional in vitro systems to study complex clock functions.PHDChemistryUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144115/1/yeguan_1.pd

Bio-inspired Dynamic Control Systems with Time Delays

The world around us exhibits a rich and ever changing environment of startling, bewildering and fascinating complexity. Almost everything is never as simple as it seems, but through the chaos we may catch fleeting glimpses of the mechanisms within. Throughout the history of human endeavour we have mimicked nature to harness it for our own ends. Our attempts to develop truly autonomous and intelligent machines have however struggled with the limitations of our human ability. This has encouraged some to shirk this responsibility and instead model biological processes and systems to do it for us. This Thesis explores the introduction of continuous time delays into biologically inspired dynamic control systems. We seek to exploit rich temporal dynamics found in physical and biological systems for modelling complex or adaptive behaviour through the artificial evolution of networks to control robots. Throughout, arguments have been presented for the modelling of delays not only to better represent key facets of physical and biological systems, but to increase the computational potential of such systems for the synthesis of control. The thorough investigation of the dynamics of small delayed networks with a wide range of time delays has been undertaken, with a detailed mathematical description of the fixed points of the system and possible oscillatory modes developed to fully describe the behaviour of a single node. Exploration of the behaviour for even small delayed networks illustrates the range of complex behaviour possible and guides the development of interesting solutions. To further exploit the potential of the rich dynamics in such systems, a novel approach to the 3D simulation of locomotory robots has been developed focussing on minimising the computational cost. To verify this simulation tool a simple quadruped robot was developed and the motion of the robot when undergoing a manually designed gait evaluated. The results displayed a high degree of agreement between the simulation and laser tracker data, verifying the accuracy of the model developed. A new model of a dynamic system which includes continuous time delays has been introduced, and its utility demonstrated in the evolution of networks for the solution of simple learning behaviours. A range of methods has been developed for determining the time delays, including the novel concept of representing the time delays as related to the distance between nodes in a spatial representation of the network. The application of these tools to a range of examples has been explored, from Gene Regulatory Networks (GRNs) to robot control and neural networks. The performance of these systems has been compared and contrasted with the efficacy of evolutionary runs for the same task over the whole range of network and delay types. It has been shown that delayed dynamic neural systems are at least as capable as traditional Continuous Time Recurrent Neural Networks (CTRNNs) and show significant performance improvements in the control of robot gaits. Experiments in adaptive behaviour, where there is not such a direct link between the enhanced system dynamics and performance, showed no such discernible improvement. Whilst we hypothesise that the ability of such delayed networks to generate switched pattern generating nodes may be useful in Evolutionary Robotics (ER) this was not borne out here. The spatial representation of delays was shown to be more efficient for larger networks, however these techniques restricted the search to lower complexity solutions or led to a significant falloff as the network structure becomes more complex. This would suggest that for anything other than a simple genotype, the direct method for encoding delays is likely most appropriate. With proven benefits for robot locomotion and the open potential for adaptive behaviour delayed dynamic systems for evolved control remain an interesting and promising field in complex systems research

Neuronal oscillations, information dynamics, and behaviour: an evolutionary robotics study

Oscillatory neural activity is closely related to cognition and behaviour, with synchronisation mechanisms playing a key role in the integration and functional organization of different cortical areas. Nevertheless, its informational content and relationship with behaviour - and hence cognition - are still to be fully understood. This thesis is concerned with better understanding the role of neuronal oscillations and information dynamics towards the generation of embodied cognitive behaviours and with investigating the efficacy of such systems as practical robot controllers. To this end, we develop a novel model based on the Kuramoto model of coupled phase oscillators and perform three minimally cognitive evolutionary robotics experiments. The analyses focus both on a behavioural level description, investigating the robot’s trajectories, and on a mechanism level description, exploring the variables’ dynamics and the information transfer properties within and between the agent’s body and the environment. The first experiment demonstrates that in an active categorical perception task under normal and inverted vision, networks with a definite, but not too strong, propensity for synchronisation are more able to reconfigure, to organise themselves functionally, and to adapt to different behavioural conditions. The second experiment relates assembly constitution and phase reorganisation dynamics to performance in supervised and unsupervised learning tasks. We demonstrate that assembly dynamics facilitate the evolutionary process, can account for varying degrees of stimuli modulation of the sensorimotor interactions, and can contribute to solving different tasks leaving aside other plasticity mechanisms. The third experiment explores an associative learning task considering a more realistic connectivity pattern between neurons. We demonstrate that networks with travelling waves as a default solution perform poorly compared to networks that are normally synchronised in the absence of stimuli. Overall, this thesis shows that neural synchronisation dynamics, when suitably flexible and reconfigurable, produce an asymmetric flow of information and can generate minimally cognitive embodied behaviours

Model order reduction techniques for circuit simulation

Includes bibliographical references (p. 156-160).Supported in part by the Semiconductor Research Corporation. SRC 93-SJ-558 Supported in part by the National Science Foundation / Advanced Research Projects Agency. MIP 91-17724Luis Miguel Silveira