<p> A unique approach for the modeling of phase noise is examined in this thesis. In previous work regarding phase noise theory, the memory property of phase is virtually ignored. The thesis introduces the Discrete Recursive Procedure (DRP): a systematic approach or methodology to predict phase noise using a discrete recursive algorithm taking into account the memory property of phase. This discrete recursive algorithm is a general extension of the Linear Time Varying (LTV) model and is referred to as the NonLinear Time Varying (NLTV) model. </p> <p> Simulations are performed using the DRP method. Phase fluctuation comparisons are made between the LTV and the NLTV models for an ideal oscillator. The simulation results show that the NLTV model taking into account the memory property of phase makes more realistic phase noise predictions than the LTV model for asymmetrical Impulse Sensitivity Function (ISF) cases. Phase noise simulation results using the NLTV model are given for a modified 810-MHz CMOS cross-coupled LC oscillator design. At 90kHz offset, the simulation prediction (-89 dBc/Hz) and the measurement readings (-93 dBc/Hz) are closely matched with a difference of approximately 4 dBc/Hz while the CAD simulation prediction ( -101. 8) has a difference of 9 dBc/Hz from the measurements. In the phase noise simulation for the 62-MHz BIT Colpitts oscillator design, the NLTV model predicts a -26 dBc/decade and -19.5 dBc/decade for the flicker noise and thermal noise regions in accordance with the theoretical -30 dBc/decade and -20 dBc/decade slopes. </p> / Thesis / Master of Applied Science (MASc)

Frequency domain models for power electronic circuits are either based on iterative techniques such as Newton's method or linearised around an operating point. Iterative frequency domain models provide great accuracy as they are capable of calculating the exact switching instants of the device. On the other hand, the accuracy of a linearised frequency domain model relies on the magnitude of input waveform to be small so that the circuit's operating point does not vary or varies very little. However, an important advantage of a linearised model is its ability to provide insight into waveform distortion interaction, more specifically, the frequency cross-coupling around a power electronic circuit. In general, a linearised model for harmonic analysis would not normally include the description of feedback control. Likewise a linearised model for control analysis would usually disregard frequency interactions above the fundamental (or the most significant component); that is assuming the cross-coupling between harmonic frequencies does not affect the dynamics of control. However, this thesis proposes that a linearised model for control analysis shall also include the complete description of frequency cross-coupling between harmonics to produce the correct dynamic response. This thesis presents a harmonic state-space (HSS) model of an HVdc converter that incorporates the full effect of varying switching instants, both through control and commutation period dynamics, while remaining within the constraints of a linear time-invariant (LTI) system. An example is given using the HSS model to explain how a close to fifth harmonic resonance contributes to the dominant system response through the frequency cross-coupling of the converter and the controller feedback loop. The response of the system is validated against a time domain model built in PSCAD/EMTDC, and more importantly, the correct response cannot be produced without including the harmonic interactions beyond the fundamental frequency component.

A systematic optimization of the Cohen class time-frequency transformation for detecting the parameters change is developed. The local moments approach to change detection is proposed and a general formula for the local moments is derived. The optimal kernel functions of the time-frequency transformation are determined based on the combined criteria of maximum sensitivity with respect to parameters change and minimum distortion of physical interpretation of the local moments. The sensitivity of the local moment with respect to a certain kind of inputs is analyzed and a most "convenient" and a "worst" input are identified. The results are presented in the form of the case studies for detecting parameters change in simple linear systems. / Graduation date: 1992

Thesis (M.S.)--Rochester Institute of Technology, 1990. / Spine title: Model reduction of complex dynamic systems. Includes bibliographical references.

Thesis (M.S.)--Rochester Institute of Technology, 1994. / Typescript. Includes bibliographical references (leaves 107-108).

Xi-Cheng Lou ... [et al.]. / Bibliography: leaf 14. / "October, 1983." / Air Force Office of Scientific Research Contract AFOSR-82-0258 Natural Sciences and Engineering Research Council of Canada Grant A-1240

by John L. Wyatt, Jr., William M. Siebert, Han-Ngee Tan. / "October, 1982." / Bibliography: p. 16-17. / National Science Foundation Grant No. ECS 800 6878

This thesis examines several problems related to singly-constrained Monotropic Network Flow Problems. In the first part, a linear time algorithm that reduces the solution of a monotropic network flow problem with an additional linear equality constraint to the solution of lower dimensional subproblems is presented. Of the subproblems, at most one is a singly-constrained monotropic network flow problem while the others are unconstrained. If none of the subproblems is constrained, the algorithm provides a linear-time transformation of constrained to unconstrained monotropic network flow problems. Extensions to nonlinear and inequality constraints are given. In the second part the qualitative theory of sensitivity analysis for Unconstrained Minimum-Cost Flow Problems presented by Granot and Veinott [GV85] is extended to Minimum-Cost Flow Problems with one additional linear constraint. The departure from the unconstrained network structure is shown to have a profound effect on computational issues. Two natural extensions of the "less-dependent-on" partial ordering of the arcs given in [GV85] are presented. One is decidable in linear time while the other yields more information but is NP-complete in general. The Ripple Theorem gives upper bounds on the absolute value of optimal-flow variations as a function of variations in the problem parameter. Moreover, it shows how changes may "ripple down" throughout the network, decreasing in magnitude as one gets "further away" from the arc whose parameter initiated the change. The Theory of Substitutes and Complements presents necessary and sufficient conditions for optimal-flow changes to consistently have the same (or the opposite) sign in two given arcs. The complexity of determining Substitutes and Complements is shown to be NP-complete in general. However, for all intractable problems, families of cases arise from easily recognizable graph structures and can be computed in linear time. The Monotonicity Theory links the changes in the value of the parameters to the change in the optimal arc-flows. Bounds on the rates of changes are discussed. We further provide a number of practical situations where our theory may apply. We discuss some Multi-Period Multi-Product Inventory-Production models that can be formulated as nonlinear parametric network flow problems with one additional linear constraint. We then apply our theory to help decision makers understand qualitatively how to respond to changes in the environment such as machine breakdown, strike or variations in inventory carrying costs without additional computation. In a second example, we show how a Cash-Flow Management model can be formulated as a nonlinear parametric network flow problem with one additional linear constraint. The theory is then recommended as a method by which a decision maker could understand qualitatively how to respond to changes in the environment such as variations in interest rates, taxes or asset prices without any additional computation. / Business, Sauder School of / Graduate

This thesis presents the formulation and solution of a new problem in systems and control theory, called the Network Realization Problem. Its relationship to other problems, such as State Realization and Structural Identifiability, is shown. The motivation for this work is the desire to completely quantify the conditions for transitioning between different mathematical representations of linear time-invariant systems. The solution to this problem is useful for theorists because it lays a foundation for quantifying the information cost of identifying a system's complete network structure from the transfer function.

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