This thesis reports the author's investigation of the effects of the injection of specific signals on the intermodulation distortion performance of microwave power amplifiers. Theory, simulation and practical results are presented, analysed and compared. The thesis gives the reader background knowledge of power amplifiers and their nonlinearities and go on to analyse the phenomena of intermodulation distortion product generation in power amplifiers. The analysis is based on a three-tone test since this highlights a second kind of third order intermodulation distortion (IMD3), which are in general higher in amplitude than the first kind of IMD3 found in a two-tone test. A mathematical analysis and a simulation of a MESFET amplifier are performed. It enables the comparison of the performance of IMD cancellation by injection of signals whose frequencies are chosen to be first, the second harmonic of the fundamental signals, second, the sum of the fundamental signal frequencies and finally the difference frequencies of the fundamental signals. A practical implementation of the difference frequency technique is then presented and practical results are compared to the other two techniques of second harmonic injection and the injection of the sum of fundamental frequencies. It is further shown that in practise these two techniques may be considered as a single technique.

We proposed new variance estimators for the poststratified estimator of the population total in two-stage sampling. The linearization or Taylor series variance estimator and the jackknife linearization variance estimator are popular for the poststratified estimator. The jackknife linearization variance estimator utilizes the ratio, ^Rc, which balances the weights for the poststrata while the linearization or Taylor series estimator does not. The jackknife linearization variance estimator is equivalent to Rao's (1985) adjusted variance estimator. Our proposed estimator makes use of the ratio, ^R c, in a different shape which is naturally derived from the process of expanding to the second-order Taylor series linearization, while the standard linearization variance estimator is only expanded to the first-order. We investigated the properties and performance of the linearization variance estimator, the jackknife linearization estimator, the proposed variance estimator and its modified version analytically and through simulation study. The simulation study was carried out on both artificially generated data and real data. The result showed that the second order accurate variance estimator and its modified version could be very good candidates for the variance estimation of poststratified estimator of population total.

For control systems that evolve on Euclidean spaces, Jacobian linearization is a common technique in many control applications, analysis, and controller design methodologies. However, the standard linearization method along a non-trivial reference trajectory does not directly apply in a geometric theory where the state space is a differentiable manifold. Indeed, the standard constructions involving the Jacobian are dependent on a choice of coordinates. The procedure of linearizing a control affine system along a non-trivial reference trajectory is studied from a differential geometric perspective. A coordinate-invariant setting for linearization is presented. With the linearization in hand, the controllability of the geometric linearization is characterized using an alternative version of the usual controllability test for time-varying linear systems. The various types of stability are defined using a metric on the fibers along the reference trajectory and Lyapunov's second method is recast for linear vector fields on tangent bundles. With the necessary background stated in a geometric framework, Kalman's theory of quadratic optimal control is understood from the perspective of the Maximum Principle. Finally, following Kalman, the resulting feedback from solving the infinite time optimal control problem is shown to uniformly asymptotically stabilize the linearization using Lyapunov's second method. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2007-12-19 16:59:47.76

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The renormalization group (RG) approach is largely responsible for the considerable success which has been achieved in developing a quantitative theory of phase transitions. This work investigates various spectral properties of the RG map for Ising-type classical lattice systems. It consists of four parts. The first part carries out some explicit calculations of the spectrum of the linearization of the RG at infinite temperature, and discovers that it is of an unusual kind: dense point spectrum for which the adjoint operators have no point spectrum at all, but only residual spectrum. The second part presents a rigorous justification of the existence and differentiability of the RG map in the infinite volume limit at high temperature by a cluster expansion approach. The third part continues the theme of the third part, and shows that the matrix of partial derivatives of the RG map displays an approximate band property for finite-range and translation-invariant Hamiltonians at high temperature. The last part justifies the differentiability of the RG map in the infinite volume limit at the critical temperature under a certain condition. In summary, the first part deals with special cases where exact computations can be done, whereas the remaining parts are concerned with a general theory and provide a mathematically sound base.

This thesis concerns the analysis and sensitivity of nonlinear eigenvalue problems for matrices and linear operators. The first part illustrates that lack of normality may result in catastrophic ill-conditioned eigenvalue problem. Linearization of rational eigenvalue problems for both operators over finite and infinite dimensional spaces are considered. The standard approach is to multiply by the least common denominator in the rational term and apply a well known linearization technique to the polynomial eigenvalue problem. However, the symmetry of the original problem is lost, which may result in a more ill-conditioned problem. In this thesis, an alternative linearization method is used and the sensitivity of the two different linearizations are studied. Moreover, this work contains numerically solved rational eigenvalue problems with applications in photonic crystals. For these examples the pseudospectra is used to show how well-conditioned the problems are which indicates whether the solutions are reliable or not.

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The interest in higher data rate systems is rising very quickly in the area of wireless communications. High data rates mean high Peak to Average Ratio, PAR. This imposes big challenge on the linearity requirement of Power Amplifiers, PAs. The simplest technique that has been used is backing off the PA. However, this leads to very inefficient performance. A lot of more complex techniques were suggested in the literatures to trick the tradeoff between linearity and efficiency. So we discuss the advantages and disadvantages of those techniques. In addition we suggest a new technique called Power Amplifier Linearization using a Mirror Predistorter. This technique is based on the use of a mirror PA that generates a copy of the main PA nonlinearity, and then feeds it in the proper phase and magnitude into the input in order to cancel the intermodulation terms at the output. Simulation and on the bench lab results validate the suggested technique. Also a hybrid PA module was designed and tested based on the suggested technique, and showed an improvement of 23 dB in the Third Order Intermodulation to Carrier ratio, IMD3 of the PA at 7.5 dB back off. / Master of Science

Orientador: Suzinei Aparecida Siqueira Marconato / Banca: Marta Cilene Gadotti / Banca: Sandra Maria Semensato de Godoy / Resumo: Neste trabalho apresentamos um estudo qualitativo do modelo feito por Ronald Ross sobre a propagação da malária em uma comunidade. O modelo encontra-se no artigo "Contribution to the Analysis of Malaria Epidemiology" de Alfred J. Lotka [1] e é dado por um sistema não linear de duas equações diferenciais ordinárias / Abstract: In this work we present a qualitative study of the model developed by Ronald Ross about the propagation of malaria in a community. The model is presented by the article "Contribution to the Analysis of Malaria Epidemiology" of Alfred J. Lotka [1] and it is given by a nonlinear system of two ordinary differential equations / Mestre

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