The purpose of this thesis is to linearize a power amplifier using digital predistortion. A power amplifier is a nonlinear system, meaning that when fed with a pure input signal the output will be distorted. The idea behind digital predistortion is to distort the signal before feeding it to the power amplifier. The combined distortions from the predistorter and the power amplifier will then ideally cancel each other. In this thesis, two different approaches are investigated and implemented on an FPGA. The first approach uses a nonlinear model that tries to cancel out the nonlinearities of the power amplifier. The second approach is model-free and instead makes use of a look-up table that maps the input to a distorted output. Both approaches are made adaptive so that the parameters are continuously updated using adaptive algorithms. First the two approaches are simulated and tested thoroughly with different parameters and with a power amplifier model extracted from the real amplifier. The results are shown satisfactory in the simulations, giving good linearization for both the model and the model-free technique. The two techniques are then implemented on an FPGA and tested on the power amplifier. Even though the results are not as well as in the simulations, the system gets more linear for both the approaches. The results vary widely due to different circumstances such as input frequency and power. Typically, the distortions can be attenuated with around 10 dB. When comparing the two techniques with each other, the model-free method shows slightly better results.

Digital predistortion is a signal processing technique used to remove undesired distortions caused by nonlinear system effects. This method is predominately used to linearize power amplifiers in communication systems in order to achieve efficient transmitter circuits. However, the technique can readily be applied to cancel undesired nonlinear behavior in other types of systems. This thesis investigates the effectiveness of digital predistortion in the context of a wideband arbitrary waveform generator. A theoretical foundation discussing nonlinear system models, predistortion architectures and system identification methods is complemented with a simulation study and followed by verification on a real system. The best predistorter is able to fully suppress the undesired distortions for any fixed two-tone sinusoidal signal. Furthermore, the results indicate the existence of a wideband predistorter which yield acceptable suppression over a frequency range of several hundred MHz. / Digital predistorsion är en signalbehandlingsteknik som används för att undertrycka oönskade distorsioner orsakade av icke-linjära effekter i elektriska system. Denna metod används i huvudsak för att linjärisera effektförstärkare i kommunikationssystem för att erhålla effektiva sändarkedjor men tekniken kan utan större problem även tillämpas på andra typer av icke-linjära system. Denna uppsats undersöker i vilken utsräckning digital predistorsion kan användas för att undertrycka oönskade signaldistorsioner i en bredbandig signalgenerator. Uppsatsen presenterar en bakgrund som utgår ifrån teorin om icke-linjära systemmodeller, arkiteturer för predistorsion och systemidentifieringsmetoder. En kvantitativ studie i en simuleringsmiljö åtföjs av en utvärdering på ett verkligt system. Det bästa predistorsionssystemet åstadkommer en fullständig linjärisering i testfallet med en fix tvåtonssignal. Resultaten indikerar även att det existerar ett system som linjäriserar signaler i ett frekvensområde som uppgår till hundratals MHz.

Neste trabalho tem por objetivo a construção de conjugações suaves de pontos fixos hiperbólicos com condições de não ressonância. Por tanto, inicialmente são apresentados alguns conceitos básicos sobre espaços de Banach e alguns resultados de equações diferenciais ordinárias em espaços de Banach e sistemas dinâmicos, apresentamos o teorema de Hartman Grobman como motivação inicial de Linearização. Apresentamos também vários exemplos como motivação para estudar o Teorema de Sternberg para contrações hiperbólicas, o principal resultado estudado nesta dissertação para contrações hiperbólicas / This work has the objetive of building smooth conjugations of hyperbolic fixed points with non-resonance conditions. So, first we present some basics of Banach spaces and some results of ordinary differential equations in Banach spaces and dynamical systems, we present the theorem of Hartman Grobman as original motivation for linearization . We also present several examples as motivation to study the Sternberg theorem for hyperbolic contractions, as main result studied in this dissertation

[pt] O presente trabalho apresenta uma estrutura balanceada em quadratura para linearização de amplificadores de potência em RF e microondas. Várias técnicas de linearização têm sido utilizadas para reduzir a intermodulação. Alguns exemplos, tais como Feedback, Pre-distorsion e Feedforward, podem ser mencionados. A característica ímpar de nosso arranjo é que ele não precisa de ajustes, enquanto que os outros métodos precisam. A desvantagem de nosso arranjo é que ele reduz apenas os produtos de intermodulação de terceira ordem. Um trabalho prático foi conduzido, mostrando que nosso arranjo é capaz de reduzir o conteúdo de intermodulação de terceira ordem em até 17 dB. / [en] The present work introduces a quadrature balanced structure for linearization of RF and microwave amplifiers. Several linearization techniques have been used to reduce intermodulation products. Some examples such as Feedback, Pre-distorsion and Feedforward may be mentioned. The unique feature of our arrangment is that it does not need adjustments, while the other methods do. The drawback of our arrangement is that it only reduces the third-order intermodulation products. A pratical work was carried out, showing that our arrangement is able to reduce the third-order intermodulation content up to 17 dB. / [es] EL presente trabajo presenta una extructura balanceada en cuadratura para linealización de amplificadores de potencia en RF y microondas. Varias técnicas de linealización han sido utilizadas para reducir la intermodulación. Algunos ejemplos como Feedback, Pre-distorsion y Feedforward, pueden ser mencionados. La principal ventaja de nuestro arreglo frente a los otros métodos es que éste no precisa de ajustes. La desventaja de nuestro arreglo es que reduce solamente los produtos de intermodulación de tercer orden. Se condujo un trabajo práctico, mostrando que nuestro arreglo es capaz de reducir el contenido de intermodulación de tercera orden en hasta 17 dB.

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This thesis presents controllers that use relative range and bearing measurements to steer unmanned aerial vehicles (UAVs) to circular trajectories around stationary, constantly moving and constantly accelerating targets. The range and bearing to the target, along with their derivaties are estimated. These, along with the estimated local heading of the UAVs, are used in the control law, and to estimate the velocity of the target. In this work, six controllers are presented. The controller for a stationary target is derived using Lyapunov's direct method, and feedback linearization is used for the constant velocity and accelerating targets. A new controller is proposed to control the direction of encirclement for moving targets, using Lyapunov's direct method. Additional terms are introduced to maintain a temporally equi-spaced formation around the targets. Theoretical proofs are provided for all controllers using Lyapunov theory. Numerical simulations show vehicles converging to circular formations around both stationary and moving targets. Results are shown using MATLAB simulations with Gaussian noise added to the measurements. Further, a technique is proposed for information exchange between UAVs, with bounds provided for the time taken to dissipate information throughout the system in a scenario with multiple groups of UAVs tracking multiple targets.

Optimization based flight control design tools depend on automatic linearization tools, such as Simulink®’s LINMOD, to extract linear models. In order to ensure the usefulness and correctness of the generated linear model, this linearization must be accurate. So a method of independently verifying the linearized model is needed. This thesis covers the automation of a system identification tool, CIFER®, for use as a verification tool integrated with CONDUIT®, an optimization based design tool. Several test cases are built up to demonstrate the accuracy of the verification tool with respect to analytical results and matches with LINMOD. Several common nonlinearities are tested, comparing the results from CIFER and LINMOD, as well as analytical results where possible. The CIFER results show excellent agreement with analytical results. LINMOD treated most nonlinearity as a unit gain, but some nonlinearities linearized to a zero, causing the linearized model to omit that path. Although these effects are documented within Simulink, their presence may be missed by a user. The verification tool is successful in identifying these problems when present. A section is dedicated to the diagnosis of linearization errors, suggesting solutions where possible.

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