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This thesis concerns polarization mode dispersion (PMD) in optical fiber communications. Specifically, we study fiber birefringence, PMD stochastic properties, PMD mitigation and the interaction of fiber birefringence and fiber nonlinearity. Fiber birefringence is the physical origin of polarization mode dispersion. Current models of birefringence in optical fibers assume that the birefringence vector varies randomly either in orientation with a fixed magnitude or simultaneously in both magnitude and direction. These models are applicable only to certain birefringence profiles. For a broader range of birefringence profiles, we propose and investigate four general models in which the stochastically varying amplitude is restricted to a limited range. In addition, mathematical algorithms are introduced for the numerical implementation of these models. To investigate polarization mode dispersion, we first apply these models to single mode fibers. In particular, two existing models and our four more general models are employed for the evolution of optical fiber birefringence with longitudinal distance to analyze, both theoretically and numerically, the behavior of the polarization mode dispersion. We find that while the probability distribution function of the differential group delay (DGD) varies along the fiber length as in existing models, the dependence of the mean DGD on fiber length differs noticeably from earlier predictions. Fiber spinning reduces polarization mode dispersion effects in optical fibers. Since relatively few studies have been performed of the dependence of the reduction factor on the strength of random background birefringence fluctuations, we here apply a general birefringence model to sinusoidal spun fibers. We find that while, as expected, the phase matching condition is not affected by random perturbations, the degree of PMD reduction as well as the probability distribution function of the DGD are both influenced by the random components of the birefringence. Together with other researchers, I have also examined a series of experimentally realizable procedures to compensate for PMD in optical fiber systems. This work demonstrates that a symmetric ordering of compensator elements combined with Taylor and Chebyshev approximations to the transfer matrix for the light polarization in optical fibers can significantly widen the compensation bandwidth. In the last part of the thesis, we applied the Manakov-PMD equation and a general model of fiber birefringence to investigate pulse distortion induced by the interaction of fiber birefringence and fiber nonlinearity. We find that the effect of nonlinearity on the pulse distortion differs markedly with the birefringence profile.

Switched mode, Class-D power amplification allows for high efficiency power amplification of an audio signal. This thesis investigates its application to high power car audio systems where there is a demand for efficient high power amplification. Examination of the present car audio power amplifiers, which comprise a switched mode power supply combined with a linear output stage, has shown that there is significant scope for improvement in efficiency and power density. A novel power stage in which the attributes of a switched-mode power supply and full bridge output stage is presented. It is demonstrated that elimination of the intermedjate DC supply results in an amplifier which has a significantly lower part count, size and cost compared to conventional designs. Two different modulation schemes are explored (PWM and PDM) with a view to finding the most suitable for the new power stage. The theoretical performances of the modulators are verified by practical measurements. The design of high order DeltaSigma modulators is difficult as they show unstable behaviour and an alternative design methodology has been presented to ease this task. The mechanisms which introduce distortion in a practical amplifier are discussed, and for the case of a PWM driven output stage, a new model is presented to predict the effect of dead time on harmonic distortion. This form of distortion is shown to be the dominant cause of open loop non-linearity. The use of feedback is also investigated and yields a factor of 20 improvement in amplifier total harmonic distortion . The design throughout has been supported with practical results and these have illustrated the importance for careful circuit layout in high frequency switching systems.

The MIUU meso-scale model has been used to evaluate a new lateral boundary condition. The new lateral boundary condition is a combination of two lateral boundary conditions used in regional models, the flow relaxation scheme and the tendency modification scheme. The impact of different lateral boundary formulations on meso-scale phenomena, such as convective boundary layers, nocturnal jets, sea breezes and mountain waves (Bora winds) has been studied. When, for instance, stably stratified air with a constant wind speed is advected through the lateral boundaries into a meso-scale model with a flat and homogenous land surface, the convective boundary layer is reduced in height and the nocturnal jet is reduced in magnitude up to a distance of 750 km from the inflow lateral boundary. This is the case, when the most common lateral boundary condition is used, namely the flow relaxation scheme, where the flow relaxation parameter is constant with height and a function of the horizontal grid points only. In the other tests a flow relaxation parameter is used that is very small up to a certain level above ground, increasing with height to a maximum value higher up, and being constant above this upper level. Then, the convective boundary layer and the nocturnal jet are fully developed already at 23 km from the inflow lateral boundary. When, for instance, islands are not represented in the large-scale model, due to the coarse grid resolution, but well represented in the meso-scale model, stably stratified air can be advected into the meso-scale model even during daytime. Then, artificial thermal circulations can arise at the lateral boundaries of the meso-scale model, and collide with a real sea-breeze circulation that develops at the coast-line. These artificial thermal circulations disappear only when the flow relaxation parameter is very small in the lowest levels. When mountain waves (Bora winds) are simulated in a relatively small model domain, the critical layer, i.e. the layer where the nonlinear large-amplitude mountain wave is generated and broken, is surprisingly displaced irrespective of the tested lateral boundary formulations. In many simulations large-scale fields have to be introduced into meso-scale models. If only the flow relaxation scheme is used, the flow relaxation parameter has to be “constant-in-height” and relatively large in order to introduce large-scale temperature and wind changes with the right time-scale at all levels. However, with the new lateral boundary condition, the flow relaxation parameter can be kept very small in the lowest kilometers above ground. A small value of the flow relaxation parameter means that the convective boundary layer and the nocturnal jet at the lateral boundaries are not affected by the boundary conditions, and furthermore, no artificial thermal circulations are created. At the same time, large-scale temperature and wind changes are correctly introduced at all heights during the prescribed time into the meso-scale model through the tendency modification scheme. / Den mesoskaliga MIUU modellen har använts för test av olika laterala gränsvillkor. Ett nytt lateralt gränsvillkor har konstruerats. Detta nya gränsvillkor är en kombination av två gränsvillkor, nämligen ’the flow relaxation scheme’ och ’the tendency modification scheme’. Inverkan av olika gänsvillkorsformuleringar på mesoskaliga fenomen som konvektiva gränsskikt, ’nocturnal’ jets, sjöbrisar och bergsvågor (Boravindar) har studerats. När stabilt skiktad luft med konstant vindhastighet advekteras in genom de laterala ränderna in till en mesoskalig modelldomän, som har en slät och homogen landyta, kommer det konvektiva gränsskiktets höjd och styrkan på ’nocturnal’ jeten att påverkas av gränsvillkoret. Randvillkoret kan påverka temperatur och hastighetsfältet upp till 750 km:s avstånd från inflödesranden. Detta sker när det vanligaste laterala gränsvillkoret används, nämligen, ’the flow relaxation scheme’. I detta schema är ’flow relaxation’-parametern konstant med höjden, dvs endast en funktion av de horisontella gridpunkterna. Sensivitetsstudier på värdet och formen av ’flow relaxation’-parametern har utförts. En ’flow relaxation’-parameter, som är mycket liten upp till en viss nivå och sedan ökar med höjden påverkar temperatur- och hastighetsfältet mycket mindre. Randvillkorets påverkan är då minimal redan på 23 km:s avstånd från inflödesranden och det konvektiva gränsskiktet och ’nocturnal’ jeten kan bli fullt utvecklade. Om till exempel öar, som är väl representerade i den mesoskaliga modellen, inte är representerade i den storskaliga modellen pga dess grova upplösning, kan stabilt skiktad luft advekteras in till den mesoskaliga modelldomänen till och med under dagtid. Det kan då uppstå en artificiell termisk cirkulation vid de laterala ränderna hos den mesoskaliga modellen. Denna artificiella termiska cirkulation kan sedan kollidera med en verklig sjöbriscirkulation. Detta kan förstöra den mesoskaliga modellösningen totalt. Denna artificiella termiska cirkulation försvinner endast då ’flow relaxation’-parametern är väldigt liten i de lägsta nivåerna. När bergsvågor (Boravindar) simuleras i en relativt liten modelldomän så är det kritiska skiktet, dvs det skikt där de icke-linjära vågorna med stor amplitud bryts och genereras, förflyttat jämfört med referensfallet där de laterala ränderna var långt borta från det studerade området. Detta sker förvånansvärt oberoenda av vilken lateral gränsvillkorsformulering som används. I många simuleringar ska storskaliga processer såsom fronter och geostrofiska vindänd-ringar införas till den mesoskaliga modellen. Om endast ’the flow relaxation scheme’ används måste ’flow relaxation’-parametern vara konstant med höjden och relativt stor. Detta för att storskaliga temperatur- och vindändringar skall kunna introduceras till den mesoskaliga modellen med rätt tidskonstant och på alla höjder. I det nya laterala gränsvillkoret behöver ’flow relaxation’-parametern inte vara lika stor och inte heller konstant med höjden. Temperatur- och vindändringar är ändå korrekt introducerade med exakt tidsskala i alla nivåer in till den mesoskaliga modellen. Detta sker genom användandet av det s.k. ’tendency modification’-schemat. Dessutom kan det konvektiva gränsskikt, ’nocturnal’ jeten och sjöbrisar utveklas korrekt i närheten av de laterala ränderna.