In this thesis I describe work on developing theoretical and numerical models of supercon- ducting thin-film microwave resonators. Superconducting resonators are used in a variety of applications, one of which is as kinetic inductance detectors (KIDs). KIDs are ultra-low noise, highly sensitive, multiplexable detectors, with uses in a wide variety of fields including astrophysics, medical imaging, and particle physics. Resonators are also crucial for supercon- ducting qubit readout, superconducting mixers and parametric amplifiers, and as multiplexers for other devices. The results described in this thesis apply to all thin film resonators, but are primarily described in the context of KIDs. I develop models of how constant absorbed power affects superconducting thin films, driving them out of thermal equilibrium with the bath. Using the Chang & Scalapino equations, I calculate numerically the steady-state quasiparticle and phonon distributions for various sources of power (sub-gap and above-gap photons and phonons, single frequency and broadband). Many new results emerge, a few of which are: the quasiparticle heating effects of microwave power, explaining the experimentally measured saturation of resonator performance; the frequency dependence of the quasiparticle generation efficiency in the sub-mm wavelength range; and the importance of phonon trapping in thin films at low temperatures. I then use these nonequilibrium results in higher-level device models. Starting from a generic framework for resonators, I present and implement a model of a KID with variable thermal isolation. I calculate the effects of quasiparticle heating on both the large-signal and small-signal behaviour, highlighting the effects of electrothermal feedback caused by readout power. Electrothermal feedback is shown to be able to increase or decrease the magnitude and bandwidth of the responsivity and noise, depending on the operating point. Finally, I propose an experimental measurement of quasiparticle heating effects in a new device – a four-port ring resonator. In such a device, unlike in the standard two-port resonator, the device can be heated and read out independently. I develop detailed models for the thermal and electrical behaviour of these devices, and suggest a scheme by which the quasiparticle heating effects of microwave power, predicted in this thesis, can be measured.

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Au cours de ces dernières années, le développement des capteurs de gaz a connu un essor grandissant pour des applications industrielles, militaires et environnementales afin d’assurer la sécurité et la protection contre les gaz nocifs et toxiques. Ces applications demandent des capteurs sensibles, sélectifs, à faible consommation d’énergie et à faible coût. Le travail de thèse présenté dans ce manuscrit, s’inscrit dans ce contexte. Il a pour objectif la réalisation d’un capteur hyperfréquence à base de nanotubes de carbone et fabriqué par technologie jet d’encre. Le principe de fonctionnement du capteur repose sur la caractérisation en fréquence d’un résonateur RF, dont un élément est sensible grâce aux nanotubes de carbone, à la présence d’un gaz environnant. Le manuscrit aborde l’ensemble des étapes nécessaires à la réalisation du capteur, à savoir : la conception des dispositifs de test, s’appuyant sur une étude théorique de leur comportement, la caractérisation des matériaux utilisées, la fabrication sur un substrat flexible par une technique d’impression jet d’encre et enfin la caractérisation du capteur de gaz en termes de comportement en fréquence et de sensibilité en présence de gaz. / In recent years, the development of gas sensors has grown rapidly for industrial, military and environmental applications to ensure safety and protection against harmful and toxic gases. These applications require sensitive, selective, low power and low cost sensors. The thesis work presented in this manuscript fits into this context. Its objective is the realization of a microwave sensor based on carbon nanotubes and manufactured by inkjet technology. The operating principle of the sensor is based on the frequency characterization of an RF resonator, one element of which is sensitive, thanks to the carbon nanotubes, to the presence of a surrounding gas. The manuscript addresses all the steps necessary for the realization of the sensor, namely: the design of the test devices, based on a theoretical study of their behavior, the characterization of the materials used, the fabrication on a flexible substrate by inkjet printing technique and finally the characterization of the gas sensor in terms of frequency behavior and sensitivity in the presence of gas.

The thesis deals with microwave resonators synthesis in Matlab environment. Due to the multi-objective optimization, the shape of the resonátor is subsequently changed to fit requested frequency properties. Particle swarm optimization and frequency domain finite element method are used. Accuracy of the different number of elements was tested. Values of several optimization parameters were balanced to reach the maximal efficiency of the optimization.

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