Universiẗat, Diss., 2005--Tübingen.

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.

Abstract In the first part of this study, determination of the dielectric properties of the low loss microwave ceramic material, barium nonatitanate (Ba2Ti9O20), around 1 GHz is discussed. The structures under test were coaxial resonators, the cores of which were made of barium nonatitanate and the metallization was realised by thick film silver. The measured value of the real part of the relative dielectric constant was εr = 37 and that of the loss tangent was tan σ = 0.00014. The change of the resonance frequency of the coaxial resonators with temperature, in the range -20 … +80 C, was 4 ppm/ C. In addition, realisation of compact interdigital and comb-line bandpass filters was demonstrated for the 900 MHz mobile phone band. Besides Ba2Ti9O20, Ba(Sm,Nd)2Ti5O14 ceramic material with a dielectric constant of εr = 78 was also employed in order to improve the miniaturisation. The volume of the smallest filter was 2 cm3 and the weight was 9 g. In the second part of this study, various measurement methods have been demonstrated to determine the real part of the relative permittivity of FR4 fibreglass circuit board. Test structures were straight asymmetric open-circuited strip lines. It was found that the real part of the relative permittivity decreased slightly with frequency. At 0.72 GHz and 4.5 GHz, εr values of 4.3 and 4.1, respectively, were measured. All the characterisation methods used gave consistent values for εr, and electromagnetic simulators were used to verify the results. In the third part of this study, the structures under test were microstrip or strip line transmission lines, the S parameters of which were measured by using on-wafer measurement techniques. It was found that the insertion loss of the 10 mm long etched Cu microstrip was slightly less than that of the Ag microstrips which were manufactured by etching and gravure offset printing techniques, respectively. The performance of the Ag microstrips was, however, similar. In addition, a theoretical basis was established for the determination of εr of the dielectric substrate and the attenuation coefficient of the transmission lines under test. The calculations were based on signal flow diagrams. The method was applied to determine the dielectric and loss properties of a commercial, Kyocera, Japan, LTCC (Low Temperature Cofired Ceramic) material up to 50 GHz. The measured value of the real part of the relative permittivity was εr = 5.7, and the loss tangent was approximately tan σ = 0.003. The essential idea behind the studies reported in this thesis was twofold. First, the studies aimed at characterising dielectric media which find usage in the realisation of UHF, microwave or millimetre wave circuits. Second, the studies aimed to obtain data of immediate value in practical design work. For this reason, the structures under test were transmission lines having extensive usage in practical high frequency circuit design.

Abstract The adaptive Helmholtz resonator for decreasing harmonic pulsating pressure in a low-pressure hydraulic system is presented in this study. Adaptivity is executed by both open loop and closed loop controls so that continuous -20dB attenuation of the peak-to-peak value of the amplitude of pressure is reached. The study begins by a theory review including the theory of effective bulk modulus, sound velocity measurements, adjustable dynamic vibration absorbers and control methods of dynamic vibration absorbers. The main target of the paper, the Helmholtz resonator, is presented in its own chapter, albeit it is noted to be one application of the dynamic vibration absorber. The review is completed by the analytical model of the hydraulic pipe with a T-filter or Helmholtz resonator. After the theory review, the test equipment and its characteristics are presented. The main parts of the test equipment were a main pipe and an adjustable Helmholtz resonator, which were both developed for this study. Certain properties of the hydraulic oils used were determined experimentally to increase understanding of the system. The experimental section includes sound velocity measurements, sonic bulk modulus definitions, measurements of the resonant frequencies of the adaptive Helmholtz resonator in the test equipment, and tests of the open loop and closed loop control of the resonator. Control is verified to maintain -20dB attenuating of pressure pulsations in the system. The presented Helmholtz resonator and controls are available for installation into a hydraulic system to damp out harmonic vibrations at low frequency. For example, the roll in the size press of a paper machine might become excited to vibrate at its resonance frequency after the paper wad has washed through the nip. In that case, tuned Helmholtz resonators in the hydraulic cylinders of the size press would damp out the pulsating pressures, and if the resonators are adaptive, as presented in this study, they can operate in a wider frequency range.

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The work presented in this thesis can be divided into two main subjects. First, lightweight designs for acoustic devices such as Helmholtz resonators and loudspeakers used for noise control in rocket payload compartments are developed. Second, active control using a hybrid control system (with structural and acoustic actuators) was tested experimentally. Due to the weight limitations for this application, Helmholtz resonators and loudspeakers are re-designed in order to reduce the device weight as much as possible while maintaining performance. For Helmholtz resonators, this is done by modeling the resonator for different structural shapes, wall materials and wall thicknesses using a finite element analysis software. The final design is then compared to the rigid resonators and is shown to perform effectively. These designs are then successfully applied to the full-scale fairing at Boeing facilities. In order to design a lightweight loudspeaker, a comparative approach was used. A standard 12' loudspeaker is taken as the reference loudspeaker and weight reduction solutions are applied to it while maintaining performance. The loudspeaker is characterized using mechanical, electrical and acoustical theories, and an optimization process is applied in order to minimize a defined cost function, which was taken as the total sound pressure output over a targeted frequency range per mass of the actuator. The results are used to build a lightweight loudspeaker together with a lightweight box, and the new designs are tested for comparison with the reference loudspeaker and shown to increase performance by 1.7 dB over 60-200 Hz band while reducing the mass by 78%. The second part of this thesis investigates the performance of a hybrid active control treatment featuring distributed vibration absorbers (DAVAs) and loudspeakers applied on a scale payload fairing. Several aspects such as causality, reference signals, and maximum controllable levels of this feedforward control scheme are the subjects of analyses. The results show that this active control approach can achieve significant amount of interior noise attenuation, and the total actuator weight required to control an external level of 138 dB can be reduced to 9.2kg using lightweight loudspeakers. However, it is shown that the attenuation levels can still be improved further by actuator positioning that gives more effective coupling of the actuators with the structural and acoustic modes and by using multiple references for the control system. / Master of Science

To properly design the microwave components such as transmission lines, filters, capacitors, inductors, and many others, it is important to know the characteristics of the construction materials at microwave frequencies. One of the most reliable techniques in material characterization at microwave frequencies is the coplaner coupled stripline resonator technique. This technique is an enhancement to the classical stripline resonator technique. In this technique, the measured resonance frequency and quality factor of the resonator are used to determine the complex permitivity. One of the main problems in this technique is the proper modeling of the coupling gaps. In this dissertation we will introduce an accurate model of the coupling gap, which will shows that the capacitive behavior of the gap is not pure capacitive as known before, but it turns into more complex one at higher frequencies depending on the dimensions of the gap primarily. The second main problem is the limitation in the frequency range for accurate measurements. At higher frequencies, the coupling reaches its peak value for a given stripline resulting in excessive loading to the resonator and thus a lowered Q value. In this frequency range, measurement of the dielectric properties looses its accuracy because the lowered Q values which means inaccuracies in determining the resonant frequencies as well as great error in determining the Qc and Qd terms. In this dissertation, attempts to remedy this problem by introducing two different approaches to get an improved design for the coplaner coupled stripline resonator are presented. The first approach to optimize the design of the coplaner coupled stripline resonator is based on optimizing the dimensions of the coplaner coupled stripline resonator three sections (coplaner, transition region, and the center stripline). In the second approach, a reactive stub (via) is introduced in the coupling gap between the coplaner line and the center stripline. The added stub is designed to improve the Q values of the structure resonances. Simulations of different designs of the coplaner coupled stripline resonator using different stub dimensions are presented. Advantages and disadvantages of these designs as well as the solution to their resonance frequency shift problems are discussed as well. / Ph. D.

La structure traditionnelle d'un oscillateur optoélectronique (OEO) s'appuie sur une boucle de fibre optique très longue, servant de ligne à retard et lui conférant la grande pureté spectrale, ou le très faible bruit de phase de l'oscillateur. Un tel oscillateur fonctionnant à la fréquence de 8 GHz a été mis en œuvre aux laboratoires SATIE/LPQM de l'ENS Cachan. Néanmoins un tel système présente des inconvénients comme les dimensions un peu grandes, la difficulté de contrôler la température et un large peigne de fréquences parmi lequel il est difficile d'extraire un seule mode. Il est en fait possible d'éliminer ses inconvénients en remplaçant la boucle de fibre par un micro-résonateur optique de grand facteur de qualité. Dans cette thèse deux types résonateurs ont été fabriqués et étudiés. Des microsphères ont été fabriquées à partir de fibres optiques de fibres optiques monomodes. Les modes de galeries de ces résonateurs sont caractérisés grâce à couplage avec une fibre effilée. L'étude expérimentale met en évidence un facteur de qualité pouvant atteindre une valeur de 106 et un intervalle spectral libre (FSR) dépendant du diamètre de la sphère. Ainsi pour un diamètre de 300 µm on obtient un FSR de 0,2 nm soit 25 GHz en fréquence. Mais pour un OEO fonctionnant à la fréquence de 8 GHz il faudrait un FSR plus petit et donc une sphère dont le diamètre serait de taille millimétrique, donc très difficile à fabriquer. Un autre type de résonateur, en forme d'hippodrome, a été conçu et étudié. L'étude expérimentale a été conduite par un couplage avec de fibres lentillées. Le spectre en transmission présente des pics de résonances avec un facteur de qualité moyen de 0,050 ± 0.003 nm (correspondant en fait à 6 GHz) sur une plage de longueurs d'onde allant de 1534 nm à 1610 nm. Les caractéristiques les plus intéressantes de ce résonateur en forme d'hippodrome sont un facteur de qualité élevé et un intervalle spectral libre tout à fait en accord avec les besoins de l'OEO étudié. Néanmoins le couplage avec les fibres lentillées induit des pertes optiques trop importantes pour satisfaire aux conditions d'oscillations. Les travaux futurs devront porter sur l'amélioration du couplage ainsi que sur l'asservissement des pics de résonnance du micro-résonateur sur la longueur d'onde du laser employé dans l'OEO. / The classical structure of an Opto-Electronic Oscillator (OEO) is based on a long fiber loop acting as a delay line and leading to the high spectral purity, or very low phase noise, of the oscillator. Such an OEO has been developed in SATIE/LPQM laboratory at ENS Cachan, operating at 8 GHz frequency. However, this system has some main disadvantages such as a bulky size, the difficulty to control temperature and a wide range of peaks among which it is difficult to select only one mode. In order to eliminate these disadvantages, high quality factor optical resonator can be used instead of the optical fiber loop. In this thesis, two resonator structures are produced and investigated. Microspheres are fabricated based on optical single mode fiber. Whispering gallery modes of these resonators are characterized by tapered fiber –resonator coupling. The experimental results show that the quality factor of the microsphere is up to 106 and FSR depends on the diameter of the resonator. A microsphere with a diameter of 300 µm, presents a FSR of 0.2 nm corresponding to a frequency of 25 GHz. However, for an OEO system which should work at 8 GHz, microsphere with a smaller FSR or with diameter of some millimeters should be fabricated- that is really difficult to obtain. Another add/drop racetrack resonator is designed and investigated. Optical experimental behavior of racetrack is characterized via fiber micro-lens coupling. The transmission spectrum shows resonance dips with average quality factor of 105 and a small FSR of 0.050 ± 0.003 nm (actually corresponding to 6 GHz) for a scanning wavelength range from 1534 nm to 1610 nm. The most promising features of the racetrack resonator are its high quality factor, and its free spectral range, which give it the high suitability for being used in the OEO system. Nevertheless the coupling with fiber lens leads to high losses and it is not possible to fulfill the oscillation conditions. Future work should be conducted for improving the coupling and for controlling the resonance dips position in agreement with the wavelength of the laser used in the OEO.

Scientists and engineers measure dielectric constant because it gives them better understanding of materials and helps them to know how to integrate these materials into their design processes;it also helps them to shorten design life cycle,and aside these two functions,it has numerous uses all of which cannot be enumerated in this section.Owing to its usefulness,various measurement methods of dielectric constant of materials have been developed over the years.Each method has its limitations which affect the accuracy of the measurement;these limitations range from frequency,temperature,and  mearsurement environment to material under test.   In this thesis,four most common methods of measuring dielectric constant were discussed and the most accurate one,the resonant method,was chosen and worked on .The project was executed by making a mathematical analysis of the ring resonator which was later simulated in HFSS to get results which would be comparable to ones obtained in  laboratory measurements.   The ring was fabricated and taken to the laboratory for measurement.Two monopole antennas were connected to the two ports of a VNA with one antenna serving as the transmitter and the other serving as the receiver.   The resonant frequencies obtained were combined with the geometric parameters of the ring resonator and that of the MUT in equations written into MATLAB scripts;this equations were used to extract the dielectric constant of the MUT.