Design, Fabrication and Characterization of a Microwave Resonator ...

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5 MeasurementsFigure 5.20: Transmission S 21 and reflection S 22 and S 11 of R36 on Silicon at 4 K.Figure 5.21: Transmission S 21 of R36 on Silicon at 4 K with full calibrated cables: Phaseshift (a) and magnitude (b) at resonance.56
5.5 Discussion of the Experimental Results5.5 Discussion of the Experimental ResultsThis subsection analyzes the results and compares the resonance frequency and quality factorsfrom theoretical predictions with measured values.Figure 5.22 shows the influence of the coupling to the environment on the resonancefrequency. For all resonators, except R27 which is designed for a different frequency, theresonance frequency decreases with increasing coupling. In the Yale design, in contrast todesign 1, the resonance frequency is lower for Sapphire. This behavior is not predicted bytheory.Figure 5.22: Measured resonance frequency versus coupling capacitance of all designs.Figure 5.23 shows the dependence of the quality factor on the coupling capacitance. Theinfluence of the design on the quality factor is clearly visible. With larger dimensions of thegap W and inner strip S the quality factor decreases. The reason for this effect can be strongercoupling to the environment, as it is the case for the resonance frequency dependence inFigure 5.22. As the loaded quality factor should approximately be the same for all designs(see tables at the end of this section) another explanation for the decrease of the quality factorcould be other losses e.g. radiation losses that have yet been neglected in the calculations.The Tables 5.11 to 5.15 compare theoretical predicted quality factors and resonance frequencieswith measured results. The uncoupled resonance frequencies are calculated using(2.31), the quality factors are derived by inserting the values from Table 2.5 in (2.32). Coupledvalues are derived from the formulas (2.29) for the loaded resonance frequency and(2.28) for the loaded quality factor.A loss tangent of 7·10 −4 was assumed for Silicon in order to have quality factors com-57
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Contents5.2.3 R27 on Silicon . . .
Page 6 and 7:
1 Motivation and Outlinethe antinod
Page 8 and 9:
2 Theoretical Description of a CPW
Page 10 and 11: 2 Theoretical Description of a CPW
Page 12 and 13: 2 Theoretical Description of a CPW
Page 14: 2 Theoretical Description of a CPW
Page 19 and 20: 2.2 Including Superconductivity in
Page 21 and 22: 2.2 Including Superconductivity in
Page 23 and 24: 2.3 Microwave Resonators2.3.2 Quali
Page 25 and 26: 2.3 Microwave ResonatorsFigure 2.11
Page 27 and 28: 2.3 Microwave ResonatorsFigure 2.13
Page 29 and 30: 2.4 The Scattering MatrixThe first
Page 31 and 32: 3 Designs Procedure for the Resonat
Page 33 and 34: 3.3 ConnectorsFigure 3.1: Coupling
Page 35 and 36: 4 Fabrication and Measurement Setup
Page 37 and 38: 4.2 Measurement SetupDevelop Resist
Page 39 and 40: 4.2 Measurement SetupFigure 4.3: Me
Page 41 and 42: 4.3 Calibration4.3 CalibrationIn or
Page 43 and 44: 5 MeasurementsThe first part of thi
Page 45 and 46: 5.1 First Experimentsname design W
Page 47 and 48: 5.2 Measurements - Design 1Figure 5
Page 49 and 50: 5.2 Measurements - Design 1The adva
Page 51 and 52: 5.2 Measurements - Design 15.2.2 R2
Page 53 and 54: 5.2 Measurements - Design 1Figure 5
Page 55 and 56: 5.3 Measurements - Yale DesignFigur
Page 57 and 58: 5.3 Measurements - Yale DesignFigur
Page 59: 5.4 Measurement - Design 2: R36 on
Page 63 and 64: 5.5 Discussion of the Experimental
Page 65 and 66: 6 SimulationsThis chapter gives a b
Page 67 and 68: 6.1 Simulations in SonnetFigure 6.4
Page 69 and 70: 6.1 Simulations in SonnetFigure 6.5
Page 71 and 72: 6.2 Simulations Done at the Institu
Page 73 and 74: 7 Conclusion and OutlookThree centr
Page 75 and 76: A Specimen OverviewDesigns for Rose
Page 77 and 78: B Masks73
Page 79 and 80: B.2 Mask for Probing StationB.2 Mas
Page 81 and 82: Bibliography[1] INFORMATIK: Quanten
Page 83 and 84: List of Figures2.1 Different realiz
Page 85 and 86: List of Figures6.6 Forward and back
Page 87 and 88: List of Tables2.1 Values where (2.1
Page 89: DanksagungVor allem möchte ich mic
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Design, Fabrication and Characterization of a Microwave Resonator ...

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