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

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2 Theoretical Description of a CPW ResonatorFigure 2.1: Different realizations of CPW: (a) the conventional CPW, (b) the conductorbacked CPW.The cross-sectional view of a CPW is shown in Figure 2.2. In this CPW structure a centerconductor and two ground planes are superimposed on a single substrate. A brief discussionof two layer substrates, like those used in this thesis, can be found in subsection 2.1.4. Wedenote the CPW center strip conductor width by S, the slot width by W. The height of thedielectric substrate is H with a corresponding relative permittivity ε r .Figure 2.2: Structure of a CPW, a conducting strip and two ground planes are placed on asubstrate. The CPW is shielded on top and bottom by conducting layer.Two metal shields are placed above the CPW conductors and on the bottom surface of thedielectric substrate. H 1 denotes the height of the upper metal cover. The shielding is realizedby the conducting inner side of the measurement-box. The side box walls can be neglecteddue to the large distance to the inner conductor. From the geometry, an effective dielectricconstantε e f f = C CPWC Air= C Air +C dielC Air= 1 + C dielC Air(2.1)can be calculated as the ratio of the capacitance of the CPW C CPW to the capacitance ofthe air-filled region C Air where the total capacitance of the CPW is a sum of a dielectriccapacitance C diel and C Air .4
2.1 The Coplanar Transmission Line2.1.1 Constitution of Air-Filled RegionsFigure 2.3: Configuration of the air capacitance of a CPW.The partial capacitance of the CPW in the absence of all dielectric layersK(k)C Air = 2ε 0K(k ′ ) + 2ε K(k 1 )0K(k1 ′ )consists of the sum of the upper and the lower regions, with heights H and H 1 , as shownin Figure 2.3.K(k) and K(k ′ ) are the complete elliptic integrals with the moduli.We reduce these formula tok =k ′ =k 1 =tanh( π·S4·H )tanh( π·(S+2·W)4·H) , (2.2)√1 − k 2 ,tanh( π·S4·H 1)tanh( π·(S+2·W)4·H 1) .k ≈π·S4·Hπ·(S+2·W)4·H=SS + 2 ·Win the case of large heights H and H 1 .The capacitance of the air-filled regions simplifies to:(2.3)C Air = 4ε 0K(k)K(k ′ )5
Page 4 and 5: Contents5.2.3 R27 on Silicon . . .
Page 6 and 7: 1 Motivation and Outlinethe antinod
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
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5.4 Measurement - Design 2: R36 on
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5.5 Discussion of the Experimental
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5.5 Discussion of the Experimental
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6 SimulationsThis chapter gives a b
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6.1 Simulations in SonnetFigure 6.4
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6.1 Simulations in SonnetFigure 6.5
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6.2 Simulations Done at the Institu
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7 Conclusion and OutlookThree centr
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A Specimen OverviewDesigns for Rose
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B Masks73
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B.2 Mask for Probing StationB.2 Mas
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Bibliography[1] INFORMATIK: Quanten
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List of Figures2.1 Different realiz
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List of Figures6.6 Forward and back
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List of Tables2.1 Values where (2.1
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DanksagungVor allem möchte ich mic
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