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

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