(a) Top view of a CPW resonator with finger capacitors (left-hand side) and gap capacitors (right-hand side). (b) Cross section of a CPW resonator design. Center conductor and lateral ground metallization (blue) on top of a double layer substrate (gray/yellow). Parameters are discussed in the main text.
Optical microscope images of an Al CPW resonator (white is metallization, gray is substrate). The red squares in the upper image indicate the positions of the input/output capacitors. Also shown are microscope images of finger and gap capacitor structures. The labels D, E, H, I, and K refer to the device ID listed in Table II.
(a) Transmission spectrum of a 4.7 GHz resonator. Data points (blue) were fitted (black) with a Lorentzian line. (b) Measured (red points) of several resonators coupled via gap capacitors with different together with a fit (blue line) to the data using Eq. (1) as fit function and as fit parameter.
transmission spectra of 2.3 GHz resonators symmetrically coupled to input/output lines. The left part of the split plot shows spectra of finger capacitor coupled resonators, whereas on the right hand side one can see spectra of gap capacitor coupled resonators. The data points (blue) were fitted (black) with the transmission matrix method, see text.
(a) Distributed element representation of symmetrically coupled TL resonator. (b) Parallel oscillator representation of TL resonator. (c) Norton equivalent of symmetrically coupled parallel oscillator. Symbols are explained in text.
(a) Dependence of on . Data points (red) are measured quality factors. These values are compared to predictions by the mapped model (solid blue line) given by Eqs. (14), (19), and (21). (b) Dependence of on . Data points (red) show measured values. The values are compared to the mapped model (solid blue line) given by Eqs. (14), (21), and (22). Dashed lines indicate the limiting cases for small and large coupling capacitances (see text).
(a) Comparison of values extracted from the measured quality factors using Eqs. (14), (19), and (21) to the EM-simulated values for (red points) for devices A–H. The blue curve is a line through origin with slope one. (b) Dependence of on . The mapped model prediction given by Eqs. (15) and (18) is shown (blue line) for resonators coupled via finger capacitors together with the measured values for (red points).
Measured quality factors for the overcoupled resonator D vs mode number (red points) together with the prediction of the mapped model given by Eqs. (18) and (21) (solid blue line). The inset shows the transmission spectrum of resonator D with fundamental mode and harmonics. The measured data (blue) are compared to the spectrum (black) obtained by the ABCD matrix method.
Designed values for resonator lengths and measured resonance frequencies corresponding to the data shown in Fig. 3.
Properties of the different CPW resonators whose transmission spectra are shown in Fig. 4. denotes the simulated coupling capacitances, is the measured resonance frequency, and is the measured quality factor.
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