Microwave characterization of a microstrip line using a two-port ring resonator with an improved lumped-element model

A two-port ring resonator is used to characterize the microwave properties of a microstrip line printed on Ferro A6-S low-temperature co-fired ceramic. The ring and its coupling gaps are simulated using a simple lumped-element model. The coupling gaps are modeled as capacitors, the values of which are extracted using a commercial two-and-one-half-dimensional electromagnetic simulator. The validity of the lumped-element model is assessed by comparing the simulated and experimental resonant frequencies and, for the first time, the simulated magnitudes of both the reflection and transmission coefficients are also compared with those obtained experimentally. A correction for the frequency pushing due to the capacitive loading of the coupling gaps is also presented. The resulting model is then shown to predict the resonant frequencies to within 0.11% from 5 to 40 GHz. The simulated and experimental reflection magnitudes are within 0.5 dB across the band, whereas the transmission magnitudes are within 3.5 dB up to 22 GHz. Experimental results indicate that the loss of the microstrip ranges from approximately 0.11 to 0.42 dB/cm across the band and that the relative permittivity of the substrate is nearly constant versus frequency with an average value of 6.17.