RF Superconducting Devices

Microwave properties of a rutile resonator between 2 and 10 K

“…where 1 is the copper geometric factor for the lower frequency mode, 2 is the geometric factor of the higher frequency mode and R Cu is the frequency-dependent microwave surface resistance of copper. The low-temperature frequency dependence of R Cu has been shown to vary as f 2/3 (anomalous skin effect) [18]. An accurate measurement of the temperature dependence of R Cu has only recently been made [19], and an empirical fit to the data shows that it varies as a function of temperature, at a frequency of 18 GHz, as: R Cu (18 GHz, T ) = 0.0115 exp(0.00615T )…”

“…If we look once again at figure 5 where the upper curve is a plot of the total permittivity mediated frequency variation with temperature (the left-hand side of equation ( 18)), and we imagine another curve drawn to indicate the value of the last term in equation ( 18) (the same as the lower curve but multiplied by 65) we note that the thermal expansion mediated term is comparable to the total term below 8 K and above 80 K. We believe that the decrease in the slope of the frequency curve above 80 K is also explained by the indirect effects of the change in the volume of the resonator. Clearly because of the difference in slopes of the upper and lower curves in the temperature range 8-80 K, the dominant permittivitytemperature dependence term will be the first term on the right-hand side of equation (18).…”