Measurement of surface impedance versus temperature using a generalized sapphire resonator technique

Abstract

An automated measurement technique to measure the surface impedance, Zs=Rs+iXs, as a function of temperature is presented. Based on the dielectric resonator measurement technique, a general purpose approach is developed which does not neglect dielectric loss and can accommodate a variety of sample sizes and measurement frequencies. By employing a parallel-plate geometry which has a known electromagnetic solution, both the surface impedance of the sample and the induced surface current can be related quantitatively to the measured Q, the resonant frequency, and the applied power. Although the measurement sensitivity depends on the system design and choice of materials, comprehensive equations are presented which serve as a useful tool for designing the system and simulating the measurement. Using a sample size of 1×1 cm2 and a measurement frequency of 19.6 GHz, a measurement uncertainty of 420 μΩ for Rs and 4800 μΩ for ΔXs is demonstrated. For superconducting samples, this translates to a measurement uncertainty of 105 μΩ for Rs and 2400 μΩ for ΔXs at 10 GHz, which is sufficient for routine measurements. Methods to improve the resolution and uncertainty of this measurement technique are discussed, and a general scheme to fully automate this measurement via computer is demonstrated.

Traceable 2-D Finite-Element Simulation of the Whispering-Gallery Modes of Axisymmetric Electromagnetic Resonators

“…z 0 |H open t | 2 dS, where z 0 is the impedance of free space. A bound on the mode's radiative Q-factor can thus be expressed as 7 It is here pointed out that, at liquid-helium temperatures, the bulk and surface resistances of metals can depend greatly on the levels of (magnetic) impurities within them [36], and the text-book f −1/2 dependence of surface resistance on frequency is often violated [37]. 8 As understood by Kippenberg [29], this observation implies that the support of equation 24 approaching equality when the WG mode's bright spot lies (in effect) at an antinode of the mode's standing wave; Λ here is exactly that given by equation 27, with H = H closed t , only now the enclosing electric wall is in the radiation zone.…”

“…In the using of equation 26, it should be pointed out that, at liquid-helium temperatures, the bulk and surface resistances of metals can depend greatly on the levels of (magnetic) impurities within them [38], and the text-book f −1/2 dependence of surface resistance on frequency is often violated [39].…”

“…Based on ref. [39], one estimates the surface resistance of copper at liquid-helium temperature to be 7 × 10 −3 Ω per square at 11.9 GHz, leading to a wall-loss Q of 3.5×10 11 for the WGE 14,0,0 mode. As this is at least an order of magnitude greater than what is observed experimentally, one concludes that wall losses do not substantially limit the UWA resonator's experimental Q.…”

“…FILLING FACTORS FOR THE WGE 14,0,0 MODE OF UWA'S SLOPING-SHOULDERS RESONATOR This mode's characteristic length Λ, as evaluated with respect to the can wall's enclosing surface, was determined to be 2.6 × 10 4 m. Based on ref [37],. one estimates the surface resistance of copper at liquid-helium temperature to be 7×10 −3 Ω per square at 11.9 GHz, leading to a wall-loss Q of 3.5 × 10 11 for the WGE 14,0,0 mode.…”

Dielectric resonators for microwave characterization of high-temperature superconductors

“…The first use of DRs to microwave characterisation of HTS materials was proposed (to the knowledge of authors) in 1989 by Fieduszko and Heideman [4]. Since then several groups [5][6][7][8][9][10][11][12][13][14][15][16] have developed variety of designs for this purpose.…”