A general approach for the calculation of intermodulation distortion in cavities with superconducting endplates

Abstract

We report on a general procedure to calculate intermodulation distortion in cavities with superconducting endplates that is applicable to the dielectric-loaded cavities currently used for measurement of surface resistance in high-temperature superconductors. The procedure would enable the use such cavities for intermodulation characterization of unpatterned superconducting films, and would remove the uncertainty of measuring intermodulation on patterned devices, in which the effect of patterning damage might influence the outcome of the measurements. We have verified the calculation method by combining superconducting and copper endplates in a rutile-loaded cavity. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1535742͔Microwave nonlinearities are important features of superconducting thin films that might limit their applicability. This is the case in high-temperature superconductors ͑HTS͒, whose use in wireless and other communication systems is limited, among other factors, by this type of nonlinearity. 1Microwave nonlinearities are enhanced when there are high current densities in the superconductor, and are most prominent in planar resonators in which magnetic field wraps around a thin superconducting film.2 There is a widespread agreement to attribute the nonlinearities to a dependence of the surface impedance on the local magnetic field or, equivalently, on the surface current density. 3There is concern regarding the possible effects of patterning superconducting films on the nonlinear behavior of the resulting planar devices, especially when considering intermodulation distortion ͑IMD͒. Besides the obvious technological implications in device fabrication, this could also affect basic studies that use the IMD of patterned resonators to probe the properties of superconductors. 4 Measurements of third-harmonic generation made on planar HTS lines of various cross sections 5 suggest that etching in HTS has a limited effect on IMD, but to completely rule out these effects, a study similar to Ref. 6 should be made. That work compares nonlinear measurements of cavities with superconducting films used as endplates with measurements of planar devices fabricated with the same films, and finds that the power dependence of the microwave surface resistance is unaffected by the patterning process. To extend such work to IMD and rule out the effects of patterning on this type of distortion, it is necessary to relate the results of a cavity IMD measurement with the properties of the superconducting film. In this letter, we address this by describing a method to calculate the power of the intermodulation products coupled out of a cavity with one or two superconducting endplates, and show experimental results that verify the method.We assume that we have a cavity, which might be dielectric-loaded as those in Refs. 6 and 7, in which one of the endplates is made of a superconducting material and the other is a normal metal. We also assume that the electric field on the superconducting endplate will be a superposition ...

Comparison between nonlinear measurements in patterned and unpatterned thin films

“…f (T , 0) = 0). Several references [5,6] use f (T , j ) = ( j/j IMD ) 2 to be consistent with their intermodulation measurements, but others claim other types of dependence like, f (T , j ) = | j/j IMD | [3,7] or f (T , j ) = |j/j IMD | 0.2 [3]. In order to deal with the various types of dependence observed, we have developed a formulation that assumes a generic variation of the penetration depth on the volume current density [8]:…”

“…The linear parameters Q 0 and κ are calculated from the measured scattering parameter S 11 . The term T α,2ω1−ω2 is equal to 0.3617 for α = 1.2 and 0.0252 for α = 0.1, being j 1 /j 2 = 1 since the two input tones have the same power [3]. With all of these parameters, the nonlinear term | R α + j ω 0 L α | has to be 2.21 × 10 −6 m α /A α for region 1 and 0.001 m α /A α for region 2, according to (4).…”

“…As done in [8], we have fed the cavity with only one port and two input tones spaced 20 kHz apart. As shown in [3], the slope of the third order intermodulation product at 2ω 1 − ω 2 sets the phenomenological parameter α. From the measurements presented below, we see two different regions depending on the input power to the resonator.…”

“…The resonator designed is like the one described in [3]: a rutile cylinder having 4 mm of diameter (2a) and 3 mm of height (h) placed on the 10 × 10 mm 2 HTS sample (b = 5). The resonance frequency of the cavity was 8 GHz and the intermodulation measurements are plotted in figure 1.…”

“…To overcome this, many experiments have been carried out over the last decade, some of which still remain unexplained. Most of the experimental work has been done measuring intermodulation products in planar patterned devices [2], but experiments have also been done on unpatterned thin films [3].…”