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Journal of Applied Physics

Intermodulation measurements in Nb superconducting microstrip resonators

R. Monaco, A. Andreone, F. Palomba

Published Sep 1, 2000• 23 citations
Publisher

Abstract

The issue of intermodulation distortion in superconducting devices for rf and microwave applications is discussed. The classical frequency conversion theory for nonlinear two-port devices in the small signal limit is shown to apply to microstrip resonators regardless of their geometry and material. Two tone, third order intermodulation measurements allow more sensitive detection of nonlinearity compared to surface impedance measurements, provided a low noise, spurious free experimental setup is adopted. Measurements carried out on high quality Nb meanderline microstrip resonators show that at very low power level nonlinearity is dominated by intrinsic device properties. Film defects start to play a predominant role above a critical power level that strongly depends on the defect’s nature.

DOI
10.1063/1.1286176

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The issue of intermodulation distortion in superconducting devices for rf and microwave applications is discussed. The classical frequency conversion theory for nonlinear two-port devices in the small signal limit is shown to apply to microstrip resonators regardless of their geometry and material. Two tone, third order intermodulation measurements allow more sensitive detection of nonlinearity compared to surface impedance measurements, provided a low noise, spurious free experimental setup is adopted. Measurements carried out on high quality Nb meanderline microstrip resonators show that at very low power level nonlinearity is dominated by intrinsic device properties. Film defects start to play a predominant role above a critical power level that strongly depends on the defect’s nature.
The penetration depth and surface resistance of a superconductor depend upon the superfluid current density. This dependence gives rise to nonlinear mixing in a superconducting microstrip resonator. Here we discuss the problem of intermodulation in which two signals at ω1 and ω2, laying within the pass band of a microstrip cavity resonance, mix and generate a signal at 2ω1−ω2. An expression relating the power generated at 2ω1−ω2 to the power transmitted at ω1 and ω2 is given. We focus on the high-Tc superconductors where it is believed that the order parameter has dx2−y2 symmetry. We find for a resonator with a large unloaded Q that intermodulation arises dominantly from the reactive nonlinear inductance of the superconducting film.
The response of nonlinear metamaterials and superconducting electronics to two-tone excitation is critical for understanding their use as low-noise amplifiers and tunable filters. A new setting for such studies is that of metamaterials made of radio frequency superconducting quantum interference devices (rf-SQUIDs). The two-tone response of self-resonant rf-SQUID meta-atoms and metamaterials is studied here via intermodulation (IM) measurement over a broad range of tone frequencies and tone powers. A sharp onset followed by a surprising strongly suppressed IM region near the resonance is observed. Using a two time scale analysis technique, we present an analytical theory that successfully explains our experimental observations. The theory predicts that the IM can be manipulated with tone power, center frequency, frequency difference between the two tones, and temperature. This quantitative understanding potentially allows for the design of rf-SQUID metamaterials with either very low or very high IM response.
Nonlinearities give rise to intermodulation distortion in superconducting microwave devices and currently limit their use to low power applications. We have developed a cryogenic imaging technique to spatially resolve intermodulation distortion and used it to image an 8.2 GHz high temperature superconducting Tl2Ba2CaCu2O8 microwave resonator. The images reveal that the fundamental and intermodulation electric fields obey a fixed relation throughout the device. We note that further refinements of intermodulation theory in resonant devices may be required to fully describe the data.
Two-dimensional scanning is combined with a method to locally excite intermodulation distortion (IMD) in a cuprate superconducting microwave resonator. The technique provides local maps of second and third order IMD. The two orders originate from distinct processes and require multiple tones in order to both be excited in a narrow passband. This is the first report where multiple orders of IMD are mapped at their points of origin at the operating frequency of the device. Two samples are shown, one pristine sample and one with an engineered defect, revealing a dominance of the defect in the nonlinearity of the device.
At the resonant frequency, superconducting resonators produce intermodulation distortion (IMD), smaller unwanted signals near the resonant frequency. These signals are a measure of the ratio between fundamental frequencies and distortion products. By inducing external microwave signals, it is possible to analyse the patterns of IMD in several different types of superconducting resonators. These measurements can be used to complement the main peak values like quality factor and frequency shift in order to understand nonlinearities present in the material of the superconductor. Once IMD measurements are taken, they were combined into a 2-dimensional raster image of the resonator chip.