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Applied Physics Letters

Frequency dependence of the nonlinear response in YBa2Cu3O7−x transmission lines

Jordi Mateu, James C. Booth, Brian H. Moeckly

Published Jan 1, 2007• 7 citations
Publisher

Abstract

The authors evaluate the frequency dependence of the nonlinear response in high-temperature superconductor YBa2Cu3O7−x thin films by simultaneously measuring the nonlinear intermodulation products and harmonic generation in broadband superconducting transmission lines at 76K. The frequencies of the two-tone incident signal are set to produce spurious signals from 1to21GHz. They extract a nonlinear term ∣ΔR2+jωΔL2∣ by applying a model of spurious signal generation in superconducting transmission lines to their measurement results. They found that this nonlinear term follows a linear dependence on frequency, indicating a dominant contribution of the nonlinear inductance ΔL2 over the nonlinear resistance ΔR2, (ωΔL2⪢ΔR2), for the superconducting nonlinear response.

DOI
10.1063/1.2430286

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The authors evaluate the frequency dependence of the nonlinear response in high-temperature superconductor YBa2Cu3O7−x thin films by simultaneously measuring the nonlinear intermodulation products and harmonic generation in broadband superconducting transmission lines at 76K. The frequencies of the two-tone incident signal are set to produce spurious signals from 1to21GHz. They extract a nonlinear term ∣ΔR2+jωΔL2∣ by applying a model of spurious signal generation in superconducting transmission lines to their measurement results. They found that this nonlinear term follows a linear dependence on frequency, indicating a dominant contribution of the nonlinear inductance ΔL2 over the nonlinear resistance ΔR2, (ωΔL2⪢ΔR2), for the superconducting nonlinear response.
We report on a technique for extracting an accurate value of the nonlinear inductance in superconducting transmission lines. This novel technique assesses the frequency dependence of the transmission line's nonlinear response. A wideband nonlinear measurement system was used to simultaneously measure the third-order spurious signals at 2f1- f2,2f2- f1+ f2, 2f2+ f1, 3f1, and 3f2frequencies. Measurements for different values of the fundamental frequencies f1and f2allow us to study the spurious signal generation from 1 to 21 GHz. We demonstrate this technique by measuring several superconducting YBa2Cu3O7-xcoplanar waveguide transmission line geometries patterned in a single chip at 80 K. The results show a linear frequency dependence of the nonlinear response, indicating a dominant contribution of the nonlinear inductance over the nonlinear resistance omegaDeltaL(i) Gt DeltaR(i). The experimentally obtained nonlinear inductances are then used to determine device-independent measures of the linearity of the thin-film material in order to provide the foundation for modeling the nonlinear response of specific devices.
The simplest model of nonlinear response of a superconducting thin film is used for modeling the nonlinear phenomena in a superconducting transmission line and a microstrip resonator. The specified characteristic power of the transmission line is suggested to use as a fitting parameter for numerical description of the microstrip line nonlinearity at microwaves. Quantitative agreement of simulated and experimental data has been obtained for the incident power dependent transmission coefficient of a microstrip line section and a high quality microstrip resonator. Numerical results have also been obtained for the power of the third harmonic radiated from the nonlinear resonator.
We examine the DC and radio frequency (RF) response of superconducting transmission line resonators comprised of very thin NbTiN films, <12 nm in thickness, in the high-temperature limit, where the photon energy is less than the thermal energy. The resonant frequencies of these superconducting resonators show a significant nonlinear response as a function of RF input power, which can approach a frequency shift of Δf=−0.15% in a −20 dB span in the thinnest film. The strong nonlinear response allows these very thin film resonators to serve as high kinetic inductance parametric amplifiers.
Superconducting planar circuits possess properties that can be very different from their normal-metal counterparts, which makes modeling efforts more complicated for superconducting components. In this paper we present closed-form expressions for the resistance and internal inductance per unit length of superconducting planar transmission lines in terms of the relevant material parameters. We also include a simple calculation of the nonlinear response of superconducting devices based on a current-dependent superconducting penetration depth. Taken together, these two descriptions can be used to predict the linear and nonlinear response of superconducting planar devices in a manner that is conducive to use in circuit design. The results of these calculations compare well with 76 K measurements of coplanar waveguide transmission lines and resonators fabricated from thin films of the high T/sub c/ superconductor YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta//.
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.
Some results of an investigation of nonlinear behavior of NbN and YBa2Cu3O7-x films at microwaves are presented. Nonlinear microwave properties of superconducting films are analyzed on the basis of dynamic Current Voltage Characteristics (CVC) measured from the film response to the short duration video pulse. Conversion loss of the microwave signal into the intermediate frequency signal under various local oscillator power has been obtained from this analysis. The experimental data for the mixing of two microwave signals are described. Mixing effect was observed on superconducting NbN and YBa2Cu3O7-x film elements in microbridge and coplanar line forms. Conversion loss of about 20 dB was obtained in the running-wave regime.