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IEEE Transactions on Applied Superconductivity

Analysis and Simulation of the Effects of Distributed Nonlinearities in Microwave Superconducting Devices

Carlos Collado, Jordi Mateu, Joan M. O'Callaghan

Published Mar 1, 2005• 62 citations

Abstract

This paper presents a comprehensive study of microwave nonlinearities in superconductors, with an emphasis on intermodulation distortion and third-harmonic generation. It contains the analysis of various resonant and nonresonant test devices and its validation using numerical simulations based on harmonic balance (HB). The HB simulations made on test devices show that the closed-form equations for intermodulation and third-harmonic generation are only valid at low power levels. The paper also contains examples of application of HB to illustrate that this technique is useful to simulate superconductive devices other than simple test devices, and that the validity of the simulations is not restricted to low drive power levels. Most of the analyses and simulations of this paper are based on electrical parameters that describe the nonlinearities in the superconducting material. These parameters are compatible with many existing models of microwave nonlinearities in superconductors. We discuss the particulars on how to relate these electrical parameters with one of the existing models that postulates that the nonlinear effects are due to a dependence of the penetration depth on the current density in the superconductor.

DOI: 10.1109/tasc.2005.844134

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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.

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.

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.

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 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.