# Modeling of nonlinear effects in HTS resonator

## DOI:

https://doi.org/10.1109/ICATT.2011.6170752## Keywords:

high temperature superconductivity, nonlinear surface impedance, integral equations, intermodulation distortions## Abstract

In recent years increasingly in a variety of radio systems the microwave devices (transmission lines, resonators, filters, etc., that are) performed with using of the phenomenon of high temperature superconductivity (HTS) are used. From the point of view of the nonlinear properties of HTS conductors, these devices are nonlinear devices that are characterized by various nonlinear effects that often degrade the properties of the whole system. Therefore, the prediction of the nonlinear characteristics of devices with HTS is a very important task still at the design stage.

In this article we consider nonlinear effects in HTS microstrip resonators. A mathematical model based on the method of nonlinear integral equations (NIE) with respect to the distribution of spectral components of current density on the surface of the HTS conductor. A procedure of numerical solution of NIE for a periodic or intermittent mode device is offered.

The results of studies of resonators with resistive and inductive nature of the nonlinearity of the surface impedance are introduced. It is shown that in resonators with inductive impedance with an increase in the level of the input there is a shift of the resonance frequency device and the response becomes asymmetric, which in turn leads to different levels of intermodulation distortion at different boundaries of bandwidth. The level of intermodulation products and the higher harmonics in the cavities of various types is analyzed.

## References

SCHRIEFFER, J.R.; BROOKS, J.S. *Handbook of High-Temperature Superconductivity*. New York: Springer, 2007, 627 p., doi: http://dx.doi.org/10.1007/978-0-387-68734-6.

CHANG K. (ed.). *Encyclopedia of RF and Microwave Engineering*. New Jersey: John Wiley & Sons, Inc, 2005, v.1-6, doi: http://dx.doi.org/10.1002/0471654507.

HEIN, M. Potential of high temperature superconductors for microwave applications. *Particle Accelerators*, 1996, v.53, p.135-197.

SATOH, K. SUZUKI, Y.; MIMURA, T.; NARAHASHI, S.; NOJIMA, T. Improvement in Capacity Performance of Mobile Communication Systems Achieved Through Cryogenic Receiver Front-End. *Proc. of 9th European Conf. on Applied Superconductivity*, 13-17 Sept. 13-17, Dresden, Germany. 2009, p.12.

LANCASTER, M.J. *Passive Microwave Device Applications of High-Temperature Superconductors*. Cambridge University Press, 1999, 337 p.

MATEU, J.; COLLADO, C.; O'CALLAGHAN, J.M. Harmonic effects in balance algorithm to model nonlinear HTS filters subject to CDMA signals. *IEEE on MTT-S Digest*, Philadelphia, 2003, p.547-550.

OATES, D.E.; ANDERSON, A.C.; SHEEN, D.M.; ALI, S.M. Stripline Resonator Measurements of Z_{s} Versus H_{rf} in YBa_{2}Cu_{3}O_{7-x} Thin Films. *IEEE Trans. Microwave Theory Tech.*, 1991, v.39, n.9, p.1522-1529, doi: http://dx.doi.org/10.1109/22.83827.

WILLEMSEN, B.A.; DEROV, J.S.; SILVAB, J.H.; SRIDHAR, S. Nonlinear Response of Suspended High Temperature Superconducting Thin Film Microwave Resonators. *IEEE Trans. Applied Superconductivity*, June 1995, v.5, n.2, p.1753-1755, doi: http://dx.doi.org/10.1109/77.402917.

DAHM, T.; SCALAPINO, D.J. Theory of Microwave Intermodulation in a High-Tc Superconducting Microstrip Resonator. *Applied Physics Letters*, 1996, v.69, n.12, p.4248-4250, doi: http://dx.doi.org/10.1063/1.116960.

VENDIK, O.G.; VENDIK, I.B.; SAMOILOVA, T.B. Nonlinearity of Superconducting Transmission Line and Microstrip Resonsator. *IEEE Trans. Microwave Theory Tech.*, 1997, v.45, n.2, p.173-178, doi: http://dx.doi.org/10.1109/22.557597.

HU, W.; THANAWALLA, A.S.; FEENSTRA, B.J.; WELLSTOOD, F.C.; ANLAGE, S.M. Imaging of microwave intermodulation fields in a superconducting microstrip resonator. *Applied Physics Letters*, 1999, v.75, n.18, p.2824-2826, doi: http://dx.doi.org/10.1063/1.125162.

WILLEMSEN, B.A.; KING, B.H.; DAHM, T.; SCALAPINO, D.J. Microwave Intermodulation in High-Tc Superconducting Microstrip Resonators. *IEEE Trans. Appl. Supercond.*, 1999, v.9, n.2, p.4181-4184, doi: http://dx.doi.org/10.1109/77.783946.

BOUTBOUL, M.; KOKABI, H.; SAUTROT, S.; DEGARDIN, A.; KREISLER, A.; FOURRIER, M. Nonlinear microwave effects in superconducting microstrip resonators based on YBCO thin films. *IEEE Trans. Applied Superconductivity*, 2001, v.11, n.2, p.139-142, doi: http://dx.doi.org/10.1109/77.919304.

OATES, D.E. Nonlinear Behavior of Superconducting Devices. *Microwave Superconductivity*, 2001, v.375, p.117-148, doi: http://dx.doi.org/10.1007/978-94-010-0450-3_5.

COLLADO, C.; MATEU, J.; O'CALLAGHAN, J.M. Computer simulation of the nonlinear response of superconducting devices using the multiport harmonic balance algorithm. *Applied Superconductivity*. Institute of Physics Publishing, 2003, p.411-414.

COLLADO, C.; MATEU, J.; O'CALLAGHAN, J.M. Analysis and Simulation of the Effects of Distributed Nonlinearities in Microwave Superconducting Devices. *IEEE Trans. Applied Superconductivity*, 2005, v.15, n.1, p.26-39, doi: http://dx.doi.org/10.1109/TASC.2005.844134.

SHIFRIN, Y.S.; LUCHANINOV, A.I.; OMAROV, M.A. Analysis of antennas with the distributed nonlinearity. *Antennas*, 2000, n.1, p.70-83.

TANG, H.Z.; SAFAVI-NACINI, S.; CHOW, Y.L. An Efficient Analysis Method for Nonlinear Effects in High-Power HTSC Planar Microwave Circuits. *IEEE Trans. Microwave Theory Tech.*, 2000, v.48, n.7, p.1280-1282, doi: http://dx.doi.org/10.1109/22.853473.

LUCHANINOV, A.I.; SHOKALO, V.M.; ZHURBENKO, V.V. The analysis of nonlinear effects in superconducting microstrip resonators. *Proc. of the Int. Conf. on Modern Problems of Radio Engineering, Telecommunications and Computer Science*, 2002. IEEE, 2002, p.35-37, doi: http://dx.doi.org/10.1109/TCSET.2002.1015846.

LUCHANINOV, A.I.; ZHURBENKO, V.V.; OMAROV, M.A. Modeling of nonlinear effects in microstrip lines with high-temperature superconductivity. *Electronics and Informatics*, 2001, n.3, p.20-23.

KRIKUN, E.V.; LUCHANINOV, A.I.; GAVVA, D.S. Nonlinear effects in microstrip power divider based on high-temperature superconductors. *Proc. of Eighth Int. Sci. Conf. on Modern Information and Electronic Technologies*, SIET 2007. Odessa, 2007, p.201.