Nonlinear RF spurious in a cylindrical cavity with superconducting endplates Jordi Mateu, Carlos Collado, Timothy J. Shaw, Juan M. O’Callaghan * Universitat Polit  ecnica de Catalunya (UPC), Campus Nord UPC-D3, Jordi Girona 1, Barcelona 08034, Spain Abstract We have developed a method to calculate the distribution of fundamental and spurious fields in a metallic cylindrical cavity with superconducting endplates in which signals at two different frequencies are injected. The nonlinearity in the superconductor produces the typical intermodulation effects if the frequencies of the injected signals are sufficiently close to each other and near a resonant mode. Our method uses harmonic balance to match the fields in the cavity with the currents on the endplates. The method can be used for a variety of nonlinear models of the superconducting endplate, and could be the base for a nondestructive procedure to extract the nonlinear parameters of an HTS sample from RF measurements. Our analysis is restricted to the TE 011 mode, but the method can be applied to any propa- gating mode in the cylindrical cavity. Closed-form equations for the case of square-law nonlinearities in the super- conductor are derived and used to check the validity of the harmonic balance calculation. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Cavity resonators; Intermodulation distortion; Nonlinear distortion; Superconducting devices 1. Introduction Most of the work on RF nonlinearities of su- perconductors has been done on planar resonators and filters. Cavity resonators are also used in filters and in devices for characterization of material properties. In both applications, the nonlinear performance of cavity resonators is of interest. This paper presents a general method to calculate the distribution of spurious fields in a metallic cylin- drical cavity with superconducting endplates in the TE 011 mode. However, with minor modifications, the method is generally applicable to any propa- gating mode in the cylindrical cavity, to cavities with other cross-sections, or to cavities with a single superconducting endplate. 2. Nonlinearities in the superconducting endplates When the signal levels are small, the electric field on superconducting endplates depends on the surface current density and the surface impedance: E L ¼ Z s J s . However, if the currents are large en- ough, the electric field has a nonlinear dependence with the surface current. Using the nomenclature in [1] we can write the following time-domain equation: Physica C 372–376 (2002) 679–682 www.elsevier.com/locate/physc * Corresponding author. Fax: +34-93-401-7232. E-mail address: joano@tsc.upc.es (J.M. O’Callaghan). URL: http://www-tsc.upc.es/eef/. 0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII:S0921-4534(02)00829-8