Lumped element modeling of nonlinear properties of high temperature   superconductors in a dielectric resonator
  Microwave properties of High Temperature Superconductors (HTS) exhibit dependence on RF power levels. Effects of nonlinear phenomena causing this dependence can be modelled using lumped element circuits. Several RLC circuits to model the surface impedance of HTS were investigated (with equations expressing transmitted power derived) and assessed. Linear, quadratic and exponential dependences of surface resistance RS and inductance LS on the RF power for the model chosen as the best have been examined and used in simulations of electromagnetic responses of superconducting films in a Hakki-Coleman dielectric resonator. 
Dimitri O. Ledenyov, Janina E. Mazierska, Greg Allen, Mohan V. Jacob
cond-mat.supr-con