Theoretical Analysis of Microwave and Millimeter Wave Integrated Circuits Basedon Magnetic Films

摘要

A macroscopic model is proposed to explain nonlinear electromagnetic phenomena insuperconductors. Nonlinear constitutive relations for electromagnetic problems are derived by modifying the linear London's equations. The superelectron number density ns is a function of the applied current density. The critical current density Jc is derived classically from a critical energy Ec. For temperature T not equal to 0, the concept of critical current Jc does not imply an abrupt transition of the whole sample from a superconducting state to a normal state when J > Jc. A rather smooth variation of ns(J) is shown instead. The relation, ns(J), is derived from the Maxwellian distribution of electron velocities at a certain temperature T and a certain macroscopic current density J. Agreement has also been found between this ns(J,T) model and the temperature dependance of ns in the two-fluid model. The nonlinear conductivities sigma s(J) and sigma n(J) are obtained from the London's equation and the ns(J) function. Nonlinear resistance R(I), kinetic inductance Lk(I) and surface impedance Zs(I) in thin wire, slab, and strip geometries of superconductors are calculated. A general scheme of solving nonlinear electromagnetic problems in superconductors is proposed. A good agreement between the theory and experiments has been found.