Inductance in Thin-Film Superconducting Structures

Thin-film superconducting components and circuits assume the form of coupled strip-transmission lines. The self and mutual inductances of these lines are important to the gain and bandwidth of the circuits. The inductances are influenced strongly by penetration of magnetic fields into the conductors. This paper gives a field solution which shows that the lowest-order mode on a thin-film superconducting strip line is a TM or E wave because of penetration effects. This mode has a non-negligible axial electric field which makes it incorrect to calculate inductance on a flux-linkage-per-unit-current basis even at low frequencies. However, the low-frequency inductance can be correctly calculated on an energy basis if the kinetic energy of the superelectrons is included in the free energy. This latter method is applied to a structure of current practical interest, that of an arbitrary number of infinitely long, very wide, thin, parallel, superimposed, closely spaced conductors above a common ground plane. All distributed self and mutual inductances with any conductor or combination of conductors in either the super or normal state are evaluated.