ALMA Memo # 533 * Improving Accuracy of Superconducting Microstrip Line Modelling at Millimetre and Sub - Millimetre Waves

This paper presents a new model to calculate the characteristic impedance and wave propagation constant of a microstrip line made of a superconducting material. Modelling provides the only tool for designing superconducting microstrip based circuits because no direct measurements of such a line can be made at millimetre and sub-millimetre waves and at cryogenic temperature of 4 K with required high accuracy. In contrast to a conventional microstrip, in the superconducting microstrip line, produced usually by a thin-film technology, the magnetic field penetration depth is comparable with the thicknesses of the dielectric and the superconductors comprising the line. As a result, the electromagnetic wave is propagating not only in the dielectric media but also partly inside the superconducting strip and ground electrodes creating dramatic changes in the line performance that should be carefully accounted for by including the superconductor material properties into the model. Niobium, as the most commonly exploited superconducting material, was used for the modelling, though the same approach would work for any different BCS superconductor. In order to evaluate the proposed model accuracy, we have made an extensive comparison study of the previously presented models and included 3D numerical electromagnetic simulation. The modelling covers different geometries of the superconducting microstrip line and address material dispersion.