Coupling inhomogeneities in the Josephson junctions of planar 0-SQUIDs and π-SQUIDs and of three-dimensional SQUIDs are considered. Starting from the properties of planar SQUIDs, it is shown that slight non-homogeneous couplings of the twelve junctions in three-dimensional superconducting interferometers do not affect the periodicity properties of voltage versus applied flux curves. The results are obtained by applying a rigorous and general analytic approach to planar and three-dimensional superconducting devices.
Thin-film Josephson-junction quantum-interference devices require only a small amount of magnetic flux to switch them between the voltage state and the superconducting state. They are sensitive to any spurious magnetic flux present at the device. The magnetic flux may be trapped in the superconducting ground plane, particularly in ground plane holes. This paper analyzes the effects of the trapped magnetic flux on the threshold curves of three-junction Josephson interferometers. The threshold curves of the interferometer are calculated automatically by using a circuit optimization program. The automatic procedure of calculating the threshold curves of an interferometer can be applied to any Josephson-junction interferometer device. The threshold curves of both symmetric and asymmetric interferometers are calculated. We find that the threshold curves of a symmetric three-junction interferometer changes periodically as a function of the effective coupled trapped magnetic flux with a period of Φ0. The threshold curves are shifted and severely distorted in shape by the presence of the coupled trapped magnetic flux. The degeneracy of the threshold curves of a symmetric interferometer makes the unique quantitative determination of the trapped magnetic flux difficult. However, the degeneracy is removed in an asymmetric interferometer. The presence of the unbalanced trapped magnetic flux greatly shifts the entire threshold curve of an asymmetric interferometer.