We have fabricated series-parallel (two-dimensional) arrays of incommensurate superconducting quantum interference devices (SQUIDs) using YBa2Cu3O7−δ thin film ion damage Josephson junctions. The arrays initially consisted of a grid of Josephson junctions with 28 junctions in parallel and 565 junctions in series, for a total of 15 255 SQUIDs. The 28 junctions in the parallel direction were sequentially decreased by removing them with photolithography and ion milling to allow comparisons of voltage–magnetic field (V–B) characteristics for different parallel dimensions and area distributions. Comparisons of measurements for these different configurations reveal that the maximum voltage modulation with magnetic field is significantly reduced by both the self inductances of the SQUIDs and the mutual inductances between them. Based on these results, we develop a computer simulation model from first principles which simultaneously solves the differential equations of the junctions in the array while considering the effects of self inductance, mutual inductance, and non-uniformity of junction critical currents. We find that our model can accurately predict V–B for all of the array geometries studied. A second experiment is performed where we use photolithography and ion milling to split another 28 × 565 junction array into 6 decoupled arrays to further investigate mutual interactions between adjacent SQUIDs. This work conclusively shows that the magnetic fields generated by self currents in an incommensurate array severely reduce its performance by reducing the maximum obtainable modulation voltage.

A model is developed to investigate the effects of mutual inductance on the voltage-field (V -B) characteristics of two-dimensional arrays of Josephson junctions. The V -B characteristics were numerically simulated for arrays with and without mutual inductance contributions. We find mutual inductances can have a strong impact on the voltage response of SQUID arrays and mutual inductance contributions from nearest neighboring SQUIDs only do not represent a good approximation.