Simulation of Series Arrays of Superconducting Quantum Interference Devices

Abstract

The voltage as a function of applied magnetic field (V-B) was calculated for arrays of superconducting quantum interference devices (SQUIDs) connected in series. Comparisons were made between arrays of equal area SQUIDs and superconducting quantum interference filters (SQIFs). The areas for the SQIFs were varied exponentially, so that the V-B had a sharp minimum at zero field. We used equations for the dc SQUID based on resistively shunted junctions, with typical parameters for YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7 - δ</sub> ion damage Josephson junctions. The maximum transfer coefficient of the central minimum <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">VB</i> = (∂ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> /∂ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> of the SQIF decreases as the area range increases. We find that the equal area array is more robust to the effects of non-uniform junction critical currents than the SQIF, for the junction parameters and SQUID area distributions chosen. Furthermore, we find that slight variations (~5%) to the area due to fabrication irregularities have little effect on the central minimum of V-B for either device.