A superconducting quantum interference devices (SQUID) comprises a superconducting inductive loop with at least two Josephson junction, whereby a magnetic flux coupled into the inductive loop produces a modulated response up through radio frequencies. Series and parallel arrays of SQUIDs can increase the dynamic range, output, and linearity, while maintaining bandwidth. Several approaches to achieving a linear triangle-wave transfer function are presented, including harmonic superposition of SQUID cells, differential serial arrays with magnetic frustration, and a novel bi-SQUID cell comprised of a nonlinear Josephson inductance shunting the linear coupling inductance. Total harmonic distortion of less than −120 dB can be achieved in optimum cases.