Operating Point and Flux Jumps of a SQUID in Flux-Locked Loop

A superconducting quantum interference device (SQUID) is a transducer with a nonlinear flux-to-voltage transfer function. This transfer function is periodic due to the quantization of the magnetic flux in a weakly connected superconducting loop. Thus, a SQUID is usually used operating in a flux-locked loop (FLL) to linearize its response. However, the periodicity of the SQUID transfer function introduces a multiplicity of allowed operating points, in FLL, for given input and output values. Furthermore, this periodicity in the open loop implies that the FLL feedback could be positive or negative, depending on the operating point. To improve the stability and linearization provided by the FLL, it is crucial to be able to determine the operating point of a SQUID in an FLL. Based on simple control considerations applied to this specific periodic system, we discuss a way to understand the FLL operating point. Measurements and simulations illustrate the point. The dynamic range of the FLL and shape with flux jumps in the flux-to-voltage transfer function is also discussed.