A formal presentation and comparative study of low-frequency noise reduction techniques for direct current superconducting quantum interference devices

We present a comparative study of existing low-frequency noise reduction techniques for dc superconducting quantum interference devices (SQUIDS). These methods are essential to applications involving high-Tc SQUIDS because they dramatically reduce the 1/f noise to useful low-frequency noise levels. We propose a formal presentation of the problem and explain mathematically the working principles of these noise reductions methods, particularly for fluctuations arising from the critical current of the junctions. An increase in the white noise level is generally observed when a sinusoidal lock-in detection is used for these methods and we give here a mathematical explanation for this peculiar effect. Finally, noise measurements made on high-Tc grain boundary dc SQUIDS are presented; the experimental results are in close agreement with theory.