Abstract
Direct-current superconducting quantum interference devices (dc SQUIDs) are ultra-sensitive flux-to-voltage convertors widely applied for biomagnetism and geophysics; they are a kind of magnetic-field-effect transistors (MFETs) with flux-modulated current-voltage characteristics. Compared to semiconductor FETs, dc SQUIDs still lack analytical expressions to interpret their inner formation mechanisms of the current-voltage characteristics. This article presents a frequency-phase-locking (FPL) model to derive the analytical expression of dc SQUIDs and reveal how the current-voltage characteristics are shaped by the circuit parameters between two Josephson junctions. The application of the analytical expression in the calculations of current-voltage characteristics is demonstrated; the results are compared with the numerical simulations. It is shown that a dc-SQUID is an FPL system inside and works as a current-modified nonlinear resistor in readout circuits; its current-voltage characteristics are the projections of three impedances of the network between Josephson currents. Those understandings enable electronic engineers to evaluate the design of dc-SQUID circuits directly through three network impedances extracted from the layout.
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