Frequency-phase-locking mechanism inside DC SQUIDs and the analytical expression of current-voltage characteristics

Direct-current superconducting quantum interference devices (dc SQUIDs) are ultra-sensitive flux-to-voltage convertors widely applied for biomagnetism and geophysics; they working as the magnetic-field-effect transistors (MFETs) their flux-modulated current-voltage characteristics. However, unlike semiconductor FETs, dc SQUIDs lack general analytical models expressions to interpret inner dynamics outside This work presents a frequency-phase-locking (FPL) model expression reveal how characteristics formed inside SQUIDs, quantitively decided by circuit parameters. The application of calculations is demonstrated; results compared with numerical simulations. It shown that dc-SQUID an FPL system current-modified nonlinear resistor outside; its mechanism projections three network impedances driven Josephson currents. Based on expression, can be simply treated resistors in practical applications; performance directly predicted evaluated according impedances.