Analytical calculation of theI-Vcharacteristics of SQUIDs with parasitic elements

Abstract

An approximate analytical calculation of the current-voltage characteristics of SQUIDs with parasitic capacitances and inductances is presented. The analytical treatment of the I -V curves is based on the approximation of harmonic signals. For bias currents I B > 1.5 I 0 (critical current of the SQUID) the approximated and the numerically calculated I -V curves are in very good agreement. From the analytical treatment of the characteristics we have derived analytical formulae for three voltages, where there is no flux modulation at the I -V characteristic. The comparison of numerically calculated and experimental characteristics shows that the equation of the upper point without flux modulation of the I -V curves is suitable for calculating parameters such as inductances and capacitances of SQUIDs with parasitic elements.