Analytical calculation of the I-V characteristics of SQUIDs with parasitic elements

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 IB>1.5 I0 (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. (author)