Noise characteristics of a dc SQUID with a resistively shunted inductance. II. Optimum damping

Abstract

Effects of a damping resistance on noise characteristics of a dc SQUID are studied theoretically, where the damping resistance is in shunt with a loop inductance of the SQUID. An analytical expression for the energy resolution of the SQUID is obtained, with which the relation between the damping resistance and the energy resolution is studied in detail. It is shown that an optimum value of the damping resistance exists, which is determined by the tradeoff between the improvement of the transfer function and the additional noise due to the damping resistance. Optimum values of the damping resistance are about twice the shunt resistance of the SQUID and vary slightly with SQUID modulation parameter β. For optimum damping, the energy resolution is improved, compared with the case without the damping resistance. This means that the SQUID with large β can be used without significant degradation of the performance, i.e., the previous restriction of β=1 can be loosened. The analytical results agree quantitatively with numerical ones.