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.

Strongly coupled, low noise dc-SQUID amplifiers

“…3.4(f) and (g). Nevertheless, the optimum working range of both additional noise and minimum noise temperature is found at much higher voltages [85][86][87], see the dashed line in the range β L > 1 of Fig. 3.5(a).…”

“…Because of the higher operation voltage of this design, the noise in the optimum working range of the shunted SQUID might be degraded compared to the non-shunted SQUID with the same β L and β C . Nevertheless, for high inductance SQUIDs β L > 1 a damping resistance in the order of γ = 0.5 can be recommended [86].…”

“…Here, the SQUID inductance L SQ is connected to a parallel resistance. This design has some interesting properties [85][86][87]. Besides possibly damping resonances, it also allows to improve the performance of sub-optimal SQUIDs with β L 1.…”

“…1.3 on page 7. On the other hand, we also included SQUID with a resistively shunted inductance [85][86][87], which is often used in practice, see section 1.4.1 on page 12. Both cases can be described by the schematic shown in Fig.…”

“…Thirdly, we performed one series of simulations without the damping resistance (γ = 0) and one with the optimum value γ = 0.5 given in literature [86,102].…”