The effect of a damping resistance on the relation between a voltage V and a magnetic flux φ of a dc SQUID is studied theoretically for the case with a large SQUID parameter βL=2LI0/φ0, where L is a loop inductance, I0 is a critical current, and φ0 is the flux quantum. An approximate analytical expression for the V-φ relation is obtained by replacing the Josephson junctions with ac current generators. It is shown that the V-φ relation becomes almost independent of the value of βL in the case of large damping. As a result, the conversion efficiency dV/dφ is not degraded even for large βL, as is not the case with a conventional SQUID without the damping resistance. This result indicates the possibility to use the SQUID with large βL for the improvement of the coupling between the SQUID and the input coil without the degradation of the conversion efficiency. Effect of the capacitance is also studied. It is shown that the effect of the capacitance becomes remarkable for the case of βc≳0.4, where βc is the McCumber parameter; for example, at βc=1 the conversion efficiency becomes about 30% of that at βc=0. These analytical results are in good agreement with numerical-simulation ones.
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