Effect of damping resistance on voltage versus flux relation of a dc SQUID with large inductance and critical current

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 β_L=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 β_L in the case of large damping. As a result, the conversion efficiency dV/dφ is not degraded even for large β_L, as is not the case with a conventional SQUID without the damping resistance. This result indicates the possibility to use the SQUID with large β_L 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 β_c≳0.4, where β_c is the McCumber parameter; for example, at β_c=1 the conversion efficiency becomes about 30% of that at β_c=0. These analytical results are in good agreement with numerical-simulation ones.