### Abstract

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}=2LI_{0}/φ_{0}, where L is a loop inductance, I_{0} is a critical current, and φ_{0} 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.

Original language | English |
---|---|

Pages (from-to) | 1691-1697 |

Number of pages | 7 |

Journal | Journal of Applied Physics |

Volume | 57 |

Issue number | 5 |

DOIs | |

Publication status | Published - Dec 1 1985 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Journal of Applied Physics*,

*57*(5), 1691-1697. https://doi.org/10.1063/1.334439

**Effect of damping resistance on voltage versus flux relation of a dc SQUID with large inductance and critical current.** / Enpuku, Keiji; Sueoka, K.; Yoshida, K.; Irie, F.

Research output: Contribution to journal › Review article

*Journal of Applied Physics*, vol. 57, no. 5, pp. 1691-1697. https://doi.org/10.1063/1.334439

}

TY - JOUR

T1 - Effect of damping resistance on voltage versus flux relation of a dc SQUID with large inductance and critical current

AU - Enpuku, Keiji

AU - Sueoka, K.

AU - Yoshida, K.

AU - Irie, F.

PY - 1985/12/1

Y1 - 1985/12/1

N2 - 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.

AB - 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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U2 - 10.1063/1.334439

DO - 10.1063/1.334439

M3 - Review article

VL - 57

SP - 1691

EP - 1697

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 5

ER -