Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Applied Physics

Voltage and current expressions for a two-junction superconducting interferometer

Robert L. Peterson, Donald G. McDonald

Published Feb 1, 1983• 29 citations
Publisher

Abstract

The average voltage and circulating current of a superconducting interferometer containing two Josephson junctions (a dc SQUID) are calculated analytically, in various approximations, as functions of bias current and applied magnetic field or control current. The results are useful in calculations of the noise characteristics of the dc SQUID, as well as in other applications.

DOI
10.1063/1.332026

Related papers

An analysis theory of symmetric dc SQUID driven by thermal noises

Ya Jia, W R Sun, J R Li

An analysis expression for the stationary probability distribution of the symmetric superconducting quantum interference device with two Josephson junctions (dc SQUID) driven by thermal noise is derived from two-dimensional Fokker–Planck equations where the potential condition is satisfied. The analytical formulae for SQUID characteristics, e.g. the circulating current, the current–voltage relationship and the transfer function, are obtained by using the probability distribution. The ‘ripple’ phenomenon of the circulating current versus the applied flux, the effects of thermal fluctuations on current–voltage relationship and the optimum operating condition of dc SQUID system are represented.

Superconductor Science and Technology•Feb 7, 2003•2 citations

Measurements of current noise in DC SQUIDS

John M. Martinis, John L. Clarke

The current noise circulating around the loop of a tunnel junction dc SQUID has been measured as a function of applied flux. The flux noise generated by this current was coupled via a superconducting transformer to a second dc SQUID that was used to measure the noise in a null-balancing configuration. The voltage noise across the SQUID was also measured, using a cooled LC-resonant circuit, and the correlation between the voltage and current noises was determined. The measured values of the noises are in good agreement with values obtained from an analog simulator.

IEEE Transactions on Magnetics•May 1, 1983•21 citations

Analysis of strong inductive coupling on SQUID systems

Claudia D. Tesche

A technique for the analysis of complex superconducting circuits containing one or more current biased inductively coupled Josephson junction interferometers is described. The equations of motion for the system are shown to separate into a set of non-linear junction equations relating the voltage drops across the junctions to the currents passing through the junctions, and a set of linear equations expressing the quantization of the fluxoid around the superconducting loops and the corresponding linear circuit equations for the normal loops. In many cases, the linear equations can be integrated, resulting in an effective elimination of the normal circuit loops from the problem. The circuit is thus reduced to that of an equivalent set of coupled SQUIDs whose device parameters are a function of the original circuit parameters and the inductive coupling strengths. The dc SQUID tuned linear amplifier is analyzed to display the method. As a result of this analysis, the optimal noise temperature of a tuned SQUID amplifier is derived as a function of the current and voltage noise spectral densities, Svand Sj, and forward transfer function, Vφ. The results obtained demonstrate that the behavior of the SQUID cannot be isolated from that of the rest of the circuit in the manner assumed in previous analyses. The existence of a quantum noise limit on the noise temperature of any phase preserving linear amplifier is used to infer that the noise figures must satisfy the constraint[(S_{v}/2LV_{\phi}^{2})(LS_{j}/2)-S_{vj}^{2}]^{1/2}>\hbarThe behavior of several simple circuits containing a pair of inductively coupled current biased interferometers is discussed to display the extension of the method to circuits containing more than one interferometer.

IEEE Transactions on Magnetics•May 1, 1983•12 citations

dc SQUID Microwave-Induced Characteristics and Magnetic Field Response, Derived Using the Stewart-McCumber Model

Seiichi Naitô

This paper describes the I-V characteristics (as a function of applied magnetic field) and magnetic field response of a dc SQUID which incorporates two weak-link Josephson junctions in a superconducting ring. These characteristics are derived by digital computer simulation, using the Stewart-McCumber model. The effects of asymmetry (dissimilarity between the junctions) on SQUID critical current I c, normal resistance R and capacitance C are also simulated. With microwave excitation applied, the Josephson oscillations of the dc SQUID are found to be “frequency-locked” to the applied microwave signal even when critical currents I c of the two junctions differed, Subharmonic voltage steps are obtained for a symmetric dc SQUID in a magnetic field even when the current-phase relationship is purely sinusoidal.

Japanese Journal of Applied Physics•Apr 1, 1985•3 citations

Dynamics of the DC-SQUID

Eshel Ben‐Jacob, Y. Imry

The dynamics of two inductively-coupled Josephson junctions, driven by a current source and by an external flux were studied. Approximate analytical arguments and numerical simulations were used. The various characteristics times of the DC-SQUID were systematically obtained as functions of the parameters of the junctions and the superconducting loop. We have studied the effects of the external magnetic field and quasiparticle conductance on the structure of the I-V characteristics. The transition times between the various branches of the I-V characteristics were calculated using approximate analytical arguments as well as numerical simulations. The results, both for the I-V characteristics and the transition times, were compared with existing experiments.

Journal of Applied Physics•Nov 1, 1981•29 citations

Stray capacitance effect in superconducting quantum interferometers

Roberto Leoni, P. Carelli, Vittorio Foglietti

The experimental results obtained with low noise dc superconducting quantum interference devices (dc-SQUIDs) are sometimes not well understood. In particular, when the critical current is high, very irregular voltage versus flux characteristics can be measured. On the other hand, when the critical current is low, the characteristics follow perfectly the resistively shunted junction model. We have studied the dynamics of a dc-SQUID in the presence of stray capacitance and shunting resistors imbalance. The equations describing a circuit model for this physical system are integrated numerically and the results are compared with voltage versus flux characteristics obtained from fabricated devices. We find that the theoretical analysis accounts very well for previously misunderstood experimental features of the dc-SQUID. This model can give more physical sense to the various regimes of behavior of the dc-SQUID giving more insight into the experimental results.

Journal of Applied Physics•Sep 1, 1988•6 citations
The average voltage and circulating current of a superconducting interferometer containing two Josephson junctions (a dc SQUID) are calculated analytically, in various approximations, as functions of bias current and applied magnetic field or control current. The results are useful in calculations of the noise characteristics of the dc SQUID, as well as in other applications.
An analysis expression for the stationary probability distribution of the symmetric superconducting quantum interference device with two Josephson junctions (dc SQUID) driven by thermal noise is derived from two-dimensional Fokker–Planck equations where the potential condition is satisfied. The analytical formulae for SQUID characteristics, e.g. the circulating current, the current–voltage relationship and the transfer function, are obtained by using the probability distribution. The ‘ripple’ phenomenon of the circulating current versus the applied flux, the effects of thermal fluctuations on current–voltage relationship and the optimum operating condition of dc SQUID system are represented.
The current noise circulating around the loop of a tunnel junction dc SQUID has been measured as a function of applied flux. The flux noise generated by this current was coupled via a superconducting transformer to a second dc SQUID that was used to measure the noise in a null-balancing configuration. The voltage noise across the SQUID was also measured, using a cooled LC-resonant circuit, and the correlation between the voltage and current noises was determined. The measured values of the noises are in good agreement with values obtained from an analog simulator.
A technique for the analysis of complex superconducting circuits containing one or more current biased inductively coupled Josephson junction interferometers is described. The equations of motion for the system are shown to separate into a set of non-linear junction equations relating the voltage drops across the junctions to the currents passing through the junctions, and a set of linear equations expressing the quantization of the fluxoid around the superconducting loops and the corresponding linear circuit equations for the normal loops. In many cases, the linear equations can be integrated, resulting in an effective elimination of the normal circuit loops from the problem. The circuit is thus reduced to that of an equivalent set of coupled SQUIDs whose device parameters are a function of the original circuit parameters and the inductive coupling strengths. The dc SQUID tuned linear amplifier is analyzed to display the method. As a result of this analysis, the optimal noise temperature of a tuned SQUID amplifier is derived as a function of the current and voltage noise spectral densities, Svand Sj, and forward transfer function, Vφ. The results obtained demonstrate that the behavior of the SQUID cannot be isolated from that of the rest of the circuit in the manner assumed in previous analyses. The existence of a quantum noise limit on the noise temperature of any phase preserving linear amplifier is used to infer that the noise figures must satisfy the constraint[(S_{v}/2LV_{\phi}^{2})(LS_{j}/2)-S_{vj}^{2}]^{1/2}>\hbarThe behavior of several simple circuits containing a pair of inductively coupled current biased interferometers is discussed to display the extension of the method to circuits containing more than one interferometer.
This paper describes the I-V characteristics (as a function of applied magnetic field) and magnetic field response of a dc SQUID which incorporates two weak-link Josephson junctions in a superconducting ring. These characteristics are derived by digital computer simulation, using the Stewart-McCumber model. The effects of asymmetry (dissimilarity between the junctions) on SQUID critical current I c, normal resistance R and capacitance C are also simulated. With microwave excitation applied, the Josephson oscillations of the dc SQUID are found to be “frequency-locked” to the applied microwave signal even when critical currents I c of the two junctions differed, Subharmonic voltage steps are obtained for a symmetric dc SQUID in a magnetic field even when the current-phase relationship is purely sinusoidal.
The dynamics of two inductively-coupled Josephson junctions, driven by a current source and by an external flux were studied. Approximate analytical arguments and numerical simulations were used. The various characteristics times of the DC-SQUID were systematically obtained as functions of the parameters of the junctions and the superconducting loop. We have studied the effects of the external magnetic field and quasiparticle conductance on the structure of the I-V characteristics. The transition times between the various branches of the I-V characteristics were calculated using approximate analytical arguments as well as numerical simulations. The results, both for the I-V characteristics and the transition times, were compared with existing experiments.
The experimental results obtained with low noise dc superconducting quantum interference devices (dc-SQUIDs) are sometimes not well understood. In particular, when the critical current is high, very irregular voltage versus flux characteristics can be measured. On the other hand, when the critical current is low, the characteristics follow perfectly the resistively shunted junction model. We have studied the dynamics of a dc-SQUID in the presence of stray capacitance and shunting resistors imbalance. The equations describing a circuit model for this physical system are integrated numerically and the results are compared with voltage versus flux characteristics obtained from fabricated devices. We find that the theoretical analysis accounts very well for previously misunderstood experimental features of the dc-SQUID. This model can give more physical sense to the various regimes of behavior of the dc-SQUID giving more insight into the experimental results.