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

IEE Proceedings G Circuits Devices and Systems

Numerical procedure for simulating the large-signal quantum behaviour of superconducting tunnel-junction circuits

S. Withington, P. Kennedy

Published Jan 1, 1991• 12 citations
Publisher

Abstract

The paper describes a numerical procedure for simulating, in the frequency domain, the large-signal quantum behaviour of superconducting tunnel-junction circuits. It is shown that the steady-state dynamics of a circuit can be decomposed by using the method of harmonic balance, and that the resulting system of coupled nonlinear algebraic equations can be solved through harmonic Newton. The presentation is generalised in a number of ways: first, the scheme is described in terms of a generic circuit comprising a tunnel junction and a Thevenin voltage source; secondly, the circuit equations are normalised to the gap voltage and the gap current of the tunnel barrier; and thirdly, an imperfect junction is modelled by convolving an ideal BCS current/voltage characteristic with a Gaussian function.

DOI
10.1049/ip-g-2.1991.0014

Related papers

CAD of Superconducting Nonlinear Circuits

S. Withington, P. R. Ke

The paper summarises preliminary work on the development of a general-purpose superconducting nonlinear-circuit simulator. After contrasting, from a CAD perspective, time and frequency domain descriptions of the macroscopic quantum behaviour of superconducting tunnel junctions, it is reported that the large-signal steady-state dynamics of a tunnel-junction circuit can be conmpletely decomposed by using the method of harmonic balance, and that the resulting system of coupled nonlinear algebraic equations can be solved through harmonic Newton. The principle is illustrated by briefly mentioning an analysis of inadvertent harmonic pumping in quasiparticle mixers.

European Microwave Conference (EuMC)•Oct 1, 1990•0 citations

An overview of superconducting nonlinear-circuit simulation

S. Withington, Philippa R Kennedy

To assist the development of superconducting millimetre and submillimetre-wave receivers, the authors have devised algorithms and written in the C programming language modular software for analysing the small-signal, large-signal and noise behaviour of SIS tunnel-junction circuits. Typical applications include the modelling of mixers, subharmonic mixers and direct detectors. To analyse the complex behaviour of a nonlinear SIS tunnel-junction circuit, it is first necessary to model the large-signal steady-state dynamics of the circuit; the underlying system of equations can then be perturbed, either numerically or analytically, to gain information about the linear relationships between signal and noise variables. A general-purpose simulator must therefore be capable of solving large systems of coupled nonlinear equations. >

•Oct 24, 1989•0 citations

Spectral-domain analysis of harmonic effects in superconducting quasiparticle mixers

S. Withington, E. Kollberg

An algorithm was developed for calculating the harmonic performance of superconducting quasiparticle millimeter-wave mixers. The scheme uses harmonic balance to determine the steady-state waveform of the large-amplitude voltage which is induced across the tunnel junction by the local oscillator source. A key feature of the algorithm is that the large-signal tunneling-current calculations are done in the frequency domain rather than in the time domain, and this approach leads to numerically efficient computer simulations. The superiority of the spectral-domain method is particularly pronounced when modeling mixers that incorporate high-quality tunnel junctions with very sharp DC nonlinearities. A simplified mixer simulation was performed to determine the range of omega CR products for which harmonic effects are likely to be important.>

IEEE Transactions on Microwave Theory and Techniques•Jan 1, 1989•33 citations

Simulation of the superconducting quasiparticle mixer using a five-port model

Edward Tong, R. Blundell

A harmonic Newton technique has successfully been used in the simulation of superconducting quasiparticle mixers in a five-port model. The steady-state large-signal waveform impressed across the tunnel junction by the incident local oscillator (LO) power is computed in the frequency domain. The three-frequency approximation provides the initial trial solution, which, together with the superlinear convergence property of Newton's method, ensures rapid convergence. A wide range of simulations based on the response function of a real superconductor-insulator-superconductor (SIS) junction is presented. The case of an SIS harmonic mixer (n=2) is also studied. Using a five-port model, the simulation explicitly takes the effect of the first harmonic into account. The algorithm and the principal results obtained for a hypothetical mixer incorporating the measured current-voltage characteristics of a real (SIS) junction are presented. The first results indicate that harmonic quasiparticle mixing may be very attractive in the submillimeter-wave band.>

IEEE Transactions on Microwave Theory and Techniques•Jan 1, 1990•15 citations

CAD techniques for superconducting millimetre and submillimetre-wave circuits

S. Withington

Over the last few years, considerable progress has been made in the development of techniques for fabricating high-quality superconducting circuits, and this success, together with major advances in the theoretical understanding of quantum detection and mixing at millimetre and submillimetre wavelengths, has made the production of CAD tools for superconducting nonlinear circuits an important new enterprise. A further motivation for modelling the behaviour of superconducting nonlinear circuits is that there is a range of circuits whose characteristics have not been studied in any detail. To model the behaviour of a quasiparticle mixer, it is first necessary to simulate the large-signal steady-state dynamics of the local-oscillator circuit. Once the large-signal operating point is known, it is then possible to perturb, either numerically or analytically, the underlying system of equations to gain information about the linear relationships between signal and noise variables. Clearly, if the simulator is to support advanced CAD facilities such as optimization, then it must be capable of calculating the large-signal behaviour of superconducting tunnel junctions efficiently.

•Oct 15, 1991•0 citations

Multitone quantum simulations of saturating tunnel junction mixers

S. Withington, Phichet Kittara, G. Yassin

When designing instruments for submillimeter-wave astronomy it is important to understand precisely how saturating superconducting tunnel-junction mixers behave. In this article, a procedure is described for calculating the behavior of tunnel-junction circuits when multitone high-level signals are applied. The procedure is based on a full quantum-mechanical description of photon-assisted tunneling, and uses Harmonic Newton to search for a set of voltages and currents that satisfy the circuit equations at every frequency present. A number of illustrative simulations are presented, and it is shown that Harmonic Newton can be used to model saturating superconductor–insulator–superconductor mixers in a robust and numerically efficient manner.

Journal of Applied Physics•Jun 6, 2003•15 citations
The paper describes a numerical procedure for simulating, in the frequency domain, the large-signal quantum behaviour of superconducting tunnel-junction circuits. It is shown that the steady-state dynamics of a circuit can be decomposed by using the method of harmonic balance, and that the resulting system of coupled nonlinear algebraic equations can be solved through harmonic Newton. The presentation is generalised in a number of ways: first, the scheme is described in terms of a generic circuit comprising a tunnel junction and a Thevenin voltage source; secondly, the circuit equations are normalised to the gap voltage and the gap current of the tunnel barrier; and thirdly, an imperfect junction is modelled by convolving an ideal BCS current/voltage characteristic with a Gaussian function.
The paper summarises preliminary work on the development of a general-purpose superconducting nonlinear-circuit simulator. After contrasting, from a CAD perspective, time and frequency domain descriptions of the macroscopic quantum behaviour of superconducting tunnel junctions, it is reported that the large-signal steady-state dynamics of a tunnel-junction circuit can be conmpletely decomposed by using the method of harmonic balance, and that the resulting system of coupled nonlinear algebraic equations can be solved through harmonic Newton. The principle is illustrated by briefly mentioning an analysis of inadvertent harmonic pumping in quasiparticle mixers.
To assist the development of superconducting millimetre and submillimetre-wave receivers, the authors have devised algorithms and written in the C programming language modular software for analysing the small-signal, large-signal and noise behaviour of SIS tunnel-junction circuits. Typical applications include the modelling of mixers, subharmonic mixers and direct detectors. To analyse the complex behaviour of a nonlinear SIS tunnel-junction circuit, it is first necessary to model the large-signal steady-state dynamics of the circuit; the underlying system of equations can then be perturbed, either numerically or analytically, to gain information about the linear relationships between signal and noise variables. A general-purpose simulator must therefore be capable of solving large systems of coupled nonlinear equations. >
An algorithm was developed for calculating the harmonic performance of superconducting quasiparticle millimeter-wave mixers. The scheme uses harmonic balance to determine the steady-state waveform of the large-amplitude voltage which is induced across the tunnel junction by the local oscillator source. A key feature of the algorithm is that the large-signal tunneling-current calculations are done in the frequency domain rather than in the time domain, and this approach leads to numerically efficient computer simulations. The superiority of the spectral-domain method is particularly pronounced when modeling mixers that incorporate high-quality tunnel junctions with very sharp DC nonlinearities. A simplified mixer simulation was performed to determine the range of omega CR products for which harmonic effects are likely to be important.>
A harmonic Newton technique has successfully been used in the simulation of superconducting quasiparticle mixers in a five-port model. The steady-state large-signal waveform impressed across the tunnel junction by the incident local oscillator (LO) power is computed in the frequency domain. The three-frequency approximation provides the initial trial solution, which, together with the superlinear convergence property of Newton's method, ensures rapid convergence. A wide range of simulations based on the response function of a real superconductor-insulator-superconductor (SIS) junction is presented. The case of an SIS harmonic mixer (n=2) is also studied. Using a five-port model, the simulation explicitly takes the effect of the first harmonic into account. The algorithm and the principal results obtained for a hypothetical mixer incorporating the measured current-voltage characteristics of a real (SIS) junction are presented. The first results indicate that harmonic quasiparticle mixing may be very attractive in the submillimeter-wave band.>
Over the last few years, considerable progress has been made in the development of techniques for fabricating high-quality superconducting circuits, and this success, together with major advances in the theoretical understanding of quantum detection and mixing at millimetre and submillimetre wavelengths, has made the production of CAD tools for superconducting nonlinear circuits an important new enterprise. A further motivation for modelling the behaviour of superconducting nonlinear circuits is that there is a range of circuits whose characteristics have not been studied in any detail. To model the behaviour of a quasiparticle mixer, it is first necessary to simulate the large-signal steady-state dynamics of the local-oscillator circuit. Once the large-signal operating point is known, it is then possible to perturb, either numerically or analytically, the underlying system of equations to gain information about the linear relationships between signal and noise variables. Clearly, if the simulator is to support advanced CAD facilities such as optimization, then it must be capable of calculating the large-signal behaviour of superconducting tunnel junctions efficiently.
When designing instruments for submillimeter-wave astronomy it is important to understand precisely how saturating superconducting tunnel-junction mixers behave. In this article, a procedure is described for calculating the behavior of tunnel-junction circuits when multitone high-level signals are applied. The procedure is based on a full quantum-mechanical description of photon-assisted tunneling, and uses Harmonic Newton to search for a set of voltages and currents that satisfy the circuit equations at every frequency present. A number of illustrative simulations are presented, and it is shown that Harmonic Newton can be used to model saturating superconductor–insulator–superconductor mixers in a robust and numerically efficient manner.