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

An overview of superconducting nonlinear-circuit simulation

S. Withington, Philippa R Kennedy

Published Oct 24, 1989• 0 citations
OpenAlex

Abstract

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. >

Related papers

Nonlinear modelling of superconducting devices and circuits

S. Withington, Philippa R Kennedy

Recent progress in the development of techniques for fabricating high-quality superconducting components, together with major advances in the theoretical understanding of quantum detection and mixing at millimetre and submillimetre wavelengths, have made the development of CAD tools for superconducting nonlinear circuits an important and exciting challenge. As a first step towards developing general purpose CAD techniques, the authors have devised algorithms, and written, in the C programming language, modular software for analysing the large-signal, small-signal and noise behaviour of quasiparticle tunnel-junction circuits. At present, they are using the software to study the complex behaviour of SIS mixers, however, the software can also be used for studying other modes of operation, and other tunnelling structures for which macroscopic quantum effects are important. >

•Jun 25, 1990•1 citation

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

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

Fast Harmonic Balance of SIS Mixers with Multiple Junctions and Superconducting Circuits

F. Rice, John S. Ward, Jonas Stasys Zmuidzinas +1 more

We have extended the spectral domain harmonic balance method of Withington and Kollberg [1] to handle quasiparticle mixer circuits of arbitrary complexity containing any number of superconducting tunnel junctions. Our algorithm uses a multidimensional Newton-Raphson technique to achieve rapid convergence, even when many harmonics are included in the analysis. Another improvement is to perform all linear circuit calculations using the scattering matrix representation typical of modern circuit modeling techniques. This algorithm has been implemented as part of an extensive C++ class library for modeling the signal and noise performance of superconducting heterodyne receivers (SuperMix). Using the common, free C++ compiler "g++" (Free Software Foundation), impressive results can be achieved on modern workstations of moderate capability. Such speeds will make complex nonlinear optimization calculations a routine part of SIS receiver design.

•Mar 1, 1999•12 citations

Non-linear two-frequency analysis of SIS mixers through harmonic balance

S. Withington, Phichet Kittara, G. Yassin

We present a numerical procedure for simulating the non-linear behaviour of Superconductor-Insulator-Superconductor (SIS) tunnel-junction mixers. Mixers of this kind are used extensively in high-performance submillimetre-wave astronomical receivers. The procedure is complete in that both the signal and local-oscillator voltages can be at high levels, with significant amounts of harmonic content; also, the full quantum mechanical behaviour of the tunnel junction is taken into account. The initial simulations show that multi-tone analysis can be carried out in a numerically efficient manner, and that saturation, and the attendant generation of IF harmonics, can be modelled rigorously. This work constitutes the first full non-linear model of an SIS mixer, and the theoretical and numerical procedures described, will be of great importance when designing the next generation of heterodyne astronomical receivers.

Journal de Physique IV (Proceedings)•May 1, 2002•1 citation

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

S. Withington, P. Kennedy

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.

IEE Proceedings G Circuits Devices and Systems•Jan 1, 1991•12 citations
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. >
Recent progress in the development of techniques for fabricating high-quality superconducting components, together with major advances in the theoretical understanding of quantum detection and mixing at millimetre and submillimetre wavelengths, have made the development of CAD tools for superconducting nonlinear circuits an important and exciting challenge. As a first step towards developing general purpose CAD techniques, the authors have devised algorithms, and written, in the C programming language, modular software for analysing the large-signal, small-signal and noise behaviour of quasiparticle tunnel-junction circuits. At present, they are using the software to study the complex behaviour of SIS mixers, however, the software can also be used for studying other modes of operation, and other tunnelling structures for which macroscopic quantum effects are important. >
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.
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.
We have extended the spectral domain harmonic balance method of Withington and Kollberg [1] to handle quasiparticle mixer circuits of arbitrary complexity containing any number of superconducting tunnel junctions. Our algorithm uses a multidimensional Newton-Raphson technique to achieve rapid convergence, even when many harmonics are included in the analysis. Another improvement is to perform all linear circuit calculations using the scattering matrix representation typical of modern circuit modeling techniques. This algorithm has been implemented as part of an extensive C++ class library for modeling the signal and noise performance of superconducting heterodyne receivers (SuperMix). Using the common, free C++ compiler "g++" (Free Software Foundation), impressive results can be achieved on modern workstations of moderate capability. Such speeds will make complex nonlinear optimization calculations a routine part of SIS receiver design.
We present a numerical procedure for simulating the non-linear behaviour of Superconductor-Insulator-Superconductor (SIS) tunnel-junction mixers. Mixers of this kind are used extensively in high-performance submillimetre-wave astronomical receivers. The procedure is complete in that both the signal and local-oscillator voltages can be at high levels, with significant amounts of harmonic content; also, the full quantum mechanical behaviour of the tunnel junction is taken into account. The initial simulations show that multi-tone analysis can be carried out in a numerically efficient manner, and that saturation, and the attendant generation of IF harmonics, can be modelled rigorously. This work constitutes the first full non-linear model of an SIS mixer, and the theoretical and numerical procedures described, will be of great importance when designing the next generation of heterodyne astronomical receivers.
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.