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.
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.
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.
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.
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.>
Over the last few years, considerable progress have 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 millimeter and submillimeter wavelengths, has made the development of CAD techniques for superconducting nonlinear circuits an important new enterprise. For example, arrays of quasioptical mixers are now being manufactured, where the antennas, matching networks, filters and superconducting tunnel junctions are all fabricated by depositing niobium and a variety of oxides on a single quartz substrate. There are no adjustable tuning elements on these integrated circuits, and therefore, one must be able to predict their electrical behavior precisely. This requirement, together with a general interest in the generic behavior of devices such as direct detectors and harmonic mixers, has lead us to develop a range of CAD tools for simulating the large-signal, small-signal, and noise behavior of superconducting tunnel junction circuits.