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IEEE Transactions on Magnetics

A general numerical analysis of the superconducting quasiparticle mixer

R.G. Hicks, M. J. Feldman, Anthony R. Kerr

Published Mar 1, 1985• 15 citations
Publisher

Abstract

Virtually all analyses of the superconductor-insulator-superconductor (SIS) quasiparticle mixer have employed the quantum theory of mixing in its three-frequency approximate form. This approximation is valid only in the limit of very large junction capacitance. For finite capacitance, these analyses may be seriously in error. To remedy this, a computer program has been developed which uses the quantum theory of mixing in its most general form, treating the large-signal properties of the mixer in the time domain. The terminating impedances at the harmonics of the local oscillator frequency and their sidebands can be arbitrary. Using this analysis, the effect of finite junction capacitance on one SIS mixer's performance is described. This gives an insight into the range of validity of the three-frequency model.

DOI
10.1109/tmag.1985.1063715

Related papers

A general numerical analysis program for the superconducting quasiparticle mixer

R.G. Hicks, M. J. Feldman, Anthony R. Kerr

A user-oriented computer program SISCAP (SIS Computer Analysis Program) for analyzing SIS mixers is described. The program allows arbitrary impedance terminations to be specified at all LO harmonics and sideband frequencies. It is therefore able to treat a much more general class of SIS mixers than the widely used three-frequency analysis, for which the harmonics are assumed to be short-circuited. An additional program, GETCHI, provides the necessary input data to program SISCAP. The SISCAP program performs a nonlinear analysis to determine the SIS junction voltage waveform produced by the local oscillator. The quantum theory of mixing is used in its most general form, treating the large signal properties of the mixer in the time domain. A small signal linear analysis is then used to find the conversion loss and port impedances. The noise analysis includes thermal noise from the termination resistances and shot noise from the periodic LO current. Quantum noise is not considered. Many aspects of the program have been adequately verified and found accurate.

•Jul 1, 1986•3 citations

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

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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.>

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Embedding impedance approximations in the analysis of SIS mixers

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The adequacy of three approximations to J.R. Tucker's (1979) quantum theory of mixers is examined. They are: (i) the usual three-frequency approximation, which assumes a sinusoidal local oscillator (LO) voltage at the junction and a short-circuit at all frequencies above the upper sideband; (ii) a five-frequency approximation, which allows two LO voltage harmonics and five small-signal sidebands; and (iii) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS (superconductor-insulator-superconductor) mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R/sub N/C for the SIS junctions used. For omega R/sub NC/ values in the range 0.5-10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, giving results very close to those of the eight-harmonic solution, and should be suitable for much design work.>

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Influence of Josephson currents on superconductor-insulator-superconductor mixer performance

Daniel G. Jablonski, Mark W. Henneberger

Superconductor-insulator-superconductor (SIS) mixers are currently the lowest-noise devices available for mixing in the 26–110 GHz frequency range. However, a major source of noise is anticipated to be the increased effects of Josephson oscillations within the mixer as higher operating frequencies are achieved. Simulations have been done to demonstrate these effects. Results indicate that the commonly used three-port analysis is valid over a wide range of conditions, but that even minimal Josephson oscillations have a deleterious effect on mixer performance. The junction shunt capacitance, which serves to short out the Josephson oscillations, is thus an extremely important parameter. However, the characterization of the mixer in terms of an ‘‘ωRC’’ product appears to be an oversimplification. A more elaborate approach to mixer characterization is suggested.

Journal of Applied Physics•Nov 15, 1985•12 citations

SIS mixer research. Final technical report, 1 Feb 89-13 May 90

A. W. Lichtenberger, M.J. Feldman

Theoretica and experimental research has been conducted to elucidate the basic physics behind the properties of superconductor-insulator-superconductor (SIS) tunnel junction receiving devices. The properties of an SIS mixer using a slightly nonideal junction, with finite LO power, were determined by analytic expansion of the equations of the quantum theory of mixing. The resulting equations have a particularly simple form. The minimum noise temperature is controlled by the leakage current of the junction. Even the most nearly ideal junctions made today require a considerable LO for best sensitivity; nevertheless, even a comparatively large leakage current allows mixer noise to be only a small factor above the quantum limit. The saturation properties of SIS mixers subjected to broad-band thermal noise obey the equations derived for monochromatic saturating signals. The Josephson junction tuning inductor was analyzed with the conclusion that such a device is not feasible with present fabrication techniques. Computer calculations using synthetic SIS junction I-V characteristics predicted the performance of an optimized receiver over its entire operating frequency range. Many aspects of the operation of SIS mixers were clarified and unexpected new phenomena were predicted. A 'photon picture' interpretation of the quantum theory of mixing is in the early stages ofmore » development. Niobium nitride edge junctions with excellent current-voltage characteristics were fabricated using novel barrier formation processes. The role of surface damage in the quality of NbN edge junction electrical characteristics was investigated and unexpected results were obtained.« less

•Nov 1, 1990•0 citations

SIS Mixer Research

Arthur W. Lichtenberger, M. J. Feldman

Abstract : Theoretical and experimental research has been conducted to elucidate the basic physics behind the properties of superconductor-insulator-superconductor (SIS) tunnel junction receiving devices. The properties of an SIS mixer using a slightly nonideal junction, with finite LO power, were determined by analytic expansion of the equations of the quantum theory of mixing. The resulting equations have a particularly simple form. The minimum noise temperature is controlled by the leakage current of the junction. Even the most nearly ideal junctions made today require a considerable LO for best sensitivity; nevertheless, even a comparatively large leakage current allows mixer noise to be only a small factor above the quantum limit. The saturation properties of SIS mixers subjected to broad-band thermal noise obey the equations derived for monochromatic saturating signals. The Josephson junction tuning inductor was analyzed with the conclusion that such a device is not feasible with present fabrication techniques. Computer calculations using synthetic SIS junction I-V characteristics predicted the performance of an optimized receiver over its entire operating frequency range. Many aspects of the operation of SIS mixers were clarified and unexpected new phenomena were predicted. A 'photon picture' interpretation of the quantum theory of mixing is in the early stages of development. Niobium nitride edge junctions with excellent current-voltage characteristics were fabricated using novel barrier formation processes. The role of surface damage in the quality of NbN edge junction electrical characteristics was investigated and unexpected results were obtained.

Final Technical Report•Nov 1, 1990•0 citations
Virtually all analyses of the superconductor-insulator-superconductor (SIS) quasiparticle mixer have employed the quantum theory of mixing in its three-frequency approximate form. This approximation is valid only in the limit of very large junction capacitance. For finite capacitance, these analyses may be seriously in error. To remedy this, a computer program has been developed which uses the quantum theory of mixing in its most general form, treating the large-signal properties of the mixer in the time domain. The terminating impedances at the harmonics of the local oscillator frequency and their sidebands can be arbitrary. Using this analysis, the effect of finite junction capacitance on one SIS mixer's performance is described. This gives an insight into the range of validity of the three-frequency model.
A user-oriented computer program SISCAP (SIS Computer Analysis Program) for analyzing SIS mixers is described. The program allows arbitrary impedance terminations to be specified at all LO harmonics and sideband frequencies. It is therefore able to treat a much more general class of SIS mixers than the widely used three-frequency analysis, for which the harmonics are assumed to be short-circuited. An additional program, GETCHI, provides the necessary input data to program SISCAP. The SISCAP program performs a nonlinear analysis to determine the SIS junction voltage waveform produced by the local oscillator. The quantum theory of mixing is used in its most general form, treating the large signal properties of the mixer in the time domain. A small signal linear analysis is then used to find the conversion loss and port impedances. The noise analysis includes thermal noise from the termination resistances and shot noise from the periodic LO current. Quantum noise is not considered. Many aspects of the program have been adequately verified and found accurate.
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.>
The adequacy of three approximations to J.R. Tucker's (1979) quantum theory of mixers is examined. They are: (i) the usual three-frequency approximation, which assumes a sinusoidal local oscillator (LO) voltage at the junction and a short-circuit at all frequencies above the upper sideband; (ii) a five-frequency approximation, which allows two LO voltage harmonics and five small-signal sidebands; and (iii) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS (superconductor-insulator-superconductor) mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R/sub N/C for the SIS junctions used. For omega R/sub NC/ values in the range 0.5-10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, giving results very close to those of the eight-harmonic solution, and should be suitable for much design work.>
Superconductor-insulator-superconductor (SIS) mixers are currently the lowest-noise devices available for mixing in the 26–110 GHz frequency range. However, a major source of noise is anticipated to be the increased effects of Josephson oscillations within the mixer as higher operating frequencies are achieved. Simulations have been done to demonstrate these effects. Results indicate that the commonly used three-port analysis is valid over a wide range of conditions, but that even minimal Josephson oscillations have a deleterious effect on mixer performance. The junction shunt capacitance, which serves to short out the Josephson oscillations, is thus an extremely important parameter. However, the characterization of the mixer in terms of an ‘‘ωRC’’ product appears to be an oversimplification. A more elaborate approach to mixer characterization is suggested.
Theoretica and experimental research has been conducted to elucidate the basic physics behind the properties of superconductor-insulator-superconductor (SIS) tunnel junction receiving devices. The properties of an SIS mixer using a slightly nonideal junction, with finite LO power, were determined by analytic expansion of the equations of the quantum theory of mixing. The resulting equations have a particularly simple form. The minimum noise temperature is controlled by the leakage current of the junction. Even the most nearly ideal junctions made today require a considerable LO for best sensitivity; nevertheless, even a comparatively large leakage current allows mixer noise to be only a small factor above the quantum limit. The saturation properties of SIS mixers subjected to broad-band thermal noise obey the equations derived for monochromatic saturating signals. The Josephson junction tuning inductor was analyzed with the conclusion that such a device is not feasible with present fabrication techniques. Computer calculations using synthetic SIS junction I-V characteristics predicted the performance of an optimized receiver over its entire operating frequency range. Many aspects of the operation of SIS mixers were clarified and unexpected new phenomena were predicted. A 'photon picture' interpretation of the quantum theory of mixing is in the early stages ofmore » development. Niobium nitride edge junctions with excellent current-voltage characteristics were fabricated using novel barrier formation processes. The role of surface damage in the quality of NbN edge junction electrical characteristics was investigated and unexpected results were obtained.« less
Abstract : Theoretical and experimental research has been conducted to elucidate the basic physics behind the properties of superconductor-insulator-superconductor (SIS) tunnel junction receiving devices. The properties of an SIS mixer using a slightly nonideal junction, with finite LO power, were determined by analytic expansion of the equations of the quantum theory of mixing. The resulting equations have a particularly simple form. The minimum noise temperature is controlled by the leakage current of the junction. Even the most nearly ideal junctions made today require a considerable LO for best sensitivity; nevertheless, even a comparatively large leakage current allows mixer noise to be only a small factor above the quantum limit. The saturation properties of SIS mixers subjected to broad-band thermal noise obey the equations derived for monochromatic saturating signals. The Josephson junction tuning inductor was analyzed with the conclusion that such a device is not feasible with present fabrication techniques. Computer calculations using synthetic SIS junction I-V characteristics predicted the performance of an optimized receiver over its entire operating frequency range. Many aspects of the operation of SIS mixers were clarified and unexpected new phenomena were predicted. A 'photon picture' interpretation of the quantum theory of mixing is in the early stages of development. Niobium nitride edge junctions with excellent current-voltage characteristics were fabricated using novel barrier formation processes. The role of surface damage in the quality of NbN edge junction electrical characteristics was investigated and unexpected results were obtained.