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

IEEE Transactions on Microwave Theory and Techniques

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

Edward Tong, R. Blundell

Published Jan 1, 1990• 15 citations
Publisher

Abstract

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.>

DOI
10.1109/22.58676

Related papers

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

Harmonic mixing in a superconducting tunnel junction

Edward Tong, Lawrence M. Chernin, R. Blundell

A theoretical analysis of harmonic mixing in a quasiparticle tunnel junction at Vbias=0 shows that harmonic mixing for submillimeter frequencies is a viable alternative to fundamental mixing. It is also shown that the signal gain from the first harmonic above the pump frequency to the intermediate frequency is independent of the embedding admittance at the pump frequency. In fact, we show that the five-port model reduces to the three-port model as a result of the inversion symmetry of the I-V curve and, moreover, no large-signal analysis is necessary. Full simulations of harmonic mixing using a five-port model confirm these results. The simulations have been done for the case of a superconductor-insulator-normal junction in which there is no pair current interference. For this type of harmonic mixer we show that the local oscillator (LO) power requirement can be less than a fundamental mixer operating at the same signal frequency, which is particularly useful in circumventing the problems of high-frequency LO power generation.

Journal of Applied Physics•Oct 15, 1990•8 citations

A general numerical analysis of the superconducting quasiparticle mixer

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

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.

IEEE Transactions on Magnetics•Mar 1, 1985•15 citations

Theoretical and numerical analysis of very high harmonic superconducting tunnel junction mixers

Phichet Kittara, S. Withington, G. Yassin

We describe a procedure for modeling the nonlinear, quantum-mechanical behavior of very high harmonic superconductor-insulator-superconductor (SIS) mixers. A typical mixer is pumped by a strong microwave source at 10–15GHz, which causes high-harmonic (20–40) currents to flow, any one of which can be used as a local oscillator to downconvert a submillimeter-wave signal to a low microwave frequency, 1–8GHz. This mode of operation is attractive for measuring the beam patterns of conventional SIS mixers, because only a single submillimeter-wave source is needed. We conducted simulations using the 20th harmonic of a 13.5GHz microwave source, downconverting a 271.4GHz signal to a 1.4GHz intermediate frequency. These simulations clearly show that linear downconversion can be achieved even for relatively high levels of rf signal power; although, care is needed when choosing the operating point. The patterns of behavior seen in the simulations are in remarkable agreement with recently published experimental results.

Journal of Applied Physics•Jan 15, 2007•14 citations

Simulating the Behavior of a 230-GHz SIS Mixer Using Multitone Spectral Domain Analysis

John Garrett, Boon-Kok Tan, Faouzi M. Boussaha +2 more

We present a new software package, called QMix, for simulating the behavior of superconductor/insulator/ superconductor (SIS) mixers. The software uses a harmonic balance procedure to calculate the ac voltage across the SIS junction and multitone spectral domain analysis to calculate the quasiparticle tunneling currents. This approach has two major advantages over other simulation techniques: 1) it can include an arbitrary number of higher order harmonics, and 2) it can simulate the effect of multiple strong nonharmonic frequencies. This allows the QMix software to simulate a wide range of SIS mixer operation, including the effects of harmonics in the local-oscillator (LO) signal and gain saturation with respect to the RF signal power. In this article, we compare the simulated results from QMix to the measured performance of a 230-GHz SIS device, both to validate the software and to investigate the experimental data. To begin, we simulated the conversion gain of the mixer and we found excellent agreement with the experimental results. We were also able to recreate the broken photon step effect by adding higher and lower order harmonics to the LO signal. We then simulated a range of incident RF signal powers in order to calculate the gain saturation point. This is an important metric for SIS mixers because we require linear gain for reliable measurements and calibration. In the simulated results, we found both gain compression and gain expansion, which is consistent with other studies. Overall, these examples demonstrate that QMix is a powerful software package that will allow researchers to simulate the performance of SIS mixers, investigate experimental results, and optimize mixer operation. We have made all of the QMix software open-source and we invite others to contribute to the project.

IEEE Transactions on Terahertz Science and Technology•Sep 2, 2019•2 citations

Investigation of the Harmonic Mixer and Low-Frequency Converter Regimes in a Superconducting Tunnel Junction

K. V. Kalashnikov, Anton A. Artanov, Gert J. de Lange +1 more

We experimentally investigate different mixing regi-mes in Nb/AlOx/Nb and Nb/AlN/NbN tunnel superconductor-insulator-superconductor (SIS) junctions. The SIS mixers were studied with regard to the following modes of operation: in an extremely low-frequency range (0.1-20 GHz) and as high harmonic mixers; n ≈ 20-30 at signal frequencies of about 500 GHz that requires high power of a local oscillator. The quasiparticle and Josephson mixing regimes have been compared. We demonstrate that, in some applications requiring high conversion efficiency, the Josephson regime can be more preferable than the quasiparticle regime due to a larger output signal and better signal-to-noise ratio. As an example of such an application, we consider the phase locking of a THz oscillator using a cryogenic harmonic phase detector, which only ought to realize all of its benefits under the Josephson mixing regime. In addition, we demonstrate that the presence of the Josephson effect results in considerable increase in conversion efficiency at the expense of the dynamic range decrease; it was measured for low-frequency up- and down-convertors, which are promising for cryogenic multiplexing systems.

IEEE Transactions on Applied Superconductivity•Feb 6, 2018•6 citations
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.>
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 theoretical analysis of harmonic mixing in a quasiparticle tunnel junction at Vbias=0 shows that harmonic mixing for submillimeter frequencies is a viable alternative to fundamental mixing. It is also shown that the signal gain from the first harmonic above the pump frequency to the intermediate frequency is independent of the embedding admittance at the pump frequency. In fact, we show that the five-port model reduces to the three-port model as a result of the inversion symmetry of the I-V curve and, moreover, no large-signal analysis is necessary. Full simulations of harmonic mixing using a five-port model confirm these results. The simulations have been done for the case of a superconductor-insulator-normal junction in which there is no pair current interference. For this type of harmonic mixer we show that the local oscillator (LO) power requirement can be less than a fundamental mixer operating at the same signal frequency, which is particularly useful in circumventing the problems of high-frequency LO power generation.
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.
We describe a procedure for modeling the nonlinear, quantum-mechanical behavior of very high harmonic superconductor-insulator-superconductor (SIS) mixers. A typical mixer is pumped by a strong microwave source at 10–15GHz, which causes high-harmonic (20–40) currents to flow, any one of which can be used as a local oscillator to downconvert a submillimeter-wave signal to a low microwave frequency, 1–8GHz. This mode of operation is attractive for measuring the beam patterns of conventional SIS mixers, because only a single submillimeter-wave source is needed. We conducted simulations using the 20th harmonic of a 13.5GHz microwave source, downconverting a 271.4GHz signal to a 1.4GHz intermediate frequency. These simulations clearly show that linear downconversion can be achieved even for relatively high levels of rf signal power; although, care is needed when choosing the operating point. The patterns of behavior seen in the simulations are in remarkable agreement with recently published experimental results.
We present a new software package, called QMix, for simulating the behavior of superconductor/insulator/ superconductor (SIS) mixers. The software uses a harmonic balance procedure to calculate the ac voltage across the SIS junction and multitone spectral domain analysis to calculate the quasiparticle tunneling currents. This approach has two major advantages over other simulation techniques: 1) it can include an arbitrary number of higher order harmonics, and 2) it can simulate the effect of multiple strong nonharmonic frequencies. This allows the QMix software to simulate a wide range of SIS mixer operation, including the effects of harmonics in the local-oscillator (LO) signal and gain saturation with respect to the RF signal power. In this article, we compare the simulated results from QMix to the measured performance of a 230-GHz SIS device, both to validate the software and to investigate the experimental data. To begin, we simulated the conversion gain of the mixer and we found excellent agreement with the experimental results. We were also able to recreate the broken photon step effect by adding higher and lower order harmonics to the LO signal. We then simulated a range of incident RF signal powers in order to calculate the gain saturation point. This is an important metric for SIS mixers because we require linear gain for reliable measurements and calibration. In the simulated results, we found both gain compression and gain expansion, which is consistent with other studies. Overall, these examples demonstrate that QMix is a powerful software package that will allow researchers to simulate the performance of SIS mixers, investigate experimental results, and optimize mixer operation. We have made all of the QMix software open-source and we invite others to contribute to the project.
We experimentally investigate different mixing regi-mes in Nb/AlOx/Nb and Nb/AlN/NbN tunnel superconductor-insulator-superconductor (SIS) junctions. The SIS mixers were studied with regard to the following modes of operation: in an extremely low-frequency range (0.1-20 GHz) and as high harmonic mixers; n ≈ 20-30 at signal frequencies of about 500 GHz that requires high power of a local oscillator. The quasiparticle and Josephson mixing regimes have been compared. We demonstrate that, in some applications requiring high conversion efficiency, the Josephson regime can be more preferable than the quasiparticle regime due to a larger output signal and better signal-to-noise ratio. As an example of such an application, we consider the phase locking of a THz oscillator using a cryogenic harmonic phase detector, which only ought to realize all of its benefits under the Josephson mixing regime. In addition, we demonstrate that the presence of the Josephson effect results in considerable increase in conversion efficiency at the expense of the dynamic range decrease; it was measured for low-frequency up- and down-convertors, which are promising for cryogenic multiplexing systems.