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Journal of Applied Physics

Multitone quantum simulations of saturating tunnel junction mixers

S. Withington, Phichet Kittara, G. Yassin

Published Jun 6, 2003• 15 citations
Publisher

Abstract

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.

DOI
10.1063/1.1576515

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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.
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 Quantum Theory of Mixing developed by Tucker provides a solid framework for understanding the behaviour of SIS mixers, and subsequent developments allow the simulation of complete mixer circuits. These methods operate, however, under the assumption of small signal levels, and so neglect the non-linear behaviour of the signal path. The non-linearity of the mixer's response to applied signals is of vital importance to the calibration of SIS receiver systems. We have previously reported a procedure for calculating the full quantum behaviour of tunnel junction circuits under multiple high-level signals, allowing the accurate prediction of the saturation characteristics of SIS mixers. In this paper, we apply our procedure to both an idealized SIS mixer and one of our previously tested 700 GHz finline mixers. We find that the small signal behaviour predicted by our procedure agrees well with other simulation methods, and that the saturation properties of both of these mixers differ from that predicted by previous estimates of saturation behaviour.
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.
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.>
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.