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IEEE Transactions on Terahertz Science and Technology

A Nonlinear Transmission Line Model for Simulating Distributed SIS Frequency Multipliers

John Garrett, Hawal Rashid, G. Yassin, Vincent Desmaris, Alexey Pavolotsky, Victor Y. Belitsky

Published Mar 30, 2020• 2 citations
Publisher

Abstract

Superconductor/insulator/superconductor (SIS) jun-ctions have extremely nonlinear electrical properties, which makes them ideal for a variety of applications, including heterodyne mixing and frequency multiplication. With SIS mixers, the SIS junctions normally have circular cross sections, but they can also be fabricated in the form of microstrip transmission lines, known as distributed SIS junctions (DSJs). By using a DSJ as an open-circuit stub, it is possible to create a large SIS junction with a low effective input reactance. This is beneficial for SIS frequency multipliers because their output power is proportional to the area of the junction. It is challenging, however, to simulate the behavior of DSJs because they have to be modeled as transmission lines and the model has to take into account the quasiparticle tunneling current, which is a nonlinear function of the ac voltage. In this article, we present a new nonlinear transmission line model to accurately describe the behavior of DSJs and to simulate the performance of distributed SIS frequency multipliers (DSMs). This model is compared to experimental data from a recent DSM device and good agreement is found between the dc tunneling currents and the output powers at the second harmonic. Based on this success, an improved DSM design is proposed that has a higher output power and a higher conversion efficiency than previous designs.

DOI
10.1109/tthz.2020.2979125

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Superconductor/insulator/superconductor (SIS) jun-ctions have extremely nonlinear electrical properties, which makes them ideal for a variety of applications, including heterodyne mixing and frequency multiplication. With SIS mixers, the SIS junctions normally have circular cross sections, but they can also be fabricated in the form of microstrip transmission lines, known as distributed SIS junctions (DSJs). By using a DSJ as an open-circuit stub, it is possible to create a large SIS junction with a low effective input reactance. This is beneficial for SIS frequency multipliers because their output power is proportional to the area of the junction. It is challenging, however, to simulate the behavior of DSJs because they have to be modeled as transmission lines and the model has to take into account the quasiparticle tunneling current, which is a nonlinear function of the ac voltage. In this article, we present a new nonlinear transmission line model to accurately describe the behavior of DSJs and to simulate the performance of distributed SIS frequency multipliers (DSMs). This model is compared to experimental data from a recent DSM device and good agreement is found between the dc tunneling currents and the output powers at the second harmonic. Based on this success, an improved DSM design is proposed that has a higher output power and a higher conversion efficiency than previous designs.
In this paper, we present the analysis, design, and characterization of the first frequency multiplier using distributed superconductor-insulator-superconductor (SIS) junctions. We derived analytical expressions describing the properties of the distributed SIS junction as a frequency multiplier. The modeling of the distributed SIS junctions shows that high conversion efficiency can be achieved when used as the multiplier. The measured output power generated by such multiplier employing the distributed SIS junction at the second harmonic of the input frequency is in good agreement with the model. Furthermore, the frequency multiplier based on the distributed SIS junction for the first time was able to pump an SIS mixer. The multiplication efficiency of the distributed SIS junction is 15-30% for a fractional bandwidth of 10% with excellent spectral line purity. The -3 dB line width of the multiplied signal is 1 Hz, which was limited by the resolution bandwidth of the spectrum analyzer. The results attained in this paper show that the distributed SIS junction frequency multiplier has considerable future potential, and could possibly be used in LO source in single-end and multipixel SIS mixer receivers.
We report the experimental study of the off-chip detection of frequency multiplication in a distributed array of Superconductor-Insulator-Superconductor (SIS) junctions. A test device consisting of a series array consisting sixty eight Nb/Al-AlOx/Nb tunnel junctions was designed for this study, and was fabricated using in-house Nb thin-film technology. The test device with SIS array was optimized for the study of second harmonic generation in 182−192 GHz output frequency band. The SIS array was exited with microwave radiation at 3 mm band using a quasi-optically coupled Gunn oscillator and the output response of the device was studied using a double sideband SIS mixer operating in 163 − 211 GHz range with 4−8 GHz. The Josephson-effect for both the SIS multiplier and the detector mixer was carefully suppressed using magnetic field. We observed very sharp second harmonic spectral signals, due to frequency multiplication by the SIS array. We also observed distinct multi-photon process in the SIS array tunnel junction response to the applied microwave signal, and the amplitude of the multiplied signal shows dependence on the bias voltage of the SIS array. We observed that the output power of the multiplied signal increases linearly with the power of the pumping signal up to certain level and them saturates. Increasing the input power beyond this level results in the heating of the chip. When the output of the test device was connected to the LO port of the SIS-mixer, an increase of 10 − 20% in the SIS -mixer dark current was observed when the SIS mixer was voltage biased in the middle of first photon step below the gap voltage. The device, although far from providing sufficient power to pump a practical SIS mixer, may be considered as a first experimental step towards SIS frequency multipliers.
This thesis focuses on the development of advanced components for the future wideband side band separating and / or multipixel receivers for radio-astronomy with ultimate sensitivity.\nIn this thesis, a novel frequency multiplier based on distributed superconducting tunnel (SIS) junctions has been demonstrated for the first time, taking advantage of the extreme inherent nonlinearity of such device. This practical demonstration is the result of an extensive theoretical exploration and modelling, showing the importance of the reactive quasi-particle tunnel current\nand its impact on the SIS tunnel junction frequency multiplier. In addition, a novel technique\nwas suggested that allows for the first time direct measurement of the reactive quasi-particle tunnel current.\nThis work comprehends the analysis, design and characterisation of the first frequency multiplier using distributed SIS junctions. The measured output power generated by the distributed SIS junction at the second harmonic of the input frequency were in good agreement\nwith the model. Furthermore, the distributed SIS junction as a frequency multiplier were for the first time able to pump an SIS mixer. An efficiency of the distributed SIS junction multiplier of 15-30 % for a fractional bandwidth of 10% with excellent spectral line purity were\ndemonstrated. The -3 dB line width of the multiplied signal is better than 1 Hz, which were the lowest resolution bandwidth of the spectrum analyser. Consequently, the results attained in this work show that the distributed SIS junction frequency multiplier has considerable future potential, and could possibly be used in LO source in single-ended and multi-pixel SIS mixer\nlayouts.\nFurthermore, in order to improve the sideband rejection ratio of cryogenically cooled sideband separating receivers for radio astronomy receivers to more than 15 dB over a wide RF and IF bandwidth, novel wideband RF and IF hybrid couplers have been developed and demonstrated\nwith very low imbalances. More specifically, a 4-8 GHz IF assembly comprising a compact 90° hybrid chip, two bias-T circuits and two transmission line circuits was designed and characterised. The compact size of the hybrid chip allows it to be integrated into virtually any sideband separating (2SB) mixer operating at cryogenic temperatures and is furthermore especially advantageous for multi-pixel 2SB receivers or low noise balanced amplifier layouts.\nThe characterisation of the hybrid assembly was performed at a cryogenic temperature of 4 K and sophisticated calibration and fixture de-embedding procedures were used. To further improve the sideband rejection ratio, a novel design for a RF 90° waveguide hybrid with very\nlow amplitude imbalance over a fractional bandwidth of 30% (159-216 GHz) was demonstrated. Both Hybrids are currently implemented in the ALMA Band 5 receivers, which\nrepresent the state-of-the-art for ultra-low noise sideband separated receivers.\nIn order to allow complete characterisation of the ALMA Band 5 cartridge a highly versatile measurement setup has been built. The measurement setup includes all necessary hardware and achieves automatic measurements for the system noise and sideband rejection with in-built\noptimisation procedures. The measurement setup additionally comprises measurements of the receiver saturation, phase and amplitude stability, as well as optical beam characterisation.
We report the first experimental off-chip detection of frequency multiplication in a distributed array of superconductor-insulator-superconductor (SIS) junctions. A test device consisting of series array of 68 Nb/Al-AlOx/Nb tunnel junctions was designed to study generation of the second harmonic in the 190-210 GHz band. The SIS array was exited with microwave radiation at 3-mm band using a quasi-optically coupled Gunn oscillator, and the output response of the device was studied using a double-sideband SIS mixer operating in the 163-211 GHz range with 4-8 GHz IF bandwidth. We measured extremely sharp spectral signals, associated with the ×2 frequency multiplication by the SIS array. Single- and multi-photon processes were observed in the response of SIS tunnel junction-array to the applied microwave radiation, confirming device operation in the quantum mode. The output power of the multiplied signal increases linearly with the power of the pumping signal up to certain level and them saturates. In attempt to verify that the device produces noticeable power, the output of the test device was connected to the LO port of the SIS mixer, and an increase of 10%-20% in the SIS mixer dark current was observed. Further development of the demonstrated principle of frequency multiplication may lead to a practical frequency multiplier device.
The superconductor–insulator–superconductor (SIS) tunnel junction based on Nb material has been investigated theoretically at frequencies of 200–1400 GHz by modeling it as a segment of a superconducting microstrip transmission line and using the Mattis–Bardeen theory of anomalous skin effect. The modeling was used to predict the performance of a flux-flow oscillator (FFO) and a SIS frequency down-converter (mixer). It is shown that in a FFO the internal loss (quasiparticle and surface) limits flux flow to the frequency band of 260–770 GHz. A SIS junction of micron size employed as a mixer for frequency down-conversion demonstrates distributed behavior at frequencies above 550 GHz. We suggest that electrically long SIS junctions of resonant size can be used as self-compensating mixing elements with attractive performance in Nb as well as NbN mixers.
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.>