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Engineering Research Express

Analytical expressions for the design of twin junction tuning in SIS mixers

Jakob Wenninger, G. Yassin, Boon-Kok Tan

Published Jun 1, 2023• 0 citations
Publisher

Abstract

Abstract We derive general analytical expressions for matching the complex impedance of the feeding radio frequency (RF) circuit to a twin junction device in Superconductor-Insulator-Superconductor (SIS) mixers. A unique feature of our analysis is that it allows for junctions of different admittance and an RF circuit with complex admittance. This provides important design flexibility and accommodates device fabrication tolerances. We then focus on special cases of identical junctions, in particular those cases that yield simple expressions for matching the twin junction to a real impedance. Finally, we derive design curves that allow the determination of the twin junction parameters for a given complex impedance of the feeding circuit. These curves allow the designer to choose different solutions than the commonly used quarter-wavelength transmission line separating the two SIS junctions, which our analysis shows is not always the optimal solution. Moreover, even when commercial software is used for designing the circuits, our analytical equations will act as an important guide to understanding the physics and guide the designer to the optimal solution.

DOI
10.1088/2631-8695/acde45

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Journal of Physics D Applied Physics•Oct 6, 2026•0 citations
Abstract We derive general analytical expressions for matching the complex impedance of the feeding radio frequency (RF) circuit to a twin junction device in Superconductor-Insulator-Superconductor (SIS) mixers. A unique feature of our analysis is that it allows for junctions of different admittance and an RF circuit with complex admittance. This provides important design flexibility and accommodates device fabrication tolerances. We then focus on special cases of identical junctions, in particular those cases that yield simple expressions for matching the twin junction to a real impedance. Finally, we derive design curves that allow the determination of the twin junction parameters for a given complex impedance of the feeding circuit. These curves allow the designer to choose different solutions than the commonly used quarter-wavelength transmission line separating the two SIS junctions, which our analysis shows is not always the optimal solution. Moreover, even when commercial software is used for designing the circuits, our analytical equations will act as an important guide to understanding the physics and guide the designer to the optimal solution.
A 600-700GHz SIS mixer with the twin-junction tuning circuit has been designed and fabricated [1] The surface impedance of thin-film superconducting microstrip lines, based on Mattis-Bardeen theory [2], is included in the optimization of RF impedance matching. The receiver noise temperature measured in the frequency range of 630-660GHz is below 200K and the lowest receiver noise temperature of 181K is achieved at 656GHz. The FTS response of the SIS mixer shows a good RF coupling from 600GHz to 700GHz. Both the noise performance and the FTS response can be quantitatively described by numerical results using the quantum theory of mixing. Some detail considerations on the mixer model calculation, such as spreading inductance around the junction tuning structure and mixer's embedding impedance, are discussed. Introduction Nb-based superconductor-insulator-superconductor (SIS) mixers have been used very successfully in sub-mm wavelength detection. Their receiver noise temperature has reached to three times the quantum limit, —3 hfrkB, below the junction's gap frequency. However, at high frequency bands, Nb SIS mixers need to be designed carefully because the photon energy is close to or higher than the gap energy of Nb, A-1.4meV. When the frequency band covers the gap frequency of Nb, —670GHz, the RF loss of Nb superconducting transmission lines increases dramatically and the surface impedance has strong frequency dependence. Usually, the RF properties of a superconducting transmission line can be described by the Mattis-Bardeen theory [2] in good accuracy. From results reported so far [4-9], the best receiver noise temperature is close to 5 hi7kB in the band of 600-700GHz. Despite of the input loss contributed by the experimental setup, some other properties of SIS mixers should be taken into account. In this paper, we characterize the performance of a 600-700GHz mixer by comparing the experimental and simulated results.
A circuit that produces broadband impedance matching with low-current-density junctions at submillimeter wavelengths for tuning superconductor–insulator–superconductor (SIS) mixers is described; it consists of half-wavelength distributed SIS junctions connected alternately by half-wavelength microstrip lines. It is made of Nb and was designed for two practical source impedances using numerical calculation based on the Mattis–Bardeen theory of the anomalous skin effect at 660 GHz, assuming SIS junctions with a current density of 5 kA/cm 2 . An SIS mixer tuned using this circuit had a large fractional bandwidth of more than 18%, below -10 dB matching, even though the assumed ω C J R N product was about 16. Investigation of the mixer performance using Tucker's quantum theory of mixing showed that it has excellent broadband and low-noise characteristics compared with conventional mixers consisting of half- or full-wavelength distributed elements.
Abstract At present, microwave transmission lines are characterized by a strong frequency dependence of loss in the subterahertz range. This work is aimed at development, research, and optimization of superconducting integrated circuits designed for matching the impedances of a long Josephson junction oscillator (a so-called “flux-flow oscillator”) and a superconductor–insulator–superconductor (SIS) detector in the subterahertz frequency range. The goal of this study is to improve and approve the numerical calculation methods, which make it possible to describe correctly experimental superconducting structures in a wide frequency range. Numerical calculations of integrated circuits have been performed in order to optimize the topology and parameters of transmission lines. The main parameters of the transmission lines and their influence on the signal propagation are determined. The results of optimization of integrated matching circuits in the range of 450–700 GHz have been experimentally confirmed. Optimization and improvement of transmission lines allow one to design new-generation integrated superconducting detectors and investigate tunnel SIS junctions more thoroughly (including shunted ones) and the properties of heterodyne oscillators based on long Josephson junctions.
Besides the sensitivity nearly approaching the quantum limit, the intermediate-frequency (IF) bandwidth is of particular interesting for Superconductor-insulator-superconductor (SIS) mixers for radio astronomy research. In this paper, we are going to present the characteristic of IF bandwidth of two type of NbN SIS mixers, Long distributed junctions and Parallel-connected twin junctions. Firstly, the relative mixer gain are measured with different IF load impedance (25Ω, 50Ω, 75Ω) for both two SIS mixers. And also the mixers gain with different IF load impedance is simulated to get the optimum IF load impedance over a relative large IF bandwidth (2-15GHz). Finally, an IF matching circuit is designed and measured associating with SIS mixers, the measurement results show that the mixers gain are flatter over a large IF bandwidth than with 50Ω IF load impedance.
Heterodyne receivers using SIS (Superconductor-Insulator-Superconductor) junctions are the most sensitive receivers for radioastronomy in the millimeter wave and submillimeter wave frequency range. These instruments use superconducting RF tuning circuits to resonate out the high shunt capacitance of the SIS junction in order to provide a good impedance match with the microwave envionment at the frequency of operation. An accurate model to determine the electrical propeties of impedance matching circuits has been developed. An analysis of superconducting microstrip lines and radial stubs taking into account the fringing fields of the thick electrode, the step discontinuities, and the Mattis-Bardeen complex conductivity for the superconductor surface impedance is presented. This model is used to calculate the resonance frequencies of the matching circuit with the capacitively-'shunted SIS junction. Good agreement is found between calculated and experimentally measured resonance frequencies at 550-600 GHz.
Abstract The wide intermediate frequency (IF) bandwidth is a core performance metric for terahertz heterodyne receivers, and a wide-IF superconductor–insulator–superconductor (SIS) mixer is key to achieving this. This paper presents the simulation-based design, optimization, and performance analysis of a 345 GHz superconducting SIS mixer developed for wide-IF applications. The mixer employs a parallel-connected twin-junction tuning structure and integrates a dedicated IF impedance matching circuit, achieving wideband impedance matching between the mixer output port and low-noise amplifier. The design is based on two tunnel junction technologies, AlO x and AlN, with critical current densities of 1 kA·cm −2 and 25 kA·cm −2 , respectively. We systematically studied the effects of different junction materials and junction areas on the RF and IF bandwidth performance of the SIS mixer. It is found that for AlN-barrier junctions with diameters of 0.6 μ m and 0.8 μ m, the receiver’s IF noise temperature slowly decreased as the IF frequency increased at a high local oscillator frequency. Furthermore, we incorporated the calculated IF output port impedance into the mixer model for correction and introduced an integrated IF circuit approach, overcoming the original IF bandwidth limitation. Simulations show that the newly designed mixer achieves the stringent sensitivity and bandwidth requirements across the 320–370 GHz range, delivering an IF bandwidth of 4–22 GHz and a receiver noise temperature of 39–73 K. Notably, the −3 dB IF bandwidth is improved by more than 1.5 times compared to conventional AlO x -based designs. These findings provide new design guidelines and quantitative criteria for next-generation wide-IF receivers and other high-frequency applications requiring a wide IF bandwidth.