Superconductor-insulator-superconductor Mixer Research Articles

Terahertz high-sensitivity SIS mixer based on Nb-AlN-NbN hybrid superconducting tunnel junctions

Abstract The terahertz band, a unique segment of the electromagnetic spectrum, is crucial for observing the cold, dark universe and plays a pivotal role in cutting-edge scientific research, including the study of cosmic environments that support life and imaging black holes. High-sensitivity superconductor-insulator-superconductor (SIS) mixers are essential detectors for terahertz astronomical telescopes and interferometric arrays. Compared to the commonly used classical Nb/AlOx/Nb superconducting tunnel junction, the Nb/AlN/NbN hybrid superconducting tunnel junction has a higher energy gap voltage and can achieve a higher critical current density. This makes it particularly promising for the development of ultra-wideband, high-sensitivity coherent detectors or mixers in various scientific research fields. In this paper, we present a superconducting SIS mixer based on Nb/AlN/NbN parallel-connected twin junctions (PCTJ), which has a bandwidth extending up to 490-720 GHz. The best achieved double-sideband (DSB) noise temperature (sensitivity) is below three times the quantum noise level.

Research on Thermal Expansion Characteristics Measurement of Launch Lock Mechanism for SIS Mixer’s Space Application

The High Sensitivity Terahertz Detection Module (HSTDM) is one of the scientific payloads of the Chinese Space Survey Telescope. The core of the HSTDM is the NbN superconducting SIS (Superconductor Insulator Superconductor) mixer, operating around 10 K. The installation structure of the SIS mixer needs to be specially designed to cope with the mechanical vibration during the launch phase and the thermal insulation requirements during the operation phase. Material thermal expansion characteristics investigation based on low-temperature LVDT (Linear Variable Differential Transformer) measurement and scratch marking measurement were carried out to confirm the validity of the thermal expansion lock mechanism design. The two methods are cross verified. The LVDT experimental measurement results show that the shrinkage rate of Teflon changes with temperature and meets the theoretical model. At the same time, we verified the LVDT results with scratch marking method. Consistently, the shrinkage rate of the material is 1.86% at 80 K, so the Teflon front-end lock mechanism of the SIS mixer can achieve effective separation after cooling down.

Development of Through-Substrate via Process for Silicon-Based Monolithic Microwave Integrated Circuits SIS Mixer

We designed and fabricated superconducting monolithic microwave integrated circuits (MMICs) at 2 mm wavelengths. Balanced superconductor-insulator-superconductor (SIS) mixers and silicon membrane-based planar orthomode transducers are incorporated into the MMICs, which is used to develop compact heterodyne array receivers for radio astronomical observations. Because of substrate cavity modes, crosstalk between the outputs of balanced mixers was observed at intermediate frequencies, which deteriorated the noise rejection ratio. Three-dimensional electromagnetic simulation proved that the cavity modes can be effectively suppressed by introducing conducting through-substrate vias (TSVs). We have been developing a TSV fabrication process compatible with that for the superconducting MMICs containing silicon membranes by using non-Bosch deep silicon etching and using sputtered Nb films. The fabricated TSVs were characterized by scanning electron microscopy and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> measurement.

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

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.

Предельные параметры СИС-переходов в теории и технологические возможности их достижения

Tunneling Josephson junctions of the superconductor-insulator-superconductor (SIS) type have a history of more than 50 years, and theoretical estimates of the ultimate parameters of devices for receiving and processing signals based on them look very promising. In practice, in many cases, the actually achieved parameters turn out to be much worse than the theoretical ones, so for niobium SQUIDs the characteristic voltage Vc=IcRn at best reaches 200 µV, and according to theory it should be up to 2 mV. For Terahertz SIS mixers and oscillators, the main problems are a large specific capacitance, hysteresis, and leakage currents. These problems may be related to the morphology and crystal structure of superconductor films. In practice, films are granular, tunnel barriers are nonuniform, the effective area is about 10% of geometric area, leakage currents, parasitic capacitances occur. The crystal structure determines fundamentally different properties of the same elements, for example, for carbon it is diamond, graphite, fullerenes, nanotubes. Important components of a promising superconducting technology are: the use of single-crystal substrates matched in lattice constant and orientation with the grown films, optimization of growth temperature conditions, controlled formation of an oxide or nitride tunnel barrier. One option is to use a Schottky barrier for the semiconductor interlayer instead of a dielectric or normal metal one. This review presents the results of studying films by X-ray diffraction diagnostics, atomic force microscopy, and electron microscopy, showing the main bottlenecks of the existing technology with the deposition of niobium, niobium nitride, and aluminum films on oxidized standard silicon substrates, as well as the results of quasi-epitaxial growth of films on single-crystal substrates at various temperature conditions. Reproducible manufacturing of high-quality tunnel junctions can be achieved by implementing atomically smooth surfaces of tunnel contacts, which will improve the signal and noise characteristics of superconducting devices for receiving and processing information.

A 230-GHz Endfire SIS Mixer With Near Quantum-Limited Performance

In this letter, we report the near quantum-limited performance of a 230 GHz endfire superconductor-insulator-superconductor (SIS) mixer utilizing a Nb/Al-AlOx/Nb trilayer. An important feature of this mixer is its use of a unilateral finline for the waveguide-to-planar circuit transition, which allows for a wide radiofrequency (RF) bandwidth, a simple waveguide structure with easy alignment, and for the mixer chip to be aligned along the optical axis. Each of these factors is beneficial in the construction of large-format focal plane arrays. We tested the new finline mixer from 210 to 260 GHz in a liquid helium cryostat at ~4 K. The best recorded noise temperature was approximately twice the quantum limit, which is comparable to conventional radial probe mixers. This suggests that endfire SIS mixers can be used in large format arrays, comprising 100s or even 1000s of SIS mixing elements, while retaining state-of-the-art quantum mixing performance.

Superconducting Receiver Technologies Supporting ALMA and Future Prospects

AbstractThis paper describes the development of superconductor–insulator–superconductor (SIS) receivers in the 787–950 GHz radio frequency (RF) range, which covers the highest frequency band of the Atacama Large Millimeter/submillimeter Array (ALMA) and is recognized as the most difficult band in terms of superconducting technology, because the conventional superconducting material of Nb cannot be used for the circuitry in the mixer devices at the frequencies. The development began at the National Astronomical Observatory of Japan (NAOJ) in 2005, and the manufacturing and testing of all the receivers to be installed in the 66 Cassegrain reflector antennas that compose ALMA was completed in 2013. This enabled the terahertz frequency observations with the highest sensitivity from the ground. To meet the stringent ALMA requirements, terahertz SIS mixers with high‐quality superconducting NbTiN films were developed, which successfully demonstrated an unpreceded noise performance less than 230 K (5 times the quantum noise) for all the receivers. After the construction of ALMA, NAOJ began development studies for ALMA enhancement such as wideband and multibeam SIS receivers according to top‐level science requirements. To increase instantaneous bandwidth of the receivers, a submillimeter‐wave multiband receiver concept with a waveguide multiplexer, wideband intermediate frequency SIS‐mixer‐amplifier, and multifrequency local oscillator (LO) source is presented. The multibeam receiver employs a planar‐integrated SIS mixer circuit that includes all the RF components except the LO distribution network and an SIS‐mixer‐based amplifier of low power consumption, which is expected to enable the wide field‐of‐view observations in the future.

The Influence of LO Power Heating of the Tunnel Junction on the Performance of THz SIS Mixers

We describe the performance of a superconductor- insulator-superconductor (SIS) mixer operating in the frequency range of 780-950 GHz. Unlike most SIS mixers, the tunnel junction employs two different superconductors, a niobium nitride top and a niobium bottom electrode sandwiching an aluminum nitride barrier layer, fabricated on a niobium titanium nitride ground plane. The mixer was tested in a pulse tube cryostat, with all the optical components, in the signal path, mounted inside the vacuum environment to avoid attenuation of the RF signal as it propagates from the hot/cold loads to the mixer. With this setup, we have measured an RF-corrected noise temperature of ~220 K. In this article, we focus on investigating the influence of local oscillator (LO) power heating on the performance of the terahertz mixer. The increase in the junction's physical temperature can be observed experimentally by noting the suppression of the gap voltage in the pumped current-voltage (I-V ) curve as the LO pumping level is increased. Similar observation has already been reported, and attempts were made to estimate the effective temperature of the device using equations of heat transfer between the mixer chip layers. Here, we present an experimental method of quantifying this effect by recovering the effective temperature of the junction through comparing the pumped I-V curves at different pumping levels and fixed bath temperature, with the unpumped I-V curves obtained at varying bath temperatures. We also estimate, for the first time, the effect of heating on the noise temperature as a function of bath temperature and frequency. We show that for typical experimental parameters, the LO heating can increase the double-sideband receiver noise temperature by as much as 20%, and that in the frequency range of the measurements, the effective temperature of the junction at fixed LO power increases linearly with frequency at a rate of 0.5 K/100 GHz.

A Compact Superconducting Heterodyne Focal Plane Array Implemented With HPI (Hybrid Planar Integration) Scheme

The article is concerned with the experimental evidence that proves technical feasibility of the hybrid planar integration (HPI) scheme that has been proposed to construct superconductor–insulator–superconductor (SIS) mixer focal plane arrays of unprecedented compactness. The scheme is characterized by the adoption of silicon membrane-based waveguide probes, which allows superconducting monolithic microwave integrated circuits to couple signal, and local oscillator (LO) from (computer numerical control)-machined waveguides through multiple paths. A $2\times 2$ dual-polarization balanced SIS mixer array has been implemented with this scheme, and assessed in $125 - \text{163}\,\text{GHz}$ RF band. This compact array has demonstrated uniform LO distribution, and low crosstalk between pixels. The RF performance of component pixels has been confirmed to be little affected by the high-degree integration. The potential implementation of the HPI scheme at THz frequencies is also discussed.

Demonstration of a wideband submillimeter-wave low-noise receiver with 4–21 GHz IF output digitized by a high-speed 32 GSps ADC

We report on a 275–500 GHz heterodyne receiver system in combination with a wideband intermediate-frequency (IF) backend to realize 17 GHz instantaneous bandwidth. The receiver frontend implements a heterodyne mixer module that integrates a superconductor-insulator-superconductor (SIS) mixer chip and a cryogenic low-noise preamplifier. The SIS mixer is developed based on high-current-density junction technologies to achieve a wideband radio frequency (RF) and IF bandwidth. The IF backend comprises an IF chain divided into two channels for 4.0–11.5 GHz and 11.3–21.0 GHz and an analog-to-digital converter (ADC) module that is capable of high-speed sampling at 32 Giga samples per second with 12.5 GHz bandwidth per channel and an effective number of bits of 6.5. The IF backend allows us to simultaneously cover the full 4–21 GHz IF range of the receiver frontend. The measured noise temperature of the receiver frontend was below three times the quantum noise (hf/kB) over the entire RF band. A dual-polarization sideband-separating receiver based on this technique could provide up to 64 GHz of instantaneous bandwidth, which demonstrates the possibility of future wideband radio astronomical observations with advanced submillimeter-wave heterodyne receivers.

Observation of Frequency Up-Conversion Gain in SIS Junctions at W Band

We have developed a test setup to measure frequency up-conversion gain in superconductor–insulator–superconductor (SIS) junctions at W band (75–110 GHz). A conventional SIS mixer with Nb/AlOx/Nb tunnel junctions was used as a frequency up-converter. An up-converted signal is measured by a room-temperature down-converter system. We observed distinct intermediate frequency responses to signal inputs from a continuous microwave source. The measured single-sideband up-conversion gain in SIS junctions was clearly positive (> 0 dB) with input frequency less than 2 GHz, which was well-calibrated by using an input from the continuous-wave source.

A Nonlinear Transmission Line Model for Simulating Distributed SIS Frequency Multipliers

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.

Fabrication of Planar-Integrated SIS Mixer Circuits with Improved Uniformity and Yield

Single-pixel prototype superconductor–insulator–superconductor (SIS) mixer integrated circuits (ICs) for multi-beam heterodyne receivers were fabricated. We introduced plasma-enhanced chemical vapor deposition (PE-CVD) for insulator layer deposition and machine-aligned via-hole etching for contact-hole definition on SIS junctions to achieve high uniformity and yield. In the PE-CVD, we applied a compressive/tensile/compressive SiO2 trilayer technique to control the film stress. The SiO2 trilayer stress was stable and negligibly low. The uniformity and junction quality yield of the single-pixel prototype SIS mixer ICs were improved in the process applying the PE-CVD and the via-hole etching.

Design and Performance of a Sideband Separating SIS Mixer for 800–950 GHz

We present the design and results of characterization of a new sideband separating (2SB) mixer for 800–950 GHz, based on superconductor–insulator–superconductor (SIS) junctions. This is the first waveguide 2SB SIS mixer demonstrated at such a high frequency. The design is following the classical quadrature hybrid architecture, meanwhile additional attention was put on the reduction of reflections in the RF structure in order to minimize the RF imbalance, to achieve a high image rejection ratio (IRR). The RF waveguide block was manufactured by micromilling and populated by single-ended SIS mixers developed earlier for upgrade of the CHAMP+ high-band array on the APEX telescope. These SIS mixers have double-sideband (DSB) noise temperatures from 210 to 400 K. The assembled 2SB mixer yields a SSB noise temperature from 450 to 900 K, with an IRR above 15 dB in 95% of the band. Comparing the DSB and the SSB sensitivities, we find that the waveguide losses are as low as expected and do not exceed 0.6 dB. The presented mixer is a prototype for use in a 2SB dual polarization receiver planned for deployment on the APEX telescope.

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

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.

125 - 211 GHz low noise MMIC amplifier design for radio astronomy

To achieve the low noise and wide bandwidth required for millimeter wavelength astronomy applications, superconductor-insulator-superconductor (SIS) mixer based receiver systems have typically been used. This paper investigates the performance of high electron mobility transistor (HEMT) based low noise amplifiers (LNAs) as an alternative approach for systems operating in the 125 — 211 GHz frequency range. A four-stage, common-source, unconditionally stable monolithic microwave integrated circuit (MMIC) design is presented using the state-of-the-art 35 nm indium phosphide HEMT process from Northrop Grumman Corporation. The simulated MMIC achieves noise temperature (Te) lower than 58 K across the operational bandwidth, with average Te of 38.8 K (corresponding to less than 5 times the quantum limit (hf/k) at 170 GHz) and forward transmission of 20.5 ± 0.85 dB. Input and output reflection coefficients are better than -6 and -12 dB, respectively, across the desired bandwidth. To the authors knowledge, no LNA currently operates across the entirety of this frequency range. Successful fabrication and implementation of this LNA would challenge the dominance SIS mixers have on sub-THz receivers.

Fabrication of Superconductor Integrated Circuits of D-Band Dual-Polarization Balanced SIS Mixers

We have fabricated prototype superconductor integrated circuits (ICs), which accommodate planar orthomode transducer (OMT) and balanced superconductor-insulator-superconductor (SIS) mixers operating at D-band (125–163 GHz). The fabrication of the ICs is different from the conventional SIS mixer fabrication process in several aspects because of new features and components being introduced and incorporated. In particular, very flat silicon membranes that mechanically support the planar OMT and the waveguide probes for local oscillator coupling were formed with a combination of dry and wet etching methods to completely remove the handle layer and the buried oxide layer of the silicon on insulator substrates. We also applied an anodization passivation of the surface of the ground plane and a via-hole etching process with an i-line stepper in the formation of low-leakage SIS junctions. The SIS junctions of moderately good quality have been fabricated with an average quality factor as high as 18, which indicate the integrity of the junction definition with the complex fabrication of ICs.

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

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.

Performance and Characterization of a Wide IF SIS-Mixer-Preamplifier Module Employing High-J c SIS Junctions

This paper reports the simulation, performance, and detailed characterization of a low-noise heterodyne module with very wide intermediate frequency (IF) bandwidth in the 385-500-GHz radio frequency (RF) range. The module integrates a superconductor-insulator-superconductor (SIS) mixer with a 3- 21-GHz cryogenic low-noise preamplifier (CLNA). The utilization of high current density SIS junctions offers wide RF bandwidth and facilitates better matching between SIS junctions and the CLNA. Based on an equivalent circuit of the SIS mixer chip, we calculate the IF output impedance and simulate how different matching conditions affect the performance of the CLNA. Simulations predict that low-noise module performance can be obtained over a 3-18GHz IF range, limited mainly by parasitic elements in theSIS mixer chip. The measurement results of the heterodyne module demonstrate flat gain and a typical noise temperature of 70-80 K over the 3-18-GHz IF range, at local oscillator frequencies of 400-480 GHz. Mixer chip output impedance and CLNA input impedance have been directly measured by recording S-parameters at cryogenic temperatures. The results enabled us to quantify the contribution of various parasitic elements in the mixer IF circuitry. Calculations based on our model are in good agreement with measurements.

Specific Capacitance Dependence on the Specific Resistance in Nb/Al–AlOx/Nb Tunnel Junctions

The junction specific capacitance (C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ) is an essential parameter in designing tuning circuitry for superconductor- insulator-superconductor (SIS) mixers. However, our knowledge of the junction capacitance only relies on the few available empirically obtained C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> versus specific normal resistance (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> A) relations, which are inconsistent especially at low R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> A values, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> A <; 40 Ω·μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . In this paper, we report the Nb/Al-AlO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> /Nb SIS junction capacitance data from our recently presented direct microwave (4 GHz) measurements at 4 K for junctions with various R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> A values ranging from 8.8 to 68 Ω·μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . New insight is provided into the extraction of the true geometrical specific capacitance of SIS junctions. We show that even at such low microwave frequencies, the so-far-neglected nonlinear susceptance is significant, especially for junctions with low R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> A values. This susceptance originates from the real part of the response function, I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">KK</sub> , which can be calculated through the Kramers-Kronig transform of the dc tunnel current. The new specific capacitance, which accounts for this contribution, is presented as a function of R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> A. We provide an improved and more accurate C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> A) relation, which can be a reliable and useful tool for circuit designers. The obtained C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> A) relation is compared with those available in the literature, and the possible reasons giving rise to the disparity among these relations are discussed. By comparing the modeled and the measured noise temperature of the APEX SHeFI band 3\(385-500 GHz) double sideband mixer, we show that the new C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> A) relation offers a great potential for improving the performance of SIS mixers.