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IEEE Transactions on Microwave Theory and Techniques

Noise parameters of SIS mixers

Larry R. D’Addario

Published Jul 1, 1988• 19 citations
Publisher

Abstract

It has been shown that low-noise receivers can be constructed at millimeter wavelengths by using mixers containing superconducting tunnel junctions as the nonlinear elements. This is possible because of both the low intrinsic noise of these devices and their potential for high conversion gain. Here, the quantum theory of mixing is used to derive the full-noise parameters and small-signal parameters of sinusoidally pumped SIS (superconductor-insulator-superconductor) junctions. These are then put into a form that allows the theory of two-port linear networks to be brought to bear, allowing calculation of such useful parameters as minimum noise temperature, optimum source impedance, available (or exchangeable) gain at minimum noise, and stability factor. These quantities are properties of the pumped junction that do not depend on the source or load impedance, but do depend on the terminations at the image and harmonic sideband frequencies. The harmonic sidebands are taken to be shorted, and the image termination dependence is studied. Numerical results are presented for both ideal (BSC theory) and practical (measured current-voltage characteristic) junctions. The noise parameters of the cascade connection of an SIS mixer and a (noisy) IF amplifier are considered, leading to a specification of the optimum coupling network between the two. It is noted that the SIS mixer is usually not unconditionally stable, but that oscillation can be avoided by careful design of the IF coupling network.< >

DOI
10.1109/22.3656

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The development of ultra-low-noise receivers at frequencies of >200 GHz is primarily driven by astronomical applications. The most sensitive millimeter-wave receivers that have presently been constructed make use of the strong mixing afforded by superconductor-insulator-superconductor (SIS) tunnel junctions. In a collaborative project between UKC and RAL, a 230 GHz laboratory receiver has been built using a lead alloy SIS junction as the mixing element, mounted in 4:1 reduced-height waveguide, terminated at one end with a circular cross-section, adjustable backshort. Best results indicate a double-sideband receiver noise temperature of T/sub R/(DSB) approximately=120 K, which represents state-of-the-art performance at this frequency. Initial difficulties in achieving good mixing performance prompted an investigation into the importance of the 'quality' of mixer block backshort tuning elements. An analysis of the mixer equivalent circuit is presented which allows for loss in a non-ideal mixer block, and 3-port mixer model calculations are discussed which incorporate this analysis into the Tucker quantum theory of mixing.

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Tucker's Quantum Theory of Mixing (QTM) is widely used to model the conversion gain and noise temperature of SIS mixers. In particular, the theory describes the phenomenon of non-classical conversion gain and that of infinite or even negative output impedances in inductively tuned SIS mixers. Common microwave noise theory is inadequate to describe the operation of the IF circuit connected to such mixers. In this paper, we report the use of the noise wave formalism to model the noise properties of a Double-Side-Band SIS mixer together with an IF isolator and low noise amplifier cascade. Starting from QTM, we derive the 4 noise parameters of the SIS mixer, together with an approximate 2-port chain matrix with an upper-side-band RF input port and an IF output port. These matrices are cascaded with the noise correlation matrix of the IF circuit to form a complete noise model of the SIS receiver. Optimum source impedance for the receiver can be derived from this noise model, which can be used in efficient CAD modeling of a complete SIS receiver.

IEEE Transactions on Applied Superconductivity•Mar 18, 2019•2 citations
It has been shown that low-noise receivers can be constructed at millimeter wavelengths by using mixers containing superconducting tunnel junctions as the nonlinear elements. This is possible because of both the low intrinsic noise of these devices and their potential for high conversion gain. Here, the quantum theory of mixing is used to derive the full-noise parameters and small-signal parameters of sinusoidally pumped SIS (superconductor-insulator-superconductor) junctions. These are then put into a form that allows the theory of two-port linear networks to be brought to bear, allowing calculation of such useful parameters as minimum noise temperature, optimum source impedance, available (or exchangeable) gain at minimum noise, and stability factor. These quantities are properties of the pumped junction that do not depend on the source or load impedance, but do depend on the terminations at the image and harmonic sideband frequencies. The harmonic sidebands are taken to be shorted, and the image termination dependence is studied. Numerical results are presented for both ideal (BSC theory) and practical (measured current-voltage characteristic) junctions. The noise parameters of the cascade connection of an SIS mixer and a (noisy) IF amplifier are considered, leading to a specification of the optimum coupling network between the two. It is noted that the SIS mixer is usually not unconditionally stable, but that oscillation can be avoided by careful design of the IF coupling network.< >
The development of ultra-low-noise receivers at frequencies of >200 GHz is primarily driven by astronomical applications. The most sensitive millimeter-wave receivers that have presently been constructed make use of the strong mixing afforded by superconductor-insulator-superconductor (SIS) tunnel junctions. In a collaborative project between UKC and RAL, a 230 GHz laboratory receiver has been built using a lead alloy SIS junction as the mixing element, mounted in 4:1 reduced-height waveguide, terminated at one end with a circular cross-section, adjustable backshort. Best results indicate a double-sideband receiver noise temperature of T/sub R/(DSB) approximately=120 K, which represents state-of-the-art performance at this frequency. Initial difficulties in achieving good mixing performance prompted an investigation into the importance of the 'quality' of mixer block backshort tuning elements. An analysis of the mixer equivalent circuit is presented which allows for loss in a non-ideal mixer block, and 3-port mixer model calculations are discussed which incorporate this analysis into the Tucker quantum theory of mixing.
Theoretical and experimental research has been conducted to elucidate the basic physics behind the properties of superconductor-insulator-superconductor (SIS) tunnel junction receiving devices. The quantum theory of mixing was employedto calculate the saturation behavior of the SIS mixer and the SIS direct detector. The direct detector was found to saturate at far higher powers than previously believed, allowing the possibility of practical application of this device. Experiments verified the saturation theory. The mixer saturation expression led to the formulation of frequency scaling regions. The origin of quantum noise sources are completely minimized. The mixer quantum noise limit was shown to be reached in only two special cases. Computer calculations determined that the behavior of SIS receivers divides into two regimes, low and high frequencies, the cross-over frequency depending upon junction quality. The properties of these two regimes were delineated. All previous SIS receivers have operated in the low frequency regime. Plasma-etched niobium nitride edge junctions have been fabricated using a novel barrier formation process. These junctions have excellent current-voltage characteristics, but their precise physical nature has not yet been determined. (Author)
It has been shown both theoretically [1] and experimentally [2,3] that the very sharp nonlinearity in the conductance of superconducting tunnel junctions can be used to implement millimeter wavelength mixers having high gain and very low noise, leading to the possibility of receivers that achieve the quantum noise limit. The junctions involved contain a thin insulating barrier between two superconductors, and are thus known as superconductor-insulator-superconductor (SIS) junctions. They are physically identical to Josephson junctions, but in this application the conductance is via the tunneling of quasiparticles (unpaired electrons), and so the Josephson effect is not involved.
Abstract : Theoretical and experimental research has been conducted to elucidate the basic physics behind the properties of superconductor-insulator-superconductor (SIS) tunnel junction receiving devices. The properties of an SIS mixer using a slightly nonideal junction, with finite LO power, were determined by analytic expansion of the equations of the quantum theory of mixing. The resulting equations have a particularly simple form. The minimum noise temperature is controlled by the leakage current of the junction. Even the most nearly ideal junctions made today require a considerable LO for best sensitivity; nevertheless, even a comparatively large leakage current allows mixer noise to be only a small factor above the quantum limit. The saturation properties of SIS mixers subjected to broad-band thermal noise obey the equations derived for monochromatic saturating signals. The Josephson junction tuning inductor was analyzed with the conclusion that such a device is not feasible with present fabrication techniques. Computer calculations using synthetic SIS junction I-V characteristics predicted the performance of an optimized receiver over its entire operating frequency range. Many aspects of the operation of SIS mixers were clarified and unexpected new phenomena were predicted. A 'photon picture' interpretation of the quantum theory of mixing is in the early stages of development. Niobium nitride edge junctions with excellent current-voltage characteristics were fabricated using novel barrier formation processes. The role of surface damage in the quality of NbN edge junction electrical characteristics was investigated and unexpected results were obtained.
We have investigated high-frequency limits of superconducting quasiparticle mixers from experiments on Al/Al-oxide-In/Al (or Ag) tunnel junctions, and from calculations based on Tucker’s quantum theory of mixing (QTM). The small superconducting energy gap of Al enabled us to study mixer performance at around the junction gap frequency, fg =(Δ1+Δ2)/h≊87 GHz, of superconductor-insulator-superconductor (SIS) mixers, and at twice the junction gap frequency for S-I-normal metal (SIN) mixers ( fg =Δ1/h) with available millimeter wave sources. Because of the low transition temperature of Al (Tc ≊1.3 K), a dilution refrigerator was used for providing temperatures below 1 K. The best mixer conversion efficiency was obtained for a low-resistance (∼34 Ω) six-junction array SIS mixer operated at f/fg ≊1 (in this case 73 GHz). The coupled single sideband conversion gain (with no image rejection) was −13.8 dB and the available conversion gain was estimated to −8.4 dB. Complicating nonequilibrium phenomena made it difficult to compare the performance of these relatively high-current-density mixers to the QTM. However, good agreement between calculated and corresponding measured conversion efficiencies and dynamic resistance values was obtained for the low-current-density mixers. Noise due to switching between rf-induced Josephson steps and interference from Josephson mixing could be quenched by a magnetic field. Several high-frequency limits are considered in this paper (such as Josephson switching noise, nonequilibrium phenomena, pair breaking, and energy gap limitations). Our results indicate that submillimeter wave SIS mixer receivers are likely to perform well, at least up to their gap frequencies, i.e., the THz region for large gap superconductors. Our QTM calculations showed that conversion gain larger than unity should be possible up to twice the gap frequency. Above this frequency the conversion loss will increase rapidly.
Tucker's Quantum Theory of Mixing (QTM) is widely used to model the conversion gain and noise temperature of SIS mixers. In particular, the theory describes the phenomenon of non-classical conversion gain and that of infinite or even negative output impedances in inductively tuned SIS mixers. Common microwave noise theory is inadequate to describe the operation of the IF circuit connected to such mixers. In this paper, we report the use of the noise wave formalism to model the noise properties of a Double-Side-Band SIS mixer together with an IF isolator and low noise amplifier cascade. Starting from QTM, we derive the 4 noise parameters of the SIS mixer, together with an approximate 2-port chain matrix with an upper-side-band RF input port and an IF output port. These matrices are cascaded with the noise correlation matrix of the IF circuit to form a complete noise model of the SIS receiver. Optimum source impedance for the receiver can be derived from this noise model, which can be used in efficient CAD modeling of a complete SIS receiver.