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IEEE Transactions on Magnetics

Optimizing double-sideband SIS quasiparticle mixers

D. P. Woody, Michael J. Wengler

Published Mar 1, 1991• 4 citations
Publisher

Abstract

Calculations based on the quantum theory of mixing in single-particle tunnel junctions show that there is a fairly simple strategy for optimizing the performance of double-sideband superconductor-insulator-superconductor (SIS) quasiparticle mixers. The best mixer noise temperature is obtained when the signal source is matched to the local oscillator (LO) admittance of the junction. This applies over a very wide range of LO and DC bias conditions. These calculations support the contention that it is the energy dissipation in the device which is important in determining the noise performance, not the small signal admittance or the power gain. This appears to be another demonstration of the Callen and Welton fluctuation-dissipation theorem. which states that it is the dissipation of energy which is responsible for the noise generation in a wide range of devices, and it is this energy dissipation mechanism to which the signal should be coupled to minimize the noise.

DOI
10.1109/20.133939

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The authors present numerical calculations of the gain and noise of a two-LO (local oscillator) mixer based on an ideal SIS (superconductor-insulator-superconductor) IV curve. They demonstrate the phase-sensitive response of the mixer with two-LO pumping and present calculations of the noise for various DC bias conditions and embedding impedances. Preliminary results indicate that for certain DC bias conditions and signal terminations, the noise added to a signal by the two-LO mixer operated in the single-sideband mode can be a factor of 25 less than that added by a conventional single-sideband single-LO mixer.>

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Noise parameters of SIS mixers

Larry R. D’Addario

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.< >

IEEE Transactions on Microwave Theory and Techniques•Jul 1, 1988•19 citations
Calculations based on the quantum theory of mixing in single-particle tunnel junctions show that there is a fairly simple strategy for optimizing the performance of double-sideband superconductor-insulator-superconductor (SIS) quasiparticle mixers. The best mixer noise temperature is obtained when the signal source is matched to the local oscillator (LO) admittance of the junction. This applies over a very wide range of LO and DC bias conditions. These calculations support the contention that it is the energy dissipation in the device which is important in determining the noise performance, not the small signal admittance or the power gain. This appears to be another demonstration of the Callen and Welton fluctuation-dissipation theorem. which states that it is the dissipation of energy which is responsible for the noise generation in a wide range of devices, and it is this energy dissipation mechanism to which the signal should be coupled to minimize the noise.
A quantum-statistical analysis of the signal and noise performance of the quasiparticle (SIS) heterodyne mixers is presented. In contrast with the earlier theories, the quantum properties of the signal source have been taken into consistent consideration. In the quantum range of sensitivity the noise properties of the mixer can be characterized by the noise parameter ΘNintroduced earlier for the parametric amplifiers. Using the conventional 3-port model of the mixer circuit and the microscopic theory of the superconducting tunnel junctions we have obtained a general expression for ΘNand evaluated it numerically for various quasiparticle current step widths, dc bias voltages, local oscillator powers, signal frequencies ωs, signal source admittances Ysand operation temperatures T. In a reasonable range of these parameters,\Theta_{N}^{DSB}has turned out to be less than the so-called quantum limith\omega_{s}/2. On the contrary, in the single sideband mode of the mixer performance, ΘNis always larger thanh\omega_{s}/2. The difference between the two modes of operation is discussed from the point of view of the quantum theory of measurements.
An analysis of the frequency dependence of superconductor-insulator-normal (SIN) and superconductor-insulator-superconductor (SIS) quasiparticle mixers is presented. Power-law expressions for conversion loss and mixer shot-noise temperature for the double-sideband SIN mixer are derived from the Tucker theory for the case of a source conductance which is small compared to the conductance of the junction. For an ideal SIN tunnel junction at T=0 the mixer conversion efficiency is shown to decrease approximately linearly with frequency up to f=Δ/h. From f=Δ/h to 2Δ/h the conversion efficiency remains approximately constant, while above f=2Δ/h it rolls off as the inverse square of the frequency. Expressions for the shot-noise contribution to the mixer noise temperature are also derived. At frequencies up to f=Δ/h the noise temperature rises as the square root of the frequency. From f=Δ/h to f=2Δ/h the noise temperature of the mixer increases linearly with frequency, whereas above f=2Δ/h it rises as the cube of the frequency. Conversion efficiency and noise temperature are also calculated numerically for the SIN mixer. Good agreement is found between the frequency dependencies calculated analytically in the limit of small local oscillator power and the numerical calculations for optimal pumping. The frequency dependence of the nonideal SIS junction is also analyzed, and shown to yield similar results, with the characteristic frequencies Δ/h and 2Δ/h for a SIN mixer transformed into 2Δ/h and 4Δ/h, respectively. Expressions also are derived for the saturation power as a function of frequency.
The authors present numerical calculations of the gain and noise of a two-LO (local oscillator) mixer based on an ideal SIS (superconductor-insulator-superconductor) IV curve. They demonstrate the phase-sensitive response of the mixer with two-LO pumping and present calculations of the noise for various DC bias conditions and embedding impedances. Preliminary results indicate that for certain DC bias conditions and signal terminations, the noise added to a signal by the two-LO mixer operated in the single-sideband mode can be a factor of 25 less than that added by a conventional single-sideband single-LO mixer.>
The properties of an SIS (Superconductor-insulator-superconductor) mixer using a slightly nonideal junction, with finite local oscillator (LO) power, are determined by analytic expansion of the equations of the quantum theory of mixing. The result is that the conversion gain using any reasonably good quality SIS junction is essentially equal to that using a perfect junction. Quite to the contrary, the minimum noise temperature is controlled by the leakage current of the junction: the increase in the minimum added-noise temperature over the quantum limit T/sub Q/=h omega /2k is given by delta T/sub Q/=(h omega /k) square root I/sub 0/I/sub 2//I/sub 1/; this minimum requires that the LO voltage across the junction is V/sub LO/=(64I/sub 0//I/sub 2/) /sup 1/4/h omega /e. (I/sub n/ is the current measured on the unpumped I-V curve of the junction at voltage V/sub 0/+nh omega /e). Therefore, although an SIS mixer using an ideal junction can reach the quantum noise limit only in the limit of zero LO power, even the most nearly ideal junctions require a considerable LO for best sensitivity.
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.
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.< >