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IEEE Transactions on Magnetics

Characteristics of a Josephson junction harmonic mixer with external pumping

Yuan Taur

Published Jan 1, 1979• 2 citations
Publisher

Abstract

Numerical calculations are carried out on harmonic mixing with an externally pumped Josephson junction. Bias conditions for optimum conversion efficiency are studied for a variety of junction parameters. The predicted noise temperature for harmonic mixing is compared with that for fundamental mixing at the same signal frequency.
DOI
10.1109/tmag.1979.1060114

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A complete characterization and optimization have been carried out for an externally pumped Josephson-junction mixer. A noise-driven nonlinear pump equation is first solved in the time domain on a computer in order to obtain a conversion matrix and noise-correlation matrix for the small-signal current and voltage. A set of linear circuit equations formed by the matrices is then solved in the frequency domain for the mixer noise temperature and conversion efficiency. Finally, optimization is made with respect to circuit, bias, and junction parameters to find the ultimate theoretical performance.
The results of extensive analog computer simulations of a Josephson junction used as a mixer with an external local oscillator are presented. The Resistively Shunted Junction model was used throughout, and the effects of intrinsic junction noise were included. When the source impedance is much greater than the junction resistance R our simulations permit predictions of conversion efficiency, noise temperature, and saturation level to be made for a wide range of experimental parameters. The possibility of harmonic mixing has also been considered. With a source resistance comparable to R (i.e., conventional matching) the behavior of the system is too complicated to permit such general predictions of performance. From the results of simulations for a particular set of parameters it appears that the best noise temperature will usually be achieved for a source impedance somewhat greater than R. An upper limit for the mixer noise temperature is approximately 40 T over a broad range of junction parameters, where T is the effective temperature of the junction. The Conversion efficiency under these circumstances should be comparable to what is potentially available from Schottky diode mixers. Our simulations show that with stronger microwave coupling it is possible to obtain conversion gain - i.e., a conversion efficiency exceeding unity. This, however, will probably be at the expense of a higher mixer noise temperature.
We present the results of extensive analog-computer simulations of a Josephson junction used as a mixer with an external local oscillator. The resistively shunted junction model was used throughout, and the effects of intrinsic junction noise were included. When the source impedance is much greater than the junction resistance R, our simulations permit predictions of conversion efficiency, noise temperature, and saturation level to be made for a wide range of experimental parameters. The possibility of harmonic mixing has also been considered. With a source resistance comparable to R (i.e., conventional ’’matching’’) the behavior of the system is too complicated to permit such general predictions of performance. From the results of simulations for a particular set of parameters, it appears that the best noise temperature will usually be achieved for a source impedance somewhat greater than R. An upper limit for the mixer-noise temperature is ∼40T over a broad range of junction parameters, where T is the effective temperature of the junction. The conversion efficiency under these circumstances should be comparable to what is potentially available from Schottky-diode mixers. Our simulations show that with stronger microwave coupling it is possible to obtain conversion gain—i.e., a conversion efficiency exceeding unity. This, however, will probably be at the expense of a higher mixer-noise temperature. Saturation can be important even for source temperatures ∼300 K. To avoid saturation it is necessary either to restrict the coupling bandwith or use an array of junctions.
This paper presents theoretical analysis and modeling of YBaCuO superconducting Josephson mixer for terahertz frequency band. The study was carried out both for the mixing at the first harmonic and for the case of high harmonic mixing. The numerical solution based on resistively shunted junction model was obtained for the YBaCuO junction with typical experimental parameters. Optimizing mixer performance included choosing the proper operating point and the local oscillator power. A study on the effect of RF input power, frequency and the harmonic number on conversion efficiency was carried out. The theoretical predictions presented in the work provide a simple method for optimal control of the Josephson mixer and demonstrate good qualitative agreement with direct modeling. For the first time, the optimum of the conversion efficiency versus signal frequency was analytically obtained.
Analog-computer studies are made on a variety of mixing and parametric effects in Josephson junctions. The predictions of the constant-voltage model are compared with the more general behavior of a junction in a resistive circuit. A simple approximate method is developed for calculating frequency conversion efficiency and the matching condition for a junction operating in the oscillator mixer mode. A similar calculation is made for the second mode of operation, in which an external local oscillator is used. In either of these modes, frequency conversion gain is possible even in a purely resistive circuit. The conditions for parametric amplification without frequency conversion are also studied and it is found that gain occurs only when the self-oscillation frequency is near the signal frequency.