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Three-port quantum mixer theory for superconductor-insulator-superconductor tunnel junctions is solved for several simple cases of practical interest. Closed form solutions are derived for the conversion gain in the low local oscillator power limit, and also the general conditions for zero and infinite gain. These results are useful in understanding more general computer calculations of predicted performance. Practical limits to gain and dynamic range are analyzed both for series arrays and single junctions.
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Smith et al. (1982) studied this question.
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