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IEEE Transactions on Magnetics

The effect of the quantum susceptance on the gain of superconducting quasiparticle mixers

C. A. Mears, Qing Hu, P. L. Richards

Published Mar 1, 1991• 7 citations
Publisher

Abstract

A detailed analysis of the effects of the quantum susceptance on the performance of superconductor-insulator-superconductor (SIS) mixers is performed. It is found that the principal effects of the quantum susceptance are to change the DC bias at which optimum coupling of the signal to the mixer occurs, and to change the output admittance at the IF frequency, thus changing the available gain. It is shown that at the signal port the principal effect is to change the bias voltage at which optimum coupling to the mixer occurs. A more dramatic effect occurs at the IF port, where the quantum susceptance leads to negative values of the output conductance, which causes the available gain to be infinite.

DOI
10.1109/20.133938

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STIN•Jan 1, 1981•0 citations
A detailed analysis of the effects of the quantum susceptance on the performance of superconductor-insulator-superconductor (SIS) mixers is performed. It is found that the principal effects of the quantum susceptance are to change the DC bias at which optimum coupling of the signal to the mixer occurs, and to change the output admittance at the IF frequency, thus changing the available gain. It is shown that at the signal port the principal effect is to change the bias voltage at which optimum coupling to the mixer occurs. A more dramatic effect occurs at the IF port, where the quantum susceptance leads to negative values of the output conductance, which causes the available gain to be infinite.
The quantum theory of mixing is essential for the interpretation of experimental superconducting quasiparticle (SIS) mixers. When the bias and tuning parameters are known, the theory is quite successful at predicting the mixer performance, gain and noise temperature. However, the theory usually predicts much higher conversion gain for some other set of bias and tuning parameters, and this is not seen in experiment. Thus the theory is less useful for engineering design of SIS mixers. We believe we have resolved this longstanding discrepancy. We find there are two distinct optimum operation modes for ideal SIS mixers. The high gain mode predicted by the theory will not be accessible in real experiments. To understand this we present the equations of a DSB SIS mixer in a novel form, in terms of the complex plane phase angle between the amplitude modulation input admittance vector and the local oscillator input admittance vector.
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.
We have measured the properties of a superconductor-insulator-superconductor quasiparticle mixer which is operated in the quantum limit. Single sideband conversion gain larger than +4 dB was observed at 36 GHz with a mixer noise temperature T = 9±6 K, which is to be compared with the (Planck) quantum limit h/ω/(k ln 2)≃2.5 K. Complete three-port mixer calculations are presented which are in good agreement with the gain measurements. The dynamic resistance was observed to become infinite and then negative as the source conductance was decreased. This implies that arbitrarily large gain is available. The negative resistance is accompanied by IF oscillations.
The authors have used the quantum theory of mixing for extensive numerical calculations to determine the mixer source conductance G/sub s/ required to optimize a superconductor-insulator-superconductor (SIS) quasiparticle heterodyne receiver. The optimum G/sub s/ matches an empirical formula which can be understood by a simple derivation. Previous work indicated that G/sub s/ should vary inversely with frequency, and this implies that the critical current density of SIS junctions used for mixing should increase as frequency squared, a stringent constraint on the design of submillimeter SIS mixers. On the contrary, it was found that G/sub s/ is more weakly dependent upon frequency, and the implications for the design of submillimeter SIS mixers are discussed.>
Virtually all analyses of the superconductor-insulator-superconductor (SIS) quasiparticle mixer have employed the quantum theory of mixing in its three-frequency approximate form. This approximation is valid only in the limit of very large junction capacitance. For finite capacitance, these analyses may be seriously in error. To remedy this, a computer program has been developed which uses the quantum theory of mixing in its most general form, treating the large-signal properties of the mixer in the time domain. The terminating impedances at the harmonics of the local oscillator frequency and their sidebands can be arbitrary. Using this analysis, the effect of finite junction capacitance on one SIS mixer's performance is described. This gives an insight into the range of validity of the three-frequency model.
We have measured the properties of a superconductor-insulator-superconductor (SIS) quasiparticle mixer which is operated in the quantum limit. Single sideband conversion gain larger than +4 dB was observed at 36 GHz with a mixer noise temperature T=9 + or - 6K, which is to be compared with the (Planck) quantum limit h-bar omega/(kln2) approx. 2.5K. Complete 3-port mixer calculations are presented which are in good agreement with the gain measurements. Negative resistance was observed which implies that arbitrarily large gain is available.