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Journal of Applied Physics

Analog-computer studies of mixing and parametric effects in Josephson junctions

C.A. Hamilton

Published May 1, 1973• 28 citations
Publisher

Abstract

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.

DOI
10.1063/1.1662568

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Performance limits of a Josephson junction mixer

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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.

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IEEE Transactions on Magnetics•Jan 1, 1979•2 citations
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.
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.
Microwave superconducting mixers operating at 10–13 GHz utilizing Josephson junctions have been investigated analytically and experimentally. Measurements on mixer sensitivity were carried out at 13 GHz using waveguide-mounted experimental point-contact Josephson junctions at 4.2 K. Results showed sensitivities of −90 dBm/MHz (10−18 W/Hz) which included mismatch losses encountered in the waveguide structure. The Josephson junction mixing mechanism was analyzed on the basis of small-signal modulation of the staircase like dc I-V characteristics. It was shown that a small-signal microwave excitation results in an ac lateral shift of the regions between steps, such that: (a) Optimum Josephson mixing occurs halfway between steps. (b) Mixing occurs between all steps with maximum conversion efficiency between the zero and first step. (c) Predicted low conversion loss and possibly internal gain for a matched mixer. The analytical model was simulated by a digital computer and the behavior of the Josephson mixer predicted for various conditions of excitation. The model chosen for the analysis and the computer simulation is based on the simplest assumptions concerning bulk-formed Josephson junctions. In the laboratory an external local oscillator set 60 MHz below the signal frequency was used to induce the well-known step structure in the dc I-V characteristic of the point-contact Josephson junction. Mixing of the Lo and signal was found to occur between constant voltage steps in agreement with both analysis and computer simulation. The correctness of the model is demonstrated by the agreement between the theory and experiment.
Conventional negative resistance effects can be generated with a Josephson junction quite similar to that obtained with Varactor diodes, with the additional advantage that the internal, self-generated oscillations serve as a pump, i. e., only a dc source is needed instead of a high frequency pump source. However, another negative resistance effect typical for a Josephson junction is possible as has been predicted recently for the current controlled, highly damped junction model. The effect has recently been demonstrated experimentally at 9 GHz. Characteristically, the pump (Josephson) frequency is smaller than the frequency of the amplified signal and the pump mechanism is effective over a broad range of frequencies in contrast to the conventional parametric negative resistance effect where the pump frequency exceeds that of the signal and idler and where the frequency of operation is limited to a narrow range. The broad-band feature renders the amplifier operation uncritical to tuning and bias voltage fluctuations. The fact that the junction is the element of lowest impedance in the circuit alleviates to a degree the matching problem generally encountered with Josephson contacts. An assessment of the competitiveness of this effect in microwave technology is given.
The high-frequency amplification properties of transformer coupled, resistively shunted Josephson tunnel junctions have been investigated. The importance of the shunt loop inductance is stressed. It allows a high cutoff frequency, of significance for good high-frequency performance. The self-pumped parametric amplifier showed none of the excessive noise rise, which has hitherto plagued the development of externally pumped Josephson junction amplifiers. Around 10 GHz, we estimated a noise temperature less than 30 K for an amplifier pumped by a Josephson oscillation with a frequency well above twice the signal frequency. The corresponding gain of 5 dB may be increased in a better impedance matched circuit. The gain was very stable against variations in the bias conditions. A gain-bandwidth product as high as 0.3 was registered. The experimental results agreed well with the established theory for self-pumped parametric Josephson amplifiers. It should be possible to extend the low noise amplification by this device to mm wave frequencies. A relaxation oscillation occurred at a subharmonic of the Josephson frequency when the shunt loop inductance became large. The amplification in this mode followed closely the predictions of a simple model, where the signal modulated the switching of the sawtooth-like (relatively low frequency) relaxation current. Gains of about 15 dB were measured around 10 GHz, but the amplification was sensitive to bias conditions and noisy in this case where the relaxation frequency fell well below the signal frequency. Much improved properties were registered when the inductance was decreased so that the relaxation frequency approached the Josephson frequency and exceeded twice the signal frequency. The behavior then resembled that of a Josephson mode parametric amplifier, but the high content of harmonics of a relaxation oscillation meant that the amplifier became noisier due to converted noise from the many idler frequencies.