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IEEE Transactions on Microwave Theory and Techniques

Nonlinear mixer gain calculations for Josephson junctions

Hoton How, Ta-Ming Fang, C. Vittoria, A. Widom

Published Jan 1, 1995• 3 citations
Publisher

Abstract

We have numerically solved the steady-state solutions of the initial value problem associated with a current-driven Josephson weak-link junction shunted by an ohmic resistance. The nonlinear mixing action of the junction leads to Shapiro steps in the DC response with step height in units of the mixing frequency. Mixer gains have been calculated with a wide range of parameter values and intrinsic chaos is observed whenever Shapiro steps are prevalent.>

DOI
10.1109/22.362987

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Journal of Applied Physics•Jul 1, 1978•42 citations
We have numerically solved the steady-state solutions of the initial value problem associated with a current-driven Josephson weak-link junction shunted by an ohmic resistance. The nonlinear mixing action of the junction leads to Shapiro steps in the DC response with step height in units of the mixing frequency. Mixer gains have been calculated with a wide range of parameter values and intrinsic chaos is observed whenever Shapiro steps are prevalent.>
Experimental I-V curves of microwave-driven Josephson tunnel junctions with resistive shunts are reported. The results are in very good agreement with numerical calculations using the resistively shunted junction model. In the low-frequency regime there are three distinct regions in the I-V curves and two different types of Shapiro steps. It is demonstrated that the overall shape of the I-V curves can be explained by using an adiabatic interpretation of the junction response. The two different types of Shapiro steps are related to a compensation effect between dc and rf bias currents.
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 report here numerical calculations on the properties of superconducting weak links as mixers with external local oscillators (LO). Our calculations are based on the resistively shunted-junction model. We assume that the LO and the signal are ideal current sources of amplitudes ILO and IS and of frequencies ωLO and ωs, respectively. We calculate the IF voltage across the weak link as a function of the bias current, the LO current amplitude ILO, and the normalized signal frequency Ωs = ħωs/(2 e Ic R), where Ic is the critical current and R is the shunt resistance. If ωIF/ωLO and Is/Ic are small, we find a linear IF response. Using this method we find the frequency dependence of the IF response, estimate the conversion efficiency for the matched case in both the absence and the presence of noise, and calculate the required LO power. We have fabricated thin-film constrictions by using electron lithography. We have made constrictions of indium films with thicknesses of ~ 1 200 A with widths as narrow as 2 000 A and lengths as short as 1 000 A and have studied their I-V characteristics in the presence of RF radiation and measured their X-band mixing properties. We have measured an NEP of 10-13 W/Hz1/2 and a dynamic range of 23 dB (3 dB deviation from linearity) and estimate that, with optimum matching, these would become 3 × 10-18 W/Hz1/2 and 74 dB, respectively.
The Josephson junction device is promising as a mixer for regions from millimeter wave to infrared. It is important to analyze Josephson devices to determine the circuit parameters and operating points of the circuits. However, it is difficult to analyze the mixer operation because of the nonlinear characteristic of the Josephson junction device. Therefore, small signal analysis has been conducted in characterizing the Josephson junction device. In this study, a detailed characterization of the IF output characteristic was obtained by introducing the concept of IF Shapiro steps. That is, it was determined that the minima that are not present in the local-oscillator Shapiro steps are present in the Josephson junction mixer output. In addition the impedance of the Josephson junction device was discussed and illustrated using a Smith chart. In this paper, the theoretical result was proved by a mixing experiment on the step-edge junction. As a result, the minima points in the IF output were confirmed. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 2, 80(3): 69–79, 1997
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.