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Proceedings of the IEEE

Analog-computer studies on microwave mixing in superconducting weak links

P. Russer, H. Bayegan

Published Jan 1, 1973• 3 citations
Publisher

Abstract

The dc characteristics of superconducting weak links, irradiated by one and two microwave frequencies and the dependence of the absorbed microwave power on the dc current, are evaluated. Within the constant voltage steps, the ac current generated in the weak link is synchronous with the incident microwaves or their mixing products. In the case of two incident microwave frequencies within the constant voltage steps, the dependence of the ratio of power-absorption variation on the impressed dc current at the two frequencies is governed by modified Manley-Rowe equations.

DOI
10.1109/proc.1973.8968

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IEEE Transactions on Magnetics•Jan 1, 1981•0 citations
The dc characteristics of superconducting weak links, irradiated by one and two microwave frequencies and the dependence of the absorbed microwave power on the dc current, are evaluated. Within the constant voltage steps, the ac current generated in the weak link is synchronous with the incident microwaves or their mixing products. In the case of two incident microwave frequencies within the constant voltage steps, the dependence of the ratio of power-absorption variation on the impressed dc current at the two frequencies is governed by modified Manley-Rowe equations.
This paper describes the I-V characteristics (as a function of applied magnetic field) and magnetic field response of a dc SQUID which incorporates two weak-link Josephson junctions in a superconducting ring. These characteristics are derived by digital computer simulation, using the Stewart-McCumber model. The effects of asymmetry (dissimilarity between the junctions) on SQUID critical current I c, normal resistance R and capacitance C are also simulated. With microwave excitation applied, the Josephson oscillations of the dc SQUID are found to be “frequency-locked” to the applied microwave signal even when critical currents I c of the two junctions differed, Subharmonic voltage steps are obtained for a symmetric dc SQUID in a magnetic field even when the current-phase relationship is purely sinusoidal.
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.
Experiments are reported in which two millimeter-wave signals incident on point-contact Josephson junctions produced changes in the junction dc voltage versus current characteristic and an intermediate frequency output whose amplitude depended sensitively on both junction bias and applied power. Equations are derived, based on Josephson's phenomenological equations, for the Josephson current in a junction exposed to two applied rf signals. When the applied signals differ appreciably in frequency, additional constant-voltage steps in the $V\ensuremath{-}I$ curve are predicted which are spaced at the difference frequency. These steps have been observed in experiments employing sources at 64 and 72 Gc/sec. Results of mixing experiments utilizing two sources nearly equal in frequency are reported at 23 and at 72 Gc/sec. In this case the two waves beat together and are equivalent in their effect to a single signal amplitude modulated at the difference frequency. Also explained on the same basis are experiments in which the third harmonic of a signal at 24 Gc/sec mixed with a signal at 72 Gc/sec. These results demonstrate the existence of the Josephson mixing mechanism as opposed to classical nonlinear mixing, and they show that it is operative at microwave and millimeter-wave frequencies over a wide range of power.
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.
We describe measurements of the 10 GHz dynamic impedance of niobium point-contact weak links at 2 K, biased below their critical currents. The measured quantity is Γ(ω), the complex reflection coefficient Of the weak link in parallel with a superconducting cavity resonator terminating a waveguide. Measurements were made at several frequencies close to resonance. In order to interpret the results it is only necessary to assume that the weak link is a two-terminal device consisting of a phase-dependent susceptance in parallel with a phase-dependent conductivity, which is connected to the waveguide through a lossless, phase-independent two-port. The data are consistent with the resistively shunted junction model including a phase-dependent conductance with a negative sign. An important feature of this study was the ability to measure the d.c. IV characteristic simultaneously. The point-contacts investigated had nearly ideal IcR products, and exhibited reproducibile structure in the differential conductance at the superconducting energy gap voltage.