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arXiv:physics/0512072 · Journal of Applied Physics

Cryogenic small-signal conversion with relaxation oscillations in Josephson junctions

Miha Furlan

Published Aug 1, 2006• 0 citations
arXivHTMLPDF

Abstract

Broadband detection of small electronic signals from cryogenic devices, with the option of simple implementation for multiplexing, is often a highly desired, although nontrivial task. We investigate and demonstrate a small-signal analog-to-frequency conversion system based on relaxation oscillations in a single Josephson junction. Operation and stability conditions are derived, with special emphasis on noise analysis, showing the dominant noise sources to originate from fluctuation processes in the junction. At optimum conditions the circuit is found to deliver excellent noise performance over a broad dynamic range. Our simple models apply within the regime of classical Josephson junction and circuit dynamics, which we confirm by experimental results. A discussion on possible applications includes a measurement of the response to a cryogenic radiation detector.

DOI
10.1063/1.2218984

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California Univ., Berkeley Report•Sep 1, 1977•0 citations
Broadband detection of small electronic signals from cryogenic devices, with the option of simple implementation for multiplexing, is often a highly desired, although nontrivial task. We investigate and demonstrate a small-signal analog-to-frequency conversion system based on relaxation oscillations in a single Josephson junction. Operation and stability conditions are derived, with special emphasis on noise analysis, showing the dominant noise sources to originate from fluctuation processes in the junction. At optimum conditions the circuit is found to deliver excellent noise performance over a broad dynamic range. Our simple models apply within the regime of classical Josephson junction and circuit dynamics, which we confirm by experimental results. A discussion on possible applications includes a measurement of the response to a cryogenic radiation detector.
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For sensitive wideband spectroscopy at THz frequencies with performance better than for Fourier Transform Spectrometer, one needs a wide-range electrically tunable, narrow linewidth THz source, and a sensitive broadband detector. To obtain a low noise level of sensor we use a superconducting normal metal cold electron bolometer (CEB). A voltage response of the bolometer is 4.108 V/W and an amplifier-limited technical noise equivalent power of the bolometer is 1.25.10-17 W/Hz1/2. The wide band electrically tuned terahertz band cryogenic oscillator is a Josephson junction. Contrary to conventional Josephson junctions based on niobium, and naturally limited in frequency by energy gap of about 700 GHz, the high critical temperature YBaCuO junctions can extend this limit by an order of magnitude. At 4 K such oscillators can radiate at frequencies exceeding 2 THz. Signals received by bolometers integrated with double-dipole and log-periodic antennas and irradiated by the Josephson oscillator show in our experiments the high frequency response corresponding to an oscillation frequency of up to 1.75 THz. Such cryogenic terahertz network analyzer is suitable for low-signal spectral evaluation of cryogenic detectors, quasioptical sub-mm cryogenic filters, planar antennas with planar microwave filters, integrated structures comprising such elements, and arrays of cryogenic receivers.
The Josephson frequency conversion in the millimeter and submillimeter wave region is studied with superconducting Nb–Nb point-contact junctions at 4.2 °K, using the contact both as the local oscillator and the mixer with intermediate frequencies of 0.1, 0.3, and 9.2 GHz. The point contact is in a nonresonant structure and fed by a constant current source: neither a strong rf coupling of the contact with a cavity nor a stabilizing shunt resistance was proved necessary. The direct observation of frequency conversion was performed with a microwave receiver at 9.2 GHz in a range of Josephson frequencies between 145 and 1600 GHz. The experiments with intermediate frequencies fi of 0.1 and 0.3 GHz indicate that conventional frequency conversion does not occur but that the observed signals are related to noise effects. An analysis of the frequency conversion mechanism in a Josephson junction operated as an oscillator-mixer is proposed which includes the noise effects and also the feedback effects induced in a junction driven by a constant current source. The results show that low-frequency current components are induced in the junction, which can give large spurious signals when small i.f. are used.
The behavior of the voltage−biased Josephosn junction coupled to a general external circuit is studied in the small−signal limit. The Josephson relations are formulated in the frequency domain in the form of an infinite set of difference equations relating the current and voltage amplitudes of different frequency components. The results are subsequently utilized to develop a general theory of the self−oscillating Josephson mixer, including noise. The noise temperature and conversion gain of the mixer are derived taking into consideration the image frequency response. A comparison is made between the operation of the negative−resistance converter in the SC regime and its operation in the OC regime.
We have studied Josephson junctions with intrinsic energy ħIc/2e (Ic being the critical current) comparable to thermal energy kT and examined their potential for electromagnetic signal conversion. In this case, moderate thermal fluctuations are sufficient to destroy Josephson oscillations but do not entirely suppress the Josephson dynamics. We have numerically calculated the DC I–V curves, their derivatives dnV/dIn, and the DC and harmonic voltage responses Vn of such Josephson junctions to the AC currents Iωsinωt. We have found that Josephson junction with γ = 2ekT/ħIc ≥ 0.5 is a nonlinear resistance at frequencies ω below characteristic Josephson frequency ωc = 2eIcRn/ħ and all current biases I0. Frequency conversion in such junctions occurs due to the classical mechanism on the nonlinearity of the DC I–V characteristics at low signal frequencies. With increasing the signal frequencies to the characteristic Josephson frequency ωc = 2eIcRn/ħ and higher, the Josephson mechanism by frequency modulation of the Josephson current gradually replaces the classical one. The classical conversion mechanism demonstrates higher conversion efficiencies than the Josephson mechanism, although it operates within a narrower bandwidth. At zero DC bias i0 and in the range of γ-values from 0.1 to 2, we have found odd harmonics Vn emerging from low signal currents. Zero-bias values of the third harmonic V3 maximize at 0.18IcRn for JJs with γ = 0.5 and Iω = 2.5Ic. Based on these findings and high-Tc Josephson junctions, a family of low-noise square-law detectors, harmonic multipliers, and linear heterodyne receivers can be developed for emerging terahertz applications.
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.