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IEEE Transactions on Magnetics

Microstrip resonances in superconducting circuits

Andrew D. Smith, Bruce J. Dalrymple, Arnold H. Silver, R. W. Simon, John F. Burch

Published Mar 1, 1987• 10 citations
Publisher

Abstract

Josephson junctions connected to high Q microstriplines display current-steps which we attribute to standing wave resonances. The step voltages of the resonances depend on sample geometry and correspond to frequencies at which the loaded microstrip is resonant. The voltages of the resonances are insensitive to applied magnetic field and junction current density. Current step amplitudes scale with the zero-voltage critical current, and are largest for zero applied magnetic field. The strength of these resonant steps has important implications for biasing weakly damped Josephson junction circuits. In addition, the resonances are a useful tool for measuring microstrip properties.

DOI
10.1109/tmag.1987.1064982

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Josephson junctions connected to high Q microstriplines display current-steps which we attribute to standing wave resonances. The step voltages of the resonances depend on sample geometry and correspond to frequencies at which the loaded microstrip is resonant. The voltages of the resonances are insensitive to applied magnetic field and junction current density. Current step amplitudes scale with the zero-voltage critical current, and are largest for zero applied magnetic field. The strength of these resonant steps has important implications for biasing weakly damped Josephson junction circuits. In addition, the resonances are a useful tool for measuring microstrip properties.
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The high frequency properties of the one-dimensional transmission line consisting of a parallel array of resistively shunted Josephson tunnel junctions have been studied in the limit of relatively low damping where this nonlinear system exhibits new and interesting phenomena. Here we report on experimental and numerical investigations of a resonant step observed at a voltage corresponding to 600 GHz in the dc current-voltage characteristic of a parallel array of 20 identical small NbAl2O3Nb Josephson junctions interconnected by short sections of superconducting microstrip line. The junctions are mutually phase locked due to collective interaction with the line sections excited close to the half wavelength resonance. The phase locking range can be adjusted by means of an external dc magnetic field and the step size varies periodically with the magnetic field. The largest step corresponds to a superconducting phase difference of π between neighboring junctions.
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The high frequency properties of the one-dimensional transmission line consisting of a parallel array of resistively shunted Josephson tunnel junctions have been studied in the limit of relatively low damping where this nonlinear system exhibits new and interesting phenomena. Here we report on experimental investigations of a resonant step observed at a voltage corresponding to 600 GHz in the dc current-voltage characteristic of a parallel array of 20 identical small NbAlO/sub x/Nb Josephson junctions interconnected by short sections of superconducting microstrip line. The junctions are mutually phase locked due to collective interaction with the line sections excited close to the half wavelength resonance. The phase locking range can be adjusted by means of an external dc magnetic field and the step size varies periodically with the magnetic field.>
We have investigated numerically a system consisting of a long Josephson junction embedded into a microstrip resonator. For such a configuration the Josephson vortex dynamics in the junction is driven by the oscillating currents in the resonator. We have calculated the complex impedance of the junction at the resonant frequency. The Q factor of the resonator and the change of the resonant frequency of the whole system can then be easily calculated knowing the parameters of the resonator without Josephson junction. The fluxon dynamics and the complex impedance of the junction are simulated for different values of the junction length, damping, dc bias current, and dc magnetic field. This allows us to explain the behavior of the impedance of the junction and different loss mechanisms. In particular, we predict a nonmonotonic dependence of the both real and imaginary parts of the impedance on the amplitude of the oscillating current in the resonator for some range of parameters. Our results show that such a combination of active and passive superconducting elements forms a rather interesting nonlinear physical system which might be useful for development of tunable/switchable superconducting resonators and suggests an experimental technique for detecting trapped vortices in long junctions.
The authors report on the design and operation of a superconducting microstrip resonator containing four series-connected highly hysteretic Josephson junctions in the top layer. This arrangement generates constant-voltage steps at X-band drive frequencies useful for a Josephson voltage standard. At 12 GHz, steps up to 5 mV have been obtained with step amplitudes of about 100 mu A. The resonator principle can be used to save microwave power and to simplify the microwave circuit. To obtain sufficiently large and stable steps the critical current density and the junction length must be matched carefully with the order of maximum step used for the operation of the Josephson voltage standard. The X-band microwave drive frequencies offer substantial advantages in terms of costs and handling of microwave equipment.>