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IEEE Transactions on Applied Superconductivity

Dynamic effects in pulse-driven Josephson junctions

H.A. Kratz

Published Mar 1, 1993• 1 citation
Publisher

Abstract

The dynamic threshold characteristics of Josephson-junction circuits operated as fast signal detectors have been simulated for a wide range of load conditions, pulse widths, and pulse amplitudes. The simulations have been carried out using the familiar resistively and capacitively shunted junction model and a modified version of an approximate Werthamer model for the Josephson junctions. Approximation formulas for the dynamic threshold characteristics are given, and a readout circuitry for inductively shunted sampling gates is presented.>

DOI
10.1109/77.233973

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arXiv:2503.20022•Mar 25, 2025•0 citations
The dynamic threshold characteristics of Josephson-junction circuits operated as fast signal detectors have been simulated for a wide range of load conditions, pulse widths, and pulse amplitudes. The simulations have been carried out using the familiar resistively and capacitively shunted junction model and a modified version of an approximate Werthamer model for the Josephson junctions. Approximation formulas for the dynamic threshold characteristics are given, and a readout circuitry for inductively shunted sampling gates is presented.>
The dynamical behavior of a balance sampling gate, consisting of two directly serially connected Josephson junctions and a common shunt resistor, has been investigated by numerical simulations and approximated equations of the resistive shunted junction model. A reduced damping parameter has been found which determines the sampler behavior alone and enables an optimization. A 2.4-ps rise time of the response to a step-function signal predicted by the approximated theory has been verified by numerical simulations. The sampling gate can be driven directly by a room-temperature generator with a rise time of a few hundred picoseconds.
We have measured Nb–AlOx–Nb Josephson tunnel junctions which have resistive shunts with different parasitic inductances. Numerical simulations reveal that specific features in the experimental current–voltage (I–V) characteristics of these devices are dc signatures of complex ac behavior. Depending on the inductance of the shunt loop and the capacitance of the junction, these features may either appear or disappear as the temperature of the device is increased. Examination of the simulated voltage waveforms allows us to map regions of the parameter space which exhibit complicated behavior. These regions should be avoided when a nearly sinusoidal voltage waveform is desired, as is the case for Josephson junction-based oscillators. The agreement of the experimental and simulated I–V curves also enables us to accurately determine the inductance of the shunts and the capacitance of the junctions.
Two-dimensional arrays of Josephson junctions have been shown to operate in a state in which the microwave oscillations of the junctions are phase-coherent. However, the performance of an array is strongly dependent on both the details of the load-coupling circuit and the characteristic parameters of the junctions. We have measured two-dimensional arrays of resistively shunted Josephson tunnel junctions which are capacitively coupled to a nearby detector junction. Changing the critical current of the junctions in our arrays, while keeping the junction parasitics and array coupling roughly the same, results in an unexpected change in device operation. We have also investigated variations of the coupling circuit. Numerical simulations of the detection circuit enable us to estimate the power output from the array and to optimize the parameters of the system.
The shunt resistors used in many Josephson junction circuits contain an inductive component that can significantly degrade high-frequency performance. Numerical simulations reveal complex dynamical behaviour, including relaxation oscillations, period-doubling sequences, and chaos, all of which are serious problems for applications as high-frequency sources and detectors. This complex AC behaviour creates features in the simulated DC current-voltage characteristics. Since these simulations closely match experimental data, they can be used to investigate the high-frequency AC behaviour of real junctions. Thus, we are able to use simple DC measurements to observe evidence of complex high-frequency dynamics. The inductance of the shunt branch can be accurately determined by comparing simulations to measurements. Simulations also allow us to map regions of the parameter space which exhibit complicated behaviour. These regions should be avoided when a nearly sinusoidal voltage waveform is desired, as is the case for Josephson junction-based oscillators.
Previously published experimental results are used to deduce an equivalent circuit for this amplifier, based on the shunted junction model. It is found that the very small inductances of the junction shunt resistors play an important role in determining the shape of the current-voltage curves in the voltage-locked region. Once the circuit is determined using the shunted junction model a combination of an approximation method (the method of slowly varying amplitudes) and the shunted junction model is used to approximately maximize the power gain of the circuit. The maximum gain achieved in these simulations of the two-junction amplifier is 11.3. This gain occurred with a negative resistance imput impedance of −0.41R and a signal source impedance of 0.167R, where R is the junction shunt resistance. It is estimated that the bandwidth of this amplifier is about 1 GHz.
Measurement of signals generated by superconducting Josephson junction (JJ) circuits require ultra-fast components located in close proximity to the generating circuitry. We report a detailed study of optimal design criteria for a JJ-based sampler which balances the highest sampler bandwidth (shortest 10\%--90\% rise time) with minimal sampled waveform distortion. We explore the impacts on performance of a sampler, realized using a single underdamped JJ as the logical sampling element (the comparator), due to the type of signal-comparator coupling scheme that is utilized (galvanic, inductive, or capacitive). In these simulations we emulate the entire waveform reconstruction sampling process, via comparator threshold detection, while sweeping the time location at which the waveform is being sampled. We extract the sampled waveform rise time (or FWHM) as a function of the comparator's Stewart-McCumber parameter and as a function of the coupling strength between the device under test and comparator. Based on our simulation results we design, fabricate, and characterize a cryocooled (3.6 K operating temperature) JJ sampler utilizing the NIST state-of-the-art Nb/amorphous-Si/Nb junctions. We separately sample a step signal and impulse generator co-located on-chip with the comparator and sampling strobe generator by implementing the same binary search comparator threshold detection technique during sampler operation as is used in simulation. With this technique the system is fully-digital and automated and operation of the fabricated device directly mirrors simulation. Our sampler technology shows a 10\%--90\% rise time of 3.3 ps and the capability to measure transient pulse widths of 2.5 ps FWHM. A linear systems analysis of sampled waveforms indicate a 3 dB bandwidth of 225 GHz, but we demonstrate effective measurement of signals well above this -- as high as 600 GHz.