### Abstract

Series-biased arrays of long Josephson junction fluxon oscillators can be phase locked by mutual coupling to a high-Q, linear distributed resonator. A simplified model of such a device, consisting of junctions described by the particle-map perturbation theory approach which are capacitively coupled to a lumped, linear tank circuit, reproduce the essential experimental observations at a very low computational cost. A more sophisticated model, consisting of partial differential equation descriptions of the junctions, again mutually coupled to a linear tank, substantially confirm the predictions of the simplified model. In the particle-map model, the locking range in junction bias current increases linearly with the coupling capacitance; in the partial differential equation (p.d.e.) model, this holds up to a certain maximum value of the capacitance, after which a saturation of the locking range is observed. In both models, for a given spread of junction lengths, the existence of a minimum value of the capacitance for locking to a tank with a given resonant frequency is evidenced. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Original language | English |
---|---|

Journal | Journal of Applied Physics |

Volume | 72 |

Issue number | 7 |

Pages (from-to) | 3179-3185 |

ISSN | 0021-8979 |

DOIs | |

Publication status | Published - 1992 |

### Bibliographical note

Copyright (1992) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.## Cite this

Filatrella, G., Rotoli, G., Grønbech-Jensen, N., Parmentier, R. D., & Pedersen, N. F. (1992). Model studies of long Josephson junction arrays coupled to a high-Q resonator.

*Journal of Applied Physics*,*72*(7), 3179-3185. https://doi.org/10.1063/1.352343