Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 4.6, Problem 4E
Interpretation Introduction

Interpretation:

a) To determine the relation between dc bias current, current through array, and current through load resistance.

b) To show that Ia=ICsinΦ1+v1r and Ia=ICsinΦ2+v2r.

c) To relate vk and Φk.

d) To show Ib=ICsinΦk+2erΦ˙k+2eR(Φ˙1+Φ˙2)......................For k=1,2.

e) To write the equation derived in part d) in standard form of Φ˙k=Ω+asinΦk+Kj=12sinΦj

Concept Introduction:

A Josephson Junction consists of two superconductors which are coupled by a week connection of insulators, a weakened superconductor, or a semiconductor.

Josephson Junctions are superconducting devices, which can produce voltage oscillations of very high frequency in the range of 10101011 Hz.

If a Josephson junction is connected to a dc current source so that a non-zero current I can be driven through the junction, it is possible to show that if this current is less than critical current IC, there will be no voltage generated across the junction. But phases of both the superconductors will have constant phase difference Φ=Φ2Φ1. Φ satisfies the Josephson current phase relation

I=ICsinΦ

When the current I exceeds the critical current IC, a constant phase difference cannot be maintained, and a potential difference is developed across the junction. The phase difference begins to slip, and the rate of slippage is given by the equation

V=2eΦ˙

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