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hw12 - ECE320 Homework 12 Cornell University Spring 2006...

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ECE320 Homework 12 Spring 2006 Cornell University T.L.Fine Please hand in this assignment at the close of lecture on Tuesday, 2 May. 1. Themes of ECE320 include: 1. functions as the mathematical model for signals and systems; 2. random signals and systems and their probability models; 3. states and state-determined systems; 4. systems approach to applications drawn from much of ECE; 5. numerical methods and visualization tools for determining and displaying complex system behavior in a comprehensible manner. For each of these five themes, cite at least three homework problems, drawn from at least two homework assignments, that support these themes. A given homework problem may support more than one theme. 2. Consider a Josephson junction device driven by a current source I ( t ), as described in Section 11.5 and in Thursday’s lecture. (a) Sketch an equivalent circuit and specify the voltages across, and the currents through, the elements of the equivalent circuit.
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Unformatted text preview: (b) Write an ode for the phase diﬀerence θ between the two quantum mechanical wave functions describing the state of the two superconducting layers. (c) What are the conditions for, and the values of, any equilibrium points? (d) At an equilibrium point, what is the voltage V e across the device? What is the equivalent resistance R e of the device? Is it superconducting? (e) In this part, assume that the Josephson junction device parameters I c = 1 , R = ~ 2 e and C = β R for β = 1 . Using pplane7.m submit phase plane plots and plots of θ ( t ) for the two cases of I = 0 . 3 I c and I = 3 I c . (f) By considering the results of (c) and (e), under what conditions on the constant current source amplitude I can a Josephson junction device produce an oscillating voltage V across itself? (g) When the Josephson junction is not oscillating, what is its eventual equiva-lent resistance? 1...
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