hw13 - ECE320 Homework 13 Cornell University Spring 2006...

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ECE320 Homework 13 Spring 2006 Cornell University T.L.Fine Please hand in this assignment by noon on Tuesday, 9 May, at my office in RH388. 1. Consider the phase locked loop (PLL) system displayed in Figure 11.17 of the class notes. The information-bearing phase modulated signal is the angle θ s ( t ) and the tracking or demodulated signal provided by the PLL is the angle θ v ( t ). The overall system S input is θ s and the system output is θ v . The goal is to have θ v ( t ) closely track θ s ( t ). (a) Write a system equation relating the error term e = θ s - θ v to the input θ s , to e itself, and to and the system elements. (This will not be an ode .) (b) Now assume that h represents an ideal integrator and, after appropriate differentiation, write an ode for the error e . Classify this ode as to order, degree, and whether or not it is autonomous. (c) Rewrite this ode in our standard vector differential equation form. (d) Identify equilibria points for the error e , if there are conditions under which they exist.
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