Electrical Engineering 20N - Fall 2002 - Lee - Midterm 2

Electrical Engineering 20N - Fall 2002 - Lee - Midterm 2 -...

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EECS 20. Midterm No. 2 Solutions November 8, 2002. 1. 40 points (10 points each part). Consider the Simulink diagram shown below: 1 Out1 1 s Integrator1 1 s Integrator .9 Gain 1 In1 y x This shows an LTI system with one input and one output, both of which are continuous-time signals. The input and output are indicated by the rounded boxes, and are labeled x and y . The gain is 0.9, and the integrators both have initial condition equal to 0. (a) Write a differential equation (with no integrals, just derivatives) that relates the input x and the output y . Answer : t Reals + , 0 . 9 x ( t )=¨ y ( t ) . (b) Give the [ A, b, c, d ] representation of this system. Solution : Let the state be the outputs of the two integrators, as follows: t Reals + ,z ( t )= " y ( t ) ˙ y ( t ) # Hence, A = " 01 00 # b = " 0 0 . 9 # c T =[1 0 ] d =0 . (c) Find the frequency response H : Reals Reals of this system. Solution : Let the input be x ( t e iωt , in which case the output must be H ( ω ) e iωt . Substituting these into the differential equation from part (a), we get 0 . 9 e iωt = H ( ω )( ω 2 e iωt ) ,
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This note was uploaded on 05/17/2009 for the course EE 20N taught by Professor Ayazifar during the Spring '08 term at Berkeley.

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Electrical Engineering 20N - Fall 2002 - Lee - Midterm 2 -...

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