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soln1 - EECS 216 SOLUTIONS TO PROBLEM SET#1 Winter 2008 1a...

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Unformatted text preview: EECS 216 SOLUTIONS TO PROBLEM SET #1 Winter 2008 1a. Using voltage divider, H ( jω ) = [1 / ( jωC )] / [ R + jωL +1 / ( jωC )] = 1 / [1 − ω 2 LC + jωRC ] Note: Units or dimensions: every term is dimensionless. This is a good check. 1b. Assume default units. L=1 H,C=1 F,R=0.1Ω → H ( jω ) = 1 / [(1 − ω 2 ) + jω . 1] → | H ( jω ) | = 1 / radicalbig (1 − ω 2 ) 2 + ω 2 / 100 and negationslash H ( jω ) = tan − 1 ω/ 100 1 − ω 2 But: Add π to phase if | ω | > 1. IF you had any trouble with this, retake EECS 215! Matlab: W=linspace(0,2);subplot(421),plot(W,abs(1./(1-W. ˆ 2+j*W/10))) subplot(422),plot(W,angle(1./(1-W. ˆ 2+j*W/10))) if have no sig. proc. toolbox. 2a. 3 − 4 j = 5 e − j. 927 = 5 negationslash − . 927. Also: 12 + j 5 = 13 negationslash . 395 (not required). 2b. [(3 − 4 j ) + (12 − 5 j )] 2 = (15 − 9 j ) 2 = 225 − 81 − 2 j 15 · 9 = 144 − 270 j = 306 negationslash − 1 . 081 2c....
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soln1 - EECS 216 SOLUTIONS TO PROBLEM SET#1 Winter 2008 1a...

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