Step Response Analysis.docx

# Step Response Analysis.docx

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Step Response Analysis By: Elias Najem Hanna Daoud Presented to: Mr. Nassif Daoud A Formal Report for the circuit lab ELEN303 Faculty of Engineering University of Balamand 16-10-2018

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Prelab: 1.a) R 2 = 10 8 > 4 L C = 10 7 α = R 2 L = 10 10 3 2 0.1 = 50000 ωo = 1 / LC = 1 0.1 0.1 10 6 = 10000 This is an over-damped case; Therefore the roots for this case are: m 1 = 2 −ω o 2 = 98989.79 m 2 = + 2 −ω o 2 = 1010.205 1.b) Due to the fact that it is a critically damped case: R 2 = 4 L C = 4000000 R = 2000 Rp = Rt −Rth−Rl = 2000 50 70 = 1880 In addition that both of the roots are equal m 1 = m 2 = −α = −R 2 L = 10000 1.c) R = 150 Ω→R 2 = 22500 R 2 < 4 L C = 10 7 α = 150 2 0.1 = 750 This is an under-damped case; wd = ωo 2 −α 2 = 10000 2 ( 750 / ( 2 0.1 ) ) 2 = 9971.835338 m 1 = −α + jwd m 2 = −α − jωd
1-Objective: Study the behavior of the three types of second order circuits (under-damped, critically-damped over-damped) and show how the time constant calculated is affected in each case.

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• Winter '19
• Quadratic equation, Elementary algebra, Characteristic polynomial, The Roots, University of Balamand

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