ECE 201 – Lecture 21

Damping r2l and write solutions regime root

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Unformatted text preview: y Oscillates forever 0<Γ< Complex Oscillate & decay Critically damped Γ= Pure real Decay Overdamped Γ> Pure real Decay Undamped Underdamped 2/29/2012 Value Range Γ=0 ECE 201-4, Prof. Bermel Special Cases: RLC Circuits • In general, one can define a quality factor: = 2Γ Measures the lifetime of an excitation • Here, Γ=R/2L, and = 1/ , so 1/ = 2 ∙ /2 = 1 As R → 0, Q → ∞, and vice versa 2/29/2012 ECE 201-4, Prof. Bermel Mathematica Demonstration Click to begin 2/29/2012 ECE 201-4, Prof. Bermel Example 1 • Consider a circuit which charges a capacitor for t<0 then switches to an RLC circuit at t=0. What is VC(t) for R=0, and 180? t=0 20 Ω 50 V + - 0.1 F 2/29/2012 + VC - R ECE 201-4, Prof. Bermel 0.1 H Solution t=0 20 Ω 50 V + VC - + - 0.1 F R 0.1 H • For t<0: VC=50 V • For t>0: I(0)=0, and: = Γ= 2/29/2012 = = .∙. = 10 rad/s = ∙ (0.1 ) 10 1 = = = Γ ∙( ) ECE 201-4, Prof. Bermel Solution t=0 20 Ω 50 V + - 0.1 F R + VC - 0.1 H • From before: = = /= + + = + Matching boundary conditions: + = −Γ + + −Γ − =0 2/29/2012 ECE 201-4, Prof. Bermel Solution t=0 20 Ω 50 V + VC - + - 0.1 F R 0.1 H • Substituting: + = + −Γ − = Γ+ −Γ + = −Γ + =0 Γ − − 2/29/2012 1− − + −Γ − = Γ− Γ = 1+ ECE 201-4, Prof. Bermel =0 Solution t=0 20 Ω + - 50 V 0.1 F • From before: = 2 = 2/29/2012 1− R + VC - 0.1 H Γ cos + 1+ + ECE 201-4, Prof. Bermel Γ sin Γ Homework • HW #19 solution posted • HW #20 due today by 4:30 pm in EE 326B • HW #21 due Wed.: DeCarlo & Lin, Chapter 8: – Problem 30 – Problem 34 2/29/2012 ECE 201-4, Prof. Bermel...
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