worksheet step response analysis.docx

worksheet step response analysis.docx

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1-PRELAB: 1. Characteristic equation: S 2 + 2*α*S + W 0 2 =0 ; W 0= LC / 1 and L R 2 / This second order equation has two solutions S1 and S2: S1= 2 0 2 and S2= 2 0 2 a- In the first case: R=10 kΩ ; L=0.25H ; C=0.1 µ F ; W 0= LC / 1 = 6324.55 L R 2 / = 20000

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S1= 2 0 2 = -1026.33 and S2= 2 0 2 = -38973.66 b- Two equal roots =0 R=Rc ; characteristic equation: S 2 + 2*α*S + W 0 2 =0 = 4 α 2 – 4W 0 =0 6 2 2 10 1 . 0 25 . 0 4 25 . 0 4 c c R LC L R So R c = 3162.27766 Ω In the second case: V c (t) = (A 1 + A 2 t) e - αt ; A 1 and A 2 constants L Rc 2 / = 6324.55 = W 0 V c (t) = (A 1 + A 2 t) e - αt = (A 1 +A 2 t) e -6324.55 t c- For R=150 Ω
In this case: W 0= LC / 1 = 6324.55 L R 2 / = 300 W 0 > α W d 2 = W 0 2 – α

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• Winter '19
• Characteristic polynomial, 0.1 10 , 

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