ECE201_25_Jung

ECE201_25_Jung - ECE 201 Lecture 25 2nd order circuits: RLC...

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ECE 201 Lecture 25 2 nd order circuits: RLC with constant inputs (continue….)

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REVIEW - Source Free 2 nd Order Circuit and given with characteristic equation Problem is reduced to solving the linear differential equation: Case 1 ( two distinct real roots s 1 , s 2 ): Case 2 ( two identical real roots s 1 =s 2 ): Case 3 ( two conjugate complex roots s 1 =- σ +j ϖ d , s 2 =- σ -j ϖ d ): 2 2 0 L L L d i di LC RC i dt dt + + =
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 -0.5 0 0.5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 -0.5 0 0.5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -20 -10 0 10 20 Typical Solutions Series LCR: Case 3 Series LCR: Case 3 (when R=0) 2 R L σ= Unstable system (Not in ECE201)

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Plot of v C (t) 0 0.05 0.1 0.15 0.2 1 0.5 0 0.5 1 1 1 - x t 0 , ( ) x t 2 , ( ) x t 5 , ( ) x t 10 , ( ) 0.2 0 t 0 0.05 0.1 0.15 0.2 1 0.5 0 0.5 0.459 1 - x t 10 , ( ) x t 20 , ( ) x t 30 , ( ) x t 40 , ( ) x t 80 , ( ) 0.2 0 t ϖ 0 ( ) 2 π 31.831 = ϖ 2 ( ) 2 π 31.791 = ϖ 5 ( ) 2 π 31.581 = ϖ 10 ( ) 2 π 30.82 = 0 2 5 10 R Series LCR 10 20 30 40 ϖ 0 ( ) 2 π 31.831 = ϖ 10 ( ) 2 π 30.82 = ϖ 20 ( ) 2 π 27.566 = ϖ 30 ( ) 2 π 21.054 = ϖ 40 ( ) 2 π 0 = Case 3 Underdamped Critically damped
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 -5 -4 -3 -2 -1 0 1

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This note was uploaded on 10/26/2010 for the course ECON 002 taught by Professor Eudey during the Spring '08 term at UPenn.

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ECE201_25_Jung - ECE 201 Lecture 25 2nd order circuits: RLC...

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