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ECE201_23_Jung

# ECE201_23_Jung - ECE 201 Lecture 23 2nd order RLC circuits...

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ECE 201 Lecture 23 2 nd order RLC circuits, Source free

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Example V S (t) R1 R2 V S (t) R1 R2 V S (t) R1 R2 C1 C2 L1 L2 L1 L2
Review of Last Lecture K, θ, K’, θ determined by the initial conditions v C (0) and i L (0) Undamped (ideal) oscillator circuit one natural frequency

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0 0 .5 1 1 .5 2 2 .5 3 -3 -2 -1 0 1 2 3 Sinusoidal Function period frequency (Hz): angular velocity (rad/s): 0 0 .5 1 1 .5 2 2 .5 3 -3 -2 -1 0 1 2 3 different phase θ
Another Example The switch is closed for a long time before it flips at time t=0 For t>0 with At time 0 - ( 29 10sin 2 2 C t t π υ = - -

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Serial RLC Circuit are given KCL KVL In terms of v C In terms of i L differentiate v C (t)=?, i L (t)=? 2 2 0 L L L d i di LC RC i dt dt + + =
General Form of the Differential Equations Equations for v C and i L are of the general form with initial conditions and given characteristic equation Guess : solutions are of the form for some constants K, s

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Characteristic Equation Characteristic equation has two roots: Case 1 ( two distinct real roots ): Case 2 (
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ECE201_23_Jung - ECE 201 Lecture 23 2nd order RLC circuits...

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