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ECE 201 – Lecture 23

ECE 201 – Lecture 23 - ECE 201 Section 3 Lecture 23 Prof...

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ECE 201, Section 3 Lecture 23 Prof. Peter Bermel October 19, 2012
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Driven Series RLC Circuits From KVL: g G ± G + ³ ´ + 1 ´µ ± = · ´ g G ¸ G + 2Γ ¸ + ¹ º G ¸ = ¹ º G · Γ = ³/2´ ; ¹ º = 1/ ´µ ; ¹ » = ¹ º G − Γ G = −¼Γ′ 10/19/2012 ECE 201-3, Prof. Bermel Regime Range Solution Behavior Under- damped Γ < ¹ º ¸ ² = ½ ¾¿À cos ¹ » ² + Á + ¶ · Oscillate & decay Critically damped Γ = ¹ º ¸ ² = ½ ¾¿À  à +  G ² + ¶ · Decay Over- damped Γ > ¹ º ¸ ² = ½ ¾¿À Â Ä ½ ¿ Å À +  ¾ ½ ¾¿ Å À + ¶ · Decay R L C + - V s
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Driven Parallel RLC Circuits From KCL: g G ± ² G + 1 ´µ ² + 1 ¶µ ± ² = ± · ¶µ g G ± ² G + 2Γ ² + ¸ ¹ G ± ² = ¸ ¹ G ± º Γ = 1/(2´µ) ; ¸ ¹ = 1/ ¶µ ; ¸ » = ¸ ¹ G − Γ G = −¼Γ′ 10/19/2012 ECE 201-3, Prof. Bermel Regime Range Solution Behavior Under- damped Γ < ¸ ¹ ± ² ³ = ½ ¾¿À cos ¸ » ³ + Á + ± º Oscillate & decay Critically damped Γ = ¸ ¹ ± ² ³ = ½ ¾¿À  à +  G ³ + ± º Decay Over- damped Γ > ¸ ¹ ± ² ³ = ½ ¾¿À Â Ä ½ ¿ Å À +  ¾ ½ ¾¿ Å À + ± º Decay R L C I s I L
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Example 10/19/2012 ECE 201-3, Prof. Bermel Consider an LC circuit connected to a voltage source at t=0. How will the current and voltage vary with time? L C + - t=0 + V C - V s I(t)
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Solution 10/19/2012 ECE 201-3, Prof. Bermel Employing our solution: g G = ± ² ³ ´ µ + ± · ³ ´ ¸ ¹ º = −Γ º Γ » − ¼ ½ » Γ = ¾ »¿ = 0 ; ¼ ½ = 1/ ÀÁ ¹ º = ºÂ¼ ½ C + - t=0 + V C - V s L I(t)
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