Wk_11_Lecture_1 - First-order Circuits Characterized by a...

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1 First-order Circuits • Characterized by a first-order differential equation RC, RL Two ways of excitations • Source-free • Independent sources (dc, sinusoidal, exponential) 1 BME 311 Network Theory John X.J. Zhang, UT Austin t RC t e V e V t v 0 0 ) ( Where, = RC Natural Response of RC Circuit Natural response: the circuit response with no external sources of excitation t t Time constant : the time required for the response to decay to a factor of 1/e or 36.8% of its initial value RC e V e V t v 0 0 ) ( Where, = RC 2 BME 311 Network Theory John X.J. Zhang, UT Austin 5 : “fully” charges or discharged v(t+ ) = v(t)/e = 0.368 v(t)
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2 • Time constant (cont.) Initial rate of decay Smaller faster response (charge or discharge) 3 BME 311 Network Theory John X.J. Zhang, UT Austin A e i t 4 2 . 0 For the following circuit: 4 BME 311 Network Theory John X.J. Zhang, UT Austin
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3 First-order Circuits • Characterized by a first-order differential equation RC, RL Two ways of excitations • Source-free • Independent sources (dc, sinusoidal, exponential) 5 BME 311 Network Theory John X.J. Zhang, UT Austin t RC t e V e V t v 0 0 ) ( Where, = RC ? The Source-Free
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Wk_11_Lecture_1 - First-order Circuits Characterized by a...

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