ECE201Lect-21

# ECE201Lect-21 - ECE201 Lect-21 1 Second-Order Circuits(7.3...

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Unformatted text preview: ECE201 Lect-21 1 Second-Order Circuits (7.3) ECE201 Lect-21 2 2nd Order Circuits • Any circuit with a single capacitor, a single inductor , an arbitrary number of sources , and an arbitrary number of resistors is a circuit of order 2 . • Any voltage or current in such a circuit is the solution to a 2nd order differential equation. ECE201 Lect-21 3 Important Concepts • The differential equation • Forced and homogeneous solutions • The natural frequency and the damping ratio ECE201 Lect-21 4 A 2nd Order RLC Circuit • The source and resistor may be equivalent to a circuit with many resistors and sources. R C v s (t ) i (t) L + – ECE201 Lect-21 5 Applications Modeled by a 2nd Order RLC Circuit • Filters – A lowpass filter with a sharper cutoff than can be obtained with an RC circuit. ECE201 Lect-21 6 The Differential Equation KVL around the loop: v r (t) + v c (t) + v l (t) = v s (t) R C v s (t ) + – v c (t) + – v r (t) L + – v l (t) i (t) + – ECE201 Lect-21 7 Differential Equation ) ( ) ( 1 ) ( ) ( t v dx x i C dt t di L t Ri s t = + + ∫ ∞- dt t dv L t i LC dt t di L R dt t i d s ) ( 1 ) ( 1 ) ( ) ( 2 2 = + + ECE201 Lect-21 8 The Differential Equation Most circuits with one capacitor and inductor are not as easy to analyze as the previous circuit. However, every voltage and current in such a circuit is the solution to a differential equation of the following form: ) ( ) ( ) ( 2 ) ( 2 2 2 t f t i dt t di dt t i d = + + ϖ ζϖ ECE201 Lect-21...
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ECE201Lect-21 - ECE201 Lect-21 1 Second-Order Circuits(7.3...

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