ECE201_Lecture23

# ECE201_Lecture23 - ECE201 Linear Circuit Analysis I Lecture...

This preview shows pages 1–4. Sign up to view the full content.

1 ECE201 Linear Circuit Analysis I Lecture 23 Topic: Second-order circuits: RLC source free case (with real characteristic roots) 1. Review of 2 nd -order Source Free LC Circuits v c i circuit equations C C v LC dt v d 1 2 2 = d 2 i L dt 2 = − 1 LC solution (general) v c ( t ) = K cos( ω + θ ) i L ( ) = cos( + ω ω = 1 ω = 1 K, θ determined by v c (t o + ) and i L (t o + v c o + ), v c (t o + i L (t o + ), i L (t o + + v c i L L + v L i c C

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 2. Source-free 2 nd -order linear networks with real characteristic roots (over-damped & critically-damped responses) In other words: Add a resistor to the LC circuit. Two cases: 3. Circuit Equations (1) Series RLC circuit Expand in terms of i L : (i R = i L = i c ) 0 ) ( 1 = + + t L L L d i C dt di L i R τ Differentiate: R di L dt + d 2 i 2 + 1 C = 0 Divide both sides by L and rearrange terms: 2 2 + + 1 LC = 0 L C R R L C R L + C v c i L kVL: v R + v L + v c = 0
3 Expand KVL in terms of v c : i R = i L = C dv c dt RC dv c dt + LC d 2 v 2 + = 0 2 2 + R L + 1 = 0 Same 2 nd -order differential equation as for i L .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/19/2011 for the course ECE 201 taught by Professor All during the Spring '08 term at Purdue.

### Page1 / 7

ECE201_Lecture23 - ECE201 Linear Circuit Analysis I Lecture...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online