&iacute;•„&ecirc;&cedil;&deg;&euml;&iexcl; #2

# &iacute;•„&ecirc;&cedil;&deg;&euml;&...

This preview shows pages 1–8. Sign up to view the full content.

13. Fr equency r esponse Sunghoon Kwon Sl i de cr edi t : Pr of essor Roger Howe, St anf or d

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

View Full Document
A Second Order System v S ( t ) L v C ( t ) + - R C i L i R i C v L + - Wher e does t he i nduct or come f r om? ( ~ 1nH/ mm “ f or any wi r e” ) Do st ep r esponse: v S ( t ) j umps t o V DD at t = 0 t = 0 V DD
“Step Response” of R-L-C circuit v S ( t ) L v C ( t ) + - R C i L i R i C v L + - I ni t i al condi t i ons: v C ( t =0 - ) = 0 V & i L ( t =0 - ) = 0 A C L i i = ( 29 dt dv C t d t v L C t L = 0 1 + - = C C DD L v R dt dv C V v I nduct or vol t age: t = 0 V DD C L R i i i = = f or t 0

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

View Full Document
Second-Order Differential Equation for  v C (t) dt dv C t d v R dt dv C V L C t C C DD = + - 0 1 Subst i t ut i ng f or v L : 2 2 1 dt v d C v R dt dv C V L C C C DD = + - Di f f er ent i at i ng bot h si des: DD C C C V v dt dv RC dt v d LC = + + 2 2 Rear r angi ng t er ms:
St eady- st at e sol ut i on: v C, ss = V DD ) ( t Tr ansi ent sol ut i on: v C, t r = ? guess v C, t r = ae st and subst i t ut e: ( 29 ( 29 0 2 = + + st st st ae ae RCs ae LCs Short Review : Solving the 2 nd  Order O.D.E. DD C C C V v dt dv RC dt v d LC = + + 2 2 ) ( t v S 0 1 2 = + + LC s L R s - ± - = LC L R L R s 1 2 2 2 2 , 1 : Char act er i st i c f unct i on Compl i cat ed…… - > Phasor anal ysi s! !

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

View Full Document
Thr ee cases f or s1 and s2 Get t wo negat i ve r eal r oot s ( over damped) - ± - = LC L R L R s 1 2 2 2 2 , 1 LC L R 1 2 LC L R 1 2 = LC L R 1 2 < Get a si ngl e negat i ve r oot s ( cr i t i cal damped) I nt er est i ng case! ( Under damped) v C, t r = ae st
Under damped case 2 2 2 , 1 2 1 2 1 2 2 - ± - = -

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 11/12/2009 for the course EE 420.402 taught by Professor Lee during the Spring '08 term at Seoul National.

### Page1 / 52

&iacute;•„&ecirc;&cedil;&deg;&euml;&...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online