Seriesrlciuits order Second transient response - PowerPoint PPT Presentation

Seriesrlciuits order Second transient response

current-voltagerelations.hr# capaoi.r.IE#=cdI 1- i - v Component symbol relation R = in Resistor a- Who . R Or + - Or I terrors L did Inductor K = + q - dt

⇒ ⇒ R L - m - mm | ¥ + a v. = i R + Vc KVL k o t = : v. =L dd÷ - L dat = ⇒ [ c daff i i Ctsdt Ck = = = I # idt Vo acct ) t L dat + I # idt Vo i. R t t o =

' ' Differentiate with t to respect . L dat + I ft ' i dt Vo i. R t t o = + I i . di d- i R L 0 + = dt at ' ' Divide by L da÷+Ed÷+ziT

⇒ ⇒ ddI÷ + Ici Eddie SOLVE o + = Differential → equation St ict ) ke Assume = ' est ddI ddt then Ks est and Ks = = - est t Ry t t Ks est k est Ks O = 5-ies-tc-fcheghauE.int ?

⇒ s 't Res t # ' Sot : = o - Eh ± s = LC = Fixate :& :Ygeae → - iz = ± or complex - T c ÷÷±=¥÷÷÷÷¥z Cracks ) frequency Define Resonant Wo = R X attenuation = constant -2L =

- d I f S . L>wo → Rootsarereal0VsEyRsDAMmPED te x=wo → Roa%segre;da¥atmFE¥ te × <wo → RjgaEGmek × UN?7?amPED *

DampedFreqnenoy# - frequency damped oscillations B of - f - FF - 4 " " h radians attenuation Per resonant constant second frequency =2T( frequency in Herty ) .