Rangkaian Orde Dua - Step Response Rangkaian RLC, Lecture notes of Electrical Circuit Analysis

Download Rangkaian Orde Dua - Step Response Rangkaian RLC and more Lecture notes Electrical Circuit Analysis in PDF only on Docsity!

STEP RESPONSE RANGKAIAN RLC

SERI DAN PARALEL

Pengantar Analisis Rangkaian

TUJUAN PEMBELAJARAN

Memahami Respon Step pada Rangkaian RLC Seri dan Paralel

Persamaan diferensial tegangan kapasitor pada rangkaian

STEP RESPONSE RANGKAIAN RLC SERI

LC

V

LC

v dt

dv L

R

dt

d vC (^) + + = s 2

2

v( t ) = vt (t)+vss(t)

STEP RESPONSE RANGKAIAN RLC SERI

vt (t ) = Aes^1 t + Bes^2 t

vt (t ) = e^ t( Acos( ot) + B sin(  o t))

vt (t) = ( At + B)e^ st

STEP RESPONSE RANGKAIAN RLC PARALEL

Perhatikan rangkaian RLC Paralel berikut KCL pada rangkaian untuk t > 0 :

Sehingga

Akhirnya diperoleh persamaan diferensial LC

I

LC

i dt

di dt RC

d i + 1 + = s 2

2

dt^ IS

i C dv R

v (^) + + =

dt

v =LdiL

IS

dt

i CLd i dt

di R

L

dt

i C dv R

v (^) + + = + + = 2

2

Persamaan diferensial arus induktor pada rangkaian

STEP RESPONSE RANGKAIAN RLC PARALEL

i( t ) =it (t)+iss(t)

LC

I

LC

i dt

di dt RC

d i + 1 + = s 2

2

Solusi Lengkap (Complete Solution) :

▪ Overdamped :

▪ Critically damped :

▪ Underdamped :

STEP RESPONSE RANGKAIAN RLC PARALEL

i (t ) = Is + Aes^1 t + Bes^2 t

i (t ) = Is +e^ t( Acos( (^) ot) + B sin(  (^) o t))

i (t) = Is +( At + B)e^ st