Matakuliah
Tahun
Versi
: H0042/Teori Rangkaian Listrik
: 2005
: <<versi/01
Pertemuan 13
Applications of the Laplace
Transform
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Menunjukkan respons transien rangkaian
RLC dengan metode transformasi Laplace
2
Outline Materi
• Materi 1 : mengenal karakteristik jaringan
dinamik
• Materi 2 : elemen dinamik kapasitor
• Materi 3 : elemen dinamik induktor
• Materi 4 : elemen dinamik resistor
• Materi 5 : aplikasi transformasi Laplace
pada jaringan dinamik.
3
Characteristics of Dynamic Network
Dynamic Elements  Ohm’s Law:ineffective
1) Inductor
4
2). Capacitor
5
• Example :
6
• Why so simple? Algebraic operation!
• Dynamic Relationships (not Ohm’s Law)
Complicate the analysis
• Using Laplace Transform
( 1)

1 I ( s ) i ( 0) 

Vs (s)  L[ (t )]  L(sI (s)  i(0 ))   
  RI (s)
C s
s 
1
 ( Ls) I (s)  I (s)  RI (s)
Cs
7
• Define ‘Generalized Resistors’
(Impedances)
Z1 (s)  Ls
1
Z 2 (s) 
Cs
 Vs ( s )  Z1 ( s ) I ( s )  Z 2 ( s ) I ( s )  RI ( s )
Vs ( s )
 I (s) 
Z1 ( s )  Z 2 ( s )  R
• As simple as resistive network!
8
• Solution proposed for dynamic network:
• All the dynamic elements  Laplace
Trans. Models.
9
3). Laplace transform models of circuit
elements.
1. Capacitor
10
2) Inductor
11
3) Resistor V(s) = RI(s)
4)Sources
12
4). Circuit Analysis: Examples
Find Norton Equivalent circuit
13
• Assumption:
*Review of Resistive Network
1) short-circuit current through the load: I s
2) Equivalent Impedance or Resistance Rs or :
A: Remove all sources
B: Replace Z L by an external source
C: Calculate the current generated by the
external source ‘point a’
Rs  Z s
D: Voltage / Current 
* Solution
1) Find I s ( s)  I sc
Zs
14
15
1
1
3
s3
 I ( s )  1   3I ( s )  (1  ) I ( s ) 
I (s)
s
s
s
s
1
2
I (s) 
 I sc  2 I ( s )  
s3
s3
• 2) Find Z s
16
Vtest ( s )
Zs 
2 I (s)
Vtest(s)
3I ( s )
I ( s)  1  
0
s
 3
 (1 ) I (s)   I (s)
s
(Will I(s) be zero? We don’t know yet!)
17
condition: 1 ohm = 3/s
or I(s) = 0
=>I(s) = 0 =>Zs = 
ZL
18
RESUME
• Jaringan dinamis dapat dianalisa dengan
sederhana menggunakan model
transformasi Laplace.
19