04. tanggapan peralihan 2015
-
Upload
ali-sadiyoko -
Category
Education
-
view
87 -
download
0
Transcript of 04. tanggapan peralihan 2015
![Page 1: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/1.jpg)
DASAR RANGKAIAN LISTRIK
TANGGAPAN RANGKAIAN PERALIHAN
(TRANSIENT RESPONSES)
Dr. Ali Sadiyoko S.T.,M.T.
Last update : 25 Mei 2016
![Page 2: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/2.jpg)
© 2015, Ali Sadiyoko, UNPAR
Peralihan Rangkaian
• Perubahan konfigurasi rangkaian akan menyebabkan perubahan nilai respons pada rangkaian.
• Perubahan nilai respons tidak terjadi secara seketika (simultaneous) karena adanya komponen komponen yang mempunyai sifat menyimpan energi.
• Kapasitor menyimpan energi dalam bentuk medan listrik sedangkan induktor menyimpan energi dalam bentuk medan magnet
• Periode perubahan nilai respons dari nilai tunak (steady state) semula menuju nilai tunak berikutnya disebut periode peralihan rangkaian (transient period)
2
![Page 3: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/3.jpg)
© 2015, Ali Sadiyoko, UNPAR
Rangkaian Peralihan
• Rangkaian Peralihan Orde Satu
• Rangkaian Peralihan Orde Dua
![Page 4: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/4.jpg)
© 2015, Ali Sadiyoko, UNPAR
Respons Orde Satu
![Page 5: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/5.jpg)
© 2015, Ali Sadiyoko, UNPAR
Respons Orde Dua
![Page 6: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/6.jpg)
© 2015, Ali Sadiyoko, UNPAR
Peralihan Rangkaian
• Kapasitor
• Nilai tegangan pada terminal kapasitor tidak dapat berubah secara seketika.
• Pada keadaan tunak (steady state) sebuah kapasitor akan berfungsi sebagai hubungan terbuka (open circuit) sehingga tidak dapat dilalui arus.
• Konstanta waktu =R.C
![Page 7: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/7.jpg)
© 2015, Ali Sadiyoko, UNPAR
Contoh 1
12 V C
2 W
t = 0 i
![Page 8: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/8.jpg)
© 2015, Ali Sadiyoko, UNPAR
t < 0
12 V C
2 W
t >= 0
12 V
C
2 W
+
-
+ -
+
- + -
I I
-12 + Vc + 2 I = 0
-12 + 0 + 2 I = 0
I = 6 A
t = 0
I = ?
JANGAN LUPA BERI TANDA POLARITAS PADA KOMPONEN
![Page 9: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/9.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t = 0 I = 6 A
Pada saat t << 0 I = 0 Pada saat t >> 0 I = 0 A
6 -
I
t
I = 6 e -t/
![Page 10: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/10.jpg)
© 2015, Ali Sadiyoko, UNPAR
t >= 0
12 V
C
2 W
+
- + -
I
-12 + Vc + 2 I = 0
-12 + Vc + 2 . 0 = 0
Vc = 12 V
t = ∞
Vc = ?
![Page 11: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/11.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t << 0 Vc = 0
Pada saat t = 0 Vc = 0
Pada saat t >> 0 Vc = 12 V
Vc
t
12 -
Vc = 12 (1 - e ) -t/
11
![Page 12: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/12.jpg)
© 2015, Ali Sadiyoko, UNPAR
Contoh 2
12 V C
2 W
t = 0
12
![Page 13: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/13.jpg)
© 2015, Ali Sadiyoko, UNPAR
t < 0
12 V
C +
-
+ -
I
t >= 0
C +
-
I
2 W
-12 + IR + Vc = 0
-12 + 0.R + Vc = 0
Vc = 12 V
2I + Vc = 0
Vc = 0
+
-
t = 0 t = ∞
![Page 14: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/14.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t << 0 Vc = 12
Pada saat t = 0 Vc = 12 V
Pada saat t >> 0 Vc = 0 V
- 12
Vc
t
Vc = 12 e -t/
I = ?
![Page 15: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/15.jpg)
© 2015, Ali Sadiyoko, UNPAR
t >= 0
C +
-
I
2 W
2I + Vc = 0
Vc = -2I
+
-
t = ∞
I = -Vc / 2
![Page 16: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/16.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t << 0 I = 0
Pada saat t = 0 I = -Vc /2 = -12/ 2 = -6 A
Pada saat t >> 0 I = 0
6 -
I
t
I = 6(1 - e ) - 6 -t/
![Page 17: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/17.jpg)
© 2015, Ali Sadiyoko, UNPAR
Contoh 3
12 V 2 W
t = 0
15 V
C
![Page 18: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/18.jpg)
© 2015, Ali Sadiyoko, UNPAR
t < 0
15 V C 12 V
C +
- +
-
t >= 0
2 W 2 W
+ - + -
+
-
+
-
I I
-15 + 2 I + Vc = 0 12 + 2 I + Vc = 0
-15 + 2 . 0 + Vc = 0
Vc = 15 V
t < 0 t = ∞
12 + 0 + Vc = 0
Vc = -12 V
![Page 19: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/19.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t << 0 Vc = 15 V
Pada saat t = 0 Vc = 15 V
Pada saat t >> 0 Vc = -12 V
- 15
Vc
t
Vc = 27 e - 12 -t/
I = ?
-12 -
![Page 20: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/20.jpg)
© 2015, Ali Sadiyoko, UNPAR
12 V C
+
-
t >= 0
2 W
+ -
+
-
I
12 + 2 I + Vc = 0 t = ∞
12 + 2I + 15 = 0
2I = -27 A
I = -13,5 A
![Page 21: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/21.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t << 0 I = 0
Pada saat t = 0 I = 27/2 A
Pada saat t >> 0 I = 0
- 13,5 -
I
t
I = 13,5 (1 – e ) – 13,5 -t/
![Page 22: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/22.jpg)
© 2015, Ali Sadiyoko, UNPAR
Peralihan Rangkaian
• Induktor
• Nilai arus yang mengalir melalui sebuah induktor tidak dapat berubah secara seketika.
• Pada keadaan tunak (steady state) sebuah induktor akan berfungsi sebagai hubungan singkat (short circuit) sehingga nilai tegangan pada terminalnya = 0.
• Konstanta waktu =L/R
![Page 23: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/23.jpg)
© 2015, Ali Sadiyoko, UNPAR
Contoh 4
12 V L
2 W
t = 0
![Page 24: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/24.jpg)
© 2015, Ali Sadiyoko, UNPAR
t < 0 t >= 0
12 V
2 W
L
12 V
2 W
L
I I
I = 0 -12 + VL + 2 I = 0
+
-
+
- + - + -
t = ∞ -12 + 0 + 2 I = 0
I = 6 A
![Page 25: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/25.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t << 0 I = 0
Pada saat t = 0 I = 0
Pada saat t >> 0 I = 6 A
I
t
6 -
I = 6 (1 – e ) -t/
VL = ?
![Page 26: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/26.jpg)
© 2015, Ali Sadiyoko, UNPAR
t < 0 t >= 0
12 V
2 W
L
12 V
2 W
L
I I
VL = 0 -12 + VL + 2 I = 0
+
-
+
- + - + -
t = 0 -12 + VL + 0 = 0
VL = 12 V I masih 0 !
![Page 27: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/27.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t << 0 VL = 0
Pada saat t = 0 VL = 12 V
Pada saat t >> 0 VL = 0
- 12
VL
t
I = 12 e -t/
![Page 28: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/28.jpg)
© 2015, Ali Sadiyoko, UNPAR
Contoh 5
12 V L
3 W
t = 0
1 W
![Page 29: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/29.jpg)
© 2015, Ali Sadiyoko, UNPAR
t < 0 t >= 0
12 V
L 3 W
1 W
+
-
+
-
+ -
L 3 W
+
-
+
- I I
-VL + I + 12 = 0
t << 0
0 + I + 12 = 0
I = -12 A
-VL + 3 I = 0
t = ∞
0 + 3 I = 0
I = 0 A
![Page 30: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/30.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t << 0 I = -12 A
Pada saat t = 0 I = -12 A
Pada saat t >> 0 I = 0 A
I
t
-12
I = 12 (1 – e ) - 12 -t/
VL = ?
![Page 31: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/31.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t = 0 VL = 3 I = -36 V
Pada saat t << 0 VL = 0 Pada saat t >> 0 VL = 0
-36 -
VL
t
VL = 36 ( 1 – e ) - 36 -t/
![Page 32: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/32.jpg)
© 2015, Ali Sadiyoko, UNPAR
Contoh 6
Latihan !
+
-
+ -
12 V
L
2 W
t = 0
15 V
_
![Page 33: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/33.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t << 0 I = 6 A
Pada saat t = 0 Vc = 6 A
Pada saat t >> 0 I = -7,5 A
- 6
I
t
I = 13,5 e - 7,5 -t/
VL = ?
-7,5 -
![Page 34: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/34.jpg)
© 2015, Ali Sadiyoko, UNPAR
Pada saat t = 0 VL = -2 I – 15 = -27 V
Pada saat t << 0 VL = 0 Pada saat t >> 0 VL = 0
-27 -
VL
t
VL = -27 ( 1 – e ) - 27 -t/
![Page 35: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/35.jpg)
© 2015, Ali Sadiyoko, UNPAR
Ringkasan Peralihan Rangkaian
• Induktor
• Nilai arus (IL) yang mengalir melalui sebuah induktor tidak dapat berubah secara seketika.
• Pada keadaan tunak (steady state) sebuah induktor akan berfungsi sebagai hubungan singkat (short circuit) sehingga nilai tegangan pada terminalnya = 0.
• Konstanta waktu =L/R
Kapasitor
Nilai tegangan (VC) pada terminal kapasitor tidak dapat berubah secara seketika.
Pada keadaan tunak (steady state) sebuah kapasitor akan berfungsi sebagai hubungan terbuka (open circuit) sehingga tidak dapat dilalui arus (I = 0).
Konstanta waktu =R.C
![Page 36: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/36.jpg)
© 2015, Ali Sadiyoko, UNPAR
Rangkaian Peralihan Orde Dua
12 V L
2W
t=0
36
![Page 37: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/37.jpg)
© 2015, Ali Sadiyoko, UNPAR
12 V L
2 W
+
- + + - -
C
-12 + VL + 2 I + VC = 0
dt
t dI L
) (
=
t
t
dt t I C 0
) ( 1
-12 + + 2 I + = 0
37
![Page 38: 04. tanggapan peralihan 2015](https://reader034.fdocument.pub/reader034/viewer/2022050800/5887284f1a28abfb0b8b6eb5/html5/thumbnails/38.jpg)
© 2015, Ali Sadiyoko, UNPAR
Respons Orde Dua
t
c(t) Allowable tolerance
ts
Mp
38