dtg2a3 teknik saluran transmisi -...
TRANSCRIPT
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Teknik Saluran
Transmisi
DTG2A3
1. PENDAHULUAN
(KONSEP DASAR SALURAN TRANSMISI)
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Where Are We?
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Content
1. Contoh-contoh Aplikasi saluran transmisi
2. Konsep/Teori Saluran Transmisi
3. Model Saluran Transmisi
4. Parameter-parameter Saluran Transmisi
5. Persamaan Umum Saluran Transmisi
6. Konsep Bandwidth Saluran Transmisi
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Contoh-contoh Aplikasi Saluran Transmisi
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Aplikasi Saluran Transmisi
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Teori Saluran Transmisi
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• Saluran transmisi didefinisikan sebagai alat untuk menyalurkan energi elektromagnet dari suatu titik ke titik lain. Saluran transmisi dapat berupa kabel koaxial, kabel sejajar/twinlead, bumbung gelombang, optik, dan sebagainya.
• Macam-macam saluran transmisi umumnya ditentukan dari daerah frekuensi operasi, kapasitas daya yang disalurkan, maupun redaman saluran per meter. Disini karakteristik saluran transmisi diturunkan atas dasar analogi dengan gelombang datar dalam medium.
• Saluran transmisi dikatakan uniform jika distribusi penampang medan listrik dan medan magnetnya tampak sama pada tiap titik sepanjang saluran transmisi tersebut. Dalam hal ini, sebagaimana pada gelombang datar uniform, keadaan tersebut memerlukan karakteristik medium dielektrik yang uniform sepanjang saluran transmisi.
• Contoh saluran transmisi adalah : kabel PLN, kabel penghubung antara sentral yang bisa berbentuk serat optik, kabel koax, strip line, twisted pair.
Teori Saluran Transmisi
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• In an electronic system, the delivery of power requires
the connection of two wires between the source and
the load. At low frequencies, power is considered to be
delivered to the load through the wire.
• In the microwave frequency region, power is
considered to be in electric and magnetic fields that are
guided from place to place by some physical structure.
Any physical structure that will guide an
electromagnetic wave place to place is called a
Transmission Line.
Teori Saluran Transmisi
Introduction
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The major deviation from circuit theory with transmission line, distributed networks is this positional dependence of voltage and current!
– Must think in terms of position and time to understand transmission line behavior
– This positional dependence is added when the assumption of the size of the circuit being small compared to the signaling wavelength
tzfI
tzfV
,
,
V1 V2
dz
I2I1
Voltage and current on a transmission line is a
function of both time and position.
Teori Saluran Transmisi
Key point about transmission line operation
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Power Plant
Consumer Home
Power Frequency (f) is @ 60 Hz
Wavelength (l) is 5 106 m ( Example length : 300 Km)
Teori Saluran Transmisi
Electrical Power Transmission Line
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Integrated Circuit
Microstrip
Stripline
Via
Cross section view taken here
PCB substrate
T
W
Cross Section of Above PCB
T
Signal (microstrip)
Ground/Power
Signal (stripline)
Signal (stripline)
Ground/Power
Signal (microstrip)
Copper Trace
Copper Plane
FR4 Dielectric
W
Signal Frequency (f) is approaching 10 GHz
Wavelength (l) is 1.5 cm ( 0.6 inches)
Micro-
Strip
Stripline
Teori Saluran Transmisi
PC Transmission Line
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Whether it is a bump or a mountain depends on the ratio of its size (tline) to the size of the vehicle (signal wavelength)
When do we need to use transmission line
analysis techniques vs. lumped circuit
analysis?
Tline Wavelength/edge rate
Similarly, whether or
not a line is to be
considered as a
transmission line
depends on the ratio of
length of the line
(delay) to the
wavelength of the
applied frequency
Teori Saluran Transmisi
When does a line become a T-Line? (analogy)
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Model Saluran Transmisi
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• The electrical characteristics of a transmission line become increasingly critical as the frequency of transmission increases
• Instead of examining the EM field distribution within these
transmission lines (Very Complex), we will simplify the discussion by
using a simple model consisting of distributed elements
(inductors,capacitors,resistor). This model called distributed
element model or transmission line model
• essentially, transmission line model needs to be used in circuits
where the wavelengths of the signals have become comparable to
the physical dimensions of the components. An often quoted
engineering rule of thumb is that parts larger than one tenth of a
wavelength will usually need to be analysed as distributed elements
Model Saluran Transmisi
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• At low frequencies, the circuit elements are lumped since voltage and current waves affect the entire circuit at the same time.
• At microwave frequencies, such treatment of circuit elements is not possible since voltage and current waves do not affect the entire circuit at the same time.
• The circuit must be broken down into unit sections within which the circuit elements are considered to be lumped.
• This is because the dimensions of the circuit are comparable to the wavelength of the waves according to the formula:
l c/f
where,
c = velocity of light
f = frequency of voltage/current
• The transmission line is divided into small units where the circuit elements can be lumped.
Low Frequency Vs High Frequency
Model Saluran Transmisi
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• The differential segment of the transmission line
R’ = resistance per unit length
L’= inductance per unit length
C’= capacitance per unit length
G’= conductance per unit length
Model Saluran Transmisi
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Parameter-parameter dalam Saluran Transmisi
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• Konstanta primer saluran :
– R’, L’, G’, C’
• Konstanta sekunder saluran :
– Konstanta propagasi ( )
– Impedansi karaketristik (Z0)
– Kecepatan fasa (Vph)
– Kecepatan group (Vg)
Parameter-parameter dalam Saluran
Transmisi
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• The transmission line has electrical resistance along its
length. This resistance is usually expressed in ohms per
unit length and is shown as existing continuously from
one end of the line to the other.
Parameter-parameter dalam Saluran
Transmisi
Konstanta primer (Resistance (R’))
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• When current flows through a wire, magnetic lines of force are set
up around the wire
• As the current increases and decreases in amplitude, the field
around the wire expands and collapses accordingly
• The energy produced by the magnetic lines of force collapsing back
into the wire tends to keep the current flowing in the same direction
• This represents a certain amount of inductance, which is expressed
in microhenrys per unit length
Parameter-parameter dalam Saluran
Transmisi
Konstanta primer (Inductance (L’))
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• Capacitance also exists between the transmission line wires.
• two parallel wires act as plates of a capacitor and that the air
between them acts as a dielectric.
• The capacitance between the wires is usually expressed in
picofarads per unit length
Parameter-parameter dalam Saluran
Transmisi
Konstanta primer (Capacitance (C’))
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• Since any dielectric, even air, is not a perfect insulator, a small
current known as LEAKAGE CURRENT flows between the two
wires.
• In effect, the insulator acts as a resistor, permitting current to pass
between the two wires.
• This property is called CONDUCTANCE (G) and is usually given in
micromhos per unit length.
Parameter-parameter dalam Saluran
Transmisi
Konstanta primer (Conductance (G’))
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TUGAS 2
1. Carilah formula konstanta primer
beberapa jenis saluran transmisi!
2. Apa saja yang mempengaruhi besarnya
nilai konstanta primer dari suatu jenis
saluran transmisi?
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dB 8,686 Np 1
(farad/m) panjangsatuan per iKapasitans
(s/m)atau (mho/m) panjangsatuan per iKonduktans
(H/m) panjangsatuan per Induktansi
(Ohm/m) panjangsatuan per Resistansi
Z
salurantik karakteris Impedansi
(rad/km) fasa konstanta ; (Np/km)redaman konstanta ,
saluran propagasi Konstanta
'
'
'
'
000
'
'
''
'
0
''''''
C
G
L
R
jXR
Y
Z
CjG
LjRZ
j
YZCjGLjR
Parameter-parameter dalam Saluran
Transmisi
Konstanta Sekunder Saluran Transmisi
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Parameter-parameter dalam Saluran
Transmisi
Konstanta Sekunder….Konstanta Propagasi
Propagation Constant
jCjGLjR )'')(''(
Menyebabkan penurunan
amplitudo gelombang karena
desipasi daya sepanjang
transmisi. Nilai a terkait
dengan resistansi saluran
Konstanta redaman
Menyebabkan perubahan
fasa dan bentuk gelombang
terkait dengan perubahan
induktansi dan kapasitansi
sepanjang saluran
Konstanta fasa
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0
' '.
' '
R j LZ
G j C
Parameter-parameter dalam Saluran
Transmisi
Konstanta Sekunder…..Impedansi Karakteristik
Impedansi Karakteristik saluran didefinisikan dari suatu saluran
transmisi yang panjangnya tak hingga
Jika saluran tersebut dicatu dengan tegangan AC maka akan
muncul arus yang mengalir di sepanjang saluran (pengaruh nilai C’
dan G’)
Perbandingan tegangan dan arus pada input saluran transmisi
dengan panjang tak hingga disebut Impedansi Karakteristik
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Parameter-parameter dalam Saluran
Transmisi
Konstanta Sekunder…..Wavelength (λ )
Wavelength (Panjang gelombang) didefinisikan sebagai jarak
dimana gelombang merambat sepanjang saluran agar pergeseran
gelombang mencapai 2π radian (satu gelombang penuh)
)(2
meter
l
Jika suatu saluran menggunakan suatu dielektrik tertentu maka
panjang gelombang bisa dituliskan :
)(0 meter
rll
l0
r
Panjang gelombang di udara
Konstanta dielektrik relatif
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Parameter-parameter dalam Saluran
Transmisi
Konstanta Sekunder…..Kecepatan Phasa (Vp)
Kecepatan Phasa (phase velocity / wave velocity/ velocity of
propagation ) didefinisikan sebagai kecepatan dimana gelombang
merambat sepanjang saluran pada frekuensi tertentu.
)sec/( ondmeterfV p l
fV p
2
V p
Jika saluran menggunakan bahan dielektrik maka
r
p
CV C = Cepat rambat gelombang di udara
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Parameter-parameter dalam Saluran
Transmisi
Konstanta Sekunder…..Kecepatan Group (Vg)
Kecepatan Group (group velocity) didefinisikan sebagai
kecepatan dari sekumpulan gelombang yang bersuperposisi
Disebut juga kecepatan envelope
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1. Suatu saluran telepon open wire memiliki R’ = 10Ω/km,
L’=0,0037 henry/km, C’=0,0083 x 10-6 , dan G’= 0,4 x
10-6 mho/km , pada frequensi 1 Khz tentukan :
a) Konstanta propagasi
b) Konstanta redaman
c) Konstanta phasa
d) Impedansi karakteristik
e) Panjang gelombang
f) Kecepatan phasa
Parameter-parameter dalam Saluran
Transmisi
Contoh Soal
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a) Konstanta propagasi
b) Konstanta redaman
c) Konstanta phasa
Parameter-parameter dalam Saluran
Transmisi
Solusi
jCjGLjR )'')(''(
jjj ))10.0083,0(1000210.4,0))(0037,0(1000210( 66
jjj ))10.15,5210.4,0)(25,2310( 66
j )56,8910.15,52)(73,6631,25( 6
j 29,15610.92,1319 6
jperKmj )(0356,000746,0145,7803633,0
)/(0000648,0)/(00746,0 mdBKmneper
)/(0356,0 Kmradian
dBneper 686,81
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a) Impedansi Karakteristik
b) Panjang Gelombang
c) Kecepatan Phasa
Parameter-parameter dalam Saluran
Transmisi
Solusi
)(88,13788,682415,1166,696
56,8910.15,52
73,6631,25
)''(
)''(0
6ohmJ
CjG
LjRZ
)(49,1760356,0
22km
l
)/(10.49,176100010.49,176 63 smfVp l
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Find the baby
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Persamaan Umum Saluran Transmisi
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),(),()''(),( tzzVtzIzLJzRtzV
),()''(),(),(
tzILJRz
tzVtzzV
Taking the limit as z tends to 0 leads to
),()''(),(
tzILJRdz
tzdV
Persamaan Umum Saluran Transmisi
),()''(),(),(
lim0
tzILJRz
tzVtzzV
z
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),()''(),(
tzVCJGdz
tzdI
),(),( tzzIItzI
zCJ
tzzV
zG
tzzVtzzItzI
'1
),(
'1
),(),(),(
Taking the limit as z tends to 0 leads to
),()''(),(),( tzzVzCJzGtzzItzI
),()''(),(),(
tzzVCJGz
tzItzzI
Persamaan Umum Saluran Transmisi
),()''(),(),(
0
tzzVCJGz
tzItzzILim
z
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0),(),(
0),(),(
2
2
2
2
2
2
tzIdz
tzId
tzVdz
tzVd
),()''(),(
tzILJRdz
tzdV
),()''(),(
tzVCJGdz
tzdI
Persamaan Umum Saluran Transmisi
0 0
0 0
( , ) cos( ) cos( )
( , ) cos( ) cos( )
z z
z z
v z t V e t z V e t z
i z t I e t z I e t z
0 0
0 0
( )
( )
z z
z z
V z V e V e
I z I e I e
Disebut Persamaan Differential saluran
transmisi
Solusi Tegangan dan arus :
Atau dalam bentuk fungsi hiperbolic:
zzez
sinhcosh
zzez
sinhcosh
zVVzVV sinhcoshV(z) 0000
zIIzII sinhcoshI(z) 0000
Disebut Telegrapher’s Equations
Ingat :
tjezV Ret)V(z, Dalam Fungsi Real Time:
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+
V(z)
-
Zo
+j
)eVe(-VZ0
1I(z)
eVeVV(z)
zz
zz
γ
0
γ
0
γ
0
γ
0
Persamaan
Umum saluran
transmisi
L
V(z) = Tegangan sejauh z dari sumber
I(z) = Arus sejauh z dari sumber
Z
Persamaan Umum Saluran Transmisi
zγ
0 eVV(z)
zγ-
0 eVV(z)
Menggambarkan ada dua
gelombang yang merambat
dalam saluran transmisi :
• V+ dan atau I+ yang merambat
pada arah (Z positif)
• V- dan atau I- yang merambat
pada arah (Z negatif)
I(z)
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)eVe(-VZ0
1I(z)
eVeVV(z)
zz
zz
γ
0
γ
0
γ
0
γ
0
o
00zz
0 0sz
Z
VV- I I
V V V V
:didapat maka 0 z Jika
Persamaan umum saluran :
Pers 1
Pers 2
2
.ZIVs V
2
.ZIVs V
0s0
0s0
2
ee.ZI
2
eeVV
e2
.ZIVe
2
.ZIVV
:didapat 1, pers ke Vdan Vkan Substitusi
γz-γz
0s
γz-γz
sz
γz0ssγz0ssz
0
-
0
γzZIγzVVssz
sinhcosh0
Persamaan Tegangan dan Arus jika
Parameter sumber diketahui
ZL
Zg
Vg
+
Vs
-
Is
+
VL
-
Zo
+j
Z=L
Z
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)eVe(-VZ0
1I(z)
eVeVV(z)
zz
zz
γ
0
γ
0
γ
0
γ
0
40
Persamaan umum saluran :
Pers 1
Pers 2
2
ee
Z
V
2
eeII
e2Z
.ZIVe
2Z
V.ZII
:didapat 2, pers ke Vdan Vkan Substitusi
γz-γz
0
S
γz-γz
sz
γz
0
0ssγx
0
S0sz
0
-
0
γzZ
VγzII s
szsinhcosh
0
Persamaan Tegangan dan Arus jika
Parameter sumber diketahui
ZL
Zg
Vg
+
Vs
-
Is
+
VL
-
Zo
+j
Z=L
Z
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41
γzZIγzVV ssz sinhcosh 0
γzZ
VγzII s
sz sinhcosh0
Persamaan Tegangan
Dan Arus Jika
Parameter
Sumber diketahui !
Persamaan Tegangan dan Arus jika
Parameter sumber diketahui
ZL
Zg
Vg
+
Vs
-
Is
+
VL
-
Zo
+j
Z=L
Z
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)eVe(-VZ0
1I(z)
eVeVV(z)
zz
zz
γ
0
γ
0
γ
0
γ
0
Persamaan umum saluran :
Pers 1
Pers 2
γL
0
γL-
0
o
L
γL
0
γL-
0L
eV eV-Z
1 I
eV eV V
:didapat maka L z Jika
γL0LL0
γL0LL0
e2
.ZIV V
e2
.ZIV V
2
eeZIe
2
eeVV
e2
.ZIVe
2
.ZIVV
e2
.ZIVe
2
.ZIVV
e2
.ZIVe
2
.ZIVV
:didapat 1, pers ke Vdan Vkan Substitusi
γd-γd
0L
γ-γd-γd
Ld
γd0LLγd-0LLd
z)-γ(L0LLz)-γ(L-0LLd
γLγz0LLγL-γz0LLz
0
-
0
γdZIγdVV LLd sinhcosh 0
Persamaan Tegangan dan Arus jika
Parameter Beban diketahui
ZL
Zg
Vg
+
Vs
-
Is
+
VL
-
Zo
+j
Z=L
d
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)eVe(-VZ0
1I(z)
eVeVV(z)
zz
zz
γ
0
γ
0
γ
0
γ
0
Persamaan umum saluran :
Pers 1
Pers 2
Dengan cara yang sama masukkan
V0 - dan V0
+ ke pers 2, maka didapat :
γdZ
VγdII L
Ldsinhcosh
0
Persamaan Tegangan dan Arus jika
Parameter Beban diketahui
ZL
Zg
Vg
+
Vs
-
Is
+
VL
-
Zo
+j
Z=L
d
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γdZIγdVV LLd sinhcosh 0
γdZ
VγdII L
Ldsinhcosh
0
Persamaan Tegangan
Dan Arus Jika
Parameter
Beban diketahui !
Persamaan Tegangan dan Arus jika
Parameter Beban diketahui
ZL
Zg
Vg
+
Vs
-
Is
+
VL
-
Zo
+j
Z=L
d
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• Pada slide sebelumnya sudah
didefinisikan mengenai
impedansi karakteristik
• Alternatif pengertian impedansi
karakteristik yang dilihat dari
persamaan umum saluran
transmisi, adalah ratio antara
tegangan dan arus yang
merambat ke satu arah (
V(z)+/I(z)+ ) atau ( -V(z)-/I(z)- )
pada setiap titik di saluran
transmisi
CjG
LjR
zI
zV
zI
zVZ
Jadi
CjG
LjR
CjGLjR
LjRLjR
LjR
zI
zVdan
LjR
zI
zV
maka
CjGLjRKarena
zIzVLjR
danzIzVLjR
eIeIeVLjR
eVLjR
eIeIeVeVLjR
eIeILjReVeV
eIeILjReVeV
eIeIzIzIzI
eVeVzVzVzV
zILjRdz
zdV
o
zzzz
zzzz
zzzz
zzzz
zz
zz
)(
)(
)(
)(
,
)(
)(
)(
)(
,
)()()()(
)(
)()(
)()()(
)()()(
)()()(
0000
0000
0000
0000
00
00
z
Impedansi Karakteristik
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• Dapat disimpulkan bahwa impedansi karakteristik bukan merupakan
fungsi dari jarak, dan besarnya hanya tergantung dari nilai R’, L’, C’,
dan G’ saja.
• Untuk mempermudah desain dan aplikasi biasanya nilai impedansi
karakteristik (Z0) dari berbagai jenis saluran sudah dibuat formula-
formula yang bisa langsung digunakan
Impedansi Karakteristik
1. Carilah formula-formula Impedansi
karakteristik (Z0) beberapa jenis saluran
transmisi!
2. Apa saja yang mempengaruhi besarnya nilai
impedansi karakteristik dari suatu jenis
saluran transmisi?
TUGAS 3
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47
coshI
1
coshI
1
dengan Kalikan
sinhcosh
sinhcosh
L
L
0
0
d
d
γdZ
VγdI
γdZIγdV
I
VZ
LL
LL
d
d
d
γdZZ
γdZZZZ
L
L
dtanh
tanh
0
0
0Didapat :
Merupakan impedansi saluran sejauh d dari beban !
Persamaan Impedansi Saluran Transmisi
ZL
Zg
Vg
+
Vs
-
Is
+
VL
-
Zo
+j
Z=L
L
d
Zd Zin
Bedakan dengan impedansi
karakteristik saluran !!!
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48
γdZZ
γdZZZZ
L
L
dtanh
tanh
0
0
0
Jika d = L maka :
γLZZ
γLZZZZZ
L
L
inLdtanh
tanh
0
0
0
Adalah Impedansi Input Saluran Transmisi !
Persamaan Impedansi Saluran Transmisi
ZL
Zg
Vg
+
Vs
-
Is
+
VL
-
Zo
+j
L
d
Zd Zin
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• A 40-m long TL has Vg=15 cos (ωt), Zo= 262,88-j137,88 W, and γ =
0,00746+J0,0356 (per m). If Zg=ZL=Z0 , find:
a) the input impedance Zin
b) the sending-end current Iin
c) the sending-end voltage Vin,
d) the receiving-end voltage VL.
e) the receiving-end current IL
f) Impedance at point 20 m from load
ZL
Zg
Vg
+
Vin
-
Iin
+
VL
-
Zo= 262,88-j137,88 W
γ= 0,00746+j0,0356
40 m
Latihan
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a) Input Impedance (Zin)
Karena saluran match dengan beban, maka Z0 = ZL = 262,88-j137,88 W
Maka:
b) Sending-end Current (Iin)
c) Sending-end voltage (Vin)
Parameter-parameter dalam Saluran
Transmisi
Solusi
W
88,13788,262
tanh
tanh0
0
00 jZ
γLZZ
γLZZZZ
L
Lin
Zin
Zg
Vg
+
Vin
-
Iin
76,27576,525
015
88,13788,26288,13788,262
015
jjjZinZ
VI
g
gin
))(68,27cos(0253,068,270253,068,2769,593
015amperetIin
Zin
Zg
Vg
+
Vin
-
Iin
015
88,13788,26288,13788,262
88,13788,262
jj
jV
ZgZin
ZV g
inin
t)(volt)( cos 7,5)(05,72
015
voltVin
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d) Receiving-end Voltage (VL)
e) Receiving-end Current (IL)
Parameter-parameter dalam Saluran
Transmisi
Solusi
γzZIγzVV ininz sinhcosh 0
40)0356,000746,0(cosh05,7 jVL
40)0356,000746,0(sinh88,13788,26268,270253,0 jj
γzZ
VγzII in
inz sinhcosh0
40)0356,000746,0(cosh68,270253,0 j
γLZIγLVV ininL sinhcosh 0
γLZ
VγLII in
inL sinhcosh0
64,5402055,040)0356,000746,0(sinh
88,13788,262
05,7j
j
yxyxyx
yxyxyx
xjjx
xjx
sinhcoshcoshsinh)sinh(
sinhsinhcoshcosh)cosh(
sinsinh
coscosh
Review Kembali!!!
))(457,62cos(522,2457,62522,2 volttVL
)64,54cos(02055,0 t
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f) Zd=20m
Parameter-parameter dalam Saluran
Transmisi
Solusi
W
88,13788,262
tanh
tanh0
0
00 jZ
γdZZ
γdZZZZ
L
Ld
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Konsep Bandwidth dalam Saluran Transmisi
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54
• Matching impedansi yang dilakukan pada frekuensi tunggal/referensi bisa saja berhasil mencapai VSWR minimum yang mendekati 1 di saluran utamanya, terutama jika salurannya lossless. Jika saluran lossy, maka matching dengan VSWR minimum mendekati 1 dapat dicapai pada pangkal saluran (titik input), sedangkan di ujung saluran (titik beban) VSWR akan cenderung membesar.
• Setelah matching dilakukan pada frekuensi referensi, saluran tersebut bagi komponen sinyal dengan frekuensi yang semakin jauh dari referensi akan semakin tidak matched.
• Dapat dibuat plot kurva respons VSWR saluran terhadap frekuensi.
VSWR
f
1.2
1.4
1.6
1.8
1.35
fref fH fL
BW1.35=fH fL
Bandwidth dalam Saluran Transmisi
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55
• Jika band-width filter didefinisikan pada respons 3 dB dari referensi, maka band-with saluran transmisi didefinisikan untuk nilai VSWR maksimum yang diijinkan sebagai referensi. Tetapi nilai VSWR maksimum referensi tersebut tidak disepakati berharga tertentu, bisa saja 1,15; 1,20; 1,35; atau 1,50 asalkan cukup baik untuk aplikasi yang bersangkutan (pantulan tidak membahayakan peralatan, khususnya pesawat pemancar).
• Matching berganda (transformator-l/4 ganda, stub ganda) bertujuan memperlebar bandwidth pada VSWR yang sama dibandingkan dengan matching tunggal.
Bandwidth dalam Saluran Transmisi
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Questions???
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