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Transcript of Smith Abagi
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T.C.FIRAT ÜNVERSTES
MÜHENDSLK FAKÜLTESELEKTRK ± ELEKTRONK MÜHENDSL BÖLÜMÜ
EMÜ ± 447 ANTENLER VE MKRODALGA TEKN DERS
SUNUMU
DERSN SORUMLUSUYRD. DOÇ. DR. H. H. BALIK
2002 ± ELAZI
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SMITH ABAI
ALPER ALKOÇ
CENK ÖZÇALIKANMEHMET ONUR GÜRSOY
HAZIRLAYANLAR
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Agenda
letim Hatlar letim Hatlarnn Genel Tanm Abaklara Neden htiyaç Duyulur
Smith Abann Türetilmesi Giri Sabit Re(Z) Çizgileri Sabit Im(Z) Çizgileri Empedans Terslemesi Karmak Elenik Smith Aba Üzerinde Empedans, Admitans ve SWR¶yi
Çizmek Güç Empedans ve Smith Aba Smith Aba ile Çeyrek Dalga Boyu Transformatör Eleme
Smith Abann Kullanlmas Sorular Kaynaklar
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1. letim Hatlar
2. Smith Abann Türetilmesi
3. Smith Abann Kullanlmas4. Sorular
5. Kaynaklar
Agenda
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LETM HATLARI
letim hatlarnn kayplar hiçbir zaman sfr olmaz.
Sürekli rejimde hat üzerinde toplanan
enerji büyüktür. Bu enerji, iletkenleri çevreleyen EM
alanlarda toplanr.
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LETM HATLARI
¼½
»¬«
!
S jZ Z
S jZ Z Z Z
L
L
F
F
tan
tan
0
0
0
letim hatt empedanslarnn matematikselçözümü zordur.
Z = hattn belli bir noktadaki empedansZL = yük empedansZ0 = hattn karakteristik empedans FS = yükten empedans deerinin hesaplanaca noktaya kadar olan mesafe
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LETM HATLARI
Neden abaklara ihtiyaç duyulur?
letim hatlarnn özelikleriningrafiksel olarak gösterilmesinde
ihtiyaç duyulur.
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LETM HATLARI
Smith aba nedir?
Smith aba üzerinde çizilen parametreler unlar içerir:
1. letim hatt üzerindeki tüm noktalardaki empedans (ya da admitans)a. Yansma katsaysnn büyüklüü (+)b. Derece cinsinden yansma katsays açs
2. Herhangi iki nokta arasnda, iletim hattnn dalga boyu cinsinden uzunluu3. Herhangi iki nokta arasndaki zayflama
a. Duran dalga kayp katsaysb. Yansma kayb
4. Gerilim ya da akm duran dalga orana. Duran dalga oranb. Duran dalgalara bal gerilim ve akm snrlar
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LETM HATLARI
Smith aba nedir?
Smith abailetim hatt hesap cetveli
Smith aba, sabitözelliklere sahip bir iletimhattnn herhangi bir noktasndaki empedansile hat üzerindeki dier tüm noktalarnempedanslar arasndakibanty gösteren özelbir empedans koordinatsistemidir.
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1. letim Hatlar
2. Smith Abann Türetilmesi
3. Smith Abann Kullanlmas4. Sorular
5. Kaynaklar
Agenda
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SMITH ABAININ TÜRETLMES
GR
Tipik devre öeleri Dikdörtgen koordinat düzlemindeçizilen empedanslar
1
1
!+
z
z
Bir iletim hattnn karakteristikempedans Z0, negatif iaretli vepozitif iaretli hem gerçek hem
de sanal bileenlerdenolumaktadr
Z = R jX
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SMITH ABAININ TÜRETLMES
Sabit Re(z) Çizgileri
Dikdörtgen grafik + düzlemi
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SMITH ABAININ TÜRETLMES
Sabit Im(z) Çizgileri
Dikdörtgen grafik+ düzlemi
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SMITH ABAININ TÜRETLMES
Empedans Terslemesi (Admitans)
Z1Y !
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SMITH ABAININ TÜRETLMES
Empedans Terslemesi (Admitans)
Empedans ve Admitans Koordinatlar
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SMITH ABAININ TÜRETLMES
Karmak Elenik
Karmak Elenik Karmakelenik, Smithabandan,
+¶nun açsnniaretinitersineçevirmek
sureliylekolaycabulunabilir.
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1. letim Hatlar
2. Smith Abann Türetilmesi
3. Smith Abann Kullanlmas4. Sorular
5. Kaynaklar
Agenda
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Empedans, Admitans ve SWR¶yi Çizmek
Z0 = 50 �Z = 25 �
0.550
25
Z
Zz
O
!!!
Omik Yük
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VSWRVoltage Standing Wave Ratio
Empedans, Admitans ve SWR¶yi Çizmek
Bir daireye karlk gelen duran dalga oranSWR, dairenin, yatay ekseni aban sayannda kestii noktadaki Z/Zo deerine eittir.
Omik Yük
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Z tamamen omikolduundan dorudan
yatay eksendebulunmak zorundadr.
Aban çevresinde 180Ûdönmek suretiyle y eldeedilir.
2Y
Yy
0
!!
Omik Yük
2!SWR
Empedans, Admitans ve SWR¶yi Çizmek
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j0.5
50
j25
Z
jX
Z
Zz
OO
!
!
!!
ndüktif Yük
Z0 = 50 �Z =+ j25 �
Empedans, Admitans ve SWR¶yi Çizmek
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Empedans, Admitans ve SWR¶yi Çizmek
ndüktif Yük
SWR, dairenin, yatayekseni aban sayannda kestii noktadakiZ/Zo deerine eittir
j2Y
YyO
!!
g!SWR
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Karmak Yük
j0.50.5
50
j2525z !
!
Z0 = 50 �Z = 25 + j25 �
Empedans, Admitans ve SWR¶yi Çizmek
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Empedans, Admitans ve SWR¶yi Çizmek
Karmak Yük
j11Y
Yy
0
!!
2.6S !
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Giri Empedans ve Smith Aba
Smith abanda en dtaki iki ölçek,dalga boyu olarak uzakl gösterir
Dtaki ölçek, yükten üretece doruuzakl verir
çteki ölçek kaynaktan yüke doru
uzakl verir
360°= 0.5 P
180°= 0.25 P
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Giri Empedans ve Smith Aba
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Giri Empedans ve Smith Aba
0.5Z
Zz
0
L !!
Z0 = 75 ;ZL = 37.5 ;
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1. letim Hatlar
2. Smith Abann Türetilmesi
3. Smith Abann Kullanlmas4. Sorular
5. Kaynaklar
Agenda
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Örnek 1
Karakteristik empedans Z0 = 50 ;
ve yük empedans ZL = 30 + j40 ;olan, 1.25 P boyundaki bir iletim hattnn
giri empedansn ve SWR¶sini bulalm.
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Örnek 1
8.0 j6
.050
40 j30
z !
!
Normalletirilmi yük empedans
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Örnek 1
3.4SWR!1.25 P uzaklkta giri empedans
0.12 P + 0.25 P = 0.37 P
D noktas
Zi = zi x Z0= 50 x (0.55 - j0.9) = 27.5 - j45
zi = 0.55 - j0.9
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Smith Aba le Çeyrek Dalga
Boyu Transformatör Eleme letim hattnn belli bir uzunluu bir transformatör gibi
hareket eder.
Yükten gerekli uzakla konulmu uygun boyda bir iletim hatt, iletim hattnn empedansna bir yüküelemekte kullanlabilir.
Smith aban kullanmak suretiyle çeyrek dalga boyutransformatörle bir yükü bir iletim hattna elemeilemi gerçekletirilebilir.
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Smith Aba le Çeyrek Dalga
Boyu Transformatör ElemeZL = 75 + j50 ;¶luk bir yük,çeyrek dalga boyutransformatörle 50 ;¶luk bir kaynaa elenebilir.Normalletirilmi yük empedans z udur:
j11.5
50
j5075z !
!
z = 1. 5 + j1 Smith aba üzerindeki A noktasdr.
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Smith Aba le Çeyrek Dalga
Boyu Transformatör ElemeC noktas 0.250 P
- B noktas - 0.192 P
uzaklk 0.058 P
zi = 2.4 (E noktas)
Zi = 50 (2.4) = 120 ;
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Smith Aba le Çeyrek Dalga
Boyu Transformatör Eleme
LZZZ !d
77.512050ZZZ LO0 !v!!d
0 Z d= Çeyrek dalga boyu transformatörün karakteristik empedans
0 Z = Elenmekte olan iletim hattnn karakteristik empedans
L Z = Yük empedans
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Smith Aba le Çeyrek Dalga
Boyu Transformatör Elemeo Çeyrek dalga boyu transformatörün, iletim hattüzerindeki duran dalgalar bütünüyle ortadan
kaldrmamaktadr.
o Çeyrek dalga boyu transformatör, yalnzcakendisiyle kaynak arasndaki duran dalgalar
bertaraf eder. iletim hattnda transformatör ile yükarasnda hâlâ duran dalgalar mevcuttur.
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Örnek 2
75 ;¶luk bir iletim hattn ZL = 25 ± j50¶lik bir
yüke elemek için SWR¶yi, çeyrek dalga boyubir transformatörün karakteristik empedansnve transformatörün kaynaktan ne kadar uzaa yerletirilmesi gerektiini bulalm.
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Örnek 2
Normalletirilmi yük empedans
66.0 j33.0
75
50 j25z !
!
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Örnek 2
4.6S !D noktas 0.5 P
- B noktas - 0.4 Puzaklk 0.1 P
zi = 2.2
Z i = 2 . 2 x 7 5 = 165 ;
24.111165750 !! Z
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1. letim Hatlar
2. Smith Abann Türetilmesi
3. Smith Abann Kullanlmas4. Sorular
5. Kaynaklar
Agenda
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ELEKTRONK LETM TEKNKLER
Wayne TOMASI, MEB ± 2002,
stanbul
ELEKTROMANYETK
J. A. EDMINISTER, SCAHUM¶SOUTLINES ± 2000, Ankara
http://www.sss-mag.com/smith.html
Yararlanlan Kaynaklar Yararlanlan Kaynaklar