Lect. 19: Smith Chart (Cheng 9-6) - Yonsei Universitytera.yonsei.ac.kr/class/2014_1_1/lecture/Lect...
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E&M 2 (14/1) W.-Y. Choi Lect. 19: Smith Chart Z 0 Z L 0 0 L L Z Z Z Z Complex numbers in general 0 Let L L Z z Z r i j , L z 1 Then , 1 L L z z 1 1 L z (Normalized load impedance) 1 1 r i L r i j z j 2 2 2 2 1 , 1 r i r i r 2 2 1 1 1 r i r i r i j j r jx (Cheng 9-6) L z r jx 2 2 2 1 i r i x Express and in terms of and r i r x Plot and in complex domain r x One-to-one correspondence
Transcript of Lect. 19: Smith Chart (Cheng 9-6) - Yonsei Universitytera.yonsei.ac.kr/class/2014_1_1/lecture/Lect...
E&M 2 (14/1) W.-Y. Choi
Lect. 19: Smith Chart
Z0 ZL
0
0
L
L
Z ZZ Z
Complex numbers in general
0
Let LL
Z zZ
r ij
, Lz
1Then ,1
L
L
zz
11Lz
(Normalized load impedance)
11
r iL
r i
jz
j
2 2
2 2
1 ,1
r i
r i
r
2 2
1 1
1r i r i
r i
j jr jx
(Cheng 9-6)
Lz r jx
2 2
21
i
r i
x
Express and in terms of and r ir x
Plot and in complex domainr x
One-to-one correspondence
E&M 2 (14/1) W.-Y. Choi
Lect. 19: Smith Chart
(-1,0)
i
r(1,0)
(0,1)
(0,-1)
2 2
2 2
1From ,
1r i
r i
r
i) )0,1
(r
r
Center :r1
1Radius :
r=0r=0.5
r=1r=2
2 22 1
1 1r ir
r r
E&M 2 (14/1) W.-Y. Choi
Lect. 19: Smith Chart
2 2
2From ,1
i
r i
x
ii) )1,1(
xCenter :
x1
Radius :
r
i
(1,0)(-1,0)
(0,1)
(0,-1)
x=0
x=0.5
x=-0.5
x=1.0
x=-1.0
2 2
2 1 11r i x x
E&M 2 (14/1) W.-Y. Choi
Lect. 19: Smith Chart
Smith Chart(Fig. 9-32In Cheng)
E&M 2 (14/1) W.-Y. Choi
Lect. 19: Smith ChartEX 9-13)
Zin=? R0=50Ω
10
L
'z
PSC
P1
'
'
2
0 2
1( ')1
j z
j z
eZ z Ze
r=0x=0.725
11Lz
,Lz
'2 ( ') j zz z e 102
in For z , move to j
e
0.725inz j
'
'
2
2
1( ')1
j z
j z
ez ze
Z 36.25in j
E&M 2 (14/1) W.-Y. Choi
Lect. 19: Smith Chart
Yonsei Univ. High-speed information transmission Lab.
EX 9-14)
R0=100Ω
434.0L
'z
180260 jZL
in
1) ?2) SWR =?3) Z ?4) ' for voltage max?z
O PM
P’2P2
P’3
P3
E&M 2 (14/1) W.-Y. Choi
Lect. 19: Smith ChartEX 9-15
R0=50Ω
'z
?LZ
L
SWR 3period for voltage 20cmFirst min. at 5cm from load
1) ?2) ?3) Z ?
PSC POO PMPm
P’L
=
?L
'z
LZ
PL
R=?
E&M 2 (14/1) W.-Y. Choi
Lect. 19: Smith Chart
PSC O
P2
P’2
Pi
P’3P’1
P1
P3
Ex. 9-16: Lossy TL
m2
R0=75Ω
)(22545 jZin
(a) ? ,
(b) If ZL= 67.5-j45,Zin=?
Homework (optional):Ex. 9-13,14,15,16
E&M 2 (14/1) W.-Y. Choi
Lect. 19: Smith Chart
(1,0)
(0,1)
(0,-1)
LOpen: z
OpenShort
(-1,0)
Z0 ZL
-circle,1 center: ( , 0) (1,0), radius 0
1 1
rr
r r
-circle1 1 center: (1, ) (1, ), radius
x
x x
(r and x 0), 1
E&M 2 (14/1) W.-Y. Choi
Lect. 19: Smith Chart
(1,0)
(0,1)
(0,-1)
LShort: z 0OpenShort
(-1,0)
Z0 ZL
-circle1 center: ( ,0) (0,0), radius 1
1 1
rr
r r
(r 0 and x 0), 1
-circle1 1 center: (1, ) (1, ), radius
x
x x
