Date post: | 16-Feb-2018 |
Category: |
Documents |
Upload: | imad-a-shaheen |
View: | 227 times |
Download: | 0 times |
of 17
7/23/2019 Notes 3 - Smith Chart Examples
1/17
Prof. David R. Jackson
Dept. of ECE
Notes 3
ECE 5317-6351
Microwave Engineering
Fall 2011
Smith ChartExamples
1
7/23/2019 Notes 3 - Smith Chart Examples
2/17
0 50
100 50L
Z
Z j
=
= +
I(-d)
V(-d)
+
d
ZL-
0 ,Z
FindZ(-d)
/ 1/ 4, 3/ 8, 1/ 2g
d =at
,
0
2 1LL nZ
Z jZ
= = +
( )
/ 4
0.4 0.2
/ 4 20 10
g
n
g
d
Z j
Z j
=
nLZ
3 / 8g
d =
/ 4g
d =
a
b
0
1/2 gd =
or
Example 1
a
2
Impedance chart
7/23/2019 Notes 3 - Smith Chart Examples
3/17
( )
3 / 8
0.5 0.53 / 8 25 25
g
n
g
d
Z jZ j
=
+
+
b
( )
/ 2
2 1
/ 2 100 50
g
n
g
d
Z j
Z j
=
+
= +
c
nLZ
3 / 8g
d =
/ 4g
d =
a
b
0
/2gd =
=0.087g
c0.5g
0.462g
0.212g
Example 1 (cont.)
3
I(-d)
V(-d)
+
d
ZL-
0 ,Z
7/23/2019 Notes 3 - Smith Chart Examples
4/17
( )0 050 20 mS
8mS 4 mSL
Z Y
Y j
= =
=
Find Y(-d)
/ 1/ 4, 3 / 8, 1/ 2gd =at
,
0
0.4 0.2LL n YY jY
= =
( )
/ 4
2 1
/ 4 40 mS 20 mS
g
n
g
d
Y j
Y j
=
+
+
nLY
3 / 8 gd =
/ 4gd =
a
b
0
1/2
gd =
or
c
Example 2
a
4
I(-d)
V(-d)
+
d
ZL-
0 ,Z
Admittance chart
7/23/2019 Notes 3 - Smith Chart Examples
5/17
( )
3 / 8
1 1
3 / 8 20 mS 20mS
g
n
g
d
Y j
Y j
=
( )
/ 2
0.4 0.2
/ 2 8mS 4mS
g
n
g
d
Y j
Y j
=
=
Example 2 (cont.)
b
c
5
I(-d)
V(-d)
+
d
ZL-
0 ,Z
nLY
3 / 8g
d =
/ 4gd =
a
b
0
1/2 g
d =
=
c
Admittance chart
7/23/2019 Notes 3 - Smith Chart Examples
6/17
Simple answer:
* When adding elements in series useZ-chart
* When adding elements in parallel use Y-chart
A B CZ Z Z+ =
A B CY Y Y+ =
ZA ZB ZC
YA YB YC
Which Chart to Use?
6
7/23/2019 Notes 3 - Smith Chart Examples
7/17
Use reactively loaded section of
transmission line.
most common to use open or short load
d
ZL0,Z
( )Z d
L LZ jX=
( )LX ( )0LX =
SC OC
d
d = 0
nLX
( )nX d
Using Reactive Loads
7
Impedance chart
7/23/2019 Notes 3 - Smith Chart Examples
8/17
d
YL0 ,Z
( )Y d
L LY j=
SC OC
d
d = 0
nL
Y
( )nY d
( ) ( )
( )
0
0/
n
n
Y d Y d Y
Y d Z
=
=
Using Reactive Loads (cont.)
8
Admittance chart
7/23/2019 Notes 3 - Smith Chart Examples
9/17
Use a short-circuited section of air-filled TEM, 50 transmission line
(= k0, g=0) to create an impedance ofZin= -j25
atf= 10 GHz.
SC
-1/2
0.42
6 g
50
0 g L
25in
Z j=
SC50 ,k0
( ),25
1/ 250
in nZ j j= =
0.426 0 0.426g g gL = =
Example 3
L= 1.28 cm
90 0 0 0
2 2c
f k
= = =
0 3.0 cm =
Impedance chart
7/23/2019 Notes 3 - Smith Chart Examples
10/17
Use an open circuited section of 75 (Y0= 1/75 S) air-filled
transmission line atf =10 GHz to create an admittance of
j1
1/75 S
OC
L
L
( )1/75inY j= +
OC75 , k0
( ), 1in nY j=
0
1
75
Y =
1S 13.3mS
75inY j j= + =
0.375cmL =
Example 4
10
00.125L = 0 3.0 cm =
Admittance chart
7/23/2019 Notes 3 - Smith Chart Examples
11/17
Y0
d
1
njb+
,A nY
,L nY
1n
G =
,in in
Z Y d
ZLYS
AY
0Z
( )0inZ Z=
,,
0 0 ,
1LL n
L
L n
L n
YY
Y Z
ZZ
Z == =
, , ,in n A n S nY Y Y= +
Note: At d we have
Want to pick dand Yssuch that Yin= Y0.
0
0
1YZ
=
Matching Circuit
11
Admittance chart
7/23/2019 Notes 3 - Smith Chart Examples
12/17
,S n n
Y jb=
, ,1 1 n S nin n YY jb= + +=
We want
Choose
( )
0
,
0
1
1 1in n n n
in
in
in
Y jb b
Y
j
Y Y
Z Z
= + =
= =
=
,in in
Z Y d
ZLYS
AY
0Z
Y0
d
1
njb+
,A nY
,L nY
1n
G =
Matching Circuit (cont.)
12Admittance chart
7/23/2019 Notes 3 - Smith Chart Examples
13/17
Example 5
ZLZ0
ls
Z0s
d
0 50[ ]Z =
100 100 [ ]LZ j= +
, 2 2L nZ j= +
( ), 1 0.25 .252 2L nY j
j= = +
/6 o0.62 0.62 30j
L e = = 0
0
1
1
L LnL
L Ln
Z Z Z
Z Z Z
= =
+ +13
In this example we will
use the usual Smith
chart, but as an
admittance calculator.
7/23/2019 Notes 3 - Smith Chart Examples
14/17
Example 5 (cont.)
0.178 g
,Y 0.25 0. 52L n j=
1 1.57j+
1 1.57j
0.322 g
0.363 g
0.219 g
0.041 g
0.219-
0.36
1.57
1.57 3
g
g
d
d
j
j
+
=
=
Solution :
Add at
or at
0.170 0.2.0 981 14 g =+
0.320 0.3.0 321 64 g =+
wavelengths toward load
wavelengths toward generator
Smith chart scale:
Admittance calculator
14
plane
SCOC
(Well use the first choice.)
7/23/2019 Notes 3 - Smith Chart Examples
15/17
Example 5 (cont.)
S / C
0 1.57j
0.09
O / C
Admittance calculator
( ), cot
1.57 cot
1cot 1.57; tan
1.57
2 0.567 [radians]
s nB l
l
l l
l l
=
=
= =
= =
0.09s gl =
From the Smith chart:
0.0903s gl =
Analytically:
15
7/23/2019 Notes 3 - Smith Chart Examples
16/17
00
0
tantan
L Tin T
T L
Z jZZ ZZ jZ
+= +
( ) 2
/ 4
4 2
g
g
g
= = =
[ ]
2
0
120
Tin
L
T in L
ZZ
Z
Z Z Z
=
= [ ]
0
12
0 0
in
T L
Z Z
Z Z Z
=
=
ZLZ0 Z0T
Zin, in ZL is real
/ 4g
Quarter-Wave Transformer
At f0 :
For in= 0
16
7/23/2019 Notes 3 - Smith Chart Examples
17/17
Match 100 load to 50 transmission Line at f0.
0 100 50
70.7
TZ = =
0
0
0
0
2 2 2g f
r rf k k
= = = =
Example 6
0 70.7TZ =
17
( )1r =, 50 Z0T
/ 4g
100