Lecture #5 Contents - GUC · 2016. 2. 28. · GUC (Dr. Hany Hammad) 2/28/2016 COMM (603) Lecture #5...
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GUC (Dr. Hany Hammad) 2/28/2016 COMM (603) Lecture #5 1 © Dr. Hany Hammad, German University in Cairo Lecture #5 Contents • Coupled Line Directional Couplers – Coupled line theory. – Design of coupled line couplers. • The Lange Coupler • Review of Smith Chart – Impedance matching. – Matching with lumped elements (L-Networks). • The quarter-wave transformer. © Dr. Hany Hammad, German University in Cairo Coupled Line Theory W S W d Ground Substrate Coupled Microstrip Transmission Line Cross Section C 12 C 22 C 11 Assume TEM propagation If the strip conductors are identical in size and location relative to the ground conductor, then C 11 =C 22 .
Transcript of Lecture #5 Contents - GUC · 2016. 2. 28. · GUC (Dr. Hany Hammad) 2/28/2016 COMM (603) Lecture #5...
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 1
© Dr. Hany Hammad, German University in Cairo
Lecture #5 Contents
• Coupled Line Directional Couplers
– Coupled line theory.
– Design of coupled line couplers.
• The Lange Coupler
• Review of Smith Chart
– Impedance matching.
– Matching with lumped elements (L-Networks).
• The quarter-wave transformer.
© Dr. Hany Hammad, German University in Cairo
Coupled Line Theory W S W
d
Ground Substrate
Coupled Microstrip Transmission Line
Cross Section
C12
C22 C11
Assume TEM propagation
If the strip conductors are identical in size and location relative to the ground conductor,
then C11=C22.
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 2
© Dr. Hany Hammad, German University in Cairo
+V +V
2211 CCCe
e
e
e
oeC
LC
C
LZ
Coupled Line Theory (even mode/odd mode)
C22 C11
Same Potential
No capacitance
+V -V
C22 C11
Same Potential
2C12 2C12
+ -
Zero
12211 CCCo
op
oCv
Z1
0
ep
oeCv
Z1
Even
Odd
© Dr. Hany Hammad, German University in Cairo
Even- and odd-mode characteristic impedance design data for coupled microstrip lines on a substrate with r = 10.
Coupled Line Theory
For a given value of W & S we can find Z0e & Z0o
For a given value of Z0e & Z0o we can find W & S
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 3
© Dr. Hany Hammad, German University in Cairo
+
_
oZ
oe ZZ 00 ,
oZ
oZ oZ
oV
3
1
4
2
Coupled
Input
Isolated
Through
Design of coupled line couplers
oe
oe
inII
VV
I
VZ
11
11
1
1
© Dr. Hany Hammad, German University in Cairo
tan
tan
00
000
jZZ
jZZZZ
e
ee
e
in
0
01ZZ
ZVV
e
in
e
ine
+
_
+
_
0Z
eZ0
0Z
0Z 0Z
0V
0V
eI3eI4
eI1
eI2
eV3 eV4
eV1 eV2
+
_
oZ
oV e
inZ
0
01
ZZ
VI
e
in
e
Design of coupled line couplers
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 4
© Dr. Hany Hammad, German University in Cairo
+
_
+
_
0Z
oZ0
0Z
0Z 0Z
0V
0V
oI3oI4
eI1
eI2
oV3 oV4
oV1 oV2
tan
tan
00
000
jZZ
jZZZZ
o
oo
o
in
0
01ZZ
ZVV
o
in
o
ino
+
_
oZ
oV o
inZ
0
01
ZZ
VI
o
in
o
Design of coupled line couplers
© Dr. Hany Hammad, German University in Cairo
oe
oe
inII
VVZ
11
11
0
2
00
2
2
ZZZ
ZZZZZ
o
in
e
in
o
in
e
inin
2
0ZZZ o
in
e
in
Design of coupled line couplers
00
00
11
ZZZZ
ZZ
Z
ZZ
Z
o
in
e
in
o
in
o
in
e
in
e
in
0
00
2ZZZ
ZZZZZZo
in
e
in
e
in
o
in
o
in
e
in
Note to have 0ZZin (matched)
2
0
00
00
00
0000
tan
tan
tan
tanZ
jZZ
jZZ
jZZ
jZZZZZZ
o
o
e
eoe
o
in
e
in
tan
tan
00
000
jZZ
jZZZZ
o
oo
o
in
tan
tan
00
000
jZZ
jZZZZ
e
ee
e
in
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 5
© Dr. Hany Hammad, German University in Cairo
tan
tan
tan
tan
00
00
0
00
00
0
eo
oe
o
oe
eo
e
o
in
e
inZjZ
ZjZZ
ZjZ
ZjZZZZ
2
000 ZZZZZ oe
o
in
e
in
Which means that all ports will be matched as long as oeZZZ 000
Design of coupled line couplers
2
000 ZZZ oe If
tan
tan
000
000
0
oee
eoe
e
e
inZZjZ
jZZZZZ
tan
tan
000
000
0
oeo
ooe
o
o
inZZjZ
jZZZZZ
© Dr. Hany Hammad, German University in Cairo
oe VVV 111
00
2
0
00
2
001
2
2
ZZZZZ
ZZZZZVV
o
in
e
in
o
in
e
in
01 VV
oeoe VVVVV 11333
0
0
0
03ZZ
ZV
ZZ
ZVV
o
in
o
in
e
in
e
in
tantan
tan
tan
tan
tan
tan
000000
000
0
00
000
00
000
jZZZjZZZ
jZZZ
ZjZZ
jZZZ
jZZ
jZZZ
eee
ee
e
ee
e
ee
tan
tan
00
000
jZZ
jZZZZ
o
oo
o
in
tan
tan
00
000
jZZ
jZZZZ
e
ee
e
in
Design of coupled line couplers
0
0
0
0ZZ
ZV
ZZ
ZV
o
in
o
in
e
in
e
in
2
000
000
ZZZZZZZ
ZZZZZZZZV
o
in
e
in
o
in
e
in
o
in
o
in
e
in
e
in
o
in
e
in
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 6
© Dr. Hany Hammad, German University in Cairo
tan2
tan2
0
2
000
2
000
ZZjZZ
jZZZ
ee
ee
tan2
tan
tan2
tan
000
00
0
2
000
00
oe
e
e
e
e
ZZjZ
jZZ
Z
ZZjZ
jZZ
Divide by Z0e
tan2
tan
000
00
0 oe
e
e
in
e
in
ZZjZ
jZZ
ZZ
Z
tan2
tan
000
00
0 oe
o
o
in
o
in
ZZjZ
jZZ
ZZ
Z
0
0
0
03ZZ
ZV
ZZ
ZVV
o
in
o
in
e
in
e
in
tan2
tan
000
0003
oe
oe
ZZjZ
ZZjVV
Design of coupled line couplers
© Dr. Hany Hammad, German University in Cairo
oe
oe
ZZ
ZZC
00
00
Let
tan1
tan
203
jC
jCVV
tan2
tan
00
0
00
00
03
jZZ
Z
ZZ
ZZj
VV
oe
oe
oe
oe ZZ
ZC
00
02 21
accordingly
Design of coupled line couplers
Divide by (Z0e+ Z0o)
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 7
© Dr. Hany Hammad, German University in Cairo
+
_
0Z 0Z
0V
eI1
eI2
eV1 eV2
01 VV
e
ee
ZZ
ZZ
00
00
e
e VVVV 10002
j
e
jjje eeVeVeVV 0001 j
e
j
e
ee
VV
1
0
j
e
j
eee
eeVV
112
jj
e
jjj
e
j
e
eeee
eeZeeZ
Z
eZZeZZ
ZZZZVV
00
0
0000
000012
2
sincos 00
012
e
ee
jZZ
ZVV
0
01ZZ
ZVV
e
in
e
ine
tan
sec
00
0
0
02
e
e
in
e
ine
jZZ
Z
ZZ
ZVV
tan
sec
tan2
tan
00
0
000
000
eoe
e
jZZ
Z
ZZjZ
jZZV
tan2
sec
000
002
oe
e
ZZjZ
ZVV
tan2
sec
000
002
oe
o
ZZjZ
ZVV
Design of coupled line couplers
© Dr. Hany Hammad, German University in Cairo
022444 oeoe VVVVV
tan2
sec2
000
00222
oe
oe
ZZjZ
ZVVVV
oe ZZ
ZC
00
02 21
tan1
sec1
2
2
02
jC
CVV
sincos1
1
2
2
02
jC
CVV
The higher the value of C the
voltage V3 (coupled port) will
increase and the V2 (Through
port will decrease), but is it also
function of .
First coupling Maximum
© Microwave Engineering 3rd ed. Pozar
,2
3,
2
Design of coupled line couplers
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 8
© Dr. Hany Hammad, German University in Cairo
2
For
2
0
2 1 CjV
V C
V
V
0
3
If
0
2
0
2
1
Z
VPin
0
2
0
2
0
2
2
2
1
2
1
2
1
Z
VC
Z
VP
0
2
0
2
0
2
3
32
1
2
1
Z
VC
Z
VP 04 P
432 PPPPin
For a given 0Z & C2
0
2
0
2
0
2
0
00
2
0
00
2
0
00
00
ZZ
ZZ
ZZZ
ZZZ
ZZ
ZZC
e
e
eoe
eoe
oe
oe
2
0
2
0
2
0
2
0 ZZCZCZ ee CZCZ e 11 2
0
2
0
C
CZZ e
1
100
C
CZZ o
1
100
Design of coupled line couplers
© Dr. Hany Hammad, German University in Cairo
Example
Design a 20 dB single-section coupled line coupler with a characteristic impedance of 50 .
1.010 20/20 C
Answer
28.55
1
100
C
CZZ e
23.45
1
100
C
CZZ o
Using Z0e and Z0o you can find the values W, S.
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 9
© Dr. Hany Hammad, German University in Cairo
Design of coupled line couplers
© Dr. Hany Hammad, German University in Cairo
The Lange Coupler
Layout in microstrip form The unfolded Lange coupler
Can achieve 3 dB or 6 dB coupling factors
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 10
© Dr. Hany Hammad, German University in Cairo
The Lange Coupler
© Dr. Hany Hammad, German University in Cairo
1 2 3 4
mC mC mC
exCinCinCexC
1 2 3 4
exCinCinCexC
+ + - mC2 mC2 mC2 mC2 mC2 mC2
- minexo CCCC 64
inexe CCC 41 2 3 4
exCinCinCexC
+ + + + 1 2 3 4
exCinCinCexC
+ + + +
1 2 3 4
exCinCinCexC
+ + - mC2 mC2 mC2 mC2 mC2 mC2
-
mex
mexexin
CC
CCCC
The Lange Coupler
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 11
© Dr. Hany Hammad, German University in Cairo
exe CC mexo CCC 2
4
4
1
ep
eCv
Z
4
4
1
op
oCv
Z
Hence eex CC 2
eom
CCC
eoe
eoee
eoe
eoe
e
mex
mexexin
CCC
CCCC
CCC
CCC
CCC
CCCC
2
2
2
oe
e
CC
C
22
The Lange Coupler
From Two Coupled Lines Slide #3 Ce and Co of two coupled lines
© Dr. Hany Hammad, German University in Cairo
oe
oee
oe
eeinexe
CC
CCC
CC
CCCCC
32 2
4
oe
eoominexo
CC
CCCCCCC
364
Similarly
oe
oeee
CC
CCCC
34
oe
oee
e
ZZ
ZZZ
Z 11
113
1
1
4
e
eo
eoe Z
ZZ
ZZZ 0
00
004
3
o
oe
eoo Z
ZZ
ZZZ 0
00
004
3
oeeo
eoeooe
ZZZZ
ZZZZZZZ
0000
2
0000440
33
The Lange Coupler
GUC (Dr. Hany Hammad) 2/28/2016
COMM (603) Lecture #5 12
© Dr. Hany Hammad, German University in Cairo
oeoe
oe
oe
oe
ZZZZ
ZZ
ZZ
ZZC
00
2
0
2
0
2
0
2
0
44
44
23
3
oeeo
eoeooe
ZZZZ
ZZZZZZZ
0000
2
0000440
33
0
2
0112
8934Z
CCC
CCZ e
0
2
0112
8934Z
CCC
CCZ o
The Lange Coupler
© Dr. Hany Hammad, German University in Cairo
The Lange Coupler
