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- Power dividers split power from one port to multiple ports, while combiners combine power from multiple ports into one port.
- S-parameters describe the scattering properties of networks and must satisfy unitary conditions for lossless, reciprocal networks.
- A directional coupler has four ports where power is coupled from one port to another according to coupling factors while ensuring isolation between other ports.
- An ideal 3 dB coupler has a 50% power split between the input and
This presentation illustrates the experience gained by me during a RF circuit design course. The course requirements included designing, fabricating and simulating various couplers, an amplifier, a low noise amplifier and an oscillator. Operating frequency was centered around 2.4 GHz.
This presentation illustrates the experience gained by me during a RF circuit design course. The course requirements included designing, fabricating and simulating various couplers, an amplifier, a low noise amplifier and an oscillator. Operating frequency was centered around 2.4 GHz.
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Use s parameters-determining_inductance_capacitancePei-Che Chang
1. Use s parameters-determining_inductance_capacitance
2. Relationship Between Common Circuits and the ABCD Parameters
3. Converts Z-parameters to S-parameters
4. Relationships Between Two-Port S and ABCD Parameters
5. Via and equivalent circuit
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
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The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
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Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
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The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
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Gopinath Rebala
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https://alandix.com/academic/papers/synergy2024-epistemic/
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https://arxiv.org/abs/2306.08302
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Elevating Tactical DDD Patterns Through Object Calisthenics
Power divider, combiner and coupler.ppt
1. Power divider, combiner and
coupler
By
Professor Syed Idris Syed Hassan
Sch of Elect. & Electron Eng
Engineering Campus USM
Nibong Tebal 14300
SPS Penang
2. Power divider and combiner/coupler
divider combiner
P1
P2= nP1
P3=(1-n)P1
P1
P2
P3=P1+P2
Divide into 4 output
Basic
3. S-parameter for power divider/coupler
33
32
31
23
22
21
13
12
11
S
S
S
S
S
S
S
S
S
S
Generally
For reciprocal and lossless network
j
i
for
S
S
N
k
kj
ki
0
1
*
1
1
*
N
k
ki ki
S
S
1
13
12
11
S
S
S
1
23
22
21
S
S
S
1
33
32
31
S
S
S
0
*
23
13
*
22
12
*
21
11
S
S
S
S
S
S
0
*
33
23
*
32
22
*
31
21
S
S
S
S
S
S
0
*
33
13
*
32
12
*
31
11
S
S
S
S
S
S
Row 1x row 2
Row 2x row 3
Row 1x row 3
4. Continue
If all ports are matched properly , then Sii= 0
0
0
0
23
13
23
12
13
12
S
S
S
S
S
S
S
For Reciprocal
network
For lossless network, must satisfy unitary
condition
1
2
13
2
12
S
S
1
2
23
2
12
S
S
1
2
23
2
13
S
S
0
12
*
23
S
S
0
23
*
13
S
S
0
13
*
12
S
S
Two of (S12, S13, S23) must be zero but it is not consistent. If S12=S13= 0, then
S23 should equal to 1 and the first equation will not equal to 1. This is invalid.
5. Another alternative for reciprocal network
33
23
13
23
12
13
12
0
0
S
S
S
S
S
S
S
S
Only two ports are matched , then for reciprocal network
For lossless network, must satisfy unitary
condition
1
2
13
2
12
S
S
1
2
23
2
12
S
S
1
2
33
2
23
2
13
S
S
S 0
13
*
33
12
*
23
S
S
S
S
0
23
*
13
S
S
0
33
*
23
13
*
12
S
S
S
S
The two equations show
that |S13|=|S23|
thus S13=S23=0
and |S12|=|S33|=1
These have satisfied all
6. Reciprocal lossless network of two matched
S21
=ej
S12=ej
S33
=ej
1
3
2
j
j
j
e
e
e
S
0
0
0
0
0
0
7. For lossless network, must satisfy unitary
condition
1
2
13
2
12
S
S
1
2
23
2
21
S
S
1
2
32
2
31
S
S
0
32
*
31
S
S
0
23
*
21
S
S
0
13
*
12
S
S
Nonreciprocal network (apply for circulator)
0
0
0
32
31
23
21
13
12
S
S
S
S
S
S
S
0
31
23
12
S
S
S
0
13
32
21
S
S
S
1
13
32
21
S
S
S
1
31
23
12
S
S
S
The above equations must satisfy the following either
or
9. Four port network
44
43
42
41
34
24
14
33
32
31
23
22
21
13
12
11
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
Generally
For reciprocal and lossless network
j
i
for
S
S
N
k
kj
ki
0
1
*
1
1
*
N
k
ki ki
S
S
1
14
13
12
11
S
S
S
S
1
24
23
22
21
S
S
S
S
1
34
33
32
31
S
S
S
S
0
*
24
14
*
23
13
*
22
12
*
21
11
S
S
S
S
S
S
S
S
0
*
44
24
*
43
23
*
42
22
*
41
21
S
S
S
S
S
S
S
S
0
*
34
14
*
33
13
*
32
12
*
31
11
S
S
S
S
S
S
S
S
R 1x R 2
R 2x R3
R1x R4
1
44
43
42
41
S
S
S
S
0
*
44
14
*
43
13
*
42
12
*
41
11
S
S
S
S
S
S
S
S
0
*
34
24
*
33
23
*
32
22
*
31
21
S
S
S
S
S
S
S
S
0
*
44
34
*
43
33
*
42
32
*
41
31
S
S
S
S
S
S
S
S
R1x R3
R2x R4
R3x R4
10. Matched Four port network
0
0
0
0
34
24
14
34
24
14
23
13
23
12
13
12
S
S
S
S
S
S
S
S
S
S
S
S
S
The unitarity condition become
1
14
13
12
S
S
S
1
24
23
12
S
S
S
1
34
23
13
S
S
S
0
*
24
14
*
23
13
S
S
S
S
0
*
34
23
*
14
12
S
S
S
S
0
*
34
14
*
23
12
S
S
S
S
1
34
24
14
S
S
S
0
*
34
13
*
24
12
S
S
S
S
0
*
34
24
*
13
12
S
S
S
S
0
*
24
23
*
14
13
S
S
S
S
Say all ports are matched and symmetrical network, then
*
**
@
@@
#
##
11. To check validity
Multiply eq. * by S24
* and eq. ## by S13
* , and substract to obtain
0
2
14
2
13
*
14
S
S
S
Multiply eq. # by S34 and eq. @@ by S13 , and substract to obtain
0
2
34
2
12
23
S
S
S
%
$
Both equations % and $ will be satisfy if S14 = S23 = 0 . This means
that no coupling between port 1 and 4 , and between port 2 and 3 as
happening in most directional couplers.
14. Physical interpretation
|S13 | 2 = coupling factor = 2
|S12 | 2 = power deliver to port 2= 2 =1- 2
Characterization of coupler
Directivity= D= 10 log
dB
P
P
log
20
3
1
Coupling= C= 10 log
dB
S
P
P
14
4
3 log
20
Isolation = I= 10 log dB
S
P
P
14
4
1 log
20
I = D + C dB
1
4 3
2
Input Through
Coupled
Isolated
For ideal case
|S14|=0
18. Example
• If source impedance equal to 50 ohm and the
power to be divided into 2:1 ratio. Determine Z1
and Z2
in
o P
Z
V
P
3
1
2
1
1
2
1
in
o P
Z
V
P
3
2
2
1
2
2
2
75
2
3
2
o
Z
Z
150
3
1 o
Z
Z
o
o
in
Z
V
P
2
2
1
50
// 2
1 Z
Z
Zo
19. Resistive divider
V2
V3
V1
Zo
Zo
P1
P2
P3
Zo V
o
o Z
Z
Z
3
Zo/3
Zo/3
Zo/3
o
o
o
in Z
Z
Z
Z
3
2
3
V
V
Z
Z
Z
V
o
o
o
3
2
3
/
2
3
/
3
/
2
1
V
V
V
Z
Z
Z
V
V
o
o
o
2
1
4
3
3
/
3
2
o
in
Z
V
P
2
1
2
1
in
o
P
Z
V
P
P
4
1
2
/
1
2
1
2
1
3
2
20. Wilkinson Power Divider
50
50
50
100
70.7
70.7
/4
Zo
/2 Zo
/2 Zo
2Zo
Zo
Zo
/4
2
2
T
e Z
Zin
o
T Z
Z 2
For even mode
Therefore
For Zin =Zo=50
7
.
70
50
2
T
Z
And shunt resistor R =2 Zo = 100
21. Analysis (even and odd mode)
2
2
1
1
Port 1
Port 2
Port 3
Vg2
Vg3
Z
Z
4
+V2
+V3
r/2
r/2
4
For even mode Vg2 = Vg3 and
for odd mode Vg2 = -Vg3. Since
the circuit is symmetrical , we
can treat separately two
bisection circuit for even and
odd modes as shown in the next
slide. By superposition of these
two modes , we can find S -
parameter of the circuit. The
excitation is effectively Vg2=4V
and Vg3= 0V.
For simplicity all values are
normalized to line characteristic
impedance , I.e Zo = 50 .
22. Even mode
Vg2=Vg3= 2V
Looking at port 2
Zin
e= Z2/2
Therefore for matching
2
Z
then V2
e= V since Zin
e=1 (the circuit acting like voltage divider)
2
1
Port 1
Port 2
2V
Z
4
+V2
e
r/2
+V1
e
O.C
O.C out
inZ
Z
Z
2
Note:
2
Z
If
To determine V2
e , using transmission line equation V(x) = V+ (e-jx + Ge+jx) , thus
V
jV
V
V e
G
)
1
(
)
4
(
2
1
1
)
1
(
)
0
(
1
G
G
G
jV
jV
V
V e
Reflection at port 1, refer to is
2
2
2
2
G
2
Z
Then 2
1 jV
V e
23. Odd mode
Vg2= - Vg3= 2V
2
1
Port 1
Port 2
2V
Z
4
+V2
o
r/2
+V1
o
At port 2, V1
o =0 (short) ,
/4 transformer will be
looking as open circuit ,
thus Zin
o = r/2 . We choose
r =2 for matching. Hence
V2
o= 1V (looking as a
voltage divider)
S-parameters
S11= 0 (matched Zin=1 at port 1)
S22 = S33 = 0 (matched at ports 2 and 3 both even and odd modes)
S12 = S21 = 2
/
2
2
1
1 j
V
V
V
V
o
e
o
e
S13 = S31 = 2
/
j
S23 = S32 = 0 ( short or open at bisection , I.e no
coupling)
24. Example
Design an equal-split Wilkinson power divider for a 50 W system
impedance at frequency fo
The quarterwave-transformer characteristic is
7
.
70
2 o
Z
Z
100
2 o
Z
R
r
o
4
The quarterwave-transformer length is
26. Unequal power Wilkinson
Divider
3
2
03
1
K
K
Z
Z o
)
1
( 2
03
2
02 K
K
Z
Z
K
Z o
K
K
Z
R o
1
R2
=Zo
/K
R
R3=Zo/K
Z02
Z03
Zo
2
3
2
3
2
port
at
Power
port
at
Power
P
P
K
1
2
3
27. Parad and Moynihan power divider
4
/
1
2
01
1
K
K
Z
Z o
2
3
2
3
2
port
at
Power
port
at
Power
P
P
K
K
K
Z
R o
1
4
/
1
2
4
/
3
02 1 K
K
Z
Z o
4
/
5
4
/
1
2
03
1
K
K
Z
Z o
K
Z
Z o
04 K
Z
Z o
05
Zo
Zo
Zo
Z05
Zo4
Zo2
Zo3
Zo1
R
1
2
3
28. Cohn power divider
VSWR at port 1 = 1.106
VSWR at port 2 and port 3 = 1.021
Isolation between port 2 and 3 = 27.3 dB
Center frequency fo = (f1 + f2)/2
Frequency range (f2/f1) = 2
1
2
3
29. Couplers
/4
/4
Yo Yo
Yo
Yo
Yse
Ysh Ysh
Branch line coupler 2
sh
2
se Y
1
Y
2
se
2
sh
sh
2
3
Y
Y
1
2Y
E
E
20
1
3 10
E
E x
x dB coupling
2
3
2
2
2
1 E
E
E
2
1
3
2
1
2
E
E
E
E
1
or
E1
E2
E3
30. Couplers
input
isolate
Output
3dB
Output
3dB 90o out of phase
3 dB Branch line coupler
/4
/4
Zo
Zo
Zo
Zo
2
/
Zo
2
/
Zo
Zo Zo
3
2 E
E
1
Ysh
2
Y
1
Y 2
2
se
sh
1.414
Yse
50
o
Z
50
sh
Z
5
.
35
se
Z
31. Couplers
9 dB Branch line coupler
355
.
0
10 20
9
1
3
E
E
2
2
1
2 355
.
0
1
E
E
935
.
0
355
.
0
1 2
1
2
E
E
38
.
0
935
.
0
355
.
0
2
3
E
E
8
.
0
sh
Y
Let say we choose
38
.
0
8
.
0
1
8
.
0
2
1
2
2
2
2
2
se
se
sh
sh
Y
Y
Y
Y
962
.
1
36
.
0
38
.
0
6
.
1
se
Y
50
0
Z
5
.
62
8
.
0
/
50
sh
Z
5
.
25
962
.
1
/
50
se
Z
Note: Practically upto 9dB coupling
32. Couplers
/4
/4
/4
/4
Input
Output in-phase
Output in-phase
isolated
1
2
3
4
•Can be used as splitter , 1 as input and 2 and 3
as two output. Port is match with 50 ohm.
•Can be used as combiner , 2 and 3 as input
and 1 as output.Port 4 is matched with 50 ohm.
Hybrid-ring coupler
OC
1
2
1
2
OC
1/2
1/2
2
2
2
2
2
2
/8
/8
/4
/4
/8
/8
Te
To
Ge
Go
33. Analysis
The amplitude of scattered wave
o
e
B G
G
2
1
2
1
1
o
e T
T
B
2
1
2
1
4
o
e T
T
B
2
1
2
1
2
o
e
B G
G
2
1
2
1
3
34. Couple lines analysis
Planar Stacked
Coupled microstrip
b
w w
s
w
s
w w
s
b
d
r
r
r
The coupled lines are usually assumed to operate in TEM mode.
The electrical characteristics can be determined from effective
capacitances between lines and velocity of propagation.
35. Equivalent circuits
+V +V
H-wall
+V -V
E-wall
C11
C22
C11
C22
2C12
2C12
Even mode Odd mode
C11 and C22 are the capacitances between conductors and the ground
respectively. For symmetrical coupled line C11=C22 . C12 is the
capacitance between two strip of conductors in the absence of ground. In
even mode , there is no current flows between two strip conductors , thus
C12 is effectively open-circuited.
36. Continue
Even mode
The resulting capacitance Ce = C11 = C22
e
e
e
e
oe
C
C
LC
C
L
Z
1
Therefore, the line characteristic impedance
Odd mode
The resulting capacitance Co = C11 + 2 C12 = C22 + 2 C12
Therefore, the line characteristic impedance
o
oo
C
Z
1
38. Stacked coupled stripline
m
F
s
b
b
s
b
s
b
C oW
r
oW
r
oW
r /
4
2
/
2
/ 2
2
11
w >> s and w >> b
m
F
s
C oW
r /
12
m
F
s
b
b
C
C oW
r
e /
4
2
2
11
m
F
s
s
b
b
w
C
C
C o
r
o /
1
2
2
2
2
2
12
11
o
o
r
1
r
o
e
oe
bw
s
b
Z
C
Z
4
1 2
2
s
s
b
b
w
Z
C
Z
r
o
o
oo
/
1
/
2
2
1
1
2
2
40. Design of Coupled line Couplers
input
output
Isolated
(can be matched)
Coupling
w
w
s
2
3 4
1
wc
/4
3 4
1 2
Zo
Zo Zo
Zo
Zoo
Zoe
2V
+V3
+V2
+V4
+V1
I1
I4
I3
I2
Schematic circuit
Layout
41. Even and odd modes analysis
3 4
1 2
Zo
Zo Zo
Zo
Zoo
V
+V3
o
+V2
o
+V4
o
+V1
o
I1
o
I4
o
I3
o
I2
o
V
_
+
+
_
3 4
1 2
Zo
Zo Zo
Zo
Zoe
V
+V3
e
+V2
e
+V4
e
+V1
e
I1
e
I4
e
I3
e
I2
e
V
_
+
+
_
I1
e = I3
e
I4
e = I2
e
Same
excitation
voltage
V1
e = V3
e
V4
e = V2
e
Even
I1
o = -I3
o
I4
o =- I2
o
V1
o = -V3
o
V4
o = -V2
o
Odd
Reverse
excitation
voltage
(100)
(99)
43. continue
Substituting eqs. (104) - (107) into eq. (101) yeilds
o
o
in
e
in
o
e
in
o
in
o
o
o
in
e
in
o
o
in
e
in
o
e
in
o
in
in
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
2
2
2
2
For matching we may consider the second term of eq. (108) will be zero , I.e
0
2
o
e
in
o
in Z
Z
Z or 2
o
oe
oo
e
in
o
in Z
Z
Z
Z
Z
(108)
Let oe
oo
o Z
Z
Z
Therefore eqs. (102) and (103) become
tan
tan
oo
oe
oe
oo
oe
e
in
Z
j
Z
Z
j
Z
Z
Z
tan
tan
oe
oo
oo
oe
oo
o
in
Z
j
Z
Z
j
Z
Z
Z
and (108) reduces to Zin=Zo
(110)
(109)
44. continue
Since Zin = Zo , then by voltage division V1 = V. The voltage at port 3, by
substitute (99), (100) , (104) and (105) is then
o
o
in
o
in
o
e
in
e
in
o
e
o
e
Z
Z
Z
Z
Z
Z
V
V
V
V
V
V 1
1
3
3
3 (111)
Substitute (109) and (110) into (111)
tan
2
tan
oo
oe
o
oo
o
o
o
in
o
in
Z
Z
j
Z
jZ
Z
Z
Z
Z
tan
2
tan
oo
oe
o
oe
o
o
e
in
e
in
Z
Z
j
Z
jZ
Z
Z
Z
Z
Then (111) reduces to
tan
2
tan
3
oo
oe
o
oo
oe
Z
Z
j
Z
Z
Z
j
V
V
(112)
45. continue
We define coupling as
oo
oe
oo
oe
Z
Z
Z
Z
C
Then V3 / V , from ( 112) will become
oo
oe
o
Z
Z
Z
C
2
1 2
tan
1
tan
tan
2
tan
2
3
j
C
jC
V
Z
Z
Z
Z
j
Z
Z
Z
Z
Z
Z
Z
j
V
V
oo
oe
oo
oe
oo
oe
o
oo
oe
oo
oe
and
sin
cos
1
1
2
2
2
2
2
j
C
C
V
V
V
V o
e
0
2
2
4
4
4
o
e
o
e V
V
V
V
V
Similarly
V1=V
46. Practical couple line coupler
V3 is maximum when = p/2 , 3p/2, ...
Thus for quarterwave length coupler = p/2 , the eqs V2 and V3 reduce to
V1=V
0
4
V
VC
j
C
jC
V
j
C
jC
V
j
C
jC
V
V
2
2
2
3
1
1
)
(
2
/
tan
1
2
/
tan
p
p
2
2
2
2
2 1
1
2
/
sin
2
/
cos
1
1
C
jV
j
C
V
j
C
C
V
V
p
p C
C
Z
Z o
oe
1
1
C
C
Z
Z o
oo
1
1
47. Example
Design a 20 dB single-section coupled line coupler in stripline with a 0.158 cm
ground plane spacing , dielectric constant of 2. 56, a characteristic impedance
of 50 , and a center frequency of 3 GHz.
Coupling factor is C = 10-20/20 = 0.1
Characteristic impedance of even
and odd mode are
28
.
55
1
.
0
1
1
.
0
1
50
oe
Z
23
.
45
1
.
0
1
1
.
0
1
50
oo
Z
4
.
88
oe
r Z
4
.
72
oo
r Z
From fig 7.29 , we have
w/b=0.72 , s/b =0.34. These
give us
w=0.72b=0.114cm
s= 0.34b = 0.054cm
Then multiplied by r
48. Multisection Coupled line coupler (broadband)
V1
V3 V4
V2
input Through
Isolated
Coupled
C1
CN-2
C3
C2 CN
CN-1
....
j
e
jC
j
jC
j
C
jC
V
V
sin
tan
1
tan
tan
1
tan
2
1
3
j
e
j
C
C
V
V
sin
cos
1
1
2
2
1
2
For single section , whence C<<1 , then
V4=0
and For = p/ 2 then V3/V1= C
and V2/V1 = -j
49. Analysis
Result for cascading the couplers to form a multi section coupler is
)
1
(
2
1
2
1
2
1
1
3
sin
...
sin
sin
N
j
j
N
j
j
j
e
V
e
jC
e
V
e
jC
V
e
jC
V
)
1
(
)
2
(
2
2
2
)
1
(
2
1
1
3
...
1
sin
N
j
M
N
j
j
N
j
j
e
C
e
e
C
e
C
e
jV
V
M
jN
C
N
C
N
C
e
jV
2
1
...
3
cos
1
cos
sin
2 2
1
1
Where M= (N+1)/2
For symmetry C1=CN , C2= CN-1 ,
etc
At center frequency
2
/
1
3
p
V
V
Co
(200)
50. Example
Design a three-section 20 dB coupler with binomial response (maximally
flat), a system impedance 50 , and a center frequency of 3 GHz .
Solution
For maximally flat response for three section (N=3) coupler, we require
2
,
1
0
)
(
2
/
n
for
C
d
d
n
n
p
From eq (200) and M= (N+1)/2 =( 3+1)/2=2 , we have
2
1
1
3
2
1
2
cos
sin
2 C
C
V
V
C
sin
)
(
3
sin
sin
sin
3
sin 1
2
1
2
1 C
C
C
C
C
(201)
(202)
52. continue
Using even and odd mode analysis, we have
63
.
50
0125
.
0
1
0125
.
0
1
50
1
1
3
1
C
C
Z
Z
Z o
oe
oe
38
.
49
0125
.
0
1
0125
.
0
1
3
1 o
oo
oo Z
Z
Z
69
.
56
125
.
0
1
125
.
0
1
50
1
1
2
C
C
Z
Z o
oe
1
.
44
125
.
0
1
125
.
0
1
2 o
oo Z
Z
53. continue
Let say , r = 10 and d =0.7878mm
63
.
50
3
1 oe
oe Z
Z
38
.
49
3
1 oo
oo Z
Z
69
.
56
2
oe
Z
1
.
44
2
oo
Z
Plot points on graph Fig. 7.30
We have , w/d = 1.0 and s/d = 2.5 , thus
w = d = 0.7878mm and s = 2.5d = 1.9695mm
Similarly we plot points
We have , w/d = 0.95 and s/d = 1.1 , thus
w = 0.95d = 0.748mm and s =1.1d = 0.8666mm
For section 1 and 3
For section 2
56. Continue/ 4 wire coupler
Even mode
All Cm capacitance will be at same potential, thus the total capacitance is
in
ex
e C
C
C
4
m
in
ex
o C
C
C
C 6
4
Odd mode
All Cm capacitance will be considered, thus the total capacitance is
Even and Odd mode characteristic impedance
4
4
1
e
e
C
Z
4
4
1
o
o
C
Z
line
on
transmissi
in
velocity
(300)
(301)
(302)
57. continue
Now consider isolated pairs. It’s equivalent circuit is same as two wire line ,
thus it’s even and odd mode capacitance is
ex
e C
C
m
ex
o C
C
C 2
Substitute these into (300) and (301) ,
we have
o
e
o
e
e
e
C
C
C
C
C
C
3
4
m
ex
m
ex
ex
in
C
C
C
C
C
C
o
e
e
o
o
o
C
C
C
C
C
C
3
4
And in terms of impedance refer
to (302)
oe
oe
oo
oe
oo
e Z
Z
Z
Z
Z
Z
3
4
oo
oo
oe
oe
oo
o Z
Z
Z
Z
Z
Z
3
4
58. continue
oo
oe
oe
oo
oe
oo
oo
oe
o
e
o
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
3
3
2
4
4
Characteristic impedance of the line is
oo
oe
oo
oe
oo
oe
o
e
o
e
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
C
2
3
3
2
2
2
2
4
4
4
4
Coupling
The desired characteristic impedance in terms of coupling is
o
oe Z
C
C
C
C
C
Z
1
/
1
2
8
9
3
4 2
o
oo Z
C
C
C
C
C
Z
1
/
1
2
8
9
3
4 2