1) The document discusses resonators and impedance matching using lumped elements. It describes series and parallel resonant circuits, quality factor, bandwidth, and loaded/unloaded Q.
2) It also covers two-element L-shaped impedance matching networks for matching a load impedance to a source impedance. Methods for determining the reactance and susceptance values are presented for cases where the source impedance is less than or greater than the load impedance.
3) The goal of impedance matching is to maximize power transfer by making the impedances seen looking into the matching network equal to the source or transmission line impedance.
Wideband CMOS Power Amplifiers Design at mm-Wave: Challenges and Case Studiesaiclab
Constant striving towards higher data rates in modern communication systems and the foreseen revolution related to the forthcoming 5G mobile communications are laying the ground for an explosion of the millimetre-wave radio market. The reason? Frequency bands are wider, less overcrowded, and cheaper. Modulation schemes can be relaxed, while very directive antennas can be exploited to realize radio hops of several hundred meters.
On the other hand, the design of all the involved high frequency components is more demanding. The power amplifier, specifically, is a fundamental block of the transmitter for its impact on the overall performance of the entire system and hence poses severe challenges to the designer.
This workshop addresses the peculiar issues involved in the design of power amplifiers in this high-frequency scenario and compares them to the ones confronted with in the traditional microwave bands.
Experts coming from leading groups actively involved in mm-wave PA design will describe and comment upon solutions of choice and real-world examples, both in compound semiconductors (GaAs and GaN) and in Si-CMOS.
Wideband CMOS Power Amplifiers Design at mm-Wave: Challenges and Case Studiesaiclab
Constant striving towards higher data rates in modern communication systems and the foreseen revolution related to the forthcoming 5G mobile communications are laying the ground for an explosion of the millimetre-wave radio market. The reason? Frequency bands are wider, less overcrowded, and cheaper. Modulation schemes can be relaxed, while very directive antennas can be exploited to realize radio hops of several hundred meters.
On the other hand, the design of all the involved high frequency components is more demanding. The power amplifier, specifically, is a fundamental block of the transmitter for its impact on the overall performance of the entire system and hence poses severe challenges to the designer.
This workshop addresses the peculiar issues involved in the design of power amplifiers in this high-frequency scenario and compares them to the ones confronted with in the traditional microwave bands.
Experts coming from leading groups actively involved in mm-wave PA design will describe and comment upon solutions of choice and real-world examples, both in compound semiconductors (GaAs and GaN) and in Si-CMOS.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Cosmetic shop management system project report.pdf
RF Circuit Design - [Ch2-1] Resonator and Impedance Matching
1. Chapter 2-1
Resonators and Impedance Matching
with Lumped Elements
Chien-Jung Li
Department of Electronics Engineering
National Taipei University of Technology
2. Department of Electronic Engineering, NTUT
Resonators
• Lump Resonators
Series resonant circuit
I R L
C
inZ
CV
1
inZ R j L
j C
21
2
RP I R
21
4
mW I L
2 2 2
2 2 2
1 1 1 1
4 4 4
e C
C
W V C I I
C C
At resonant frequency 0 02 f
m eW W 0
1
LC
0inZ R
Resonance occurs when the
average stored magnetic and
electric energies are equal, and
the input impedance is a purely
real impedance.
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3. Department of Electronic Engineering, NTUT
Series Resonant Circuit
• Quality Factor:
average energy stored
energy loss/sec
m e
R
W W
Q
P
At resonance 0
2
0
0 0
2
1
22 4
1
2
m
R
I L LW
Q
P RI R
2
2
0
0 0
2
0
1 1
2
2 4 1
1
2
e
R
I
W C
Q
P CRI R
X
Q
R
where
0
0
1
orX L
C
Q is a measure of the loss of
a resonance circuit, and lower
loss implies higher Q.
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4. Department of Electronic Engineering, NTUT
Comparisons
X L
Q
R R
L R
C R
1X
Q
R CR
Although the Q is defined, but the resonant frequency can’t be defined
(they are not resonators).
• For series RL and series RC Circuits
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5. Department of Electronic Engineering, NTUT
Define the Bandwidth
• For series resonant circuits, as 0
1
inZ R j L
j C
0
Let 0 0
1
LC
2 2
0
22 2
2
0
1 1
1 1inZ R j L R j L R j L
LC
0 0 0
2
0
2
R j L R jL
0
2 2
QR
R j L R j
0L
Q
R
I L R
C
inZ
CV
where
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6. Department of Electronic Engineering, NTUT
3-dB Bandwidth
0
2
BW
0
0
2
2
in
BW QR
Z R j R jBW QR
when
1
BW
Q
2inZ R jR R
0
03-dB Bandwidth BW
Q
1
3-dB Bandwidth in % BW
Q
inZ
0
R
2R
2
• Define the bandwidth
When resonance occurs, the absolute
value of impedance is minimum in the
series resonant circuit.
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7. Department of Electronic Engineering, NTUT
Parallel Resonant Circuit
Parallel resonant circuit
1 1
inY j C
R j L
2
2
R
V
P
R
21
4
eW V C
2 2
2
2 2 2
1 1 1
4 4 4
m L
V V
W I L L
L L
At resonance, the angular resonant frequency 0 02 f
m eW W 0
1
LC
0
1
inY
R
LI
LR C
inY
V
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8. Department of Electronic Engineering, NTUT
Parallel Resonant Circuit
• Quality Factor:
average energy stored
energy loss/sec
m e
R
W W
Q
P
At resonance 0
B
Q
G
where
0
0
1
orB C
L
1
G
R
Comparisons:
B R
Q
G L
B
Q CR
G
L
R
C
R
and
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9. Department of Electronic Engineering, NTUT
3dB Bandwidth
• For parallel resonant circuits, as 0
1 1 1
2inY j C jC
R j L R
0
2
BWDefine
0
0
1 1
2
2
in
BW Q Q
Y j jBW
R R R R
when
1
BW
Q
1 1 2
inY j
R R R
0
03-dB Bandwidth BW
Q
1
3-dB Bandwidth in % BW
Q
inY
0
1
R
2
R
2
When resonance occurs, the absolute
value of admittance is minimum
(maximum impedance) in the parallel
resonant circuit.
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10. Department of Electronic Engineering, NTUT
Loaded and Unloaded Q
LR
Resonant
Circuit
Unloaded Q
• For series RLC circuit
• For parallel RLC circuit
0
0
1
L
L L
L
Q
R R C R R
0
0
//
//L
L L
R R
Q C R R
L
• Define the external Q eQ
0
0
1
e
L L
L
Q
R R C
for series RLC
0
0
L
e L
R
Q R C
L
1 1 1
L eQ Q Q
for parallel RLC
for both cases
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11. Department of Electronic Engineering, NTUT
Impedance Matching
Matching
Network
in sZ R
sV
sR
LZo sZ R
0in
Goal:
• The matching network is ideally lossless, to avoid unnecessary loss of
power, and is usually designed so that the impedance seen looking
into the matching network is Zo (matched with the transmission line) or Rs
(matched with the source impedance when no line connected).
• Maximum power is delivered when the load is matched to the line
(assuming the generator is matched), and power los in the feed line is
minimized.
• Impedance matching may be used to improve the signal-to-noise
ratio or amplitude/phase errors in some applications.
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12. Department of Electronic Engineering, NTUT
Eight Ell Matching Sections (L-Shape)
LZ1C
2C
LZL
C
LZ1L
2L
LZC
L
LZC
L
LZ2C
1C
LZL
C
LZ2L
1L
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13. Department of Electronic Engineering, NTUT
Lump Element Matching
• Two element (L-shape) matching
sV
sR
jX
jB LY L L LY G jB
inZ
X : matching reactance
B : matching susceptance
We want to find X and B
Case (a)
1
ors s L
L
R R R
G
in sZ R
0in s
in s
Z R
Z R
Goal:
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14. Department of Electronic Engineering, NTUT
L-Shape Matching – Case (a) Rs < RL
1
in s
L L
Z jX R
G jB jB
Real part: 1s L LR G X B B
Imaginary part: 0s L LR B B XG
sV
sR
jX
Lj B B LG
lQsQ
Use the resonator concept:
Series RC or RL
Parallel RC or RL
s
s
X
Q
R l
L
L
B B
Q
G
When the impedances are matched,
the imaginary part of the input
impedance looking into the matching
network is equal to zero.
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15. Department of Electronic Engineering, NTUT
L-Shape Matching – Case (a) Rs < RL
Imaginary part: 0s L LR B B XG
L
s
s L
X B B
Q Q
R G
lReal part: 1s L LR G X B B
2
1 1s LR G Q
1
1
s L
Q
R G
Choose l
1
1s
s L
Q Q Q
R G
1
1s s
s L
X R Q R
R G
and
1
1L L L L
s L
B G Q B G B
R G
(>0, capacitance)
(<0, inductance)
(>0, inductance)
or 1L
s
R
R
When Q is chosen, X and B are also
decided.
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16. Department of Electronic Engineering, NTUT
L-Shape Matching – Case (b) Rs > RL
sV
sR
jX
jB LZ L L LZ R jX
inY
X : matching reactance
B : matching susceptance
1
in
s
Y
R
1
0
1
in
s
in
s
Y
R
Y
R
Again, we want to find X and B
Case (b) s LR R
Goal:
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17. Department of Electronic Engineering, NTUT
L-Shape Matching – Case (b) Rs > RL
1 1
in
L L s
Y jB
R jX jX R
Real part: s L s LBR X X R R
Imaginary part: 0L s LX X BR R
Use resonator concept:
s sQ BR l
L
L
X X
Q
R
sV
sR
Lj X X
jB LR
lQsQ
Parallel
RC or RL
Series RC or RL
When the impedances are matched,
the imaginary part of the input
admittance looking into the matching
network is equal to zero.
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18. Department of Electronic Engineering, NTUT
L-Shape Matching – Case (b) Rs > RL
Imaginary part: l
L
s s
L
X X
Q BR Q Q
R
Real part:
2
L s LQ R R R 1s
L
R
Q
R
Choose l 1s
s
L
R
Q Q Q
R
1s
L L L L
L
R
X R Q X R X
R
(>0, inductance)
1
1s
s s L
RQ
B
R R R
(>0, capacitance)
(<0, capacitance)
0L s LX X BR R
s L s LBR X X R R
When Q is chosen, X and B are also
decided.
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19. Department of Electronic Engineering, NTUT
Series-to-Parallel Transformation
• Series-to-Parallel transformation
sR
sjX
pR
pjX
s
s
s
X
Q
R
s s sZ R jX
p
p
p
R
Q
X
p p
p
p p
R jX
Z
R jX
ps
s p
s p
RX
Q Q Q
R X
p p
s p s s
p p
R jX
Z Z R jX
R jX
2
1s pR Q R
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20. Department of Electronic Engineering, NTUT
Matching Bandwidth (I)
Case (a)
1
ors s L
L
R R R
G
sV
sR
jX
jB LY L L LY G jB
inZ
in s
in s
Z R
Z R
sV
sR
jX
Lj B B LG
sV
sR
jX eqjB
eqR
2
1 1
1
eq
L
R
G Q
2
11 L
eq
eq
G Q
B
QR Q
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21. Department of Electronic Engineering, NTUT
Matching Bandwidth (II)
sV
sR
jX eqjB
eqR
Impedance matching at 0
0
1
in eq s
eq
Z jX R R
jB
Imaginary part:
1
0
eq
jX
jB
1eqXB
Let 0X L 0eqB C 0
1
LC
Real part: eq sR R
2
1 1
1
s
L
R
G Q
1
1
L s
Q
G R
and ,where
and
Series resonant circuit
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22. Department of Electronic Engineering, NTUT
Matching Bandwidth (III)
sV
sR
jX eqjB
eq sR R
inQ
1
2
L inQ Q
• Define QL and Qin for RLC resonator
2
1in s L
eq
X
Q R Q G Q Q
R
Find 3-dB bandwidth for
Let X L eqB C
as 0 ,let 0 0
1
LC
0
1
2
1 2 22
eqin s
in s s
s
eq
jX
jBZ R jL
Z R jL RjX R
jB
and
where and
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23. Department of Electronic Engineering, NTUT
Matching Bandwidth (IV)
3-dB bandwidth for 2 occurs when
2 2 sL R
02 2
2 s sR R
L X
3-dB Bandwidth in % BW
0
22 2 1 2
1
1
s
L
s L
R
BW
X Q Q
R G
Similarly, for case (b)
1 2 2
1
1L
s L
BW
Q Q
R G
0
1
2
1
2
1
1
s L
Q
R G
Case (a)
1
s
L
R
G
1s
L
R
Q
R
Case (b)
s LR R
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24. Department of Electronic Engineering, NTUT
Example – L-Shape Matching (I)
• Find element values and 3-dB fractional bandwidth of the two-element
matching network.
1 2000
1 1
50s L
Q
R G
s
L
1
R < , choose case (a)
G
6.245Q
6
6
50 6.245 2 100 10
6.245/ 2000 0 2 100 10
s
L L
X R Q L
B G Q B C
1st Solution: choose
Matching
Network
100in sZ f MHz R
sV
50sR 2000LR
100 0in f MHz
Goal:
LR
LR 4.9696C pF
496.96L nH
sV
50sR
-9
12
496.96 10 ( ) 496.96 ( )
4.9696 10 ( ) 4.9696 ( )
L H nH
C F pF
6.245
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25. Department of Electronic Engineering, NTUT
Example – L-Shape Matching (II)
6
6
50 ( 6.245) 1/(2 100 10 )
( 6.245)/ 2000 0 1/(2 100 10 )
s
L L
X R Q C
B G Q B L
6.245Q 2nd Solution: choose
12
9
5.097 10 ( ) 5.097 ( )
509.7 10 ( ) 509.7 ( )
C F pF
L H nH
LR
sV
50sR
509.7L nH
5.097C pF
3dB
1 2 2
32%
| | 6.245L
BW
Q Q
9dB 15dB16%, 8%BW BWand
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26. Department of Electronic Engineering, NTUT
Three Elements Matching (High Q)
Case (a) Pi-Shape Matching
sV
sR
2jX
3jB LY L L LY G jB
inZ in sZ R
0in s
in s
Z R
Z R
1jB
sV
sR
1jX
LZ L L LZ R jX
inZ in sZ R
0in s
in s
Z R
Z R
2jB
3jX
Case (b) T-Shape Matching
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27. Department of Electronic Engineering, NTUT
Pi-Shape Matching
sV
sR
2ajX
3jB LY L L LY G jB
VR
1jB
2bjX
VR
2 2 2a bX X X
VR : virtual resistance (designed by yourself)
1
V
L
R
G
V sR R
Splitting into 2 “L-shape” matching networks
sV
sR
2ajX
3jB LY
L L LY G jB
1jB
2bjX
VR
sV
sR
in sZ R 0 in VZ R 0
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28. Department of Electronic Engineering, NTUT
Pi-Shape Matching
sV
sR
2ajX
3jB LY
L L LY G jB
1jB
2bjX
VR
sV
VR
in sZ R 0 in VZ R 0
1 1s
V
R
Q
R
2
1
1
V L
Q
R G
Since is small, you can get a high QVR
1
1
2
BW
Q
2
2
2
BW
Q
1 2min ,BW BW BW
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29. Department of Electronic Engineering, NTUT
T-Shape Matching
VR : virtual resistance (designed by yourself)
sV
sR
1jX
LZ L L LZ R jX
VR
2ajB
3jX
2bjB
VR V LR RV sR R
sV
sR
1jX
LZ
L L LZ R jX
in sZ R 0
2ajB
3jX
VR 2bjB
sV
VR
in VZ R 0
Splitting into 2 “L-shape” matching networks
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30. Department of Electronic Engineering, NTUT
T-Shape Matching
sV
sR
1jX
in sZ R 0
2ajB VR LZ
L L LZ R jX
3jX
2bjB
sV
VR
in VZ R 0
1 1V
s
R
Q
R
2 1V
L
R
Q
R
Since is large, you can get a high QVR
1
1
2
BW
Q
2
2
2
BW
Q
1 2min ,BW BW BW
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31. Department of Electronic Engineering, NTUT
Example – Pi and T Matching Networks
• Use Pi and T matching networks to achieve a matching BW<5%.
Matching
Network
100in sZ f MHz R
sV
50sR 2000LR
100 0in f MHz
Goal:
LR
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32. Department of Electronic Engineering, NTUT
Example – Pi Matching Network (I)
sV
50sR
2ajX
3jB1jB
2bjX
1.249VR
sV
1.249VR
100 50inZ f MHz
100 0f MHz
100 1.2492inZ f MHz
100 0f MHz
VR LG
1
50
1 1 6.247
1.2492
s
V
R
Q
R
2
1 2000
1 1 40
1.2492V L
Q
R G
1
2000
LG
Pi-section matching network
1 2max(| |,| |) max( 50/ 1, 2000/ 1) 2000/ 1v v vQ Q Q R R R
2
5% 1.249
(2000/ ) 1
v
v
BW R
R
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33. Department of Electronic Engineering, NTUT
Example – Pi Matching Network (II)
sV
50sR
2ajX
1jB
1.249VR
100 50inZ f MHz
100 0f MHz
VR
1 6.247Q
1
1 0
s
Q
B C
R
198.85C pF
2 1 0a VX R Q L 12.42L nH
1 6.247Q
1
1
0
1
s
Q
B
R L
203.95C pF
2 1
0
1
a VX R Q
C
12.74L nH
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34. Department of Electronic Engineering, NTUT
Example – Pi Matching Network (III)
3jB
2bjX
sV
1.249VR
100 1.2492inZ f MHz
100 0f MHz
1
2000
LG
2 40Q
3 2 0L LB G Q B C 31.83C pF
2 2 0b VX R Q L 79.53L nH
2 40Q
3 2
0
1
L LB G Q B
L
79.58L nH
2 2
0
1
b VX R Q
C
31.85C pF
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37. Department of Electronic Engineering, NTUT
Example – T Matching Network (I)
sV
50
1jX
100 50inZ f MHz
100 0f MHz
2ajB VR
3jX
2bjB
sV
T-section matching network
1 2max(| |,| |) max( ( /50) 1, ( / 2000) 1) ( /50) 1v v vQ Q Q R R R
2
5% 80050
( /50) 1
v
v
BW R
R
80050VR
100 80050inZ f MHz
100 0f MHz
80050VR
LR
2LR k
1
80050
1 1 40
50
V
s
R
Q
R
2
80050
1 1 6.247
2000
V
L
R
Q
R
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38. Department of Electronic Engineering, NTUT
Example – T Matching Network (II)
sV
50
1jX
100 50inZ f MHz
100 0f MHz
2ajB 80050VR
1 40Q
1 1 0sX R Q L 3.183L H
1
2 0a
V
Q
B C
R
0.795C pF
1 1
0
1
sX R Q
C
0.796C pF
1
2
0
1
a
V
Q
B
R L
3.185L H
1 40Q
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39. Department of Electronic Engineering, NTUT
Example – T Matching Network (III)
3jX
2bjB
sV
100 80050inZ f MHz
100 0f MHz
80050VR
2LR k
2 6.247Q
3 2 0L LX R Q X L 19.884L H
2
2 0b
V
Q
B C
R
0.124C pF
3 2
0
1
L LX R Q X
C
0.127C pF
2
2
0
1
b
V
Q
B
R L
20.394L H
2 6.247Q
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40. Department of Electronic Engineering, NTUT
Example – T Matching Network (IV)
2k0.795pF
3.183 H
sV
50 19.884 H
0.124pF
2k3.185 H
0.796pF
sV
50 19.884 H
0.124pF
2k0.795pF
3.183 H
sV
50 0.127pF
20.394 H
2k3.185 H
0.796pF
sV
50
0.127pF
20.394 H
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42. Department of Electronic Engineering, NTUT
Cascaded L-Shape Matching (Low Q)
Case (a)
1
s V
L
R R
G
sV
sR
1jX
1jB LY L L LY G jB
in sZ R
2jX
2jB
0
VRVR
sV
VR
2jX
LY
L L LY G jB
2jB
sV
sR
1jX
1jB VR
in sZ R
0
in VZ R
0
Splitting into 2 “L-shape” matching networks
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43. Department of Electronic Engineering, NTUT
Cascaded L-Shape Matching (Low Q)
sV
VR
2jX
2Lj B B LG
sV
sR
1jX
1jB VR
in sZ R
0
in VZ R
0
1 1V
s
R
Q
R
2
1
1
L V
Q
G R
We want to have the maximum bandwidth (find minimum Q)
Let 1 2Q Q Q s
V
L
R
R
G
2 2 2
2 1
1
s L
BW
QQ
R G
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44. Department of Electronic Engineering, NTUT
Cascaded L-Shape Matching (Low Q)
Case (b) s V LR R R
sV
sR
1jX
1jB LZ L L LZ R jX
in sZ R
2jX
2jB
VRVR
0
sV
sR
1jX
1jB LZ
L L LZ R jX
in sZ R
2jX
2jB
0
VR
sV
VR
in VZ R 0
Splitting into 2 “L-shape” matching networks
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45. Department of Electronic Engineering, NTUT
Cascaded L-Shape Matching (Low Q)
sV
sR
1jX
1jB
in sZ R
2 Lj X X
2jB
0
VR
sV
VR
in VZ R 0
VR
1 1s
V
R
Q
R
2 1V
L
R
Q
R
Let 1 2Q Q Q V s LR R R
2 2 2
2 1
1
s L
BW
QQ
R G
We want to have the maximum bandwidth (find minimum Q)
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46. Department of Electronic Engineering, NTUT
Example – Cascaded L-Shape Matching (I)
• Use Cascaded L-shape matching networks to achieve BW>60%.
Matching
Network
100in sZ f MHz R
sV
50sR 2000LR
100 0in f MHz
Goal:
LR
Choose RV to let
50 2000 316.23V s LR R R
2 2
61.29%
1 2000 50 11
s L
BW
R G
s V LR R R
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47. Department of Electronic Engineering, NTUT
Example – Cascaded L-Shape Matching (II)
sV
50sR
1jX
1jB
100 50inZ f MHz
2jX
2jB
100 0f MHz
VR
sV
316.23VR
100 0f MHz
100 316.23inZ f MHz
LR
1
316.23
1 1 2.3075
50
V
s
R
Q
R
2
2000
1 1 2.3075
316.23
L
V
R
Q
R
1 2.3075Q
1 1 0sX R Q L 183.63L nH
1
1 0
V
Q
B C
R
11.61C pF
1 2.3075Q
1 1
0
1
sX R Q
C
13.79C pF
1
1
0
1
V
Q
B
R L
218.11L nH
2 2.3075Q
2 2 0VX R Q L 1.161L H
2
2 0L
L
Q
B B C
R
1.836C pF
2 2.3075Q
2 2
0
1
VX R Q
C
2.181C pF
2
2
0
1
L
L
Q
B B
R L
1.379L H
316.23VR 2LR k
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48. Department of Electronic Engineering, NTUT
Example – Cascaded L-Shape Matching (III)
2k11.61pF
183.63nH
sV
50 1.161 H
1.836pF
2k218.11nH
13.79pF
sV
50 1.161 H
1.836pF
2k11.61pF
183.63nH
sV
50
2.181pF
1.379 H
2k218.11nH
13.79pF
sV
50
2.181pF
1.379 H
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50. Department of Electronic Engineering, NTUT
Matching For Larger Bandwidth
L-Shape
Matching
Network
sV
50sR
LR
L-Shape
Matching
Network
L-Shape
Matching
Network
• Use multi-section L-shape matching networks to extend BW.
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51. Department of Electronic Engineering, NTUT
Summary
• Impedance matching is a procedure of transforming the
complex load impedance ZL to match with the source
impedance Zs or characteristics impedance Zo of the
transmission line (Generally, Zs = Rs = Zo).
• The lossless lumped element matching networks that are
commonly used include L-section, Pi-section, T-section,
and cascaded L-section. L-section has medium but not
adjustable matching bandwidth. Pi and T sections have
rather small and adjustable matching bandwidth.
Cascaded L-section can increase bandwidth as the
number of stages increases.
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