Nghiên cứu thiết kế chế tạo mảng anten 8 cổng tự cấu hình dựa trên bộ dịch pha khả trình kiểu phản xạ

..

MINISTRY OF EDUCATION AND TRAINING
NGUYEN CONG THUAN

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY
---------------------------------------

Nguyen Cong Thuan

COMPUTER SCIENCE

STUDY AND DESIGN OF 8-PORT RECONFIGURABLE
PHASED ARRAY ANTENNA USING PROGRAMABLE
REFLECTION TYPE PHASE SHIFTER

MASTER THESIS OF SCIENCE
COMPUTER SCIENCE

2016A
Hanoi – 2018


MINISTRY OF EDUCATION AND TRAINING
HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY
---------------------------------------

Nguyen Cong Thuan

STUDY AND DESIGN OF 8-PORT RECONFIGURABLE PHASED
ARRAY ANTENNA USING PROGRAMMABLE REFLECTION TYPE

PHASE SHIFTER

Specialty: Computer Science
International Research Institute MICA

MASTER THESIS OF SCIENCE
COMPUTER SCIENCE

SUPERVISOR:
Dr. Nguyen Thanh Huong

Hanoi – 2018


Declaration of Authorship
I, NGUYEN Cong Thuan, declare that this thesis titled, “Study and design of 8-port
reconfigurable phased array antenna using programmable reflection type phase shifter”
and the work presented in it are my own. I confirm that:
 This work was done wholly or mainly while in candidature for a research degree
at this University.
 Where any part of this thesis has previously been submitted for a degree or any
other qualification at this University or any other institution, this has been clearly
stated.
 Where I have consulted the published work of others, this is always clearly
attributed.
 Where I have quoted from the work of others, the source is always given. With the
exception of such quotations, this thesis is entirely my own work.
 I have acknowledged all main sources of help.
 Where the thesis is based on work done by myself jointly with others, I have made
clear exactly what was done by others and what I have contributed myself.

Signed:

Date:

i


Abstract
Indoor positioning systems based on radio wave have attracted a lot of research
interest over the last decade. One of methods, named Angle of Arrival, locating object based
on the relative angle of object to the reference points, requires a design of directional
antenna. Recently, antenna designs for this method mainly focus on sectorized antennas,
reconfigurable antennas and switched-beam array antenna with limited number of
predefined beams, which lowers the accuracy of indoor positioning system. From this
situation, I present in this thesis a design of 8-port phased array antenna using reflection
type phase shifter. The input power is split to each antenna through 8-port Wilkinson power
divider with insertion loss of about 11dB and isolation of about 20dB. To extract more
accurate position, the main beam direction of phased array antenna can be steered smoothly
by a design of a continuous and full 360o reflection type phase shifter with low insertion
loss variation. Microstrip patch antennas are used as elements in phased array antenna. The
steering of main beam from -45o to 45o with step 5o have been presented by radiation
patterns of phased array antenna, measured in anechoic chamber. The measured results
show that the main beam direction is quite close the desired direction in simulation. In most
case, the side lobe level is less than main lobe about 10dB.

ii


Acknowledgements

It is an honor for me to be here to write thankful words to those who have been
supporting, guiding and inspiriting me from the moment, when I started my work in
International Research Institute MICA, until now, when I am writing my master thesis.
I owe my deepest gratitude to my supervisor, Dr. Nguyen Thanh Huong. Her
expertise, understanding and generous guidance made it possible to work in a new topic for
me. She has made available her support in a number of ways to find out the solution to my
works. It is a pleasure to work with her.
Special thanks to Prof. Eric Castelli, Dr. Dao Trung Kien, Dr. Nguyen Viet Tung and
all of members in the Pervasive Space and Interaction Department for their guidance which
help me a lot in how to study and to do research in right way, and also the valuable advices
for my works.
I would like to show my gratitude to Prof. Vuong Tan Phu at University of Grenoble,
France for his supporting. His suggestions enable me to keep my thesis in the right
direction.
Finally, this thesis would not have been possible if there were no encouragement from
my family and friends. Their words give me power in order to overcome all the
embarrassment, discouragement and other difficulties. Thanks for everything helping me
to get this day.

Hanoi, 15/01/2018
Nguyen Cong Thuan

iii


Table of Contents
Declaration of Authorship ........................................................................................ i
Abstract ....................................................................................................................ii
Acknowledgements ................................................................................................. iii
Table of Contents .................................................................................................... iv

List of Tables ..........................................................................................................vii
List of Figures ...................................................................................................... viii
List of Abbreviations ................................................................................................ x
Chapter 1 -

INTRODUCTION ........................................................................................ 1

1.1

Application and Technical Area ................................................................... 1

1.2

Problem Statement and Technical Issue ....................................................... 1

1.3

Research Aim and Objective ........................................................................ 2

1.4

Thesis Outline ............................................................................................... 3

Chapter 2 -

LITERATURE REVIEW ............................................................................. 4

2.1

Basics of Microwave Engineering ................................................................ 4

2.1.1 Transmission Line Impedance.................................................................. 4
2.1.2 Microstrip Discontinuity .......................................................................... 7
2.1.3 Scattering Matrix .................................................................................... 11
2.2

Fundamental Parameters of Antennas ........................................................ 12

2.2.1 Return Loss and Voltage Standing Wave Ratio ..................................... 12
2.2.2 Radiation Pattern .................................................................................... 13
2.2.3 Polarization ............................................................................................. 15
2.3

Phased Array Antenna ................................................................................ 16
iv


2.3.1 Array Geometry ...................................................................................... 18
2.3.2 Array Factor............................................................................................ 20
2.3.3 Grating Lobe and Mutual Coupling ....................................................... 21
2.3.4 Feed Network ......................................................................................... 23
Chapter 3 -

DESIGN OF PHASED ARRAY ANTENNA ............................................ 26

3.1

Structure ...................................................................................................... 26

3.2

Power Divider ............................................................................................. 27

3.2.1 Requirement for Power Divider ............................................................. 27
3.2.2 Power Divider ......................................................................................... 28
3.3

Phase Shifter ............................................................................................... 31

3.3.1 Requirement for Phase Shifter ............................................................... 31
3.3.2 Phase Shifter Types ................................................................................ 32
3.3.3 Reflection Type Phase Shifter ................................................................ 33
3.3.4 Design of Controller for Reflection Type Phase Shifter ........................ 44
3.4

Antenna Element......................................................................................... 46

3.4.1 Requirement for Antenna Element ......................................................... 46
3.4.2 Microstrip Patch Antenna ....................................................................... 47
Chapter 4 -

EXPERIMENTAL RESULT...................................................................... 49

4.1

Wilkinson Power Divider ........................................................................... 49

4.2

Reflection Type Phase Shifter .................................................................... 53

4.3

Microstrip Patch Antenna ........................................................................... 57

4.3.1 Return Loss and VSWR ......................................................................... 57
4.3.2 Radiation Pattern .................................................................................... 58
4.4

Phased Array Antenna ................................................................................ 61
v


Chapter 5 -

CONCLUSION AND FUTURE WORK ................................................... 67

5.1

Conclusions ................................................................................................. 67

5.2

Future Works .............................................................................................. 68

PUBLICATIONS ............................................................................................................... 69
REFERENCES ................................................................................................................... 70
Appendix A: Calibration Procedure ................................................................................... 72
Appendix B: Antenna Radiation Pattern Measurement System ........................................ 74
Appendix C: Main beam angle versus DC bias look up table............................................ 76

Appendix D: Dimension of parts in phased array antenna ................................................. 77

vi


List of Tables
Table 4-1: Comparison of main beam angle and side lobe level in simulation and
measurement ....................................................................................................................... 62
Table 4-2: Comparison with previous antenna design for indoor localization .................. 63

vii


List of Figures
Figure 2-1: A transmission line terminated in a load impedance [6] ................................... 5
Figure 2-2: Bend: (a) geometry; (b) equivalent circuit[7] .................................................... 7
Figure 2-3: Mitered Bends [8] .............................................................................................. 8
Figure 2-4: Open-Ends[7]..................................................................................................... 9
Figure 2-5: Gaps[7] .............................................................................................................. 9
Figure 2-6: Step in Width[7] .............................................................................................. 10
Figure 2-7: T-junction discontinuity compensation configuration[8] ................................ 10
Figure 2-8: Fields regions of an antenna ............................................................................ 14
Figure 2-9: Radiation pattern of array antenna: (a) in linear scale; (b) in dB .................... 15
Figure 2-10: PLF according to different transmitter/receiver polarizations ...................... 16
Figure 2-11: Phased array antenna geometry: (a) Linear, (b) Planar, (c) Circular, (d)
Spherical ............................................................................................................................. 18
Figure 2-12: Total field patterns of two dipole antenna array with element spacing λ/4 and
different phase excitation β = -90o [10] .............................................................................. 21
Figure 2-13: Series Feed Network for Phased Array Antenna ........................................... 24
Figure 2-14: Parallel Feed Network for Phased Array Antenna ........................................ 24

Figure 2-15: 4×4 Butler matrix network ............................................................................ 25
Figure 3-1: Directivity as a function of the element spacing of linear array antenna [11] 27
Figure 3-2: T-junction divider: (a) Lossless; (b) Resistive ................................................ 29
Figure 3-3: The Wilkinson power divider: (a) Microstrip line form, (b) Equivalent
Transmission Line Circuit .................................................................................................. 30
Figure 3-4: An N-way, equal-split Wilkinson power divider[6] ........................................ 30
Figure 3-5: An 8-way equal-split Wilkinson power divider .............................................. 31
Figure 3-6: Types of phase shifter: (a) Switched Line; (b) Switched Network; ................ 32
Figure 3-7: 3dB Hybrid Coupler ........................................................................................ 34
Figure 3-8: Structure of RTPS ............................................................................................ 35
Figure 3-9: Schematic Diagram of RTPS. .......................................................................... 37
Figure 3-10: Reflection Load of RTPS. ............................................................................. 38
Figure 3-11: The results of the first ZT1 survey: (a) Phase Shift, (b)

d S 21
..................... 41
dVR

Figure 3-12: The results of the second ZT1 survey: (a) Phase shift, (b)

d S 21
................. 42
dVR

Figure 3-13: Impedance of DC Block VJ0603D8R2CXP ................................................. 43
Figure 3-14: Block Diagram of controller .......................................................................... 46
Figure 4-1: The 2-way WPD in theory: (a) Schematic Circuit; (b) Forward gains S21, S31
............................................................................................................................................ 49
viii

Figure 4-2: The 2-way WPD: (a) Schematic Circuit; (b) Forward gains S21, S31 .............. 50
Figure 4-3: 8-way Wilkinson Power Divider ..................................................................... 51
Figure 4-4: Forward gain at port 2, 3, 4: S21, S31, S41. ....................................................... 52
Figure 4-5: Forward gain at port 5, 6, 7: S51, S61, S71. ....................................................... 52
Figure 4-6: Forward gain at port 8, 9: S81, S91. ................................................................... 52
Figure 4-7: Isolation between output ports ......................................................................... 52
Figure 4-8: Equivalent model of SMV1247: (a) on SPICE; (b) on ADS .......................... 54
Figure 4-9: C-V curve of SMV1247 on: (a) technical document; (b) ADS ....................... 54
Figure 4-10: Schematic circuit of Reflection type phase shifter ........................................ 55
Figure 4-11: Reflection type phase shifter fabricated on Roger4003c ............................... 55
Figure 4-12: S21 of RTPS ................................................................................................... 56
Figure 4-13: Phase shift of RTPS ....................................................................................... 56
Figure 4-14: Fabricated microstrip patch antenna .............................................................. 57
Figure 4-15: Microstrip patch antenna paramters: (a) VSWR; (b) Return Loss ................ 58
Figure 4-16: Structure of measuring chamber .................................................................... 59
Figure 4-17: Measurement in Anechoic chamber in reality ............................................... 60
Figure 4-18: Radiation Pattern of microstrip patch antenna: (a) on simulation; (b)
comparison between simulated and measured result. ........................................................ 60
Figure 4-19: Radiation pattern of phased array antenna at different angles ...................... 66
Figure A-1: Elements of 85052D calibration kit ................................................................ 72
Figure A-2: OPEN, SHORT, BROADBAND elements of 85052D calibration kit .......... 73
Figure B-1: Block diagram of ARPM system .................................................................... 74
Figure B-2: Rotating structure ............................................................................................ 74
Figure B-3: Controller ........................................................................................................ 75
Figure B-4: Program on PC ................................................................................................ 75

ix

List of Abbreviations
GPS

Global Positioning System

GLONASS

Globalnaya Navigatsionnaya Sputnikovaya Sistema

RSS

Received Signal Strength

ToF

Time of Flight

ToA

Time of Arrival

AoA

Angle of Arrival

E-field

Electric Field

H-field

Magnetic Field

PLF

Polarization Loss Factor

RL

Return Loss

VSWR

Voltage Standing Wave Ratio

AF

Array Factor

D

Element Spacing

WPD

Wilkinson Power Divider

RTPS

Reflection Type Phase Shifter

DC

Direct Current

ADS

Advanced Design System

PNA

Precise Network Analyzer

EM Simulation

Electromagnetic Simulation

EM Cosimulation

Electromagnetic Cosimulation

ARPM

Antenna Radiation Pattern Measurement

x


Chapter 1 - INTRODUCTION
1.1

Application and Technical Area
Nowadays, positioning has played an important part in human life, and is the

foundation for many other applications such as navigation, tracking, location-based
services and games. While outdoor positioning has become widespread and popular
with satellite-based navigation systems such as GPS, GLONASS and Galileo, indoor
positioning systems have attracted a lot of research interest over the last decade.
Indoor localization promises to create a lot of new services such as guiding users in
museum, preventing theft from expensive devices, locating products in supermarket,
navigating in mall, saving power consumption of devices, and so on.
Due to the scattering and attenuation of microwave on roofs, walls and other
object, the systems for outdoor positioning are infeasible solutions when applying to
indoor positioning. Instead, indoor positioning systems have been implemented based
on several technologies: infrared (IR), Bluetooth, radio-frequency identification
(RFID), wireless local area networks (WLAN), ultra-wideband, ultra-sound,
magnetic positioning and audible sounds. Among them, WLAN-based approach
receive more attention thanks to its wide range and popularity of equipment.
Nowadays, the number of WLAN devices has reached billions of devices and
continues to increase, hence the study in WLAN-based indoor positioning promise to
be applied and spread in the near future.

1.2

Problem Statement and Technical Issue
For WLAN-based approach, indoor localization techniques are classified into

RSS scene analysis, ToA, TDoA, RToF and AoA [1]. While the highly unstable
feature of RSS in indoor environments is the major challenge of RSS scene analysis
technique and ToA, TDoA, RToF are based on a precise clock synchronization of

devices, the AoA technique requires a directional antenna design to estimate the
relative angle of object to reference points.

1


There have been several antenna designs for AoA-based indoor localization
presented in past few years. G.Giorgetti and A.Cidronali [2] introduced a switchedbeam directional antenna, including 6 circular antennas to cover 6 areas in a room.
M.Rzymowski et al [3] also introduced an antenna design using twelve passive
elements electrically steerable parasitic array radiator antenna with one active
monopole in the center of the ground plane. By controlling single-pole, single-throw
switches, parasitic elements connect to the ground and act as reflectors, which change
the main lobe’s directions. With twelve passive elements, this antenna has twelve
different directions. Kamarudin et al [4] proposed a reconfigurable antennas using
PIN diodes to switch lumped components such as inductors and capacitors in order
to change the structure of antennas and switch between four beams. Bui et al [5] built
a switch-beam array antenna based on 4x4 Butler matrix to create four beams toward
four angles. It is found that these designs are based on switching between the limited
number of predefined beams, which limits the resolution in determining the location
of object and leads to significant errors in positioning.

1.3

Research Aim and Objective
For indoor localization, the system needs to determine the location of object

with high accuracy, therefore an antenna design with high resolution steering beam
ability is very essential in the AoA technique. As discussed above, the current antenna
designs for indoor localization system mainly focus on switched-beam antenna
structures. With these structures, the resolution of angle of arrival primarily depends

on the number of antenna elements. Therefore, to create a system with high resolution
of beam scanning, the number of antennas as well as switching elements such as PIN
diode, FET also increases, which makes the system more cumbersome and complex.
In order to improve the accuracy for AoA-based indoor localization, the aim of this
thesis is to study and develop a phased array antenna at Wi-Fi band (2.4GHz to
2.484GHz), capable of finely steering beam without increasing the number of
antennas. Therefore, main objectives of thesis are:

2


+ To determine the structure of phased array antenna for AoA technique.
+ To develop the 360o continuous reflection type phase shifter that is
controllable.
+ From above structure and phase shifter, I develop the phased array antenna
that can steer the main beam in high resolution without the increase of antenna
elements as well as switching elements.

1.4

Thesis Outline
This thesis work has been organized as follows:
In chapter 2, a brief introduction and basic concepts like Array Geometry, Array

Factor, Grating lobes and Mutual Coupling of phased array antennas are presented.
Further, the principle of steering beam and several methods to feed antennas and
control the phase differences have been discussed. Additionally, antenna’s important
parameters relevant to my thesis are presented to support the next parts of thesis.
Chapter 3 discusses the structure of phased array antennas used for indoor
localization. After that, power dividers for feed networks are designed, followed by

principle and design of the proposed phase shifter. Next, antenna elements are chosen
in order to create the total beam suitable for indoor localization issue. Finally, the
structure of my positioning system is mentioned.
The simulation, fabrication and measurement are mentioned in Chapter 4. While
power divider and phase shifter are simulated on ADS software, CST Microwave
Studio is used to design antennas and phased array antenna system. The substrates
used for fabrication are FR4 and Roger4003c. Next, characteristics of power dividers,
phase shifters and antennas are measured by the Network Analyzer, and radiation
pattern of antenna have been examined in an anechoic chamber.
Chapter 5 completes the thesis by providing conclusions and perspectives for
future works.

3


Chapter 2 - LITERATURE REVIEW
In this chapter, part 1 introduces some basic knowledge about microwave and
antenna engineering that are directly relevant to designs and experiments in my thesis.
Firstly, the microwave theory, shown in section 2.1, is mainly used in designing two
important parts in my thesis, power divider and phase shifter. Secondly, I present
some fundamental parameters of antennas that need to be paid attention in indoor
localization. Finally, basic concepts and principle of phased array antenna, enabling
me to choose the suitable structure and some parameters in my design, is shown.
Obviously, these knowledge should be presented before designing and evaluating my
phased array antenna for indoor localization in detail.

2.1

Basics of Microwave Engineering
In terms of microwave engineering, there are a lot of important concepts such

as smith chart, waveguides, modes of waves and impedance matching. However, this
thesis just shows three issues, mainly related to my design, transmission line
impedance, microstrip discontinuity and scattering matrix. Other concepts can be
effortlessly figured out in some books [6], [7] and other theses. The transmission line
impedance allows me to calculate the equivalent impedance of circuits, including
transmission lines, and I can take advantage of special lengths to create short point or
open point in microwave circuit. Next, the discontinuity of microstrip lines is a big
problem in microwave engineering in general. This problem will be more obvious
when frequency increases. Section 2.1.2 will show some typical kinds of microstrip
discontinuity, and some techniques overcoming this problem. Finally, scattering
matrix is usually used to present the characteristics of a microwave circuit.
2.1.1

Transmission Line Impedance
Consider a lossless line, length l, terminated with a load ZL. Assume that an

incident wave of the form Vo e jz is generated from a source at z<0. We have seen
that the ratio of voltage to current for such a travelling wave is Z0, the characteristic

4


impedance of the line. However, when the line is terminated in an arbitrary load
Z L  Z 0 , the ratio of voltage to current at the load must be ZL.

Figure 2-1: A transmission line terminated in a load impedance [6]

The input impedance is simple the line impedance seen at the beginning (z = l) of transmission line.
Z in  Z ( z  l ) 

V ( z  l )
I ( z  l )

(2-1)

To determine Zin, we first must determine the voltage and current at the
beginning of the transmission line (z = -l).
V ( z  l )  Vo [e  jl  L e  jl ]
V
I ( z  l )  o [e  jl  L e  jl ]
Zo

(2-2)
(2-3)

While L is the reflection coefficient of a load, determined by its impedance ZL,
and the impedance toward the source.
Z L  Zo
Z L  Zo

(2-4)

e  jl  L e  jl
V ( z  l )
 Z o (  jl
)
I ( z  l )
e  L e  jl

(2-5)

L 

Therefore:
Z in 

Combining two expressions (2-4), (2-5), we get:
Z in  Z 0

( Z L  Z 0 )e  jl  ( Z L  Z 0 )e  jl
( Z L  Z 0 )e  jl  ( Z L  Z 0 )e  jl

Z L (e  jl  e  jl )  Z 0 (e  jl  e  jl )
 Z0
Z L (e  jl  e  jl )  Z 0 (e  jl  e  jl )

5

(2-6)


We have the Euler’s equations:
e  jl  cos l  j sin l
e  jl  cos l  j sin l

(2-7)

Using Euler’s relationship, we can likewise write the input impedance without
complex exponentials:

Z in  Z 0

Z L cos l  jZ0 sin  l
Z 0 cos l  jZ L sin  l

Z  jZ0 tan l
 Z0 L
Z 0  jZ L tan l

(2-8)

Next, we consider some special case of lossless terminated transmission line.
If the length of transmission line is exactly one-half wavelength, l   / 2 , we
find that:
Z in  Z 0

Z L (1)  jZ0 (0)
 ZL
Z 0 (1)  jZ L (0)

(2-9)

In other words, if the transmission line is precisely one-half wavelength long,
the input impedance is equal to the load impedance, regardless of Z0 or  .
If the length of the transmission line is exactly one-quarter wavelength,
l   / 4 , we find that:

Z in  Z 0

Z L (0)  jZ0 (1) Z 02


Z 0 (0)  jZ L (1) Z L

(2-10)

In other words, if the transmission line is precisely one-quater wavelength long,
the input impedance is inversely proportional to the load impedance. If the load
impedance is a short circuit, ZL = 0. The input impedance at beginning of the  / 4
transmission line is:
Z 02 Z 02
Z in 


ZL
0

6

(2-11)


That means the quater-wave transmission line enables us to transform a shortcircuit into an open-circuit and vice versa.
If the transmission line is electrically small, its length l is small with respect to
signal wavelength  , we find that:
Z in  Z 0

Z L (1)  jZ0 (0)
 ZL
Z 0 (1)  jZ L (0)

(2-12)

In other words, if the transmission line length is much smaller than a
wavelength, the input impedance Zin will always be equal to the load impedance ZL.
2.1.2

Microstrip Discontinuity
Surface waves, electromagnetic waves propagating on the dielectric interface

layer of the microstrip, are generated at any discontinuity. Surface waves couple with
other microstrip, decrease isolation between different networks and cause crosstalk,
coupling and attenuation on microstrip circuit. A discontinuity is caused by an abrupt
change in geometry of the strip conductor. Electromagnetic field distributions near
the discontinuity are changed, which leads to a change in capacitance and inductance.
Discontinuities commonly encountered in the layout of practical microstrip circuits
are: Bends, Open-Ends, Gaps, Steps, T-junction.
Bends are the most frequently encountered discontinuities. The 90° bend, can
be modeled by T-network circuit for a short line length, as shown in Figure 2-2.

(a)

(b)

Figure 2-2: Bend: (a) geometry; (b) equivalent circuit[7]

The values of the components are as follows [7].
 (14 r  12.5)W / h  (1.83 r  2.25) 0.02 r

for W/h  1
W

W /h
C ( pF )  
W /h
(9.5  1.25)W / h  5.2  7.0
for W/h  1
r
r






L(nH )  100 h 4 W / h  4.21

7

(2-13)


The accuracy on the capacitance is quoted as within 5% over the ranges of

2.5   r  15 and 0.1  W / h  5 , and on the inductance is about 3% for 0.5  W / h  2 .
To compensate the excess capacitance, we can use increased inductance or
decreased capacitance techniques by cutting the corner (Figure 2-3).

Figure 2-3: Mitered Bends [8]

Open-Ends, encountered any time a microstrip, is open terminated (Figure 2-4).
Because of the effect of fringing field, the fields extend slightly instead of stopping

abruptly, which affect as a shunt capacitor or a shortly extended transmission line Δl.
A closed-form expression is below with the accuracy better than 2% for the
range of 0.01  W / h  100 and  r  128 .
l 

3e11Z cC p

 re

h

135
4

(2-14)

Where

1  0.434907
2  1 
3  1 

 re0.81  0.26(W / h) 0.8544  0.236
 re0.81  0.189 (W / h) 0.8544  0.87

(W / h) 0.371
2.35 r  1
0.5274 tan 1[0.084 (W / h)1.9431/ 2 ]

 re0.9236

 4  1  0.037 tan 1[0.067 (W / h)1.456](6  5e ( 0.036(1 )) )
r

 5  1  0.218 e ( 7.5W / h )
The simplest way to compensate for the increase in line length is to reduce the
length of the designed line by the correct amount.

8


Figure 2-4: Open-Ends[7]

Gaps can be equivalently represented as a π capacitor circuit (Figure 2-5), while
the shunt (Cp) and series (Cg) capacitors can be defined by:
C p  0.5Ce

(2-15)

C g  0.5Co  0.25Ce
o
e
   s 
   s 
Co ( pF )   r    e k o ; Ce ( pF )  12 r    e k e
 9. 6   W 
 9.6   W 
For 0.1  s/W  1.0
W
mo  [0.619 log( W / h)  0.3853 ]; ko  4.26  1.453 log( W / h)

h
For 0.1  s / W  0.3

0.8

m

0 .9

m

me  0.8675 ; ke  2.043 (W / h)0.12
For 0.3  s / W  1.0
1.565
0.03
me 
 1; ke  1.97 
0.16
(W / h)
W /h

Figure 2-5: Gaps[7]

The accuracy of these expression is within 7% for 0.5  W / h  2 and

2.5   r  15 . For narrow gaps, Cp is approximately zero and Cg increases, and
practical series capacitor is from 0.01pF to 0.5pF. For large gaps, the capacitance
value Cg is ignored, and gaps become an open-end circuit.
Step in Width is also affected by fringing effect in microstrip lines and has
equivalent circuit as shown in Figure 2-6, while capacitor and inductors can be

calculated as:
9


L1 

Lw1
Lw1  Lw 2

 re1 

W    0.3  W1 / h  0.264 

1  2  re1

Z c1  W1   re1  0.258  W1 / h  0.8 
Lw 2
L; L2 
L
Lw1  Lw 2

C ( pF )  0.00137 h


Z
Lwi  Z ci  rei / c; L(nH )  0.000987 h1  c1
 Zc2

 re1
 re2

(2-16)






Where Lwi for i = 1, 2 are the inductances per unit length of the appropriate
microstrips, having widths W1 and W2, respectively. While Zci and εrei denote the
characteristic impedance and effective dielectric constant corresponding to width Wi,
c is the light velocity in free space, and h is the substrate thickness in micrometers.

Figure 2-6: Step in Width[7]

In terms of distributed elements, the discontinuity capacitance C has the effect
of an increase in length of the wide line W1, and an equal decrease in length of the
narrow line W2. To compensate for the excess capacitance, we can make the W1 line
to be electrically longer by a correct length.
T-Junction is also a component, usually encountered in microwave circuits as
impedance matching, power divider and hybrid coupler. T-junction can be
compensated by cutting a part at the intersection area as shown in Figure 2-7.

Figure 2-7: T-junction discontinuity compensation configuration[8]

10


2.1.3

Scattering Matrix

In conventional circuit theory, the fundamental quantities of interest are voltage
and current, and the parameters used to express relationships between them are called
impedances (Z), admittances (Y), hybrid (H) or ABCD parameters. A single twoterminal circuit element may be characterized by a complex impedance, representing
the ratio between the voltage and the current at its two terminals. More complicated
multi-terminal networks may be represented at a given frequency by an equivalent
circuit, consisting of a number of simple two-terminal elements in certain
combinations, such as equivalent tee, pi or ladder networks. However, Z, H, Y and
ABCD parameters cannot be measured at microwave frequencies. The main reason
is that at microwave frequency, the length of cables is comparable to the signal
wavelength. Currents at opposite ends of a cable begin to differ in magnitude and
phase, and it becomes difficult to specify the scalar potential difference between two
terminals uniquely. In addition, the short circuit and open circuit are difficult to
achieve over a wide range of frequencies, and the presence of active devices such as
transistors, tunnel diodes makes the circuit unusable for short or open circuit. One is
thus led to look for simpler and more refined analysis techniques for handling
microwave circuits; such techniques are provided naturally by the use of the
scattering parameter that is first mentioned by Campbell and Foster in 1922.
Scattering parameters are defined in terms of incident and reflected waves at
ports of networks [6], [7]. It seems logical to treat the incident waves as the
independent quantities, denoted as Vm and express their contributions to the reflected
wave Vn at port n by a series of scattering coefficients, as:
V1  S11V1  S12V2  ...  S1nVn
V2  S 21V1  S 22V2  ...  S 2 nVn
...
Vn  S n1V1  S n 2V2  ...  S nnVn

V   S V 




(2-17)

In two port networks, other parameters such as Z, Y, H, ABCD can be
transformed from scattering parameters. These equations is expressed by D.M.Pozar
in [6].
11


2.2

Fundamental Parameters of Antennas
With regard to antenna engineering, there is also many parameters of an antenna

such as bandwidth, directivity, gain, axial ratio, efficiency, antenna efficiency,
radiation pattern and so on, but in this thesis, I just mention to three parameters,
primarily impacting on designing phased array antenna for indoor localization
system, in below. Return Loss and Standing Wave Ratio can be switched together,
and they used to determine frequencies that an antenna can operate well. Radiation
Pattern shows graphical representation of the radiation properties of antenna as a
function of space coordinates. Finally, the affection of relative angle between two
antennas to the transmission loss is presented in section 2.2.3, polarization.
2.2.1

Return Loss and Voltage Standing Wave Ratio
In transmission, the source generates a wave, traveling along the transmission

line to antenna. Ideally, antenna would radiate all energy to surrounding space.

However, due to impedance mismatch, a part of energy will be reflected, which
reduces transmission efficiency. Obviously, all the reflected energy is wasted, so
minimizing the reflection at the antenna port is one of criteria when designing
antennas. Assuming that the amplitude of the incident wave and reflected wave are
V+ and V-, respectively. The reflection coefficient is given by   V



V

.

In microwave theory, the scattering matrix, as discussed in section 2.1.3, is used
to describe a network. From the circuit perspective, an antenna is a single port device,
so the definition of S11 is identical to the reflection coefficient, S11   . In engineering,
the S11 is usually used in the decibel (dB) scale.
S11 (dB)  20 log 10 ( S11 )  20 log 10 (  )

(2-18)

The absolute value of S11(dB) is called the Return Loss: RL = |S11(dB)|
Another way to indirectly observe the amplitude of reflected wave is through
Voltage Standing Wave Ratio (VSWR) parameter. This parameter is ratio between
maximum voltage and minimum voltage on transmission line. With same frequency,
12


the maximum voltage is the sum of amplitudes of incident and reflected voltage, and
the minimum voltage is the subtraction of amplitudes of incident and reflected
amplitude.

VSWR 

V V
V V



1 
1 

(2-19)

About the quantitative evaluation, an antenna with 10% maximum reflected
power is acceptable, so the return loss of 10dB or VSWR of approximate 2 is a
commonly used specification for antennas. Therefore, the designed antenna need to
have the return loss higher than 10dB or VSWR less than 2 at operating frequency.
2.2.2

Radiation Pattern
Before introducing to radiation pattern, I need to consider to field regions of an

antenna. The fields surrounding an antenna are divided into 3 regions: reactive nearfield, radiating near-field and far-field regions as shown in Figure 2-8.
Reactive near-field region is the portion of the near-field region in the
immediate vicinity of the antenna. In this region, the fields are predominately reactive
fields, which means that the relationship between the strengths of E-field and H-field
is often too complex to predict. The out boundary is commonly given as 0.62 D3 ,
where λ is the wavelength and D is the largest dimension of antenna.
Radiating near-field region is the region between the reactive near-field region
and far-field region. If the antenna has a maximum dimension that is not large
compared to the wavelength, this region may not exist. The region is commonly given

by 0.62 D3  R  2D 2 /  , where λ is the wavelength and D is the largest dimension
of antenna and must be large compared to the wavelength.
Far-field region is the most important, since this determines the antenna’s
radiation pattern. In practice, antennas are used to wirelessly communicate from long
distances, so this is the region of operation for the most antennas. In this region, the

13