Numerical Analysis of Electromagnetic Textiles and Application in 
Emergency Communication Network 
 
by 
 
Houmin Li 
 
 
 
 
A dissertation submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Doctor of Philosophy 
 
Auburn, Alabama 
May 9, 2011 
 
 
Keywords: electromagnetic textile; artificially electromagnetic surface;  
textile antenna; emergency communication network; wireless sensor network 
 
Copyright 2011 by Houmin Li 
 
 
Approved by 
 
Gwynedd Thomas, Chair, Associate Professor of Polymer and Fiber Engineering 
Lloyd Riggs, Professor of Electrical and Computer Engineering 
Peter Schwartz, Professor of Polymer and Fiber Engineering 
Ann Beth Presley, Associate Professor of Consumer Affairs 
Xinyu Zhang, Assistant Professor of Polymer and Fiber Engineering 
 
 ii
 
 
 
Abstract 
 
In this paper, we presented a new type of textile antenna with new radiation 
mechanism that is capable of resonating at 1/9 the size of a corresponding microstrip 
antenna due to the woven structures. Further study of this phenomenon suggests 
development of textile electromagnetic structures with artificially magnetic conductor 
(AMC) and frequency selective surface (FSS) characteristics. Full-wave finite element 
method (FEM) simulation of the antennas as well as textile FSS and textile AMC are 
carried out and compared with existing electromagnetic structures.  The results suggest 
conventional electromagnetic structures such as FSS and AMC can be realized with 
flexible textile materials. These textile electromagnetic materials possess unique 
electromagnetic properties that can be applied to a variety of electromagnetic problems, 
including new kinds of low-profile antennas, standalone FSS and artificial electromagnetic 
surfaces. 
On the other hand, efforts toward development of a novel wireless emergency 
communication network have been made. Public communication infrastructures are 
vulnerable to catastrophic events and are usually incapacitated when disaster hits. An 
airborne Wireless Sensor Network (WSN) with Global Special Mobile (GSM) Short 
Message Service (SMS) capability is proposed to provide rapidly deployable emergency 
wireless communication solution. A SMS-WSN node prototype is developed and 
encapsulated in a weatherproof and airdrop enabled shell. A cargo aircraft loaded with the 
 
 iii 
SMS-WSN nodes can be deploy to an affected area within hours, distribute thousands of 
nodes to form a complimentary SMS network which is capable of relaying text messages 
among all cellular users. Although more work is needed to improve the design, our results 
have demonstrated the viability of providing text messaging service among cellular users 
during emergency to help saving people?s lives. 
 
 
 
 
  
 
 iv
 
 
 
Acknowledgments 
 
Foremost I would like to thank God for giving me the strength and determination to 
achieve my graduate degree. I would like to express deepest appreciation to Dr. Thomas 
and Dr. Riggs for their continual tutoring, support, and encouragement for every step in the 
process. I would also like to thank Dr. Schwartz, Dr. Presley, and Dr. Zhang for their 
contribution to this dissertation by serving on my graduate committee, and Dr. Baginski for 
serving as my outside reader. To all of the professors and staff that helped me, I am forever 
grateful. To my research colleagues, David Branscomb, Jeff Thompson, Ashton Johnson, 
and Joshua Hamilton, I am thankful for all your help throughout my research. 
I also would like to express great thanks to my family, for their endless support, 
encouragement, and love. 
 
 
 
  
 
 v
 
 
 
Table of Contents 
 
Abstract ............................................................................................................................... ii 
Acknowledgments.............................................................................................................. iv 
List of Tables .................................................................................................................... vii 
List of Figures .................................................................................................................. viii 
List of Acronyms .............................................................................................................. xii 
Chapter 1. Preface..........................................................................................................1 
Chapter 2. Antenna and Artificial Electromagnetic Surface Fundamentals ..................5 
2.1. Introduction ......................................................................................................5 
2.2. Maxwell?s Equations .......................................................................................6 
2.3. Fundamental Theory of EM Radiation ............................................................9 
2.4. Microstrip Antenna Basics .............................................................................14 
2.5. Surface Waves ...............................................................................................20 
2.6. Artificially Electromagnetic Surface Basics ..................................................25 
2.7. Artificially Magnetic Conductor Basics ........................................................32 
2.8. Frequency Selective Surface Basics ..............................................................39 
2.9. Important Parameters of Antennas.................................................................44 
2.10. Summary ........................................................................................................47 
Chapter 3. Numerical Modeling of Electromagnetic Textiles .....................................49 
3.1. Numerical Modeling Methods .......................................................................49 
 
 vi
3.2. Numerical Modeling of Woven Antennas .....................................................51 
3.3. Numerical Modeling of Woven Frequency Selective Surface ......................68 
3.4. Numerical Modeling of Textile Artificial Magnetic Conductor ....................76 
Chapter 4. Emergency Communication Network........................................................81 
4.1. Introduction ....................................................................................................81 
4.2. Overall System Design ..................................................................................85 
4.3. Wireless Sensor Network Basics ...................................................................88 
4.4. Wireless Sensor Network Design ..................................................................95 
4.5. Microcontroller Firmware ............................................................................111 
4.6. Graphic User Interface .................................................................................111 
4.7. Results ..........................................................................................................113 
4.8. Summary ......................................................................................................113 
Chapter 5. Conclusion and Future Work ...................................................................115 
5.1. Conclusion on Electromagnetic Textile Research .......................................115 
5.2. Conclusions on Emergency Communication Network Development .........116 
References ........................................................................................................................117 
Appendix A FSS Simulation Using Periodic Boundary Conditions in Ansoft HFSS .....122 
Appendix B AMC Simulation Using Floquet Modal Analysis in Ansoft HFSS .............128 
 
 
 
 vii
 
 
 
List of Tables 
 
Table 2-1 Surface impedance and boundary conditions of different EM surfaces ........... 27 
Table 3-1 Design Summary of MSA ................................................................................ 56 
Table 4-1 Received SMS in PDU format and decoded text. .......................................... 113 
  
 
 viii 
 
 
 
List of Figures 
 
Figure 2.1 Diagram for computing EM fields [2]. ............................................................ 10 
Figure 2.2 Microstrip antenna structure and electric field lines ....................................... 15 
Figure 2.3 Microstrip antenna cavity model coordination selection ................................. 18 
Figure 2.4 Surface wave on a general interface between two media ................................ 20 
Figure 2.5 Classic corrugated surface ............................................................................... 26 
Figure 2.6 Soft surface diagram ........................................................................................ 28 
Figure 2.7 Hard surface diagram ...................................................................................... 29 
Figure 2.8 One, two, and three dimensional EBG structures............................................ 31 
Figure 2.9 Sievenpiper mushroom structure and equivalent circuit [21].......................... 33 
Figure 2.10 Corrugated surface analysis ........................................................................... 35 
Figure 2.11 Impedance and phase of a parallel resonant circuit [21] ............................... 37 
Figure 2.12 Dispersion diagram for bound surface waves [21] ........................................ 37 
Figure 2.13 Circuit model of leaky TE waves [21] .......................................................... 38 
Figure 2.14 Complete dispersion diagram, including leaky modes [21] .......................... 38 
Figure 2.15 Surface wave band structure for a two-layer AMC [21] ............................... 38 
Figure 2.16 Capacitive and inductive FSS ........................................................................ 39 
Figure 2.17 Coordination set up of the FSS problem ....................................................... 40 
Figure 2.18 Problem set up of FSS ................................................................................... 41 
Figure 2.19 Equivalent circuit of transmitting antenna .................................................... 45 
 
 ix
Figure 2.20 Radiation pattern of antenna .......................................................................... 47 
Figure 3.1 Interface of Ansoft HFSS ................................................................................ 51 
Figure 3.2 Boundary conditions of MSA cavity mode ..................................................... 54 
Figure 3.3 Resonance modes of MSA (a)uni0009TM010x, (b)uni0009TM001x, (c)uni0009TM020x, and 
(d)TM002x. ........................................................................................................... 55 
Figure 3.4 Design scheme of MSA ................................................................................... 56 
Figure 3.5 MSA design scheme. ....................................................................................... 57 
Figure 3.6 Woven antenna design scheme. ....................................................................... 57 
Figure 3.7 Picture of fabricated MSA. .............................................................................. 58 
Figure 3.8 Picture of fabricated woven antenna. .............................................................. 58 
Figure 3.9 Simulated (solid) and measured (dashed) S11 return loss of MSA................. 60 
Figure 3.10 Measured S11 of woven antenna (solid) and MSA (dashed) ........................ 60 
Figure 3.11 Simulation model of (a) grating MSA and (b) woven antenna ..................... 61 
Figure 3.12 Simulated S11 of woven antenna (solid) and grating MSA (dashed) ........... 62 
Figure 3.13 Picture of fabricated grating MSA. ............................................................... 62 
Figure 3.14 Measured S11 of woven antenna (solid) and grating MSA (dashed) ............ 63 
Figure 3.15 Simulated (solid) and measured (dashed) radiation pattern of MSA uni0009TM010x 
mode. (a) XZ plane. (b) YZ plane......................................................................... 64 
Figure 3.16 Simulated (solid) and measured (dashed) radiation pattern of MSA TM002x 
mode. (a) XZ plane. (b) YZ plane......................................................................... 64 
Figure 3.17 Simulated (solid) and measured (dashed) radiation pattern of woven antenna 
TM002x mode. (a) XZ plane. (b) YZ plane. ....................................................... 64 
Figure 3.18 Simulated woven antenna radiation pattern at 886MHz ............................... 67 
Figure 3.19 Model setup of aperture FSS ......................................................................... 70 
Figure 3.20 Model setup of textile FSS ............................................................................ 71 
Figure 3.21 Magnitude of S11 and S21 of textile FSS and Aperture FSS........................ 72 
 
 x
Figure 3.22 Phase shift of S11 and S21 of textile FSS and Aperture FSS ....................... 72 
Figure 3.23 Aperture FSS incident angle dependence TE mode ...................................... 73 
Figure 3.24 Aperture FSS incident angle dependence TM mode ..................................... 73 
Figure 3.25 Woven FSS incident angle dependence TE mode ......................................... 74 
Figure 3.26 Woven FSS incident angle dependence TM mode ....................................... 74 
Figure 3.27 Model setup of PEC strip grating .................................................................. 78 
Figure 3.28 Model setup of woven strip grating ............................................................... 78 
Figure 3.29 Dispersion diagram of grating AMC/AEC .................................................... 79 
Figure 3.30 Dispersion diagram of textile AMC/AEC ..................................................... 80 
Figure 4.1 Wireless emergency communication network concept ................................... 85 
Figure 4.2 Overall emergency communication system architecture ................................. 87 
Figure 4.3 WSN network structure ................................................................................... 89 
Figure 4.4 Major components of sensor node ................................................................... 90 
Figure 4.5 WSN protocol stack ......................................................................................... 91 
Figure 4.6 WSN node system structure diagram .............................................................. 96 
Figure 4.7 Schematics of SPI interface ............................................................................. 98 
Figure 4.8 MCU pin configuration ................................................................................... 98 
Figure 4.9 Manufactured WSN node PCB board ............................................................. 99 
Figure 4.10 Populated WSN node .................................................................................... 99 
Figure 4.11 GSM module attached to WSN node through breadboard .......................... 101 
Figure 4.12 Solar panel under test .................................................................................. 103 
Figure 4.13 Improvement schematic of the energy harvest interface ............................. 103 
Figure 4.14 Components of pneumatic system ............................................................... 104 
Figure 4.15 Multi-functional braided tether with pneumatic tubing and wires .............. 105 
 
 xi
Figure 4.16 Braiding machine during manufacture of multi-functional tether ............... 106 
Figure 4.17 Impact resisting polyurethane foam ............................................................ 107 
Figure 4.18 Weatherproof shell constructed from recycled soda bottle ......................... 108 
Figure 4.19 Air holes drilled in bottle to cause separation during deployment .............. 108 
Figure 4.20 Air pressure separation experiment ............................................................. 110 
Figure 4.21 Top and bottom separation .......................................................................... 110 
Figure 4.22 Start up data through GSM-UART-RF-USB link ....................................... 112 
Figure 4.23 SMS Received in PDU format through GSM-UART-RF-USB link .......... 112 
 
xii 
 
 
 
 
List of Acronyms 
 
8PSK 8-Phase Shift Keying 
ACN Airborne communications node 
ADC Analog to digital converter 
AEC Artificial electric conductor 
AMC Artificial magnetic conductor 
AUT Antenna under test 
BTS Base station 
CDMA Code division multiplexing 
EBG Electromagnetic bandgap 
ECN Emergency communication network 
EM Electromagnetic 
FDTD Finite difference time domain 
FEM Finite element method 
FSS Frequency selective surface 
GMSK Gaussian minimum shift keying 
GSM Global special mobile 
 
 xiii 
GUI Graphic user interface 
IC Integrated circuit 
LCS Longitudinal corrugated surface 
LNA Low noise amplifier 
MCU Microcontroller 
MEMS Microelectromechanical systems 
MOM Method of moments 
PA Power amplifier 
PBG Photonic bandgap 
PEC Perfect electric conductor 
PGA Programmable gain amplifier 
PLL Phase locked loop 
PMC Perfect magnetic conductor 
PML Perfect matched layer 
QoS Quality of service 
RF Radio frequency 
SACCH Slow associated control channel 
SDCCH Standalone dedicated control channel 
SMS Short text messaging 
TCP Transmission control protocol 
TCS Transverse corrugated surface 
UDP User datagram protocol 
 
 xiv
USB Universal serial bus 
VCO Voltage controlled oscillator 
WINS Wireless integrated network sensors 
WSN Wireless sensor network 
 
 
 
 
 
 
 
 
1 
 
 
 
 
Chapter 1.Preface 
 
Due to the development of technology, today?s society has become an information 
society in which the creation, distribution, diffusion, use, integration and manipulation of 
information is a significant economic, political, and cultural activity. The communication 
of information needs conduits. Physically, there are only two ways to communicate 
information: wired transmission, and wireless transmission. Land line telephones, cable 
TV, cable internet falls into the wired category, while cellular communication, satellite 
communication, wireless local area network, falls into wireless category. As the 
communication requirement from society grows, wired transmission especially optical 
fiber technology has become the preferred communication network backbone solution 
due to the enormous bandwidth it can provide. Meanwhile, wireless technology has 
become the preferred ?last mile? solution to the end user due to its mobility and 
multi-access capability [1].  
A wireless communication system utilizes EM wave to transmit information, and the 
EM wave transmission and reception is done by means of antennas. Two major functions 
of antennas are to convert electrical energy to EM wave energy and directionally transmit 
or receive EM radiation [2, 3]. The antenna is a critical component of a wireless 
communication system because its properties have direct impact on overall system 
performance. Ever since the first pair of antennas were developed by Heinrich Hertz in 
 
 2
1887, and especially after the Second World War, antenna theory, design, and application 
has been developed drastically and has entered a relatively mature stage [3]. However, 
the development of antenna never ceased, research, exploration and application of 
wireless technology has placed new requirements on antenna systems including 
miniaturization, high mobility, and conformity [4].  
There is currently much interest in textile antenna systems for body-worn 
communication or communication off body to fixed and mobile networks. The most 
widely used portable antennas are whip antennas or ducky antennas. However, these 
antennas have to be placed perpendicular to a ground plane and do not conform to device 
surfaces. There are two solutions toward conformal antennas, one is the printed circuit 
board microstrip antenna, and the other is the textile antenna. The textile antenna has 
significant advantage over the microstrip antennas in that it is flexible can be integrated 
into cloth and other textile products. However, the current numerical modeling method on 
textile antenna is confined to mimicking microstrip antenna using the transmission line 
model. The transmission line model uses the simplest approximation to study microstrip 
antennas and only applies to the fundamental radiation mode. Shown in this study, the 
textile antennas can behave in a far more complicated manner than the microstrip antenna 
and can operate in radiation mode other than the fundamental mode. To reveal the physics 
behind the textile antennas, a more strict and useful cavity model is utilized and the higher 
mode radiation of the textile antenna is used to study the resonant modes higher than the 
fundamental mode, meanwhile the leaky wave antenna model is used to study the modes 
lower than the fundamental mode. The results have suggested that by arranging the 
 
 3
conductive yarns properly, the designed textile patch can also be used as frequency 
selective surfaces.  
An effort toward numerical modeling of textile frequency selective surfaces is also 
given in this study. The periodicity of textile materials makes it a perfect candidate for 
frequency selective surfaces implementations. However, the current researches on 
frequency selective surfaces are mostly focused on the hard dielectric backed PCB 
approach, not much research is done on flexible textile based frequency selective surfaces. 
The implementation of textile based frequency selective surfaces can be applied to any 
communication system, large to small, very easily by just covering it with the textile. 
Moreover, the fabrication process of textile frequency selective surface can also be easily 
incorporated into advanced composite manufacturing to integrate FSS into composite 
structures in a one-step process.  
Another work presented here is the effort toward developing a solution to the real 
world problem of emergency communication congestion using the textile antenna and 
FSS. From the lessons learn through hurricane Katrina, the Select Bipartisan Committee 
to Investigate the Preparation for and Response to Hurricane Katrina suggests the ECN in 
the future should rapidly deploy, be portable and easily configured, require low power, 
and should be integrated into humanitarian aid infrastructure. The recent advances in 
ultra-low power integrated circuit (IC) technologies have created low cost, low-power, 
and multi-functional devices, which can be configured and programmed to fulfill the 
requirements of future terrestrial ECN. 
The low-power requirements imply that such communication system must be 
battery/solar operated, and can only have very limited communication range. Due to the 
 
 4
broadcasting nature of the ECN, omnidirectional antennas must be used. The only ways 
to improve the communication range for the ECN nodes are either to increase the 
transmitting power, which is prohibited by the low-power requirement, or to use more 
efficient antenna and FSS. Whip or ducky antennas are widely studied and efficient. 
However, they require a size too large (a quarter of the wavelength) being perpendicular 
to a ground plane, thus do not meet the conformity requirement. Microstrip antennas are 
conformal, but they are rigid and vulnerable to weather, and generally contained inside 
the communication device. Their small sizes determined they can only have low radiation 
efficiency.  
In our research, we propose to develop a network containing a large set of relay 
nodes scattered over a wide area to serve the people in need of emergency 
communication. The proposed ECN consists of a number of relay nodes that collaborate 
to accomplish the task of transmitting and receiving data packages such as text messages 
using the radio link to an emergency responding center node (sink node, such as satellite 
phone station or 911 station) under conditions when the conventional communication 
infrastructure is destroyed, a common situation caused by natural disasters. The ECN can 
serve both survivors and emergency responders for real time communication needs.  
In this specific application of ECN, the proposed relay nodes can be deployed in 
several different ways depending on the scale and severity of the disaster, the population 
density of the affected area, and the total population affected. The overall system 
architecture design is presented, a relay node prototype is developed, and the feasibility 
of applying textile antenna and FSS to the relay nodes is discussed. 
  
 
 5
 
 
 
Chapter 2.Antenna and Artificial Electromagnetic Surface Fundamentals 
 
2.1.Introduction 
Accompanied by the discovery of electromagnetism, antennas have been widely 
studied for over one hundred years. As electromagnetic (EM) theory develops in depth, the 
understanding of radiation mechanism of various existing antenna structures has become 
more mature while new antenna structures has been suggested and tested.  Through 
sophisticated application of the Maxwell equations, antenna design has come to the stage 
of replacing expensive prototyping and field testing with simulation and numerical 
analysis [2] .  
Meanwhile, Artificial Electromagnetic Surface (AES) as a promising way to further 
improve antenna and microwave circuit performance, has been widely studied. The 
hypothetical concept of the Perfect Magnetic Conductor (PMC) has been suggested by 
mathematicians and applied in EM modeling for years. However, the emergence of High 
Impedance Surface (HIS), a special type of AES, has brought the possibility to realize the 
characteristic of PMC as a part of AES and is named Artificially Magnetic Conductor 
(AMC). With its unique surface wave bandgap property and in phase reflection property, it 
is possible to drastically reduce sizes of antennas while improving performance and has 
drawn significant interest from the EM research society.  
 
 6
In particular, frequency selective surface (FSS) is another promising application area 
of AES or AMC. FSS is typically a large scale periodic planar array with metallic elements 
or periodic aperture array in a metallic screen. FSS has certain frequency selecting 
characteristic to EM wave and can be considered as an open space EM filter. FSS itself 
does not absorb RF energy. Its scattering characteristic is frequency dependent. It is almost 
transparent to pass band EM wave but opaque to stop band EM wave. The frequency 
selecting characteristic depends on the shape of the individual array element. Due to its 
unique property and promising application potentials, FSS with AMC integration has 
become another popular topic of the EM research area.  
As computer technology developed in the past decades, the numerical method has 
become the preferred way to analyze antenna and AES properties. With powerful 
computing and optimized differential equation solvers, modern antenna and AES design 
has become more efficient and accurate. However, no matter what method people use, 
antenna and AES will always follow the fundamental laws of electromagnetism. This 
chapter will briefly introduce the fundamental laws of electromagnetism, EM radiation 
theories, microstrip antenna theories including transmission line model and cavity model, 
AES in general and FSS theories. 
2.2.Maxwell?s Equations 
An antenna is a conductive component designed to send and receive radio waves. It is 
a transitional structure between the circuit and the free space. Antenna properties can be 
analyzed with basic laws of physics. These laws have been collected into a set of equations 
commonly referred to as Maxwell?s equations.[5] 
 
 7
The time domain Maxwell?s equations can be show as 
??g2319=??g2316?t ?g2327 (2-1) 
(2-2) 
(2-3) 
(2-4) 
??g2322=??g2318?t +g2324 
??g2318=?(t) 
??g2316=m 
The cross and dot operators are referred to as the curl and divergence respectively. 
Another equation can be derived from equation (2-2) and (2-3) is 
??g2324=???(t)?t  (2-5) 
Equation (2-5) is denoted as the continuity equation to describe the electric current 
density g2276 in terms of the movement of volumetric electric charge, ?. A similar 
relationship also exists for the magnetic current density ? and volumetric magnetic 
charge m. The other quantities ?, ?, g2270, ?, are electric and magnetic field intensity, 
and the electric and magnetic field densities respectively. 
In most antenna applications, the EM analysis is based on sinusoidal varying sources 
in a linear environment. For time-harmonic fields with a single radian frequency of g185, 
we can use the phasor form of the electrical field 
g2319=Re(g1779?eg2920g2985g2930) (2-6) 
and the phasor form of Maxwell?s equations can be derived as 
??g1779=?j?g1776?g2327 (2-7) 
??g1782=j?g1778+g2324 (2-8) 
 
 8
??g1778=? (2-9) 
??g1776=m (2-10) 
and the phasor form continuity equation 
??g1784=?j?? (2-11) 
If there is more than one frequency present, the solution to the Maxwell?s equations 
may be found for each individual frequency separately and the results combined for the 
total solution. The linearity environment restriction is to ensure that the analysis should be 
restricted to a single frequency. For nonlinear environment, it is advantageous to solve the 
time-domain equations first and obtain the frequency-domain form through a Fourier 
transform process.  
Maxwell?s equations define relationships between the field quantities, but do not 
provide information about the media in which these fields exist. The material can be 
characterized by three quantities: permittivity ?, permeability ?, and conductivity ?. 
Sometimes the material conductivity is given in the form of resistivity ?= g2869g2978. These 
quantities define the relationship between the density and intensity quantities as well as 
the portion of the current due to conduction. Thus we have g1778=?g1779, g1776=?g1782, and 
g1784=?g1779. Applying these to the Maxwell?s equations give 
??g1779=?j??g1782?g1787 (2-12) 
??g1782=(?+j??)g1779+g1784g1809 (2-13) 
(?? ?j?)??g1779=?g2919 (2-14) 
???g1782=m (2-15) 
and 
 
 9
??g1784g1809 =?j??g2919 (2-16) 
The i-subscript denotes the impressed sources in the system, equivalent to the 
independent sources of circuit theory. The medium is described by scalar quantities, 
which implicating the media is isotropic. And the material parameters are extracted from 
the derivatives, which implicating the media is constant and homogeneous. Such 
simplifications are valid for common antenna problems. 
2.3.Fundamental Theory of EM Radiation 
EM Radiation is caused by current source and magnetic source. Given the 
distribution of current and magnetic source, the EM field distribution of any arbitrary 
position can be determined by solving Maxwell?s equation. When analyzing a radiation 
problem, it is typical to solve radiation source, then calculate the radiation field 
accordingly. The auxiliary potential function method is most widely used in solving such 
problems [2]. The most commonly used auxiliary function pair is A (magnetic vector 
potential) and F (electric vector potential). It is common practice to solve auxiliary 
functions, and then solve the EM field to simplify the problem. 
Figure 2.1 shows the relationship between the different function pairs. Normally the 
integration and differentiation of path 2 is easier than the integration of path 1 alone. 
 
 10
 
Figure 2.1 Diagram for computing EM fields [2]. 
2.3.1.Source Current Densities J and M 
The vector potential A is widely used when solving the EM field generated by 
current density J. We define  
g1782g3002uni0009=1g2020??g1775 (2-17) 
Solving A and J using vector identity and Maxwell equation (2-13) gives 
?g2870g1775+uni006Bg2870g1775=?g2020g1784 (2-18) 
The E-field satisfies  
g1779g3002 =?g2744g2038g3032uni0009?uni0009g1862g2033g1775=?g1862g2033g1775?g1862 1g2033g2020g2035?(??g1775) (2-19) 
Once A is known, HA can be found from (2-17) and EA from (2-19).  
Although magnetic current source M is considered physically unrealizable, the 
volume or the surface equivalent magnetic currents is widely used when solving real EM 
problems. 
 
 11
Harmonic magnetic current M generates potential vector F. F satisfies the following 
relationship: 
?g2870g1780uni0009+g1863g2870g1780uni0009=uni0009?g2035g1787 (2-20) 
If we define 
g1779g3007 =?1g2035??g1780 (2-21) 
Apply vector identity and Maxwell equation (2-12)(2-12) 
g1782g3007 =?g1862g2033g1780? g1862g2033g2020g2035?(??g1780) (2-22) 
Once F is known, EF can be found from (2-21) and HF from (2-22). 
In order to solve EM field, the source currents J and M must be solved first, then A 
and F can be solved, and finally using the above equations, E and H field generated by J 
and M can be solved accordingly.  
Electric current density J and vector potential A satisfies the following relationship  
g1775= g20204g2024g3512g1784
g3049
g1857g2879g3037g3038g3019
g1844 g1856g1874? (2-23) 
While magnetic current density M and vector potential F satisfies the following 
relationship  
g1780= g20354g2024g3512g1787
g3049
g1857g2879g3037g3038g3019
g1844 g1856g1874? (2-24) 
 
 
 12
Where g1863g2870uni0009=uni0009g2033g2870g2020g2035 and R is the distance from any point in the source to the 
observation point. Then we can find HA from (2-17), EA from (2-19), HF from (2-22), and 
EF from (2-21).  
The total fields are then determined by 
g1779uni0009=uni0009g1779g3002uni0009+g1779g3007uni0009=uni0009?g1862g2033g1775?g1862 1g2033g2020g2035?(??g1775)?1g2035??g1780 (2-25) 
g1782uni0009=uni0009g1782g3002uni0009+g1782g3007uni0009=uni00091g2020??g1775?g1862g2033g1780? g1862g2033g2020g2035?(??g1780) (2-26) 
 When computing using the far field approximations, the second term in EA and HF 
expressions can be negligible, and thus further simplify the problem. 
2.3.2.Far Field Radiation 
The radiated wave can be considered as spherical plane wave from an antenna with 
finite sizes. The solution of the vector wave equation under spherical coordination can be 
expressed as: 
g1775uni0009=uni0009g1801g3548g3045g1827g3045(g1870,g2016,g2030)uni0009+uni0009g1801g3548g3087g1827g3087(g1870,g2016,g2030)uni0009+uni0009g1801g3548g3101g1827g3101(g1870,g2016,g2030) (2-27) 
The amplitude variations of r in each component has the form of g2869g3045g3289,g1866=1,2,? and 
(2-27) can be reduced to 
g1775uni0009?g3427g1801g3548g3045g1827g3045g4593(g2016,g2030)+uni0009g1801g3548g3087g1827g3087g4593 (g2016,g2030)+uni0009g1801g3548g3101g1827g3101g4593 (g2016,g2030)g3431g1857
g2879g3037g3038g3045
g1870 ,g1870?? (2-28) 
Substituting (2-28) into (2-17) and (2-19) we get 
g1779uni0009=1g1870g3419?g1862g2033g1857g2879g3037g3038g3045g3427uni0009g1801g3548g3045(0)+uni0009g1801g3548g3087g1827g3087(g2016,g2030)+uni0009g1801g3548g3101g1827g3101(g2016,g2030)g3431g3423+ 1g1870g2870g4668?g4669+? (2-29) 
 
 13
g1782uni0009=1g1870g3420?g1862g2033g2015g1857g2879g3037g3038g3045g3427uni0009g1801g3548g3045(0)+uni0009g1801g3548g3087g1827g3087(g2016,g2030)+uni0009g1801g3548g3101g1827g3101(g2016,g2030)g3431g3424+ 1g1870g2870g4668?g4669+? (2-30) 
  Where g2015=g3493g2020/g2035 is the intrinsic impedance of the medium. 
Neglecting higher order terms of 1/g1870g3041, the radiated E- and H- fields have only ? 
and ? components. They can be expressed as 
 
g1832g1853g1870?g1832g1861g1857g1864g1856uni0009g1844g1857g1859g1861g1867g1866uni0009
g4688
g1831g3045 ?uni00090
g1831g3087 ??g1862g2033g1827g3087
g1831g3101 ??g1862g2033g1827g3101
uni0009uni0009uni0009g1871g1867uni0009g1872?g1853g1872uni0009g1779g3002uni0009??g1862g2033g1775 
(2-31) 
g1749g1750
g1748
g1750g1747
g1834g3045 ?uni00090
g1834g3087 ?+g1862g2033g2015g1827g3101 =?g1831g3101g2015
g1834g3101 ??g1862g2033g2015g1827g3087 =+g1831g3087g2015
uni0009uni0009uni0009g1871g1867uni0009g1872?g1853g1872uni0009g2164g3002uni0009?g1801g3548g3045g2015 ?g1779g3002
=?g1862g2033g2015g1801g3548g3045 ?g2157uni0009
(2-32) 
Radial field components exist only for higher order terms of 1/g1870g3041. 
In a similar manner, the far-zone fields due to a magnetic source M (potential F) can 
be written as 
g1782g3007 ?uni0009uni0009?g1862g2033g1780 (2-33) 
g2161g3007 ?uni0009uni0009?g2015g1801g3548g3045 ?g1782g3007 =g1862g2033g2015g1801g3548g3045 ?g2162uni0009 (2-34) 
  Finally combining the two corresponding parts gives the total EM field. It can be 
easily shown that the E and H fields are orthogonal in the far field and thus forms a TEM 
wave. The radiation field can be subdivided into near field, transition zone, and far 
 
 14
radiation field based on the distance from the radiator. In practice the smallest radial 
distance of far field is 2g1830g2870/g2019 where D is the largest dimension of the radiator. 
2.4.Microstrip Antenna Basics 
The MSA is a low profile antenna.  It is also named as patch or planar antenna.  The 
MSA is a popular built-in antenna for electronics because of it is lightweight, inexpensive, 
and offers conformal structures [6].  The fundamental radiation mechanism can be 
explained by studying a rectangular flat plate over a substrate with a ground plane using 
transmission line model or cavity model.  
2.4.1.Transmission Line Model 
As shown in Figure 2.2, the microstrip has a dimension of g1849?g1838, dielectric thickness 
of ?, ?g1575g2019g2868,uni0009g2019g2868 is the free space wavelength.  The radiating patch can be considered as 
a microstrip transmission line. Since the terminal edge (W) is open circuit, a standing wave 
will be generated on the patch. The length of the transmission line L can be approximated 
as g1838g3406 g3090g3282g2870 , g2019g3034 is the wavelength on the transmission line, so that the other terminal edge 
(W) is open circuit too.  
The electric field of MSA can be approximately expressed as  
g1831g3051 =g1831g2868g133g145g149uni0009(g2024g1877/g1838) (2-35) 
Also shown in Figure 2.2, the electric field of the MSA is zero at the center, maximum 
(positive) at one side, and minimum (negative) on the opposite side, according to (2-35).  
When a signal is applied, the minimum and maximum continuously change sides 
according to the instantaneous phase of the signal [6].  The length L of MSA is the factor 
 
 15
that causes resonance at its half-wavelength frequency.  The radiating edges are the two 
edges at the ends of the L-dimension of the patch.  Radiation that occurs at the ends of the 
W-dimension is far less compared to those at L-dimension edges, and is normally ignored. 
There are several keys to successfully design a MSA structure.  First, the structure 
needs to be a half-wavelength length resonator.  Second, a low dielectric constant 
substrate for the MSA is preferred.  Third, a thicker dielectric substrate could broaden the 
bandwidth, but the substrate thickness should always be just a fraction of a wavelength [2]. 
The resonant frequency of MSA is inversely proportional to its size.  Because of this, 
MSA are mostly used for frequencies of microwave and above.  For frequencies lower 
than microwave, MSA application is very limited because of the sizes required.  For 
example, an MSA to receive FM radio at 100 MHz would have a size on the order of 1 
meter long, which is a very large circuit for any type of substrate.  To receive AM radio at 
1000 KHz, the MSA would have the size of a football field [2].  One application example 
of MSA is in satellite radio receivers (XM and Sirius) [6]. 
 
Figure 2.2 Microstrip antenna structure and electric field lines 
 
 16
The radiation efficiency is determined by the patch width W and the impedance 
matching network.  In order to achieve best radiation efficiency, W can be calculated 
according to (2-36).  
0
( 1)2
2
r
cW
f ?
= +
 
(2-36) 
Where c is the speed of light, f0 is the resonant frequency, and g2013g3045 is the dielectric constant. 
Once the resonant frequency f0 is set by the application requirement, patch length L 
can be calculated based on effective dielectric constantuni0009g2013g3045g3032g3033g3033uni0009according to (2-37) through 
(2-40). 
1
21 1[1 12 ]
2 2
r r
reff
h
W
? ?? ?+ ?= + + ?
 
(2-37) 
02
eff
reff
cL
f ?=  (2-38) 
( 0.3)( 0.264)
0.412
( 0.258)( 0.8)
reff
reff
W
hL h
W
h
?
?
+ +
? = ?
? +  
(2-39) 
2effL L L= ? ??
 
(2-40) 
To match the antenna impedance to the 50g563 transmission line and feed structure, the 
edge impedance can be calculated using (2-41) and a quarter wave transformer can be 
designed accordingly. 
2
290 ( ) ( )
1
r
L
r
LZ
W
?
?= ? ??
 
(2-41) 
 
 17
2.4.2.Cavity Model 
The transmission line is the simplest model used to study MSA. However, it only 
applies to the fundamental radiation mode. To study the higher mode radiations, a more 
strict and useful cavity model must be utilized. The cavity model is first suggested by Y. T. 
Lo et al. in 1979 [7].  Based on the feature of ?g1575g2019g2868, MSA can be considers as 
dielectric-loaded cavities bounded by electric conductors (above and below it) and by 
magnetic walls (to simulate an open circuit) along the perimeter of the patch. The radiated 
field can be calculated from the equivalent magnetic current around the cavity, while the 
input impedance can be calculated from cavity field and feed source boundary condition. 
The cavity model has been successfully utilized in computing antenna pattern, input 
admittance, and resonant frequencies and compare well with measurements [7-9] . This 
model provides a more detailed physical insight into the radiation mechanism of MSA 
and generates many novel designs and applications. The cavity model can be applied not 
only to rectangular patch, but also applicable to other regular shape patches. The cavity 
model is conformant to the transmission line model in that the latter is merely the 
fundamental radiation mode of the cavity model.  
The approximation method used is the cavity model is the two step method. First, 
calculate the source field distribution on the radiator or equivalent source field 
distribution on a closed surface surrounding the source. Second, solve the far field 
distribution based on the solution of the source field distribution to. The second step is a 
strict mathematical solution based on Huygens principle, but because it is based on the 
 
 18
approximation result from step 1, the overall solution is an approximate solution. The 
overall accuracy depends on the accuracy of step 1.  
First solve for the near field: 
Select the coordination as shown in Figure 2.3, whenuni0009?g1575g2019g2868, it can be assumed that: 
(1) the E-field has only Ez component, while the H-field has only Hx and Hy components, 
in other words, the field inside the cavity is has only TM mode in z direction. (2) The 
field inside the cavity does not vary with z. (3) the current around the cavity does not 
have normal components, thus the tangential component of H-field is zero, so the side 
walls of the cavity can be considered as PMC boundaries. This is assumption is made for 
ease of calculation, in reality MSA has a fringing effect like microstrip transmission lines, 
the fringing effect can be accounted for by calculating the equivalent effective sizes.  
 
Figure 2.3 Microstrip antenna cavity model coordination selection 
The assumptions result in a modified form of the Maxwell equation: 
 
 19
??g1782=?j??g1779+g1784 
(2-42) 
??g1779=?j??g2868g1782 
??g1782=0 
??g1779=0 
Since ?g1575g2019g2868, current source Jz can be considered constant along z direction, so uni0009
??g1784=?g1862g2033g2025=0, thus  ??g1779=0. From (2-42) we can get 
?g2870g1779+g1863g2870g1779=g1862g2033g2020g2868g1784
 
(2-43) 
Where g1863 =g2033g3493g2020g2868g2013=g1863g2868g3493g2013g2868(1?g1862tg131g144g2012), tg131g144g2012 is the loss tangent of the 
dielectric material. Since g1784=g1878uni0302g1784g3053, g1779=g1878uni0302g1779g3053, (2-43) can be simplified into a scalar 
equation: 
(?g2870+g1863g2870)g8g3053 =g1862g2033g2020g2868g13g3053
 
(2-44) 
To solve (2-44), we can use the eigenmode expansion method. This method solves 
the equation by expressing the solution as a superposition of the eigenvalues. The 
eigenfunction is derived from the homogeneous wave equation: 
(?g2870+g1863g3040g3041g2870)g2006g3040g3041 =0
 
(2-45) 
g2006g3040g3041 must satisfy the PMC boundary condition g3105g3077g3288g3289g3105g3041 =0, the n on the denominator 
is the normal vector of the PMC boundary. For regular shape cavities, variable separation 
can be used to solve for g2006g3040g3041 and corresponding g1863g3040g3041. 
After solving (2-44), we can get g8g3053, then using Maxwell Equation (2-42) we can 
solve for Hx and Hy thusly: 
 
 20
g1749g1750
g1748
g1750g1747g1834g1876=?
g1862
g2033g2020g2868
g2034g1831g3053
g2034g1877
g1834g1877=? g1862g2033g2020
g2868
g2034g1831g3053
g2034g1876  
(2-46) 
 
2.5.Surface Waves 
A surface wave is a type of EM wave. Its intrinsic property is an exponential decay 
away from the surface along the surface normal direction, in other words, the energy is 
bound in close proximity to the surface.   
2.5.1.Conditions of Existence 
 
Figure 2.4 Surface wave on a general interface between two media 
As shown in Figure 2.4, g2013g2869 and g2013g2870 are the dielectric constant of the two media 
respectively. For the instance of TM mode, assume the surface wave is propagating along z 
direction and decay in x direction, with g1857g3037g3050g3047 term implicit the E-field components in 
region I can be written as:  
 
 21
g1831g3051 =g1827?g1857g2879g3037g3038g3053g2879g3080g3051uni0009
g1831g1877=0uni0009
g1831g1878=uni0009g1828?g1857g2879g3037g3038g3053g2879g3080g3051 
(2-47) 
In material II, the electric field has the same form, given below. 
g1831g3051 =g1829?g1857g2879g3037g3038g3053g2878g3082g3051uni0009
g1831g1877=0uni0009
g1831g1878=uni0009g1830?g1857g2879g3037g3038g3053g2878g3082g3051 
(2-48) 
Where A, B, C, D, are constants, and k, g2009, g2011 are unknown variables. Recall Maxwell 
equation 
??g1776= g578g3045g1855g2870g2034g1831g2034g1872uni0009
??g1779=?g2034g2158g2034g1872 
(2-49) 
Where = g2869g3493g3091
g3116g3084g3116
 , is the speed of light in vacuum, and from  
????g1779= g578g3045g1855g2870?g2870g1779 (2-50) 
Expanding (2-50) yields 
xg3548g4678?g2034
g2870g1831g3051
g2034g1878g2870 +
g2034g2870g1831g3053
g2034g1876g2034g1878g4679+g156g3548(
g2034g2870g1831g3051
g2034g1876g2034g1878?
g2034g2870g1831g3053
g2034g1876g2870 )=
g578g3045?g2870
g1855g2870 (xg3548g8g3051 +g156g3548g8g3053) (2-51) 
Since the x and z derivatives equal respectively 
?g2034
g2870g1831g3051
g2034g1878g2870 +
g2034g2870g1831g3053
g2034g1876g2034g1878=
g578g3045?g2870
g1855g2870 g8g3051 
g2034g2870g1831g3051
g2034g1876g2034g1878?
g2034g2870g1831g3053
g2034g1876g2870 =
g578g3045?g2870
g1855g2870 g8g3053 
(2-52) 
Substituting (2-47) and into (2-52) we can get 
 
 22
g1863g2870g1827+g1862g1863g2009g1828=g578g2869?
g2870
g1855g2870 g1827 
g1862g1863g2009g1827?g2009g2870g1828=g578g2869?
g2870
g1855g2870 g1828 
(2-53) 
And substitute (2-48) and into (2-52) we can get 
g1863g2870g1829?g1862g1863g2011g1830=g578g2870?
g2870
g1855g2870 g1829 
?g1862g1863g2011g1829?g2011g2870g1830=g578g2870?
g2870
g1855g2870 g1830 
(2-54) 
Tangential component of E-field and normal component of D have to be continuous 
across the dielectric interface, so that 
g578g2869g1827=g578g2870g1829 
g1828=g1830 
(2-55) 
Substituting (2-55) into (2-54) yields 
g578g2869g1863g2870g1827?g1862g1863g2011g578g2870g1828=g578g2869g578g2870?
g2870
g1855g2870 g1827 
?g1862g1863g2011g578g2869g1827?g578g2870g2011g2870g1828=g578g2870
g2870?g2870
g1855g2870 g1828 
(2-56) 
Combining equations (2-53) and (2-56) we have four equations and four unknowns g1863, 
g2009,  g2011, g3002g3003. Solving these we can get  
g1863 =g3496 g578g2869g578g2870g578
g2869 +g578g2870
?
g1855  
g2009 =g3496 ?g578g2869
g2870
g578g2869+g578g2870
?
g1855 (2-57) 
 
 23
g2011=g3496 ?g578g2870
g2870
g578g2869+g578g2870
?
g1855  
Generally speaking region I is air, so that g578g2869 =1, and let g578g3045 =g578g2870, (2-57) can be 
simplified into 
g1863 =g3496 g578g30451+g578
g3045
?
g1855  
g2009 =g3496 ?11+g578
g3045
?
g1855 (2-58) 
g2011=g3496?g578g3045
g2870
1+g578g3045
?
g1855  
According to (2-58), for air-dielectric interface, if g578g3045 g34080, g2009 and g2011 are pure 
imaginary numbers, the EM Field does not decay in the x direction, and the TM mode 
surface wave is not supported, so the plane waves simply propagate through the dielectric 
interface. On the other hand, if g578g3045 g3407?1 (air-metal interface), the solution describes a 
wave that is bound to the surface. A TM mode surface wave is supported. 
Similarly, the solution for TE surface waves can be obtained according to the 
principle of duality [2]. If the electric and magnetic fields are exchanged, and g2020 is 
substituted for g2013, the solution above can be applied to the TE case. 
 
 24
2.5.2.Surface Impedance of TE and TM Mode Surface Waves 
Referring to Figure 2.4, assume that a surface wave is propagating along the z 
direction and exponentially decaying in the x direction. The surface impedance g1852g3046 is the 
impedance looking down on the surface. For the TM mode surface wave: 
g1852g3046g3021g3014 = g1831g3053g1834
g3052
 (2-59) 
Let,  
g1831g3053 =g1829g1857g2879g3037g3038g3053g2879g3080g3051 (2-60) 
Recall Maxwell equation  
??g2164=g578g2034g1831g2034g1872 (2-61) 
Plug (2-60) into (2-61) we can get  
g1834g3052 =?g1862g2033g2013g2009 g1829g1857g2879g3037g3038g3053g2879g3080g3051 (2-62) 
So the TM mode surface impedance is  
g1852g3046g3021g3014 = g1862g2009g2033g2013 (2-63) 
Applying the same procedure to the TE mode surface wave we get 
g1852g3046g3021g3006 =?g1831g3052g1834
g3053
=?g1862g2033g2020g2009  (2-64) 
It is obvious that the TM mode is supported only when the surface has positive 
impedance (inductive), and TE mode is supported only for negative impedance 
(capacitive). 
  
 
 25
2.6.Artificially Electromagnetic Surface Basics 
2.6.1.Definitions 
In the field of Electromagnetism and microwave research, new terminologies such as 
soft and hard surfaces, electromagnetic band-gap (EBG) structures, Negative Index 
Materials (NIM), and artificial magnetic/electric conductors (AMC/AEC) have arisen and 
attracted much interest from the research community.  These structures or materials do not 
occur in nature and possess valuable EM properties. Their unique properties have shown 
great advantages in the applications of high performance antennas and microwave devices.  
This work addresses all these structures or materials as Artificially Electromagnetic 
Surface (AES). The following is a brief definition and introduction of a few AES. 
2.6.2.Corrugated Surface 
Corrugated surfaces emerged in the 1960s, and were considered the first type of AES. 
They were mainly designed for corrugated horn antennas. In 1996, Simmons, Rumsey, and 
Minnett successfully designed hybrid-mode horn antennas with low cross-polarization and 
symmetrical radiation patterns using corrugated surface [10-12]. Until now, corrugated 
horn antennas are still widely used as feed source for satellite ground station antennas.  
The diagram of classic corrugated surface is shown in Figure 2.5. It is a 
one-dimensional periodic structure formed by infinite long slots with a quarter 
wavelengths depth, and the width of slot is far less than a wavelength. Every slot can be 
considered as a parallel plate waveguide, where the bottom of the slot is a shorted terminal. 
When the depth of waveguide is greater than a quarter wavelength, the surface impedance 
 
 26
appears to be capacitive and does not support TM mode propagation, while the TE mode 
can only propagate along y direction. The overall performance is equivalent to a bandstop 
filter to the surface wave in z direction, thus is called transversely corrugated surface 
(TCS).  
It is worth note that because the depth of the slot is a quarter wavelength, when a 
z-polarized surface wave incident on the TCS is in the negative x direction, the reflected 
wave is in phase with the incident wave, which is a characteristic of the ideal Artificial 
Magnetic Conductor (AMC). The TCS is merely a 1D structure, Lee and Jones further 
developed a 2-D periodic structure with grating arranged metallic rods, and analyzed its 
scattering characteristics [13]. While Kildal et al developed the soft and hard surface 
theory based on these findings and acoustic principles [14, 15].  
 
 
Figure 2.5 Classic corrugated surface 
 
 27
2.6.3.Soft and Hard Surfaces 
Starting in 1986, Kildal et al began to investigate the application of the corrugated 
surfaces in varies of antennas and found that the bandstop characteristic of the corrugated 
surface is similar to the soft surface in acoustic research, which means the Poynting vector 
is zero on the corrugated surface within the stop band [16]. Due to the similarity of acoustic 
and EM waves, a question on whether there is an EM structure similar to acoustic hard 
surface has been suggested. Based on simple physics reasoning, Kildal et al suggested a 
modified corrugated surface with the slots filled with dielectric materials, when the EM 
wave propagates along the y direction (see Figure 2.7), the surface has hard surface 
characteristic and is called a longitudinal corrugated surface (LCS). Kindal concluded the 
work on TCS and LCS as well as the corresponding theory in 1988, thus defined the 
artificially soft and hard surfaces for electromagnetic waves [14].  
 
Table 2-1 Surface impedance and boundary conditions of different EM surfaces 
 Transverse Impedance (Z
t) 
Longitudinal 
Impedance (Zl) 
Boundary 
Condiction (Et) 
Boundary 
Condiction (En) 
PEC 0 0 g1831g3047 =0 g2034g1831g3041g2034g1866 =0 
PMC ? ? g2034g1831g3047g2034g1866 =0 g1831g3041 =0 
Artificially  
Soft Surface 0 ? g1831g3047 =0 g1831g3041 =0 
Artificially  
Hard Surface ? 0 
g2034g1831g3047
g2034g1866 =0 
g2034g1831g3041
g2034g1866 =0 
 
To define artificial soft and hard surfaces, anisotropic surface impedance has to first 
be defined as   
 
 28
g1852g3039 =?g1831g3039/g1834g3047
 
g1852g3047 =?g1831g3047/g1834g3039 (2-65) 
Where Zl and Zt correspond to the longitudinal and transverse surface impedances, 
respectively. The subscript l stands for the longitudinal component, while subscript t stands 
for the transverse component, referring to Figure 2.6 and Figure 2.7 for coordinate 
definitions. Table 2-1 also gives the surface impedance and boundary conditions of PEC, 
PMC, and artificial soft and hard surfaces.    
 
 
 
Figure 2.6 Soft surface diagram 
 
 
 29
 
Figure 2.7 Hard surface diagram 
Soft surface 
Figure 2.6 shows the classic soft surface formed by transverse corrugated metal strips. 
A soft surface can stop surface wave propagation of any polarization thus is typically used 
for reduction of cross-polarization and generating symmetrical radiation patterns for 
corrugated horn antennas. However, since the thickness of the classic soft surface has to be 
a quarter wavelengths, it is very costly to make and limited in applications. This issue can 
be solved by dielectric loaded soft surfaces. 
Hard surface 
Figure 2.7 shows the classic hard surface formed by longitudinal dielectric filled 
corrugated metal straps. A hard surface can enhance the surface wave propagation on the 
surface with any polarization, and once rolled up to form a wave guide, the TEM wave 
mode will be supported. A hard surface horn antenna can be formed if the outlet of the 
wave guide is broadened, which is one of the most important applications of hard surfaces.  
 
 30
2.6.4.Electromagnetic Bandgap Structures 
The electromagnetic Bandgap (EBG) structure, analogous to the Photonic Bandgap 
(PBG) structure or photonic crystal in the RF and microwave domain, was originated by Eg303g289
Yablonovitch from Bell labs and S. John from Princeton University independently in 1987 
[17, 18] .  
Both electrons and photons have wave?particle duality, and obey Schr?dinger?s 
equation and Maxwell?s equations [19]. Within crystals, the periodic potential around the 
atoms causes discretization of electron energy, dividing the energy bands into pass bands 
and stop bands. Meanwhile, it is possible to create an artificial crystal with periodic 
dielectric constants so that when light passes through it photon energy may separate into a 
pass band and a stop band as well. For the photon, its energy is proportional to frequency 
squared, so stop band means photon propagation is prohibited within certain frequency 
bands. This type of artificial crystal is named as the Photonic Crystal and the band stop 
feature is named PBG.  
Since the EM wave is the same as photons (accordance with Maxwell Equation), PBG 
can be reproduced in RF and microwave frequencies, so the structure thus is named as 
EBG structure. EBG structure in general is formed by a series of unit cells periodically 
arranged inside a substrate material. Proper selection of substrate material, unit cell 
structure, and unit cell arrangement can result in a band stop feature to surface waves with 
arbitrary incident angles and polarizations [20].  
In 1987, E. Yablonoviteh first proved the band stop feature of 3D PBG through 
experiment. 1995 J. Joannopoulos in his book explained properties and applications of 1, 2, 
 
 31
3D photonic crystals in detail, and proved that Diamond/BCC structure can provide 
complete band stop characteristic over three dimensions [19]. 
EBG structures can be applied in varies fields including microwave circuit, antenna, 
and optical devices. Its band stop characteristic over RF made it possible to eliminate or 
reduce surface EM waves to reduce coupling between devices, and improve RF device 
performance.  
EBG can be categorized by the axis dimensions of the unit cell arrangement as shown 
in Figure 2.8.  
   
Figure 2.8 One, two, and three dimensional EBG structures 
Different dimensional arrangement results in different properties when interacting 
with surface waves. 1-D EBG, identical to corrugated surface, is the easiest to make and is 
mostly applied in corrugated antenna and waveguide designs. While 2-D and 3-D EBG 
require more sophisticated manufacturing processes and are mostly used as AMC/AEC in 
antenna reflection surfaces or microwave circuits. 
Based on the materials used, EBG can also be categorized as dielectric EBG, metal 
EBG, and hybrid EBG. The 2-D and 3-D dielectric EBG are widely used as patch antenna 
substrates, suppressing the surface wave on the patch or ground plane thus improving 
antenna gain and reducing side and back lobes. Metal EBGs are usually etched on the 
 
 32
ground plane and used as microwave transmission lines or in circuit bandstop filters. 
Hybrid EBG i.e. Sievenpiper mushroom or coplanar EBG also finds application in 
microstrip antenna ground planes for surface wave reduction.  
 
2.7. Artificially Magnetic Conductor Basics 
PEC and PMC are very important concepts in classic EM theory. Because the PEC 
boundary condition requires the tangential E-field to be zero, the reflected wave and the 
incident wave are always 180g953 out of phase. This property determines when using metal as 
reflective surface to improve antenna gain, the antenna and the reflective surface must be a 
quarter wavelength apart. If not, the reflected wave E-field will cancel out the radiated 
wave E-field and reduce antenna efficiency, which is a constraint on reducing antenna 
dimensions. According to the reciprocity of EM theory, if plane wave is incident on the 
PMC surface, the reflected wave will be in phase with the incident wave, thus making PMC 
an ideal choice for an antenna reflection surface. However, PMC do not exist in nature and 
left PMC exists only in EM theory and an ultimate goal for EM researchers.  
In the 1960s, the emergence of the corrugated surface has made in phase reflection 
possible. However, corrugated surfaces require a quarter wavelength depth to behave like 
PMC, making it less attractive to the solution of the antenna reflective surface. In 1999, D. 
Sievenpiper from UCLA suggested a novel EBG structure named High Impedance Surface 
(HIS). The HIS is based on microstrip substrate, is intrinsically low profile and light weight, 
and has in phase reflection characteristic just like PMC. The discovery of HIS has attracted 
much interest from the EM society, and was named Artificial Magnetic Conductor, a 
 
 33
subcategory of Artificial Electromagnetic Material.  For convenience purposes, AMC will 
be used throughout this discussion. The AMC structure suggested by D. Sievenpiper is 
relatively simple. It consists of an array of metal protrusions on a flat metal sheet arranged 
in a two-dimensional lattice which are connected to the continuous lower conductor by 
vertical posts [21]. Due to its shape, the structure is also known as the ?Sievenpiper 
mushroom?. The Sievenpiper mushroom is a type of EBG periodic structure, however, the 
bandgap mechanism is different from PBG?s Bragg diffraction mechanism, which requires 
the unit cell dimension be one half of the corresponding wavelength. The AMC unit cell is 
much less than a wavelength and has a resonator structure, which makes it a very practical 
solution to antenna reflective surface problems. 
 
 
 
Figure 2.9 Sievenpiper mushroom structure and equivalent circuit [21] 
 
 34
The AMC structure developed by Dg303g289Sievenpiper was first called HIS because AMC 
has high surface impedance at certain frequency range. From the equivalent circuit shown 
in Figure 2.9, the equivalent circuit suggests a shunt LC resonant circuit, where the gap 
between patches are coupled to provide capacitance while patch, ground, and plated vias 
provide equivalent inductance. The surface impedance can be written as 
g1852 = g1862g2033g18381?g2033g2870g1838g1829 (2-66) 
When surface wave frequency is equal or close to the resonant frequency, the surface 
will have high impedance and prevent surface wave propagation.  
To understand the mechanism of the AMC, first we have to look back at corrugated 
surfaces. The corrugated slots can be considered as a parallel-plate transmission line 
terminated with shorted load, as shown in Figure 2.10. Assume the plane wave incident 
along the ?x direction, so reflection occurs at the discontinuity at x=0. Let g1831g3036 and g1834g3036 
represent the incident field, g1831g3045 and g1834g3045 represent reflected field vectors respectively, the 
incident and reflected fields overlap and form the standing wave: 
g1831(g1876)=g1831g3036g1857g3037g3038g3051 +g1831g3045g1857g2879g3037g3038g3051 
(2-67) 
g1834(g1876)=g1834g3036g1857g3037g3038g3051 ?g1834g3045g1857g2879g3037g3038g3051uni0009
 
 35
 
 
 
Figure 2.10 Corrugated surface analysis 
Wave impedance of the transmission line g2015 can be written as the ratio of E and H 
field components:  
g2015=g3628g1831g3036(g1876)g1834
g3036(g1876)
g3628=g3628g1831g3045(g1876)g1834
g3045(g1876)
g3628 (2-68) 
 
The input impedance at x=0, can be written as  
g1852= g1831(g1876)g1834(g1876) (2-69) 
And since the boundary is a short, g1852(0)=0, plug into (2-69) we get 
 
 36
g1831g3045(0)=?g1831g3036(0) 
g1834g3045(0)=?g1834g3036(0) 
(2-70) 
The phase difference between incident and reflection wave can be written as: 
g2038=g1835g1865g3420g142g144uni0009(g1831g3036g1831
g3045
)g3424=g1835g1865g3420g142g144uni0009(g1852g3046 ?g2015g1852
g3046 +g2015
)g3424 (2-71) 
When g2015g1575g1852g3046, phase difference is g3399g2024, the surface can be considered as PEC. When 
g2015g1576g1852g3046, the phase difference is 0, the reflected and incident wave are in phase, so the 
surface can be considered as PMC. In other words, low impedance surface is equivalent to 
PEC, while high impedance surface is equivalent to PMC. In reality, good conductors can 
realize g3399g2024 phase difference over entire frequency range, but AMC can only be realized in 
phase reflection in a very limited frequency band. As a result, the AMC can be considered 
as PMC only in a limited bandwidth. In general, bandwidth of AMC is defined by the 
frequency range where uni007Cg2038uni007Cg3407g2024/2, as shown in Figure 2.11 [21]. 
Combining (2-67) (2-68) (2-69), we can also get 
g1852(g1856)= g1831(g1856)g1834(g1856)= g1831g3036(g1857
g3037g3038g3031 ?g1857g2879g3037g3038g3031)
g1834g3036(g1857g3037g3038g3031 +g1857g2879g3037g3038g3031)=g1862g2015tg131g144(g1863g1856) (2-72) 
From (2-72), when the depth of slot g1856 g3407g2019/4, Z(d) is positive (inductive) and 
supports the TM mode surface wave only. When g1856=g2019/4, g1852(g1856)??, all surface wave 
modes are suppressed thus the EM bandgap is formed. When g1856g3408g2019/4, Z(d) is negative 
(capacitive), and only the TE mode surface wave is supported. This can be shown in the 
dispersion diagram in Figure 2.12 [21]. 
 
 37
  
Figure 2.11 Impedance and phase of a parallel resonant circuit [21] 
 
Figure 2.12 Dispersion diagram for bound surface waves [21] 
The above analysis is applicable to the surface wave bound to the surface only. For the 
complete dispersion diagram, the leaky wave mode must be taken into consideration. From 
Figure 2.12, the TE band begins as a branch out of the light line at the resonance frequency, 
which is contrary to wave physics. The TE waves that lie to the left of the light line must 
exist and the only explanation is radiative leaky TE waves.  
The radiation from these leaky TE modes can be modeled as a resistor in parallel with 
the AMC and the modified the equivalent circuit model is shown in Figure 2.13. The 
circuit equations are satisfied at the resonant frequency. Therefore, the leaky modes that 
 
 38
exist to the left of the light line can be represented by a horizontal line as shown in Figure 
2.14. 
 
Figure 2.13 Circuit model of leaky TE waves [21] 
 
Figure 2.14 Complete dispersion diagram, including leaky modes [21] 
A simulated band structure for a two-layer AMC is shown in Figure 2.15. The band 
gap is clearly shown between the lowest TM and TE modes.  
 
Figure 2.15 Surface wave band structure for a two-layer AMC [21] 
  
 
 39
2.8. Frequency Selective Surface Basics 
One of the major applications of AES is to make Frequency Selective Surface (FSS).  
The concept of FSS was first suggested by physicist David Rittenhouse over 200 years ago 
[22]. FSS is typically a single layer or multi-layer planar structure with 2-D periodic 
elements placed on top of dielectric backing. There are generally two types of FSS: the 
capacitive FSS (patch-type) and the inductive FSS (aperture-type) as shown in Figure 2.16. 
FSS has a frequency selecting characteristic which is similar to that of passive EM wave 
filters. At resonating frequencies, it can be totally reflective (capacitive FSS) or totally 
transparent (inductive FSS) to the incoming wave.  
 
Figure 2.16 Capacitive and inductive FSS 
In general, patch-type FSS is transparent at low frequencies but reflective at high 
frequencies, which is similar to low pass filters, while aperture-type FSS is the opposite of 
patch-type and similar to high pass filters. For non-dielectric backed FSS, the frequency 
response curves of patch-type and aperture-type are complimentary, in accordance with 
Babinet?s principle [23]. 
 
 40
Theoretically, scattering of the EM wave will occur for any planar surface with 
periodically arranged patches or apertures. The scattering characteristic depends on the 
form of array element, distance between elements, and dielectric layer properties [23]. The 
periodic structure can be optimized for any particular application with certain 
characteristics by designing the elements as well as the way they are placed in the 
periodic array. When the form of the 2-D array is determined, resonance will occur at a 
certain frequency when the incident EM wave hits the surface. In free space, the resonance 
usually occurs when the dimension of the element is an integer number of half wavelengths 
of the incident wave. The scattering is strongest at the first harmonic. As wavelength 
become smaller, higher order harmonics will occur with less energy scattered, until 
scattering reaches zero [22, 23].  
 
Figure 2.17 Coordination set up of the FSS problem 
The research on FSS theory began in the 1960s. With decades of development, several 
theories have been suggested to analyze FSS properties. Before we formulate the FSS 
 
 41
scattering problem, several assumptions of the FSS have to be made. In general, FSS is 
assumed to have a 2-D periodic distribution of elements, the elements are infinitely thin 
PEC patches or apertures, and the incident wave is a homogenous plane wave. The 
coordination is set up according to Figure 2.17, and the FSS problem set up is shown in 
Figure 2.18. 
 
Figure 2.18 Problem set up of FSS 
In the same way we treated antenna problems, we can use auxiliary functions to solve 
FSS problems. Let g1784 be the induced surface current density on the FSS and g1775 be the 
magnetic vector potential generated by g1784. In general, due to the planar nature of the FSS, 
the induced surface current g1784 is nonzero only in the transverse direction [22].  
Assuming the time convention is g1857g1876g1868uni0009(g1862g2033g1872), the transverse (to z) components of g1775 
and g1784 should have the following relationship:  
 
 42
g3428g1827g3051(g1876,g1877)g1827
g3052(g1876,g1877)
g3432=g2163g3368(g1876,g1877)g1499g3428g1836g3051(g1876,g1877)g1836
g3052(g1876,g1877)
g3432
 
(2-73) 
Where 
g2163g3368 =exg146uni0009(?g1862g1863g2868g1870)4g2024g1870 g2165g3367, g1870=g3493g1876g2870 +g1877g2870
 
(2-74) 
g1863g2868 =g1858g1870g1857g1857uni0009g1871g1868g1853g1855g1857uni0009g1875g1853g1874g1857uni0009g1866g1873g1865g1854g1857g1870 
g2165g3367=g1861g1856g1857g1866g1872g1861g1872g1877uni0009g1872g1857g1866g1871g1867g1870   
g1499uni0009g1861g1871uni0009g1872?g1857uni0009g1855g1867g1866g1874g1867g1864g1873g1872g1861g1867g1866uni0009g1867g1868g1857g1870g1853g1872g1867g1870 
Next, the transverse components of the scattered electric field g2161g3046 in the plane of the 
screen, i.e., at z = 0, can be expressed in terms of the transverse components of the vector 
potential A: 
g3428g1831g3051
g3046
g1831g3052g3046g3432=
1
g1862g2033g2020g2868
g1743
g1742g1742
g1742
g1741g2034
g2870
g2034g1876g2870 +g1863g2868
g2034g2870
g2034g1876g2034g1877
g2034g2870
g2034g1876g2034g1877
g2034g2870
g2034g1877g2870 +g1863g2868g1746
g1745g1745
g1745
g1744
g3428g1827g3051g1827
g3052
g3432
 
(2-75) 
In order to take full advantage of the periodicity of the geometry, it is convenient to 
rewrite the above equation in the spectral domain [24, 25]. Fourier transform of (2-75) 
gives: 
g4680g1831
g3364g3051g3046(g2009,g2010)
g1831g3364g3052g3046(g2009,g2010)g4681=
1
g1862g2033g2020g2868g4680
g1863g2868g2870 ?g2009g2870 ?g2009g2010
?g2009g2010 g1863g2868g2870 ?g2010g2870g4681g2163g3368g4680
g1836uni0305g3051(g2009,g2010)
g1836uni0305g3052(g2009,g2010)g4681 (2-76) 
Where 
g2163g3368 = ?1
2g3493(g1863g2868g2870 ?g2009g2870?g2010g2870)
g2165g3367
 
(2-77) 
g2009 and g2010 are the transform variables corresponding to the x and y coordinates, 
respectively.  
 
 43
To take advantage of the periodicity of FSS, we can implement the Floquet Modal 
analysis.  Since FSS is assumed to be infinitely periodic in both x and y directions, the 
Fourier transform of the induced current J is nonzero only for an infinite set of discrete 
values of the spectral variables g2009 and g2010. These values, designated here as g2009g3040g3041 and g2010g3040g3041, 
are associated with the Floquet harmonics for the doubly periodic screen, named after the 
nineteenth century French mathematician Floquet who introduced the concepts of these 
harmonics in the context of his work on the periodic solution of differential equations. The 
g2009g3040g3041 and g2010g3040g3041 can be expressed as: 
g2009g3040g3041 =2g2024g1865g1853 +g1863g2868g149g139g144g2016g133g145g149g2038
 
(2-78) 
g2010g3040g3041 = 2g2024g1866g1854g149g139g144g563?2g2024g1865g1853 g133g145tg563+g1863g2868g1871g1861g1866g2016g149g139g144g2038uni0009 (2-79) 
 Where g2016 and g2038 are the angles of the incident plane wave, and according to Figure 
2.18, g1853 is g1846g3086g3117 and g1854 is g1846g3086g3118.  
The inverse Fourier transform of (2-76) and the boundary condition g2161g4652g4652g1318g3046 =?g2161g4652g4652g1318g3036 on the 
PEC surface of FSS obtains the following [24]: 
?g4680g1831g3051
g3036(g1876,g1877)
g1831g3052g3036(g1876,g1877)g4681=
1
g1862g2033g2020g2035g2868g3533g3533g4680
g1863g2868g2870?g2009g3040g3041g2870 ?g2009g3040g3041g2010g3040g3041
?g2009g3040g3041g2010g3040g3041 g1863g2868g2870?g2010g3040g3041g2870 g4681g3041g3040
?g2163g3368(g2009g3040g3041,g2010g3040g3041)g2166uni033F(g2009g3040g3041,g2010g3040g3041)g1857g3037g3080g3288g3289g3051g2878g3037g3081g3288g3289g3052uni0009
=g3533g3533g4680g1833
uni0305g3051g3051 g1833uni0305g3051g3052
g1833uni0305g3052g3051 g1833uni0305g3052g3052g4681g3041g3040 g4680
g1836uni0305g3051(g2009g3040g3041,g2010g3040g3041)
g1836uni0305g3052(g2009g3040g3041,g2010g3040g3041)g4681g1857
g3037g3080g3288g3289g3051g2878g3037g3081g3288g3289g3052
 
(2-80) 
Equation (2-80) can then be solved with Galerkin?s procedure [24]. Once the induced 
currents have been solved, other quantities of practical interest, such as reflection and 
 
 44
transmission coefficients for the dominant harmonics, as well as the scattering matrix, can 
be readily calculated. A practical approach to solving the above equations under various 
conditions of illumination is to use FEM simulation programs on computers. 
The coplanar AMC can also be considered as an FSS with the ground plane. Such an 
AMC can be formed by using capacitive FSS coupled with the ground plane utilizing the 
reflection property of the capacitive structure (patch-type). The structure can also be 
considered as a Sievenpiper mushroom structure without vias, thus has similar phase 
reflection property as the Sievenpiper mushroom. Because the metal patches are separated 
from each other on the capacitive FSS, current cannot flow across the gap between the 
patch elements thus surface wave propagation is prohibited at resonant frequencies and act 
as AMC.  
2.9.Important Parameters of Antennas  
2.9.1.Input impedance 
The input impedance of an antenna is the impedance presented by an antenna at its 
terminals or the ratio of the voltage to the current at the pair of terminals or the ratio of the 
appropriate components of the electric to magnetic fields at a point [2].  Hence the 
impedance of the antenna can be written as: 
g1852g3036g3041 =g1844g3036g3041 +g1862g1850g3036g3041
 
(2-81) 
Where Zin is the antenna impedance at the terminals 
Rin is the antenna resistance at the terminals 
Xin is the antenna reactance at the terminals 
 
 45
2.9.2.Voltage Standing Wave Ratio 
Figure 2.19 shows an equivalent circuit of transmitting antenna.  For an antenna to 
radiate efficiently, the power transferred from the transmitter to the antenna must be 
maximized.  Maximum power transfer can only occur when the impedance of the antenna 
(Zin) is matched to that of the transmitter (ZS).   
When such a matching condition is not satisfied, some of the power will be reflected 
to the transmitter.  This could cause standing waves, which can be characterized by the 
parameter Voltage Standing Wave Ratio (VSWR). 
 
 
Figure 2.19 Equivalent circuit of transmitting antenna 
The VSWR can be expressed as [26]: 
1
1VSWR
+ ?=
? ?
 
(2-82) 
in Sr
i in S
Z ZV
V Z Z
?? = =
+ uni0009 (2-83) 
 
 46
 Where ? is called the reflection coefficient, Vr is the amplitude of the reflected wave, 
and Vi is the amplitude of the incident wave. 
The VSWR represents the impedance mismatch between the transmitter and the 
antenna.  The higher the VSWR, the greater the mismatch will be.  The theoretical 
minimum VSWR which corresponds to a perfect match is unity.  A practical antenna 
design should match an input impedance of 50uni2126 which is the impedance of the coaxial 
cable. 
2.9.3.Return Loss 
The Return Loss (RL) is a parameter similar to VSWR.  It is a parameter indicating 
the amount of power that is lost to the load and does not return as a reflection.  As 
explained in VSWR section, reflected waves lead to the formation of standing waves when 
the transmitter and antenna impedance do not match.  So the RL is a parameter indicating 
how well the transmitter and antenna matches.  RL can be expressed as [26]: 
1020logRL =? ?  (dB)
 
(2-84) 
When the transmitter and the antenna are perfectly matched, ?=0 and RL=-g286which 
means no power is reflected.  On the other hand, when ?=1, RL=0dB, which means all 
input power is reflected.  For practical antenna applications, a VSWR of 2 is acceptable, 
this equivalent to a RL of -9.5dB. 
 
 47
2.9.4.Radiation Pattern 
In the field of antenna design, radiation pattern refers to the directional (angular) 
dependence of radiation from the antenna [2].  The radiation pattern is directly related to 
the surface current and the radiation mechanism of the antenna.  The radiation pattern is 
usually presented in polar form with a dB strength scale.  Patterns are normalized to the 
maximum graph value, 0 dB, and directivity is given for the antenna.  The plot is typically 
represented as a three-dimensional graph as shown in Figure 2.20. 
 
Figure 2.20 Radiation pattern of antenna 
 
2.10.Summary  
This chapter first introduced the fundamental EM theories including the Maxwell 
equations and EM radiation theory. The general routine of solving EM radiation problem 
was given. Then we introduced the fundamental theory of MSA with transmission line 
model and cavity model. Transmission line model is easy to understand and easy to use, but 
 
 48
lacked the physical details of how MSA works. The cavity model is stricter than the 
transmission line model, which offers greater insight into the radiation mechanism of MSA. 
After that we introduced the fundamental theories of surface wave, AES and AMC. And 
then FSS was introduced as well as a general routine to solve FSS problems. Lastly the 
definitions of a few important antenna parameters were introduced. Overall, this chapter 
serves a basis for the research work that follows. 
 
 
g3
 
 
49 
 
 
 
Chapter 3.Numerical Modeling of Electromagnetic Textiles 
 
3.1.Numerical Modeling Methods 
Among the numerical modeling methods, FEM, MOM, and FDTD are the most 
popular ones.  The fundamental concept of FEM is based on the decomposition of the 
domain and its corresponding boundary condition into a finite number of subdomains 
(elements) for which the systematic approximate solution is constructed by applying the 
variational methods [27]. The assumed approximating functions within each element can 
be expressed by the unknown field variables. These functions are defined in terms of the 
values of the field variables at the points along the element boundaries and connecting 
adjacent elements. The discretize procedure greatly reduces the requirement on the 
computer as well as the calculation time, which makes the method a valuable and 
practical analysis tool for the solution of boundary, initial, and eigenvalue problems.  
In order to analyze antenna problems, the following procedure can be followed. First, 
establish antenna models by using approximations or empirical formula, calculating the 
initial design parameters. Second, define metallic, vacuum, dielectric materials and their 
corresponding properties. Next, define boundary conditions i.e. PEC, PMC, radiation 
boundary, symmetry planes, and excitation ports i.e. discrete ports, wave guide ports, 
plane wave sources. Then, define calculation parameters for optimizing system resource 
 
50 
and improving calculation speed and efficiency. Finally, post processing allows analysis 
for antenna parameters such as S parameters, field distribution, energy distribution etc.  
Meanwhile, in order to analyze FSS problems, an alternative procedure has to be 
followed. First, establish FSS models by calculating the initial design parameters of a unit 
cell with upper and lower PML layers. Second, define materials, same as antenna 
simulation. Next, for boundary conditions, besides PEC, PMC, periodic boundaries and 
PMLs must be defined. Calculation parameters and post processing are the same as 
antenna simulations. 
 In order to shorten the research time required, we used commercial FEM software 
package HFSS from Ansys for CAD and EM field analysis. (See Figure 3.1 for the 
interface of HFSS) Ansys HFSS is a mainstream FEM based solver package for EM 
structures from Ansys Corporation.  The acronym originally stood for High Frequency 
Structural Simulator.  It is one of the most popular and powerful EM simulation 
softwares, and among one of the earliest commercialized. Due to its highly mature 
algorithm, high simulation precision, and relatively high speed, it has been widely 
utilized in scientific research, technical designs, as well as other applications. When 
using HFSS for numerical design, the calculation precision and time is highly dependent 
on the size of the object and its mesh sizes. The finer meshes will result in more precise 
results, but requires longer computing time as well as larger RAM. As a result, during 
early simulation stages, it places high requirements on computers.    
 
51 
 
Figure 3.1 Interface of Ansoft HFSS 
 
 
3.2.Numerical Modeling of Woven Antennas 
3.2.1.Introduction 
Over the past decades, woven antennas have drawn significant attention from 
researchers for their intrinsic flexibility, conformity, mount-ability, low manufacturing 
cost, and ease of fabrication. Various types of antennas made of textile materials have been 
developed during the past few years [28-35]. Most of these antennas are designed based on 
the assumption that woven antennas have the same radiation characteristic as microstrip 
antennas (MSA) and are designed and analyzed using conventional the MSA transmission 
line model.  However, such an assumption has to be investigated with care because there 
are intrinsic differences between conductive woven conductive structure and PEC 
boundary. By introducing different weave patterns into the radiating patch, the woven 
 
52 
antenna has the capability of eliminating the fundamental mode of MSA while operating 
under higher order modes, with its performance changed dramatically from MSA. 
The goal of this research was to reveal the effect of weave arrangement and crimp on 
the radiation mechanism of woven antennas. In this paper we fabricated a woven antenna 
using plain weave method and compared it to reference microstrip antenna (MSA).  Prior 
to the antenna fabrication we also carried out finite element method (FEM) simulation 
using Ansoft High Frequency Simulation Software (HFSS) to confirm our findings.   
The resonance characteristics of the antennas under test (AUT) are measured by a 
vector network analyzer.  The radiation patterns of the AUTs are measured in a 
microwave anechoic chamber.  The impacts of the plain weave configuration on radiation 
modes are discussed.   
3.2.2.Materials 
3.2.2.1.Non-conductive Yarns 
The textile material we chose for this research is a generic polypropylene yarn 
acquired from Belton Industries.  The yarn has a width of 2 mm and thickness of 0.1 mm.  
The standard configuration of the textile fabric is 9 picks per cm of 1000 denier 
polypropylene monofilament yarn according to qualifications for the American 
Association of State Highway & Transportation Officials (AASHTO) standardized Class 1 
Stabilization standards. 
 
53 
3.2.2.2.Conductive Wires 
In order to study the impact of weave configuration on antenna performance, a 
conductive wire with the same dimension of the non-conductive yarn was carefully chosen.  
The wire we chose was designed to be used as solar cell interconnecting wires 
(photovoltaic ribbon wire) acquired from Ulbrich Industries. It was a double side coated 
ribbon wire with 62% tin 36% lead and 2% silver soldering coating of 0.001-0.0015mm 
per side.  The conductive wire was 2 mm wide and 0.1 mm thick, which is the same as the 
non-conductive yarn. 
3.2.2.3.Dielectric Substrate 
The substrate provides the dielectric between the antenna patch and the ground plane.  
The general requirements for the substrate include low electrical loss, homogenous 
thickness, low moisture absorption, and uniform electrical properties over frequency.  For 
our proposed application, chemical resistance and resilience are also important.  
Accordingly, the dielectric substrate material we chose was a 1.72mm thick Rogers 
RT5880 high frequency laminate. It has ?r of 2.2 with a loss tangent (tan?) of 0.0009. 
3.2.3.Antenna Design 
In this study, higher order modes of the MSA are studied.  To describe the higher 
order resonances, a cavity model in which the MSA resembles dielectric-loaded cavities 
needs to be used [2].  In this model, the MSA is defined as a cavity with length of L, width 
of W, and height of h.  Since the height-to-width ratio is usually very small, the cavity is 
considered generating only transverse current density Jt at the bottom and top surfaces 
 
54 
underneath the patch, and the E field inside the cavity is considered constant across the 
patch.  The fringing field close to the edges of the patch are approximated as constant and 
normal to the surface of the patch. As a result, no TE mode will be generated in the cavity 
mode.  The side walls are approximated as having no tangential magnetic field component 
and thus are modeled as perfect magnetic conducting (PMC) walls.  The resulting cavity 
model is defined by perfect electrically conducting (PEC) boundaries in the yz plane 
separated by h, PMC boundaries in the xz plane separated by W, and PMC boundaries in 
the xy plane separated by L, as shown in Figure 3.2, the yellow color represents conductive 
material, the gray color represents non-conductive material, as is the convention 
throughout the paper.  The resonant frequencies predicted by the cavity model are given 
by 
(g1858g3045)g3040g3041g3043 = g2869g2870g3095uni221Ag3091g3084g3495(g3040g3095g3035 )g2870+(g3041g3095g3013 )g2870+(g3043g3095g3024)g2870 
 
(3-1) 
 
Figure 3.2 Boundary conditions of MSA cavity mode 
 
 
55 
The radiation mode of the MSA depends on the dimension of the radiating patch. For 
different cases of L, W, h arrangements, usually the fundamental and secondary modes are 
among uni0054uni004Dg2868g2869g2868g2934 , uni0054uni004Dg2868g2868g2869g2934 , uni0054uni004Dg2868g2870g2868g2934 , and uni0054uni004Dg2868g2868g2870g2934  as shown in Figure 3.3, respectively.   
  
Figure 3.3 Resonance modes of MSA (a)uni0009uni0054uni004Dg2868g2869g2868g2934 , (b)uni0009uni0054uni004Dg2868g2868g2869g2934 , (c)uni0009uni0054uni004Dg2868g2870g2868g2934 , and (d)uni0054uni004Dg2868g2868g2870g2934 . 
The parameters of MSA is designed based on the equations (3-2) and (3-3) assuming 
uni0054uni004Dg2868g2869g2868g2934  as the fundamental mode, taking into account the fringing effects 
g1849 = g2869g2870g3033
g3293g3493g3084g3116g3091g3116
g3495 g2870g3084
g3293g2878g2869
 
 
(3-2) 
g1838 = 12g1858
g3045g3493g2013g3045g3032g3033g3033g2013g2868g2020g2868
?2uni0394g1838uni0009 (3-3) 
 Where uni0066g2928 is the fundamental uni0054uni004Dg2868g2869g2868g2934  mode resonance frequency.  The width W 
determines the input impedance of the radiating patch and is carefully chosen so that one of 
the yarns in the warp direction can be used as quarter wave transformer to connect the 
patch to the 50uni2126 transmission line. 
As for the antenna feed structure, we used a 50uni2126 microstrip transmission line and a 
microstrip quarter wave transformer in series to match the impedance of the microstrip 
patch to a SubMiniature version A (SMA) coaxial cable.  The widths of the transmission 
line and microstrip transformer were computed using the microstrip transmission line 
formulas given in Balanis [2].  The final parameters of the MSA design are listed in Table 
3-1, and the resulting scheme of MSA is shown in Figure 3.4 Design scheme of MSA 
 
56 
 
Table 3-1 Design summary of MSA 
Microstrip ?/4 Transformer Feed Structure Substrate 
W=102.7mm Wqw=2mm W50=5.24mm Wsub=190mm 
L=58mm Lqw=32.9mm L50=10mm Lsub=140mm 
 
 
 
Figure 3.4 Design scheme of MSA 
3.2.4.Antenna Manufacturing 
The MSA is fabricated with copper single clad RT5880 board and adhesive copper 
foils.  To fabricate the woven antenna, a plain weave process is carried out on a wooden 
loom, which is normal practice for textile product prototype manufacturing. 
Since it is easier to manipulate the weft yarns, the radiating patch forming wires are 
woven from the weft direction.  Before the weaving begins, the warp yarn in the middle is 
replaced with a conductive wire for antenna feed structure and the conductive wires are 
inserted as weft yarns.  The resulting scheme of the radiating patch of the MSA and woven 
antenna are shown in Figure 3.5 and Figure 3.6 .  After the radiating patch is woven, the 
 
57 
excessive yarns outside the radiating patch are trimmed off, and the dielectric substrate is 
attached to the patch using adhesives.  Photographs of the MSA and woven antenna are 
shown in Figure 3.7 and Figure 3.8 respectively. 
 
Figure 3.5 MSA design scheme. 
 
Figure 3.6 Woven antenna design scheme. 
 
58 
 
Figure 3.7 Picture of fabricated MSA. 
 
Figure 3.8 Picture of fabricated woven antenna. 
 
59 
3.2.5.Simulation and Measurement Results 
In order to validate the antenna performance, we conducted full-wave FEM 
simulations using Ansoft HFSS. The antenna model of reference MSA is established with 
the 3d modeler of HFSS. The MSA model is relatively simple: for the radiation patch it has 
a feed structure, quarter wave transmission line, and square patch with dimensions listed in 
Table 3-1, plus dielectric substrate and ground plane. A waveguide port is added 
perpendicular to the patch as radiation source. An air box with radiation boundary is 
established to enclose the entire structure.  
To confirm the simulation result, first we measured the S11 return loss of the woven 
antenna and MSA to find out possible correspondent radiation modes.  A HP8753C vector 
network analyzer is used for S11 measurement.  The data is extracted to a laptop computer 
using an Agilent 82357 USB/GPIB interface and Agilent Intuilink data capture software.  
First the simulated S11 of MSA is compared with the measured data to find out the 
corresponding resonances as shown in Figure 3.9. The measured S11 of woven antenna 
and MSA are shown in Figure 3.10. 
 
 
 
60 
0.0 0.5 1.0 1.5 2.0 2.5
-40
-30
-20
-10
0
 
 
Re
tur
n L
os
s [
dB
]
Frequency [GHz]
 Simulated MSA
 Measured MSA
 Figure 3.9 Simulated (solid) and measured (dashed) S11 return loss of MSA 
0.0 0.5 1.0 1.5 2.0 2.5
-40
-35
-30
-25
-20
-15
-10
-5
0
 
 
Re
tur
n L
os
s (
dB
)
Frequency (GHz)
 Measured Woven Antenna
 Measured Reference MSA
 Figure 3.10 Measured S11 of woven antenna (solid) and MSA (dashed) 
In order to study the effect of crimp on radiation characteristics, a woven antenna and 
a grating MSA are also modeled separately. The woven antenna is modeled with analytical 
curve sweeping, and the wires are modeled as a sine function of y in z direction with 
uni0054uni004Dg2868g2869g2868g2934  uni0054uni004Dg2868g2868g2870g2934  
uni0054uni004Dg2868g2868g2870g2934  uni0054uni004Dg2868g2869g2868g2934  
 
61 
0.1mm spacing between the wires. The lengths of wires are set the same as width of 
reference MSA, and the number of wires is chosen carefully to match the patch size of 
reference MSA. For the grating MSA, the patch is modeled as individual microstrips with 
the same size as the conductive wires in woven antenna and 0.1mm spacing in between, we 
call it grating MSA for convenience. The simulation models and the simulated S11 return 
loss are shown in Figure 3.11 and Figure 3.12 respectively. To confirm the simulation 
result, a grating MSA is fabricated as shown in Figure 3.13 and the measured S11 of the 
grating MSA comparing with woven antenna is shown in Figure 3.14.  
 
Figure 3.11 Simulation model of (a) grating MSA and (b) woven antenna 
 
 
62 
0.0 0.5 1.0 1.5 2.0 2.5
-25
-20
-15
-10
-5
0
 
 
Re
tur
n L
os
s (
dB
)
Frequency (GHz)
 Simulated Grating MSA
 Simulated Woven Antenna
 
Figure 3.12 Simulated S11 of woven antenna (solid) and grating MSA (dashed) 
 
 
Figure 3.13 Picture of fabricated grating MSA. 
uni0054uni004Dg2868g2868g2870g2934  
 
63 
 
Figure 3.14 Measured S11 of woven antenna (solid) and grating MSA (dashed) 
Next, we loaded the AUTs onto the Desktop Antenna Measure System (DAMS) in the 
anechoic chamber to acquire radiation patterns.  An L-band horn antenna is used as source 
antenna and the HP8753C is tuned into continues wave mode and act as the power source.  
At the receiving end, a DAMS x100 turn table system is used as the testing platform.  The 
AUT is connected to a power amplifier and then to an Agilent 34401A multi meter for 
signal reading.  The data is collected by DAMS software for further processing.  The 
entire experiment is set up in the anechoic chamber to minimize reflection and external 
interferences.  
0.0 0.5 1.0 1.5 2.0 2.5
-30
-25
-20
-15
-10
-5
0
 
 
Re
tur
n L
os
s (
dB
)
Frequency (GHz)
 Measured Woven Antenna
 Measured Grating MSA
uni0054uni004Dg2868g2868g2870g2934  
 
64 
0
30
60
90
120
150
180
210
240
270
300
330
-40
-30
-20
-10
0
-30
-20
-10
0
 
 
0
30
60
90
120
150
180
210
240
270
300
330
-40
-30
-20
-10
0
-30
-20
-10
0  
Figure 3.15 Simulated (solid) and measured (dashed) radiation pattern of MSA uni0009uni0054uni004Dg2868g2869g2868g2934  mode. (a) XZ 
plane. (b) YZ plane.  
0
30
60
90
120
150
180
210
240
270
300
330
-40
-30
-20
-10
0
-30
-20
-10
0  
0
30
60
90
120
150
180
210
240
270
300
330
-40
-30
-20
-10
0
-30
-20
-10
0  
Figure 3.16 Simulated (solid) and measured (dashed) radiation pattern of MSA uni0054uni004Dg2868g2868g2870g2934  mode. (a) XZ 
plane. (b) YZ plane. 
-40
-30
-20
-10
0
0
30
60
90
120
150
180
210
240
270
300
330
-30
-20
-10
0
-40
-30
-20
-10
0
0
30
60
90
120
150
180
210
240
270
300
330
-30
-20
-10
0
 
Figure 3.17 Simulated (solid) and measured (dashed) radiation pattern of woven antenna uni0054uni004Dg2868g2868g2870g2934  mode. 
(a) XZ plane. (b) YZ plane. 
 
65 
The simulated and measured radiation patterns of MSA uni0054uni004Dg2868g2869g2868g2934  mode, uni0054uni004Dg2868g2868g2870g2934  mode, 
and the woven antenna uni0054uni004Dg2868g2868g2870g2934  mode are shown in Figure 3.15 through Figure 3.17, 
respectively.   
3.2.6.Discussion 
Based upon the results, herein the radiation characteristic of the woven antenna is 
drastically different from the MSA. Figure 3.9 shows the dominant radiation mode of the 
MSA is uni0054uni004Dg2868g2869g2868g2934  and the next higher mode is uni0054uni004Dg2868g2868g2870g2934  as the cavity model predicted. 
However, the dominant mode of the woven antenna is shown to be uni0054uni004Dg2868g2868g2870g2934  mode instead of 
uni0054uni004Dg2868g2869g2868g2934 , as shown in Figure 3.10.  
uni0054uni004Dg2868g2869g2868g2934  mode is generated by transverse current density Jt in Y direction. (Refer to 
Figure 3.2 and Figure 3.3).  Continuous Jty requires a continuous PEC boundary condition 
in Y direction, which is disrupted by the periodic crimps introduced by the weaving 
method. From the cavity model, the PEC boundary on top of the cavity is replaced with a 
periodic PEC and crimp boundary, the transverse current in the Y direction is disrupted by 
the crimps, while a tangential E-field is allowed in the openings, making the uni0054uni004Dg2868g2869g2868g2934  mode 
a prohibited mode. Meanwhile, the uni0054uni004Dg2868g2868g2870g2934  mode is generated by Jtz which requires a 
continuous PEC boundary in the z direction.  Although there are open slots introduced by 
the crimp between the conductive wires, they remain parallel to the current flow, and since 
the size of the openings is electrically small, the Jtz current is undisrupted and uni0054uni004Dg2868g2868g2870g2934  
became the preferred mode in woven antenna.  
 
66 
A careful examination of the crimp effect is made by comparing a grating MSA with a 
woven antenna. The simulation and measured results are shown in Figure 3.12 and Figure 
3.14 respectively, which suggests the elimination of uni0054uni004Dg2868g2869g2868g2934  mode is common for both the 
grating MSA and the woven antenna. However, the crimp introduces strong resonances 
below 1GHz, which is not present in the grating MSA. The simulated result shows a -7dB 
resonance of woven antenna at 886MHz and -5dB resonance of grating MSA at 979MHz. 
However, the measured result shows -28dB resonance at 478MHz for the woven antenna 
and the grating MSA has a -11dB resonance at 745MHz. The crimps in the structure have 
drastically changed the radiation mechanism of the antenna, and allow a highly efficient 
mode at 478MHz, which is much lower than cavity model prediction. This result appears to 
be a unique behavior of woven antenna. The result suggests that a woven antenna is able to 
replace an MSA nine times its size, 24g890?210g1865g1865 MSA compared to 10g885?
g887g890g1865g1865woven antenna for the same design with the same efficiency. The woven antenna is 
even superior to a Planar Inverted-F Antenna (PIFA), which is widely used in cellular 
designs nowadays, in that PIFA operates one quarter the size of MSA with the trade off of 
lower efficiency and more sophisticated structure [2].  
Although the FEM simulation is inaccurate, the simulation can still give some insights 
into its radiation mechanism. The simulated radiation pattern of 886MHz is shown in 
Figure 3.18. The radiation pattern suggests a 45 degree main lobe in the xz plane which is 
different from any MSA model predictions but similar to microstrip slot antenna. The 
travelling wave g1846g1831g3051 mode of the slot antenna allows the main lobe direction to be pointed 
in any direction, from broadside to end-fire, by varying the width of the slots [4]. Such 
 
67 
behavior can also be explained with an artificially electromagnetic surface. An artificial 
soft surface prevents certain modes of surface waves from propagating in the stop band. In 
this case, the grating strips are in the transverse direction, thus the g1846g1839g3051 mode wave is 
prohibited, while the g1846g1831g3051 mode surface wave becomes a leaky wave and causes the 
radiation pattern shown in Figure 3.18. Further investigation is needed to confirm this 
hypothesis. 
 
Figure 3.18 Simulated woven antenna radiation pattern at 886MHz 
3.2.7.Conclusion 
The characteristics of MSA and woven antennas were measured.  The simulation and 
experimental results confirm that the radiation characteristic of the MSA has been changed 
dramatically by the incorporation of plain weave.  The weave configuration eliminates the 
uni0054uni004Dg2868g2869g2868g2934  mode, while it preserves the uni0054uni004Dg2868g2868g2870g2934  mode.  The weave structure also enabled the 
woven antenna to operate in an unknown mode, one ninth of the size of a conventional 
MSA. It is possible that the grating weave configuration introduced an electromagnetic 
 
68 
bandgap structure, preventing TM mode surface mode, and made the antenna to operate in 
leaky-wave TE mode as microstrip slot antenna. 
 
3.3.Numerical Modeling of Woven Frequency Selective Surface 
3.3.1.Introduction 
Artificial surfaces have numerous applications in antenna design and microwave 
engineering [36]. Among these, the frequency selective surface (FSS) is considered one of 
the most promising, and the interest in the integration of FSS into composite materials has 
led to various kinds of frequency selective fabric structures [37-44]. An FSS is an 
artificially engineered surface, comprising of periodic metallic structures with selective 
EM wave transmission or reflection characteristics. Research into frequency selective 
fabric has inspired many new applications, especially in new generation wireless 
communication systems and radar systems. However, most of the current research has 
been focused on microwave absorption properties of the resulting composite material. In 
this paper, we suggest a new class of FSS that can be manufactured with the weaving 
process, which gives rise to novel devices including self-supported standalone FSS. Some 
other advantages of woven FSS include: relatively light weight, flexible (conformal) 
substrates, and simple integration into other textile or composite products. Therefore FSS 
formed of special fabrics can be considered as a substitute for conventional printed circuit 
devices. 
 
69 
In this work, a textile FSS has been studied using the numerical analysis method for 
the first time. The goal of this research was to reveal the effect of weave arrangement and 
crimp on the EM wave interaction mechanism of textile FSS. We modelled a textile FSS 
together with a conventional aperture type FSS using a commercial finite element method 
(FEM) simulation package - Ansoft High Frequency Simulation Software (HFSS). HFSS 
has been proven to be an efficient and accurate way to calculate EM field under various 
conditions. Based on the simulation result, the impacts of the plain weave configuration on 
FSS performance is discussed.   
3.3.2.Floquet's Modal Analysis 
Due to its periodic nature, FSS may comprise patch type or aperture type. The 
aperture type FSS is studied herein for the ease of fabrication using the weaving technique. 
To model the periodic FSS structure, one can take advantage of Floquet-Bloch theorem. In 
this study we used periodic boundary conditions in HFSS, which essentially set up a 
Bloch boundary along the unit cell walls. The fields at one wall of the cell are related to 
the fields at the opposite wall by the wave vector. A frequency sweep can be set up to 
scan the entire frequency band of interest, which yields scattering parameter data for FSS 
performance analysis.  
3.3.3.Simulation Model Setup 
The geometry of the aperture FSS and textile FSS are shown in Figure 3.19 and Figure 
3.20, respectively. The aperture FSS structure consists of periodic apertures 2.g887?2.g887mm 
in size and placed 2.5 mm apart uniform along x and y direction. The textile FSS consists 
 
70 
of two types of yarns, conductive copper yarn and non-conductive Teflon yarn, both of 
which are 1.25mm wide and 0.05mm thick. The plain weave structure is modeled with an 
analytical curve, sweeping with the yarns, and modeled as a sine function in the z direction. 
The arrangement of the copper and Teflon yarns is a two by two repeating pattern in both 
warp and weft directions, thus making a 2.5 non-conductive aperture in the middle of the 
unit cell, matching that of the conventional aperture FSS. The non-conductive Teflon yarns 
are hidden in Figure 3.20 to show the copper yarns more clearly.  
 
 
Figure 3.19 Model setup of aperture FSS 
 
 
71 
 
Figure 3.20 Model setup of textile FSS 
 
 
3.3.4.Simulation Results and Discussion 
The simulated S-parameter (S11 and S21) results of the aperture and textile FSS are 
shown in Figure 3.21 and Figure 3.22. The primary interests in this case are the 
S-parameter results, which represent the reflection from and transmission through the FSS. 
The results show significant differences between the aperture and textile FSS. From Figure 
3.21, the transmission of textile FSS was almost completely blocked at 14.5 GHz, as seen 
from the Textile FSS S21 of about -54 dB, and the reflection was almost complete, as seen 
from Textile FSS S11 of 0 dB. On the other hand, the first reflection of aperture FSS was 
not present until 24.2GHz. Moreover, the aperture FSS behaves like a high-pass filter 
(reflect incident wave <10GHz) as FSS theory predicted, but the textile FSS appears to be 
low-pass filter, which is contrary to the theory on an aperture type FSS.  
 
72 
0 5 10 15 20 25 30
-50
-40
-30
-20
-10
0
 
 
Ma
gn
itu
de
 of
 S
11
 an
d S
21
 (d
B)
Frequency (GHz)
 Textile FSS S11
 Textile FSS S21
 Aperture FSS S11
 Aperture Aperture FSS S21
 Figure 3.21 Magnitude of S11 and S21 of textile FSS and Aperture FSS 
0 10 20
-200
-150
-100
-50
0
50
100
150
200
 
 
Ph
as
e S
hif
t o
f S
11
 an
d S
21
 (d
eg
)
Frequency (GHz)
 Textile FSS S11
 Textile FSS S21
 Aperture FSS S11
 Aperture Aperture FSS S21
 
Figure 3.22 Phase shift of S11 and S21 of textile FSS and Aperture FSS 
Moreover, the dependence of the FSS resonant frequency on the angle of the incident 
plane wave is of interest. The incident angle stability of both aperture and woven FSS is 
investigated as shown in Figure 3.23 through Figure 3.26.  
 
73 
0 5 10 15 20 25 30
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
 
 
Th
eta
 sw
ee
p o
f S
21
 (d
B)
 - A
pe
rtu
re 
FS
S 
TE
 m
od
e  
Frequency (GHz)
 theta=10
 theta=20
 theta=30
 theta=40
 theta=50
 Figure 3.23 Aperture FSS incident angle dependence TE mode 
0 5 10 15 20 25 30
-50
-40
-30
-20
-10
0
 
 
Th
eta
 sw
ee
p o
f S
21
 (d
B)
 - A
pe
rtu
re 
FS
S 
TM
 m
od
e  
Frequency (GHz)
 theta=10
 theta=20
 theta=30
 theta=40
 theta=50
 Figure 3.24 Aperture FSS incident angle dependence TM mode 
 
74 
0 5 10 15 20 25 30
-60
-50
-40
-30
-20
-10
0
 
 
Th
eta
 sw
ee
p o
f S
21
 (d
B)
 - W
ov
en
 FS
S 
TE
 m
od
e  
Frequency (GHz)
 theta=10
 theta=20
 theta=30
 theta=40
 theta=50
 Figure 3.25 Woven FSS incident angle dependence TE mode 
0 5 10 15 20 25 30
-60
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
 
 
Th
eta
 sw
ee
p o
f S
21
 (d
B)
 - W
ov
en
 FS
S 
TM
 m
od
e  
Frequency (GHz)
 theta=10
 theta=20
 theta=30
 theta=40
 theta=50
 Figure 3.26 Woven FSS incident angle dependence TM mode 
For the aperture FSS, the transmission coefficient (S21) of the TE mode (24GHz) 
shows greater dependence on variation of the scan angle in theta than the TM mode 
(24GHz) does. This is to be expected since the shape of the aperture changes to rectangle 
 
75 
when incidence is not normal. For the TE mode, the E-field is perpendicular to the width of 
the rectangle, which is varying with scan angle, thus the frequency of the TE mode 
transmission coefficient mode varies with scan angle. While for the TM mode, the E-field 
is parallel to the width of the rectangle, so the amplitude instead of the resonant frequency 
changes with scan angle. Either way, this incident angle dependency is undesirable for FSS 
applications. 
On the other hand, for the textile FSS, both the TE and TM mode at 15GHz are 
independent of scan angle. The incident angle stability is possibly due to the sine and 
cosine cross section of the textile aperture. The complimentary curvatures in the aperture 
cross section have a similar effect of ring resonators which is well known for incident angle 
stability. Further investigation needs to be carried out including the investigation of an 
equivalent lumped element circuit model. 
3.3.5.Conclusion 
A new type of textile FSS with unique EM properties has been simulated using the 
FEM method. It is characterized by an inverted filtering behavior and much lower 
fundamental resonant frequency than its aperture FSS counterpart. The incident angle 
stability of textile FSS is also comparable with ring resonators. It can be easily 
manufactured by weaving technology and even indicates the feasibility of standalone FSS 
manufacturing. The previously unpredicted EM behavior of such a material might lead to 
further development of the FSS theory and novel applications including electromagnetic 
textiles and artificially magnetic conducting textiles.  
  
 
76 
3.4.Numerical Modeling of Textile Artificial Magnetic Conductor 
3.4.1.Introduction 
High Impedance Surface (HIS) such as the Sievenpiper mushroom is capable of 
providing in-phase reflection for plane wave incidence. This is an important characteristic 
of a perfect magnetic conductor (PMC), and so HIS is also called Artificial Magnetic 
Conductor (AMC). Due to its surface wave suppression characteristic [21], it is widely 
studied in the applications of low profile antennas [45], high performance IC filters [46], 
and high Q resonators [47].  
There is also much interest in the integration of wireless communication systems into 
wearable products, which lead to various kinds of body worn antenna structures [28, 29, 31, 
32, 34, 35, 48-54]. It is a logical to attempt to integrate AMC structures into body worn 
antennas to improve their performance. Bashir et al. [33] has suggested flexible frequency 
selective surface (FSS) by incorporating HIS into fabric structures. However, the work is 
done by using fabric felt material as substrate and the traditional printed circuit technique 
(PCB) technique to form the periodic pattern, thus is not a purely textile AMC/AEC. 
In this paper, we address the impact of fabric nature on the electromagnetic 
performance of textile AMC/AEC structures. Yarns in a piece of fabric are periodic in 
nature. To the author?s best knowledge, study of textile AMC/AEC structure has never 
been done. Arranging conductive fibers in the weft direction only and attaching the fabric 
to a suitable substrate results in an AMC/AEC composite surface. The comparison between 
periodic conducting-strip grating and a woven AMC/AEC surface was studied for the first 
time. Based on this study, several distinct phenomena regarding weave-introduced crimps 
 
77 
were observed which lead to conclusions regarding the feasibility of textile AMC/AEC 
and other electromagnetic textiles. 
3.4.2.Eigenmode Analysis 
To study the behavior of a textile AMC/AEC surface, a finite-element model with 
detailed weave geometry of the textile surface is included. In the FEM model, the 
structure of the unit cell is discretized, and the electric field at all points on the grid can 
be reduced to an eigenvalue equation, which may be solved numerically. In this study we 
used periodic boundary conditions in HFSS, which essentially set up Bloch boundary 
along the unit cell walls. The fields at one wall of the cell are related to the fields at the 
opposite wall by the wave vector. The calculated eigenvalue is essentially the allowed 
frequencies for a particular wave vector. The procedure can be repeated for each wave 
vector to produce the entire dispersion diagram. The structures analyzed herein are a PEC 
strip grating and a woven grating, shown in Figure 3.27 and Figure 3.28 respectively. The 
straight strips and woven strips are infinitely long and uniform along the x direction, and 
periodic in the y direction. The lattice constant was 5 mm, the strip width is 2.5 mm, and 
the substrate thickness is 1.8 mm. 
The textile AMC/AEC structure consists of two types of yarns, conductive copper 
yarn and non-conductive Teflon yarn, both of which are 1.25mm wide and 0.05mm thick. 
The plain weave structure is modeled with analytical curve sweeping with the yarns 
modeled as a sine function in the z direction. The copper and Teflon yarns are inserted 
repeatedly in weft direction to form the grating, and the warp has only Teflon yarns to form 
 
78 
the plain weave patch. The Teflon yarns in Figure 3.28 are hidden in order to better show 
the copper yarn structure. 
 
Figure 3.27 Model setup of PEC strip grating 
 
Figure 3.28 Model setup of woven strip grating 
3.4.3.Numerical Results and Discussion 
The primary interests in AMC/AEC study are the dispersion diagrams, which 
represent the EBG of the AMC/AEC structure. A dispersion diagram is a plot of the 
propagation constant versus frequency. It indicates how much phase shift a material has at 
 
79 
a given frequency. For background on Brillouin zone and details of how to generate 
dispersion diagram, please refer to Appendix B. The simulated dispersion diagrams of the 
grating AMC/AEC and textile AMC/AEC are shown in Figure 3.29 and Figure 3.30, 
respectively.  
For the grating AMC/AEC, the band gap between first TM and TE mode is clearly 
shown from uni0393 to g1850 and g1839 to uni0393, which suggest the structure is AMC for these wave 
vectors in the Brillouin zone. However, the bandgap collapsed from g1850 to g1839, which 
suggests the structure is AEC for these wave vectors. For the textile AMC/AEC, the 
behavior of uni0393 to g1850 and g1839 to uni0393 are the same as the grating AMC/AEC. However, for g1850 
to g1839, the bandgap does not collapse, which means the textile AMC/AEC is really an entire 
AMC structure. In other words, by incorporating a weave pattern into a grating structure, 
the 1-D EBG is transformed into a 2-D EBG, meaning it is possible to reproduce the 
behavior of the more complicated Sievenpiper mushroom with a simple weave pattern. 
 
Figure 3.29 Dispersion diagram of grating AMC/AEC 
 
80 
 
Figure 3.30 Dispersion diagram of textile AMC/AEC 
3.4.4.Conclusion 
A new type of textile AMC/AEC structure with unique EM properties has been 
simulated using the FEM method. It is characterized by having a 2-D EBG dispersion 
property on a 1-D periodic structure, and is able to turn an AMC/AEC structure into a full 
AMC structure. The simulated textile structure can be manufactured easily using weaving 
technology, providing the feasibility of pure textile AMC/AEC structure by incorporating 
the conductive yarns into a fabric dielectric substrate. The discovery of such unique EM 
behavior of the novel textile material might lead to further development of AMC theory 
and novel applications including electromagnetic textiles and flexible low profile high 
performance textile antennas.  
 
 
81 
 
 
 
Chapter 4.Emergency Communication Network 
 
4.1.Introduction 
In recent disasters such as hurricane Katrina, and the Wenchuan and Haiti earthquakes, 
we have witnessed great losses of human life due to lack of communication.  Many 
sources emphasize that the most common problem in disasters is the deficiency of 
communication, equipment, and ultimately the ability to respond [55-59]. Pursuing a 
solution to this recurring problem was the inspiration to develop this project.   
The function of communication networks to disseminate reliable information to the 
public, and enable the survivors to be connected to the "outside" world is critical during 
catastrophes [56]. Because transportation and power infrastructures are often damaged or 
destroyed during such times, it is impossible to restore the entire communication 
infrastructure immediately. Meanwhile, the first responders primarily acquire critical 
information from 911 calls, and are required to communicate quickly because their 
reaction speed means life or death to those in danger [56, 59]. Thus a rapidly deployable, 
easily reconfigurable, low power and low cost ECN that can provide temporary bandwidth 
to physically breach the communication gap is highly desired for such relief effort. 
Wireless sensor network (WSN), enabled by the recent advances in electronics, 
networking, information processing, is a promising technology toward the solution of an 
effective ECN. 
 
82 
A WSN featuring air-drop enabled nodes that can be distributed to any terrain 
promptly was investigated. With its performance and protocols dedicated for emergency 
text messaging service, a reliable emergency network among survivors and first responders 
can be established to improve emergency management effectiveness. 
4.1.1.Impact on Humanity 
Technology is best administered when it involves helping people, especially those in 
danger. The project addresses primarily the need for sustainable communications during 
disaster.  In the event of a catastrophe, access to reliable communication systems is critical 
for the survivors. During Hurricane Katrina, much of the wireless and landline network 
infrastructure was destroyed or severely damaged, resulting in an overload of the 
remaining infrastructure as first responders, and rescue personnel, and the general public 
were all attempting simultaneous access. Moreover, the failure of backup 911 networks 
resulted in many unanswered emergency calls which confused the public about the relief 
effort while leaving life threatening situations unresolved.  
The proposed approach provides rapid-deployable wireless communication capability 
during an emergency until the public communication infrastructure can be systematically 
restored. In this study, a WSN prototype that can be deployed to the affected area within 
hours by aircraft is designed.  The WSN nodes will form a self-organized text messaging 
network, disseminate public safety information, and relay text messages among the 
survivors and responders. By re-establishing communications, capable survivors will also 
be enabled to assist in rescue effort before responding force arrives.  
The solution could provide a reliable emergency communication method among 
survivors and first responders.  The system will increase people?s confidence when facing 
 
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disaster, increase awareness among survivors and responders, and relieve anxiety and 
combat rumors, thus improving morale in affected communities.  Local and national 
government agencies can make more efficacious and informed decisions.  Finally, and 
most importantly this communication system can save people?s lives. 
4.1.2.General Solution 
The developed prototype involves the construction of a novel, rapidly-deployed, 
ultra-low power, distributed wireless communication network utilizing recycled 
post-consumer products and off-the-shelf components.  The solution could enable 
survivors to communicate critical, lifesaving information with emergency responders via 
text messages using this network.  The solution involves a multi-disciplinary scientific 
and engineering approach, combining electrical, computer, mechanical and textile 
engineering in an innovative way.   
How it works: As soon as initial report of disaster is received, thousands of the 
communication nodes can be loaded on aircraft within minutes and air-dropped to the 
affected area. The air-dropped nodes will form a self-organized network to provide SMS 
service to the area. Based on the SMS feedback, humanitarian aid as well as additional 
nodes can be effectively distributed according to need.   
The benefits of this concept are as follows. First, this approach facilitates saving of 
lives by serving as an interim communication network to quickly restore wireless 
communications during a time critical event. Next, the concept utilizes standardized 
components and works well with existing infrastructure, i.e. relief agencies are familiar 
with airborne relief methods. This system can be easily deployed over a large area from 
aircraft and utilized by existing cell phones with text messaging. Finally, the scale and 
 
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topology of the network are versatile such that they can be adapted to any emergency 
event.  
SMS has become an overwhelmingly popular method of mobile communication 
nowadays (~5 billion cell phones worldwide); therefore utilizing SMS eliminates special 
training required for the survivors to operate the interim system. Moreover, unlike 
walkie-talkies and conventional landline telephones which may be left unanswered, text 
messages will be stored in a responder?s cell phone memory, thus not easily ignored. The 
text messages from the survivors can also help the first responders, local and national 
governments in assessing the damage and dispatching aid efficiently.  
The ultra-low power feature of the WSN node ensures full capacity communication 
for over two weeks with a single AAA battery. By adding solar-cells and rechargeable 
batteries, an energy harvest interface can ensure the service be extended almost indefinitely 
if needed. The WSN node prototype is designed to be fabricated with post-consumer 
products including recycled soda bottles.  
The solution comprises the following modules: WSN node, GSM, power harvest, 
pneumatic control, multi-functional tether, and protective shell and base. The WSN node 
module comprises the fundamental elements forming the backbone of the WSN radio link 
and provides a backhaul of text message data to the sink node. The GSM module provides 
?Um? radio interface to the mobile users, allowing users to register with the emergency 
network for peer-to-peer or cell broadcast text messaging. The power harvest module 
integrates off-the-shelf rechargeable batteries, solar panels, and onboard voltage regulators 
to sustain system operation under varying conditions. The pneumatic control module 
utilizes off-the-shelf hardware to fulfill safe descending while providing antenna elevation 
 
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thus increasing communication range. The multi-functional tether facilitates balloon filling, 
power transmission, and load carrying between the balloon and base. Such a 
multi-functional tether is developed to connect the balloon, transmitter, and enclosure. The 
protective shell and base module provides supporting hardware surrounded by impact 
absorbing polyurethane foam and is also designed to act as an anchor to the ground by 
arranging the heavy components appropriately. 
Based on testing, the developed WSN node will provide critical time-sensitive 
information to rescue responders and help save lives amid disaster and crisis. A computer 
aided imaginary deployment of the system is shown in Figure 4.1.  
 
Figure 4.1 Wireless emergency communication network concept 
4.2.Overall System Design 
When catastrophic disaster strikes, the quickest way to deliver external responding 
force is by airborne methods [55]. An airborne communication network at this time is one 
of the best ways to relieve the communication needs of the people affected and the local 
 
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first responders for situation assessment.  An airborne cellular communication network in 
such a situation is most desirable due to interoperability, wide spread availability, and 
ubiquity. Deaton et al. have suggested an ACN, which has a cell phone BTS loaded on 
aircraft to fly over the affected area and provide communication services [60]. However, 
the feasibility of such a solution for large scale disasters needs further investigation. First 
of all, a single aircraft will not be able to cover the affected area. For example, during 
Hurricane Katrina, Federal disaster declarations covered 233,000 km2 of affected area in 
U.S. However, the ideal coverage of a WC-130 is 730 km2 according to Deaton, et al [60]. 
In order to service the entire affected area, a fleet of over 300 aircraft need to be prepared 
and deployed when the hurricane hits. The cost for modifying aircraft, fuel, pilots and crew 
is significant. Therefore the ACN solution can only support emergency communication for 
small areas and relatively short periods of time. 
Although ACN is not economically preferred, airborne methods are still the quickest 
and at times the only possible way to get help into the affected area. As a matter of fact, the 
C-130 Hercules has participated in countless humanitarian aid operations and has far 
superior performance especially in fierce weather conditions. The Lockheed WC-130 
Weatherbird is configured with palletized weather instrumentation for penetration of 
tropical disturbances and storms, hurricanes and winter storms, and will be able to provide 
real-time humanitarian aid under virtually any weather condition. In our project, we 
propose to utilize specially designed air-drop WSN relay nodes in an airborne deployable 
form to provide emergency communication capability. Clusters of the WSN relay nodes 
can be loaded on a C-130 and precisely delivered to the affected area quickly. The nodes 
have all the circuitry built in a protective shell for weather proofing. It also employs a 
 
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multi-functional tether and helium balloon for safe descending and antenna elevation. 
Once dropped from the carrier, the balloon on the node will start to inflate and slow the 
descent. The helium tank, pneumatic valve, and other heavy components are built into the 
bottom compartment of the protective shell, while the communication module and solar 
panel (optional) will be attached to the balloon.   
 
Figure 4.2 Overall emergency communication system architecture 
Once landed, the WSN node will remain aloft at 20 feet above ground (lower than 
power lines) by the balloon for increased communication range. The tether prevents the 
balloon from being blown away by the wind and protects the connecting components. The 
WSN nodes will automatically form self-organized networks and gather SMS from GSM 
users and send them through the WSN to the sink node which will have connection to the 
public network. Please see Figure 4.2 for proposed overall system architecture. 
 
 
88 
4.3.Wireless Sensor Network Basics 
Recent advances in low-power highly integrated digital electronics, microprocessors, 
and low-power radio frequency (RF) technologies have created low cost, low-power, and 
high performance devices that enable battery operated wireless signals transmission over 
long distances. With conventional data acquisition methods evolved from single wired 
mode to highly integrated, miniaturized, automated, and interconnected modes, these 
devices have drawn significant attention from researchers. They have integrated sensor 
technology, embedded computing, distributed information technology, and 
telecommunication technology. They could cooperatively and in real-time monitor, sense, 
and gather any information about the environment or an object under test, process this 
information, and convey them to the end users.  
Wireless Sensor Network (WSN) is typically a self-organized network. It bloomed in 
late 90s, and can be applied to national security, environmental monitoring, traffic control, 
modern logistics, medical care, smart homes and many other fields. It has great potential 
for improving people?s lives.  WSN has become a new hot topic since then and will 
impact the way people live in the near future. 
4.3.1.WSN System Structure 
4.3.1.1.WSN Networking Structure 
WSN is typically composed of a sensor node, sink node, and management node. A 
great number of sensor nodes randomly scattered inside or around the sensing field, form 
a network using self-organize capability, real-time monitoring and capture of information 
about objects. They send data back to the sink node through multi-hopping or other 
 
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mechanisms. The data can be processed during transmission, and then passed to the 
internet or a satellite to the management node. The end user can configure and manage 
the whole sensor network remotely, setting monitor tasks or change objectives on the fly. 
A basic WSN network structure is shown in Figure 4.3. 
Sensor nodes are usually micro embedded systems, they have very limited processing 
power, memory storage and communication capability. They are usually equipped with a 
small battery, a radio transceiver, and a microprocessor used to control and process 
wireless data packages. The hardware and software of sensor nodes are the key research 
area of WSN. On the other hand, sink nodes usually have better processing power, 
memory storage, and communication capability. They may have connectivity to an 
external network such as the internet, implement interconnectivity between different 
protocols, disseminating tasks to the sensor nodes, and convey the gathered data to 
external network. 
 
Figure 4.3 WSN network structure 
 
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4.3.1.2.WSN Sensor Node Structure 
WSN has emerged as an independent computer network, and its basic unit is the 
node. Every node has its own sensor unit, processing unit and communication module. 
The functions of each node are to sense data, process data, and transmit data. A sensor 
node can have up to five major components as shown in Figure 4.4. 
. 
 
Figure 4.4 Major components of sensor node 
Microprocessors or microcontrollers control all the processes and the behavior of the 
device, and can execute any code. The storage unit stores the gathered data and the 
relayed data. Normally programs and data use different memory allocations. Sensors are 
the units used to gather information from the environment or data on specific object. The 
communication modules are used to convey the data out to the external network and end 
users. The power system is usually a battery, with or without energy harvest devices.  
 
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4.3.1.3.WSN Protocol Stack 
The protocol stack of WSN utilizes a simplified open system interface (OSI) model, it 
usually consists of a Physical Layer, Data Link Layer, Network Layer, Transport Layer, 
and Application Layer as shown in Figure 4.5. Besides, the stack should also include a 
power management platform, mobility management platform, and task management 
platform. These platforms enable the sensor node to work efficiently and utilize the least 
energy, thus prolonging the system battery life. 
 
Figure 4.5 WSN protocol stack 
Physical Layer 
The Physical Layer consists of the basic hardware transmission technologies of a 
network such as signal modulation/demodulation, transmission and reception. The main 
 
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functions of the Physical Layer include frequency selection, signal modulation, and data 
encryption. For long range telecommunication, it is a critical component in term of 
implementation complexity and energy consumption.  
Data Link Layer 
The Data Link Layer is focused on solving multiple access problems. It provides the 
functions and procedures to transfer data between network entities without contention and 
might provide the means to detect and correct errors that may occur in the Physical Layer. 
Network Layer 
The Network Layer takes care of the data routing from the Transportation Layer. With 
many sensor nodes scattered around the observation area, a routing protocol is necessary to 
be used for the communication between sensor nodes and sink node. 
Transportation Layer 
To ensure QoS of the WSN, the Transportation Layer is utilized to maintain data 
stream throughout the WSN.  Refer to the protocol diagram in Figure 4.5. When the WSN 
needs to be connected to another type of network, the Transportation Layer allows the sink 
node to communicate with the Task Management node with conventional TCP or UDP 
protocols. However, since the sensor nodes have very limited power and memory 
resources, the WSN itself needs a resource efficient protocol. 
Application Layer 
Based on the task requirement of the WSN, different applications can be added to the 
Application Layer. It can include a series of application softwares for monitoring purposes. 
Because of their limited computing power, memory storage and communication 
capability, each individual sensor node can only acquire a very limited topology of the 
 
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network, so the protocol cannot be over complicated. Meanwhile, WSN topology may be 
constantly changing, i.e. wireless mobile sensor network, with a requirement of dynamic 
networking resource reallocation, thus places an even higher requirement of the WSN 
protocol. The WSN protocol must also ensure that each individual node forms a multi-hop 
data transportation network, and the current key research areas are Network Layer and 
Data Link Layer protocols.  
4.3.2.Characteristics of Wireless Sensor Network 
Large Scale 
To acquire precise real-time information, it is necessary to deploy a large number of 
sensor nodes to the area of interest, the number of nodes can be thousands or more. For 
example, with the nodes loaded on and deployed by aircraft, WSN can be installed over 
thousands of acres of land for geological survey or oceanic environmental survey.  
Energy Limitation   
Every node in the network has access to limited energy. WSN typically works in rural 
areas with sparse populations or even in hazardous environments. Sometimes it is 
impossible to change their battery, thus they requires ultra-low power consumption to 
prolong the operation life of the network. 
Self-organization 
Self-organization includes functions of auto network association, node and terminal 
identification, and hack prevention. Compared to a fixed point wireless network, the 
configuration of WSN is more similar to ad hoc networks, with the prerequisite of a 
suitable communication protocol for unmanned operation.  
Self-management 
 
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In WSN, data processing is done within the nodes in preference to reducing data rate 
on the wireless medium, so that only the data related to other nodes are sent over the RF 
link. The data centric character is another feature of WSN. Since the positions and 
deployment of the nodes are not pre-planned, it is possible that some nodes will go out of 
service due to errors or accidents during deployment.  To ensure undisturbed services, 
redundant nodes must be included in a WSN design. Moreover, data sharing and 
cooperation between nodes must be implemented to guarantee complete monitoring of the 
subject. 
Differences from ad hoc networks  
WSN is similar to an ad hoc network in the feature of distributed network. However, 
there are many differences between them. Generally speaking, WSN nodes have more 
limited access to resources compared to handheld devices, but the computing requirement 
is only optional. When a computational task is needed, if the cost of communication is 
lower, it could be possible to transfer the computing task to the sink node to improve 
overall performance. 
4.3.3.Wireless Sensor Network Applications 
WSN nodes have the capability of continuously gathering data, detecting events, and 
marking events, monitoring position, and controlling other nodes. These features plus the 
wireless communication capability ensure broad applications of WSN. It can be applied in 
environmental monitoring and prediction, geological survey, health monitoring, smart 
homes, building monitoring, control of complex machinery, metropolitan traffic control, 
space exploration, garage management, industrial park safety, etc. A very important 
feature of WSN nodes is that they can be air-dropped to any designated area for different 
 
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missions including humanitarian missions. As the research and application of WSN 
deepens, it will have great impact on every aspect of human lives.  
4.3.4.Current Research on Wireless Sensor Network  
The earliest WSN research effort was funded by NSF and DARPA, and was carried 
out by the University of California and Cornell University. Starting in the year 2000, much 
industrial research on WSN has been reported, including work from Intel [61] and 
Microsoft [62].  
Nowadays, WSN research has gone through two stages of developments. The first 
stage is focused on the utilization of a micro-electro-mechanism system (MEMS) 
technology and miniaturization of the nodes. Example works include Wireless integrated 
network sensors [63] (WINS), and Smart Dust [64].  The second stage of the research is 
mostly about the network itself and has become a popular study area currently. From the 
network architecture point of view, every layer has to be studied separately to optimize the 
overall performance of the WSN. Current research is mainly focused on Network Layer 
and Link Layer with special interest in establishing robust p2p or meshed network through 
different MAC protocols.  
4.4.Wireless Sensor Network Design 
In general, WSN is a large scale, multiple-node network with all the nodes 
independent and maintenance-free.  There are at least two types of nodes in a WSN, the 
WSN nodes and the sink nodes. For testing purposes, an off-the-shelf USB Dongle with 
C8051F342 MCU and Si4431 radio from Silicon Labs connected to a laptop computer was 
used as a sink node.  
 
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4.4.1.WSN sensor node module 
As for the WSN nodes, they should be small, portable, of low power consumption, 
and have a highly robust wireless link. A compact design is also desirable for control of 
cost and large scale production. The WSN node must have MCU, RF module, GSM 
module, power module, and pneumatic control module (power deployment hardware). A 
design schematic is shown in Figure 4.6. 
 
Figure 4.6 WSN node system structure diagram 
For the MCU and RF module we used a Silicon Labs C8051F912 MCU and a Si4431 
radio [65]. This combo features ultralow power and voltage operation. A single AAA 
battery can support the module in full active mode (24.5 MHz clock) for over 14 days. The 
C8051F912 has an on-chip dc-dc converter to allow operation from a single cell battery 
with a supply voltage as low as 0.9 V. The dc-dc converter is configured to enable bypass 
mode when VBAT is greater than VDD for use with solar panel. A power harvest interface 
is utilized for solar panel connection. The Si4431 radio is connected to the MCU through 
SPI and is controlled by Silicon Labs EZMacPro library, as shown in Figure 4.8. A PCB 
meander line antenna from Silicon Labs EZRadioPro reference design is used together 
 
97 
with the Si4431 radio. The MCU also has a C2 interface for debugging and firmware 
updates. The schematic of the MCU configuration is shown in Figure 4.8. The PCB design 
is sent to Advanced Circuit for fabrication, and the fabricated board is shown in Figure 4.9. 
Keeping the board to a minimal size, leadless QFN-based ICs and surface mount passive 
components sized down to 0402 based packages are chosen for the prototype. An 
advantage to using standard surface mount components is that the board can be assembled 
on a larger scale using standard manufacture assembly lines for electronics because they 
are easily handled using automated ?pick and place? machines.  Using components this 
small, hand-soldering is less than ideal for populating the board; therefore, the reflow 
soldering technique is used to fabricate the PCB assembly. This method requires that a 
solder paste to be applied to each of the component pads on the circuit board. To place the 
correct solder paste in the right location, a solder paste stencil made of 3mm thick clear 
Mylar for relatively low cost at Pololu Robotics and Electronics is designed and applied to 
the fabrication process. Upon placing the components, the circuit board is place in an oven 
to flow the solder, which will harden when cooled.  The unpopulated circuit board is 
shown in Figure 4.9. The fully assembled board is shown in Figure 4.10. 
 
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Figure 4.7 Schematics of SPI interface 
 
Figure 4.8 MCU pin configuration 
 
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Figure 4.9 Manufactured WSN node PCB board 
  
Figure 4.10 Populated WSN node 
4.4.2.GSM module 
Since IS-95-style CMDA is a tightly controlled intellectual property, adapting CDMA 
is out of the question. GSM modules have become our main focus since they are proven to 
be working well and over 80% of the world's carriers are using it [66]. 
The greatest challenge presented in our project was to accommodate the GSM ?Um? 
air interface into WSN design. Although the GSM industry is one of the largest industries 
in the world, there are only few implementations and most of them are close source. We 
have investigated OpenBTS?, which is a promising open source project. However, 
operation of OpenBTS stack requires a computer with Linux OS and Universal Software 
Radio Peripheral hardware. Accommodating entire GSM stack into WSN nodes with 
limited computing capability and battery operation requirement can be an extremely 
challenging task even for expert wireless companies, if at all possible. Our solution to this 
problem was to develop a low power mixed-signal GSM transceiver IC supporting 
SDCCH and SACCH channels. 
 
100 
Although SMS is defined in five layers of ?Um?, only L1 and L2 layers are necessary 
to provide SMS to mobile users in our setup. The function of L3 and above can be passed 
on to the WSN network layer to relay text messages and using WSN as the SMS backhaul. 
The proposed GSM chip should contain the following components: Analog TX: PA, VCO, 
filters, oscillators; Analog RX: LNA, Mixers, PGA, PLLs, ADC; Digital: GMSK or 8PSK 
modem, and interface control. The GSM IC can be interfaced with popular low power 
microprocessors such as the C8051F series or the ARM series with simplified OpenBTS 
stack to provide registration and SMS services. For this experiment, only off-the-shelf 
components are utilized to prove the concept. However, attention and help from the 
transceiver IC industry is welcome in the future.  
Alternatively, to prove we could extract text messages from a ?Um? air interface, we 
modified a commercial GSM module with only SMS multicasting capability and 
interfaced it to the WSN node module. The cellular module we used was a GSM SM5100B 
from SpreadTrum and is powered by an external LiPo battery. It is a quad-band GSM 
module with SMS, GSM/GPRS, two UARTs, and an SPI interface. The SM5100B is 
connected to the WSN node?s MCU using two wires UART at 9600bps baud rate, (8-N-1), 
and no flow control. The breadboard prototype test is shown in Figure 4.11.  
 
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Figure 4.11 GSM module attached to WSN node through breadboard 
4.4.3.Power harvest module 
For the wireless node to be able to operate in varying environmental conditions, we 
chose to implement two sources of power: photovoltaic cells and a secondary battery. 
Using this combination, it is possible to sustain system operations for an extended time 
period. The secondary batteries provide power to the system in times of darkness, as well 
as any periodic high current demand need by the RF transceiver. The solar cells power 
operations during times of sunlight, as well as replenish the charge of the secondary 
batteries from the excess power generated. The solar panel tested is shown in Figure 4.12. 
Looking at the simplified diagram below in Figure 4.13 we see that in times of sunlight, the 
solar cell will develop a voltage potential across the cells and this voltage is greater than the 
voltage of the batteries, the Schottky diode will start conducting and will allow current to 
flow from the solar cell and into the battery and/or the voltage regulator. Excess power not 
 
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needed by the voltage regulator is then diverted into the battery. Over time, the battery will 
reach a voltage level that is associated with being fully charged. To prevent from 
over-charging, which may cause irreversible damage, a Zener diode has been placed in 
parallel with the battery. By selecting the correct reverse breakdown voltage of this Zener 
diode, any excess power generated by the solar cells that is not needed by the battery or the 
system will be dissipated.  
Since the voltage of the battery or the solar cells is not controlled, a voltage regulator 
must be used in order to adjust and control the voltage supplied to the rest of the system. To 
achieve this regulation as efficiently as possible, the DC/DC convertor onboard the 
C8051F912 MCU is utilized for this purpose. Using this convertor, the system can be 
correctly powered from the batteries and solar cell when their voltages weaken to 0.9 volts. 
When the voltage supplied by the solar cell/battery combination reaches the design 
regulator output voltage, the regulator will bypass itself to operate at the utmost efficiency. 
Since the DC/DC convertor is flexible within the input voltage range, this allows for 
different combinations of batteries and solar cells for the system if other power source 
options are desired.  
 
103 
 
Figure 4.12 Solar panel under test 
 Figure 4.13 Improvement schematic of the energy harvest interface 
 
104 
4.4.4.Pneumatic control module 
Since the WSN node will be dropped into high population areas, safe descent must be 
emphasized in the design. Normally parachutes or balloons are the only two options. We 
have chosen an inflatable weather balloon approach because it has a twofold benefit: it 
provides elevation to the sensor module to increase communication range and serves to 
slow the descent. The balloon is inflated via a helium cartridge, with a pressure regulator, 
and a low power solenoid valve.  A fixed pressure regulator was selected because it 
weighs less than a conventional regulator with a gauge. The solenoid valve is controlled by 
the MCU through GPIO port P0.0.  The pneumatic module is shown in Figure 4.14.  The 
pneumatic off-the-shelf hardware was selected as being most well suited to fulfill our 
design requirements.  The individual components are justified as follows:  the smallest 
OTS helium cartridge is chosen.  The helium is stored in a burst resistant, high pressure 
container and thus requires a pressure regulator or reducer.  A fixed pressure regulator 
with safety relief features is chosen because it is lighter than an adjustable regulator.  A 
micro-solenoid valve controllable by the MCU to inflate the balloon is also included. 
 
Figure 4.14 Components of pneumatic system 
 
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4.4.5.Multi-functional Tether 
An important piece of hardware was not available commercially to connect the 
balloon and WSN node with the base module.  Instead we developed a novel 
multi-functional tether using a textile technology called braiding to incorporate pneumatic 
tubing, electrical conductors, a protective layer and strength members in a single 
manufacturing process, see Figure 4.15.  16 Nylon yarns were braided over the tubing and 
electrical conductors using a Wardwell Maypole style braiding machine to consolidate 
these components, see Figure 4.16.  The Nylon yarns serve as primary strength members, 
as well as provide environmental protection against abrasion and ultraviolet degradation. 
 
Figure 4.15 Multi-functional braided tether with pneumatic tubing and wires 
 
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Figure 4.16 Braiding machine during manufacture of multi-functional tether 
4.4.6.Weather Proof Protect Shell and Base Module 
The bottom portion of the protective shell and base module contains the pneumatic 
control module and protects against impact by shock absorbing polyurethane foam, see 
Figure 4.17.  The protective shell is also designed to act as an anchor to the ground by 
arranging the heavy components appropriately.  Although weight is important, it is 
intended to optimize the physical arrangement of components throughout the design, so 
that each component serves multiple design needs. A two liter soda bottle is utilized to 
serve as a protective shell and housing for the primary components during deployment and 
end use, see Figure 4.18. The advantages of using a recycled bottle as a protective shell 
are manifold:  First, it is an off-the- shelf component that can be easily provided from 
many sources. Second, as a component benefitting from mass production, it is inexpensive.  
Third, it is lightweight, strong, and can provide sufficient protection against moisture and 
environmental hazard.  We have modified the bottle to produce top and bottom sections.  
 
107 
Each of the aforementioned modules is inserted and the top and bottom section 
re-combined, see Figure 4.18.   
 
Figure 4.17 Impact resisting polyurethane foam 
 
108 
 
Figure 4.18 Weatherproof shell constructed from recycled soda bottle 
 
Figure 4.19 Air holes drilled in bottle to cause separation during deployment 
The top and bottom are designed to separate automatically during airborne 
deployment.  Holes have been placed along the sides of the bottom section in such a way 
 
109 
that air pressure is exerted during descent causing a separation, see Figure 4.19.  The 
design is such that as the bottle begins to descend, the top and bottom separate, the balloon 
begins to inflate, and the multi-functional tether unspools.  Although a high altitude 
deployment test is not scheduled at this time, each system component was tested 
individually with success.  For example, an air nozzle test at various air velocities is 
carried out to test the separation and found minimal air pressure causes the top to separate 
from the bottom. Figure 4.20 shows the initial separation experiment.  The bottle was 
dropped from a second story and the separation was observed as well. The separated top 
and bottom compartments are shown in Figure 4.21. 
 
 
110 
 
Figure 4.20 Air pressure separation experiment 
 
Figure 4.21 Top and bottom separation 
 
 
 
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4.5.Microcontroller Firmware 
The MCU firmware is developed using Silicon Labs Integrated Development 
Environment. The WSN protocol stack is developed based on Silicon Labs EZMacPro 
library with MAC layer and partially hardware supported PHY layer.  
The communication protocol we used has a star topology with the USB Dongle as 
master and WSN node as slave. The nodes are self-organized using contention sensing 
method provided by the EZMacPro library (Listen-before-talk). Multi-hopping mode is 
also enabled for nodes to relay received text messages. The implemented routing protocol 
uses a simple flood-and-forwarding algorithm. The advantage of using EZMacPro library 
allows us focus more on the design rather than ?reinventing the wheel?; it also supports 
multiple addressing modes, contention detection, CRC, and frequency hopping.  For each 
network, it can address up to 255 WSN nodes. EZMacPro implements its own state 
machine using two interrupt routines. The timer can realize different timed tasks, while 
External INT supports RF related interrupt requests. The behavior of EZMacPro is 
determined by the parameter of a series of EZMacPro registers. APP layer can easily 
access and control low level behavior using C functions.  
 
4.6. Graphic User Interface 
Our GUI is written in Visual C# based on the Silicon Labs P2P UART 
communication demo with SLABHIDDevice.dll USB dynamic library. We added in an 
addressing mode so that it will be compatible with the star topology. The GUI provides 
ASCII and HEX input/output through the wireless link to the WSN nodes. 
 
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Figure 4.22 Start up data through GSM-UART-RF-USB link  
 
Figure 4.23 SMS Received in PDU format through GSM-UART-RF-USB link 
 
 
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4.7.Results 
Communication with the GSM module using AT commands and retrieval of SMS 
from GSM module are successfully carried out through the WSN RF link. An AT 
?command request for receive? SMS is sent from the master to the WSN node through the 
RF link, and then transmitted to the GSM module via UART. The gathered SMS in PDU 
form is then transferred to the WSN node through UART and then transmitted over the RF 
link to the sink node. Figure 4.22 shows the received start up data indicating the GSM 
module is successfully registered to the cellular network. Figure 4.23 shows the received 
text message in PDU format and Table 4-1 shows the decoded text message. The result 
proves that a WSN RF link can be used to receive, transmit, and relay GSM text messages.  
Table 4-1 Received SMS in PDU format and decoded text. 
PDU format Decoded text 
07912180958729F3000B818156721453F8000090907
18083420A31C43728FFAE83D6EEF71D1476E7E9E8B4
FB0C0A8BDF753A089E2EEBDF65365D9E1E83DA617
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SMSC#+12085978923 
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TimeStamp:17/09/09 08:38:24 
TP_PID:00 
TP_DCS:00 
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Do you know anything about piezoeltric materials? 
Length:49 
 
4.8.Summary 
Utilizing off-the-shelf components is very important in a research and development 
environment.  However, these products are not always ideal for their intended application.  
Weight is critical in this design.  Although helium balloon payloads are sufficient for the 
prototype design, no intuition about helium balloon payload before this project was taken 
into account seriously. A further design iteration and testing where minimal weight is the 
 
114 
primary objective will be carried out and save even more weight.  It is also learned that the 
manufacturer?s specification can be misleading in design work of this type.   
A novel rapidly deployable communication network concept has been proposed and 
prototype developed.  The design is a result of a multi-disciplinary efforts including 
mechanical, electrical, computer, and textile engineering.  The concept is developed with 
laboratory testing and proven in the field.  The software and hardware are developed with 
both laboratory equipment and field testing.  The concept of transmitting text message 
data between Um radio interface and WSN radio interface is proven. A novel 
multi-functional tether is also developed to facilitate communication, allow pneumatic 
control of the balloon, and provide the necessary tensile strength and environmental 
protection.  Although we have proven the concept by developing a deployable scheme for 
emergency communication during disaster relief, we have also learned many lessons, and 
realize future work is needed including increasing communication range and developing 
application specific components optimized for this endeavor.  We sincerely hope this 
technology can be developed further and implemented to save lives, improve emergency 
management and response, and that our effort may truly benefit humanity in the future. 
 
115 
 
 
 
 
Chapter 5.Conclusion and Future Work 
 
5.1.Conclusion on Electromagnetic Textile Research 
This dissertation explored the radiation mechanism of woven antennas by conducting 
simulations and antenna testing.  The results suggest that the structure of the woven 
antenna disturbed the fundamental resonant mode of the MSA, while the second lowest 
resonant mode remained. The designed woven antennas also possess an efficient resonant 
mode much lower than all MSA model predictions. Thus, it is a novel type of compact, low 
profile, and highly efficient antenna.  
Meanwhile, such phenomena also lead to the numerical research of textile FSS and 
AMC/AEC structures. This research is among the first to discover the unique 
electromagnetic properties of both materials. Based on these findings, this new type of 
material is defined as the Electromagnetic Textile distinguishing from the common 
E-textile, which merely provides DC connectivity of computing, digital components, and 
electronics to be embedded in fabrics.  
The development of a novel electromagnetic material is accomplished. The unique 
material is applicable to a variety of electromagnetic problems, including novel low-profile 
antennas, frequency selective surfaces, and artificially electromagnetic surfaces. The 
 
116 
author hopes this research will draw interest from both textile and electromagnetism 
researchers and start a new era of electromagnetic textile material research.  
5.2.Conclusions on Emergency Communication Network Development 
Efforts on development of novel ECN resulted in desirable outcome. The hypothesis 
that WSN RF link can be used to relay GSM text messages was proven. The protective 
shell and tether have shown adequate strength during field testing. The feasibility of using 
air-drop SMS-WSN to form emergency communication network was successful. However, 
due to the complexity of the ECN system, significant work remains from both a theoretical 
and an experimental perspective. We are very interested in furthering this entire project to 
develop what is necessary so that it might be implemented.  Presently we are considering 
new design iteration, incorporating the lessons learned to improve the design.  Future 
research will be strongly advanced by partnering with industry to leverage their knowledge, 
resources, and experience to extend the present capabilities to include mixed-signal IC 
design among other possibilities. 
 
117 
 
 
 
 
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APPENDIX A. FSS Simulation Using Periodic Boundary Conditions in Ansoft HFSS  
 
An overview of the full-wave analysis of frequency selective surfaces using Periodic 
Boundary Conditions (PBCs) in Ansoft HFSS is presented in this appendix. This tutorial is 
based on the resources provided by Ansys Corporation.  
The characteristics of Frequency selective surfaces (FSSs) are their incident wave 
reflection and transmission properties. FSSs in general are 2-D planar, periodic arrays with 
an infinite extent. According to the Floquet?s theorem, the scattering properties from the 
entire infinite array can be derived from the field information of a single period of the array 
(unit cell). This condition assumes a plane-wave excitation. 
Ansys HFSS utilizes the Floquet theorem to simulate antenna array and FSSs. This 
can be done through the modeling one unit cell and applying the periodic boundary 
conditions (PBC) to the unit cell. The excitation is usually set up as a plane-wave port on 
one side of the unit cell. The procedure we used to simulate an FSS in HFSS 12 is provided 
here through an example, including all the steps for modeling. Example considered here is 
the surface presented in Chapter 3, the square aperture FSS. 
Simulation Model Setup  
The example considered here is a single sided array of metallic aperture on top of a 
substrate. After drawing the unit cell, the PBC is assigned as the boundary condition to 
each pair of the opposite side walls of the unit cell to set up the infinitely array 2-D space. 
 
123 
Perfectly-matched layers (PMLs) are set up over the top and bottom sides of the box 
outgoing wave absorption. Finally, the excitation is chosen to be the incident plane-wave. 
These steps are summarized in the following. 
1) Model the unit cell, including the substrate and the metallic aperture on top of the 
substrate. 
2) Draw an air box which includes the unit cell. The box sides must touch the 
substrate edges. 
 
Figure A.1 The unit cell geometry inside the simulation air box 
3) Assign the Master and Slave boundaries to the air box. Select the face shown in 
Figure A.2, and click HFSS>Boundaries>Assign>Master or right click on Boundaries in 
the Project tree and select Assign>Master. Click the drop down menu for the U vector, and 
click, New Vector. The Measure dialog and the Create Line prompt appear. Draw the U 
vector of the coordinate system on the selected face. Click on the lower left corner as the 
starting point, and drag the cursor to the right corner and click. In the Master Boundary 
dialog, for the V Vector, check the box for Reverse direction, and OK to close the dialog. 
 
124 
Select the opposite face, and HFSS>Boundaries>Assign Slave or right click on Boundaries 
in the Project tree and select Assign>Slave. The Slave dialog appears with the General Tab 
selected. Select Master1 as the Master boundary. Draw the U Vector as shown. Accept the 
other settings and OK to close the dialog. Repeat the procedure for the Master2 and Slave 2 
boundaries.  
 
Figure A.2 Assign master and slave boundary 
Assign the Floquet Ports 
This section shows how to assign the Floquet ports to the top and bottom faces of the 
model.  
Select the top face of the model, and click HFSS>Excitations>Assign>Floquet Port. 
The Floquet Port wizard appears, showing the General page. For the Lattice Coordinate 
System, from the drop down menu for g2183 direction, select New Vector. The Measure Data 
dialog appears, and the Create Line dialog tells you to draw the g2183 lattice vector on the 
plane of the face as shown in Figure A.3, clicking on the corner nearest the Z axis to start, 
and then clicking on the corner along the X direction. When you make the second click to 
 
125 
complete the vector, the Measure Data and Create line dialogs disappear, and the 
Floquet Port wizard reappears, showing that the g2183 vector is Defined. Repeat the process 
to draw the g2184uni0009vector as shown. 
 
Figure A.3 Assign Floquet port 
Click Next in the Floquet wizard to set the Phase Delays. Select the Input Lattice 
Phase Delays radio button, and click Next to go to the Modes setup page. On the Modes 
setup page, enter 6 as the Number of Nodes. This fills out the Mode table to 6 entries with 
initial 0 values. Click the Modes Calculator button for assistance in setting up the modes. 
Accept the values by clicking OK to close the Calculator. This fills out the table with 
calculated values. Accept default set up for the rest of Floquet port wizard. 
Setup the Analysis 
To setup this analysis, Right click on Analysis in the project tree, and select Add 
Solution Setup. This opens the Solution Setup dialog. On the General tab, set the Solution 
frequency to 10 Ghz. Set the Maximum Number of Passes to 10, and the Maximum 
Delta S as 0.02 as shown in Figure A.4. On the Options tab, check the Do Lamda 
Refinement box, and set the Lambda target as 0.2. Set the Maximum Refinement Per 
 
126 
Pass to 20%, the Minimum Number of Passes to 6, and the Minimum Converged 
Passes to 2. Select First Order Basis function, and click OK to accept the Setup.  
 
Figure A.4 Solution setup dialog 
 
Figure A.5 Solution setup option dialog 
 
 
127 
Setup the Sweep 
To setup the Sweep, Rightclick on Setup1 in the Project tree, and select Add 
Frequency Sweep. The Edit Sweep dialog appears. For the Sweep Type, select 
Interpolating. For the Frequency Setup, select Linear Step. Then set the Start as 8 GHz, 
the Stop as 20 GHz, and the Step Size as 0.2 GHz. For the Interpolating Sweep options, 
set the Max Solutions as 50, and Error Tolerance at 0.5%. Click the Advanced Options 
button to display the Interpolating Sweep Advanced Options dialog. Set the Minimum 
Solutions to 5, and the Minimum number of Subranges to 1. Click OK to close the 
Interpolating Sweep Advanced Options, and OK to close the Edit Sweep dialog. Right 
click on the Sweep in the Project tree and click Analyze on the shortcut menu to start the 
simulation. This will take some time. 
 
Figure A.5 Sweep setup dialog 
 
  
 
128 
 
 
APPENDIX B. AMC Simulation Using the Floquet Modal Analysis in Ansoft HFSS 
 
The Sievenpiper mushroom structure has been widely studied in the microwave 
engineering field due to its unique properties. The Sievenpiper mushroom structure 
basically consists of a metallic patch connected to ground with a shorting post. The general 
model is shown in Fig. 1.  
 
Figure B.1 General model of Sievenpiper mushroom surface 
 
It can be used as a high-impedance surface and act like an artificial magnetic 
conductor. The Sievenpiper mushroom structure has also been widely used to realize AMC 
since it can be designed to have in phase reflection characteristic. In this appendix, the 
dispersion diagram of a Sievenpiper mushroom structure is generated using HFSS's 
eigenmode solver. 
 
 
 
129 
Dispersion Diagram Basics 
We want to use HFSS to obtain a dispersion diagram for the Sievenpiper mushroom. 
A dispersion diagram is a plot of propagation constant versus frequency; a dispersion 
diagram basically tells you how much phase shift a material has at a given frequency. 
Since a Sievenpiper mushroom allows for waves to travel in two-dimensions, its 
propagation constant can be written as a vector quantity, ? = xkx + yky. In order to 
generate the dispersion diagram, a unit-cell has to be defined and the appropriate periodic 
boundary conditions (PBCs) have to be applied.  
The Brillouin zone is shown with the high-symmetry points defined as 
uni0413uni0009=uni0009(g1863g3051g1868uni0009=uni0009g1863g3052g1868uni0009=uni0009uni0030g4667uni0009
uni0425uni0009=uni0009(g1863g3051g1868uni0009=uni0009g2024uni002Cg1863g3052g1868uni0009=uni0009uni0030g4667uni0009
uni041Cuni0009=uni0009(g1863g3051g1868uni0009=uni0009g1863g3052g1868uni0009=uni0009g2024)uni0009
The Brillouin zone is the most fundamental region for defining the propagation vector 
for a unit-cell; basically if one can define all the propagation vectors in the Brillouin zone, 
one obtains the entire characteristic of the entire periodic structure. Therefore the 
dispersion diagram will start at uni0413 then to uni0425 then to M and back to uni0413 as indicated by the path 
depicted on the Brillouin zone. 
 
Figure B.2 Brillouin zone 
 
 
 
130 
Model Setup 
First we must configure HFSS to use its eigenmode solver; HFSS>Solution 
Type...>Eigenmode. Next, the unit-cell of the Sievenpiper mushroom structure has to be 
drawn in HFSS. It consists of a square patch, a via, and a square block of substrate as 
shown in Figure B.3. The dimension of the patch is 4.8x4.8 mm2 and is assigned a PEC 
boundary condition. The via has a radius of 0.12 mm, a height of 1.27 mm, and is assigned 
a perfect conductor material. In the case of the substrate, its dimensions are 5.0x5.0x1.27 
mm3 and the substrate material is Rogers RT/duroid 6010/6010LM. 
 
Figure B.3 HFSS model of Sievenpiper mushroom structure 
Since the Sievenpiper structure is open to air in the positive z-direction, an airbox has 
to be defined for the simulation. To simulate an infinite free space, a perfect matched layer 
(PML) boundary is defined on top of the airbox as shown in Figure B.4. Radiation 
boundary cannot be used in the eigenmode simulation. The height of the airbox has to be 
approximately six times the substrate thickness. The default values for the PML boundary 
condition are used. 
 
 
131 
 
Figure B.4 Airbox and PML added to unit-cell 
 
Periodic Boundary Conditions 
Periodic boundary conditions must be applied to the face of the entire structure, 
which includes the airbox and the PML. Therefore, another airbox has to be created with 
encloses the original airbox and PML.  
1. Select the negative y-z face of the unit-cell and assign a Master Boundary 
Condition (mx); you have to define the U Vector which starts at (-2.5, -2.5, 0) and ends at 
(-2.5, 2.5,0). The completed boundary assignment should look like Figure B.5. Next 
select the positive y-z face of the unit-cell and assign a Slave Boundary Condition (sx). 
Again define the U Vector which starts at (2.5, -2.5, 0) and ends at (2.5, 2.5, 0). Then 
input the phase delay using a variable (px) as shown in Figure B.6. 
 
132 
 
Figure B.5 Completed master boundary condition 
 
Figure B.6 Phase delay 
 
 
133 
2. Do the same to the x-z faces of the unit-cell. Label the master as my and the slave 
as sy. For sy make sure to reverse the V Vector and use a variable (py). 
Analysis/Optometrics Setup 
Before the eigenmode analysis can be started, several steps need to be completed 
first. First, add a solution setup and input the values as depicted in Figure B.7. In addition, 
in the options tab of the Solutions Setup, input a minimum converged passes of 2. Note 
that the mesh gets large (around 30,000 tets) for each eigenpoint. As a result, this 
simulation takes several hours even for only one mode. 
 
Figure B.7 Solution setup dialog 
 
134 
Next, parametric sweeps are added for each design in the simulation file. 
For the first parametric sweep, we will go from uni0413 to uni0425 and. Add a linear step sweep for 
the variable px from 15 deg to 180 deg with 15 deg steps. In the Options tab make sure to 
check both Save Fields and Mesh and Copy geometrically equivalent meshes. 
For the second parametric sweep, we will go from uni0425 to M and this will be labeled 
2_X2M. Add a linear step sweep for the variable py from 15 deg to 180 deg with 15 deg 
steps. We have to set px to 180 deg. To do this go to General tab and check override for px 
and input 180 deg as shown in Figure B.8.  In the options tab make sure to check both Save 
Fields and Mesh and Copy geometrically equivalent meshes. 
 
Figure B.8 Override px variable 
For the third parametric sweep, we will go from M to uni0413 and this will be labeled 
3_M2Gamma. Add a linear step sweep for the variable px from 15 deg to 180 deg with 15 
deg steps and also for the variable py. Select both of these sweeps and Sync them as shown 
 
135 
in Figure B.9. In the options tab make sure to check both Save Fields and Mesh and Copy 
geometrically equivalent meshes. 
 
Figure B.9 Sync up sweeps 
Plotting Results 
Plots for each parametric sweep have to be made. For the uni0413 to uni0425 parametric sweep, 
create a report and use the default values (Eigenmode Parameters, Rectangular Plot). In the 
Sweep tab, choose Sweep Design and Project variable values and choose px values from 
15 deg to 180 deg and for py select only 0 deg. For the Y tab, choose Eigen 
Modes>Mode(1) through Mode(4)>re. We only wish to look at the real part of the 
eigenmode, the imaginary part is due to loss which is ignored since a parallel plate 
waveguide?s loss is negligible for the fundamental mode. The finished plot should look 
like Figure B.10. 
 
136 
 
Figure B.10 Plot of uni0413 to uni0425 
To plot the X to M parametric sweep, do the same as for the uni0413 to uni0425 parametric sweep 
report. However, make py as the primary sweep and set px to 180 deg. The finished plot 
should look like Figure B.11. 
 
Figure B.11 Plot of uni0425 to M 
 
 
 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00px [deg]2.00E+009
4.00E+009
6.00E+009
8.00E+009
1.00E+010
1.20E+010
1.40E+010
1.60E+010
Y1
Ansoft LLC 1_Gamma2XXY Plot 5
Curve Info
re(Mode(1))Setup1 : LastAdaptive
py='0deg'
re(Mode(2))Setup1 : LastAdaptive
py='0deg'
re(Mode(3))Setup1 : LastAdaptive
py='0deg'
re(Mode(4))Setup1 : LastAdaptive
py='0deg'
 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00px [deg]2.00E+009
4.00E+009
6.00E+009
8.00E+009
1.00E+010
1.20E+010
1.40E+010
Y1
Ansoft LLC 2_X2MXY Plot 5
Curve Info
re(Mode(1))Setup1 : LastAdaptive
re(Mode(2))Setup1 : LastAdaptive
re(Mode(3))Setup1 : LastAdaptive
re(Mode(4))Setup1 : LastAdaptive
 
137 
To plot the M to uni0413 parametric sweep, do the same as for the previous plots, but this 
time select values of 15 deg to 180 deg for both px and py. However, the resulting plot will 
just be a series of unconnected dots. This is because HFSS?s plotting function does not 
know which order to connect them. You can easy export the data and plot it yourself or 
create another HFSS design and only add an M to uni0413 parametric sweep. HFSS will then 
connect the dots in the results as shown in Figure B.12. The complete dispersion diagram is 
shown in Figure B.13; it was plotted by exporting the eigenvalues obtained from HFSS and 
using an external plotting program. 
 
Figure B.12 Plot of M to uni0413 
 
 
 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00px [deg]2.50E+009
5.00E+009
7.50E+009
1.00E+010
1.25E+010
1.50E+010
Y1
Ansoft LLC 3_M2GammaXY Plot 5
Curve Info
re(Mode(1))Setup1 : LastAdaptive
py='0deg'
re(Mode(1))Setup1 : LastAdaptive
py='15deg'
re(Mode(1))Setup1 : LastAdaptive
py='30deg'
re(Mode(1))Setup1 : LastAdaptive
py='45deg'
re(Mode(1))Setup1 : LastAdaptive
py='60deg'
re(Mode(1))Setup1 : LastAdaptive
py='75deg'
re(Mode(1))Setup1 : LastAdaptive
py='90deg'
re(Mode(1))Setup1 : LastAdaptive
py='105deg'
re(Mode(1))
 
138 
 
Figure B.13 Complete dispersion diagram