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THESIS

905;

This is to certify that the

thesis entitled

A CHARACTERIZATION AND APPLICATIONS OF HIGH
IMPEDANCE GROUND PLANES WITH CONFORMAL ANTENNAS

presented by

BENJAMIN RUSSELL NI LMHOFF

has been accepted towards fulﬁllment
of the requirements for

MS degree in ELECTRICAL ENGINEERING

 

 

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Major professor

 

Date 7/31/02

 

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6/01 c:/CIRC/DaIeDue.p65-p. 15

A CHARACTERIZATION AND APPLICATIONS OF HIGH IMPEDANCE
GROUND PLANES WITH CONFORMAL ANTENNAS

By

Benjamin Russell Wilmhoff

A THESIS

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Electrical Engineering

2002

UMI Number: 1410744

®

UMI

 

UMI Microform 1410744

Copyright 2002 by ProQuest Information and Learning Company.

All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.

 

ProQuest lnfonnation and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, MI 48106-1346

ABSTRACT
A CHARACTERIZATION AND APPLICATIONS OF HIGH IMPEDANCE GROUND
PLANES WITH CONFORMAL ANTENNAS

By

Benjamin Russell Wilmhoff

Current conformal antenna designs often incorporate features which protect
surrounding devices from unwanted radiation from the antenna. These antennas include
patch antennas and printed dipoles, amongst others. These features, in the form of larger
ground planes or absorber-loaded quarter-wave cavities, oﬁen are detrimental to the
performance of the antenna itself. A relatively new advance in electromagnetic
engineering, physics and optics, called the photonic band-gap (PBG) structure and the
high impedance ground plane (HIGP) have proven useful in alleviating these effects.

This thesis ﬁrst highlights the operation of HIGPs and provides computational
analysis, using the Finite Element Method (FEM), of a hybrid HIGP/conformal antenna
design. Secondly, a novel four-layer design concept for HIGP/antenna structures is
presented. This concept uses electric-type or real-source antennas, such as a dipole,
placed parallel in close proximity to the HIGP structure separated by a thin layer of low-
dielectric material. This design concept helps to better match the antenna by eliminating
the phase-reversed reﬂected wave off of the bottom of the ground plane, thereby allowing
an electric-type antenna to be used in close proximity to the ground plane that shields it,

and allowing for a lower-proﬁle surface mounted antenna.

For the ol’ folks at home

iii

ACKNOWLEDGEMENTS

I would like to thank Dr. Leo Kempel for his guidance through my career at Michigan
State. I thank him for giving me the opportunity to attend Michigan State, and for his
mentoring during my career here. I would like to thank Dr. Ed Rothwell for his wise
tutoring and patience. I would like to thank Dr. Dennis Nyquist for his bottomless pool of
electromagnetic knowledge.

A thanks to Dr. Stephen Schneider and Capt. Keven Golla of the Air Force Institute of
Technology for their support for and work on this project.

I thank Dr. John Burke, formerly of Mission Research Corp. and now an assistant
professor at Western New England College. John, it was your guidance and mentoring at
MRC that sparked an interest in me for electromagnetics, and ultimately led me to pursue
a higher degree.

A special thanks to my wonderﬁrl family for their support, patience and positive
attitudes while I worked to attain this degree. I have been blessed in so many ways, and I
am so happy to have the opportunity now to spend more time with all of you. Finally, to
my girlfriend Kristen and her family: thank you for your support and all you have done
for me in the past few months. The gloomy days in Mid-Michigan have been brighter

because of you.

iv

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................ vii
LIST OF FIGURES ...................................................................................................... viii
CHAPTER 1 ................................................................................................................... 1
INTRODUCTION ........................................................................................................... 1
1.1 Problem Statement ....................................................................................... l
1.2 Overview ..................................................................................................... 3
CHAPTER 2 ................................................................................................................... 5
HISTORY OF HIGH IMPEDANCE GROUND PLANES .............................................. 5
2.1 Problems With Conventional Conformal Antennas ...................................... 5
2.2 Photonic Band Gaps ..................................................................................... 9
2.3 High-Impedance Ground Planes ................................................................. 15

2.4 Electric Source Antennas (Type 1) and High Impedance Ground Planes ....21
2.5 Magnetic Source (Type 2) Antennas and High Impedance Ground Planes..28

2.6 Summary .................................................................................................... 34
CHAPTER 3 ................................................................................................................. 36
COMPUTATIONAL RESULTS OF PREVIOUSLY BUILT STRUCTURES .............. 36

3.1 Method of analysis ..................................................................................... 36

3.2 Wideband Hexagonal Patch with Normal Dielectric Border ....................... 40

3.3 Wideband Patch with HIGP Border ............................................................ 46

3.4 Wideband Patch with PEC border .............................................................. 51

3.5 Conclusions ............................................................................................... 53
CHAPTER 4 ................................................................................................................. 54
PROPOSED FOUR LAYER ANTENNA/HIGP DESIGN METHOD ........................... 54

4. 1 Introduction ............................................................................................... 54

4.2 Bowtie Dipole over HIGP Substrate ........................................................... 56

4.3 Bowtie Dipole over Grounded Dielectric Substrate .................................... 68

4.4 Optimized Bowtie Dipole/HIGP Design ..................................................... 72

4.5 Proposed Design not Computationally Tested ............................................ 81
CHAPTER 5 ................................................................................................................. 84
CONCLUSIONS AND GROUNDS FOR FUTURE WORK ......................................... 84
APPENDIX A ............................................................................................................... 88
CREATING INPUT FILES FOR PRISM ...................................................................... 88

Al Methodology .............................................................................................. 88

A2 ReadXY Z F ortran Code for Reading DXFZXYZ Ouptut ............................ 97

REFERENCES ............................................................................................................ 101

LIST OF TABLES

Table A-1: Sample Output from DXFZXYZ .................................................................. 90
Table A-2: Sample Skymesh .pts File ............................................................................ 92
Table A-3: Sample Skymesh .edg File ........................................................................... 93
Table A-4: Sample Skymesh .ref File ............................................................................ 94
Table A-5: Sample Skymesh .prj File ............................................................................ 94
Table A-6: Flowchart for Creating the Prism Input Files ................................................ 96

vii

LIST OF FIGURES

Figure 2-1: Printed probe-fed bowtie dipole on dielectric substrate .................................. 6
Figure 2-2: Cavity-Backed Printed Type I Antenna Conﬁguration ................................... 7
Figure 2-3: E-plane pattern of a printed dipole over dielectric slab .................................. 8

Figure 2-4: Actual and Imaged Sources Above Perfect Electric (PEC) and Perfect

Magnetic (PMC) Conductors ........................................................................ 9
Figure 2-5: Patch antenna (left) and printed dipole (right) over PBG substrates ............. 10
Figure 2-6: Radiation pattern of a bowtie-dipole over PBG substrate ............................. 11
Figure 2-7: Microstrip-fed Patch .................................................................................... 12
Figure 2-8: Surface Fields for Microstrip-fed Patch ....................................................... 12
Figure 2-9: Microstrip—fed Patch with PBG Border ........................................................ 13
Figure 2-10: Surface ﬁelds for Microstrip-fed Patch with PBG Border .......................... 13
Figure 2-11: Hexagonal-based HIGP surface ................................................................. 16
Figure 2-12: HIGP Geometry ........................................................................................ 17
Figure 2-13: Reﬂection Phase of a Wave from a Resonant HIGP ................................... 18

Figure 2-14: TM Surface Wave Measurements of a Flat Copper Sheet (a) and a HIGP

Surface (b) ................................................................................................ 20
Figure 2-15: Wideband Zigzag Dipole Over a Wideband HIGP structure ...................... 22
Figure 2-16: Probe-fed Monopole Over HIGP surface ................................................... 22

Figure 2-17: Broadside Transmission Measurement of a Wideband Zigzag Antenna over

Wideband HIGP surface ........................................................................... 25

viii

Figure 2-18: Broadside Frequency Response of Copper Tape Monopoles Connecting 4

HIGP Elements, with and without Vias ..................................................... 27
Figure 2-19: Wideband Hexagonal-Based Patch Antenna .............................................. 28
Figure 2-20: Wideband Patch with HIGP Border ........................................................... 29
Figure 2-21: Wideband Patch with PEC border ............................................................. 31

Figure 2-22: Broadside Transmission Measurement of Hexagonal Based Wideband

Figure 3-1:

Figure 3-2:

Figure 3-3:

Figure 3-4:

Figure 3-5:

Figure 3-6:

Figure 3-7:

Figure 3-8:

Figure 3—9:
Figure 4-1:

Figure 4-2:

antennas with three different borders ........................................................ 33
A sample ﬁnite element model of a square patch ......................................... 38
Sample Mesh for Wideband Patch used from 2-4 GHz ................................ 41

Input Impedance of Wideband Hexagonal-based Patch with simple Dielectric
Border ......................................................................................................... 42
Normalized tangential (a) and z-directed (b) substrate-level E-ﬁeld strength

for hex-based Wideband patch antenna at 4.4186 GHz ................................. 43

Normalized tangential (a) and z-directed (b) substrate-level E-ﬁeld strength

for hex-based Wideband patch antenna at 6.2685 GHz ................................. 44
Mesh used for Wideband Patch with HIGP border ﬁ'om 24 GHz ................ 47
Input Impedance for Wideband Patch with HIGP border ............................. 48

Normalized Tangential (a) and Z-directed (b) Substrate-Level E-ﬁeld

Strength for Wideband Patch with HIGP Border at 4.32645 GHz ................ 50
Input Impedance for the Wideband Patch with PEC Border ......................... 52
A Bowtie Antenna with HIGP Substrate ...................................................... 56

Cross Section of Proposed Four-Layer Design for a Dipole over a HIGP

Substrate ..................................................................................................... 57

Figure 4—3: Measured Resistance (a) and Reactance (b) vs. Electrical Length for
Triangular Dipole with 60° Flare Angle (from [13]) .................................... 61
Figure 4-4: Computed Input Impedance for the Bowtie Antenna with HIGP substrate 63
Figure 4-5: Expanded view of Input Impedance of Bowtie Dipole over HIGP substrate
ﬁom 4.2 — SGHz ......................................................................................... 64
Figure 4-6: Bowtie Dipole with HIGP-Substrate with Reduced Number of Elements 66
Figure 4-7: Input Impedance of Bowtie Dipole with Reduced-Size HIGP Substrate ....... 67
Figure 4-8: Diagram of a Printed Bowtie over Grounded Dielectric Substrate ................ 68
Figure 4-9: Input Impedance of a Probe-fed Bowtie Antenna over Grounded Dielectric
Substrate ..................................................................................................... 70
Figure 4-10: Expanded Input Resistance of the Bowtie over HIGP and Grounded
Dielectric Substrate ﬁom 4.2 - 5.0 GHz ................................................... 71
Figure 4-11: Input Resistance for Bowtie Antenna over HIGP and Grounded Dielectric
Substrates ................................................................................................. 74
Figure 4-12: Broadside Normalized E-plane Pattern (gain, db) of the Bowtie Antenna
with HIGP Substrate and Grounded Dielectric Substrate, F=5.58 GHz ..... 77
Figure 4-13: Broadside Normalized H-plane Pattern (gain, db) of the Bowtie Antenna
with HIGP Substrate and Grounded Dielectric Substrate, F=5.58 GHz ..... 78
Figure 4-14: Normalized Tangential (a) and z-Directed E-ﬁelds for Antenna over HIGP
Substrate ................................................................................................... 79
Figure 4—15: Normalized Tangential (a) and z-Directed E-ﬁelds for Antenna over
Grounded Dielectric Substrate .................................................................. 80

Figure 4-16: Untested Antenna/HIGP Four Layer Design .............................................. 81

Figure A-l: Square Patch Drawn in CAD ...................................................................... 89

xi

CHAPTER 1

INTRODUCTION

1.1 Problem Statement

Antennas can generally be classiﬁed into two categories: electric current (Type 1) and
equivalent magnetic current or aperture (Type 2) antennas [1]. In surface mount
applications, as in the skin of an aircraft, both these types of antennas require a reﬂector
or ground plane of some sort. A printed dipole (Type 1), for example, requires a ground
plane or reﬂector to direct radiation into a particular half-space, usually in the form of an
absorber-loaded quarter-wave cavity. A patch antenna (Type 2) requires a ground plane
to direct the electromagnetic wave to its radiation point. The ﬁnite ground plane in both
these cases is known to have negative effects on the performance of the antenna. In the
past thirteen years, there have been developments in optics, physics and electromagnetics
that have proven to alleviate some of the issues with antenna ground planes. These
developments include the discovery of photonic band gaps (PBG) [2] and high-
impedance ground planes (HIGP) [3].

A photonic band gap is a band of frequencies for which electromagnetic waves do not
propagate in a particular medium. A HIGP is a device that utilizes PBG theory to create a
structure that forbids the ﬂow of surface waves. HIGPs also have the interesting property
that they reﬂect incident electromagnetic energy with no phase reversal when the
incoming wave is within the PBG of the surface. There have been numerous efforts to

improve the bandwidth of the HIGP, i.e., increase its PBG [4].

The purpose of this thesis is, ﬁrst, to shed light onto the operation of a HIGP in the
RF/microwave range. Computational results have been obtained on a number of hybrid
HIGP/planar antenna structures using a custom Finite Element Method (FEM) code
called Prism [5]. With this code, the ﬁelds inside the aperture and under the HIGP surface
can be analyzed. The normal and tangential (with respect to the surface of a planar
antenna) electric ﬁelds for several antennas are plotted. These plots provide valuable
insight to how a HIGP/planar antenna structure works at resonance. Secondly, it is shown
how a high-impedance ground plane can help to reduce the overall volume that a surface-
mounted antenna consumes, and can even improve the performance of the antenna. A
novel four-layer design concept for a hybrid HIGP/antenna structure is introduced. This
design has the advantage of being low-proﬁle in volume and surface area, and fairly well
matched over a broad band (~28%). This concept places a Wideband electric/real source
antenna in the form of a bowtie-dipole parallel and in close proximity to a HIGP surface.
It is seen how this concept enhances the performance of dipoles placed near the ground
plane that shields them, thus making the printed dipole more conducive to surface-

mounting environments.

1.2 Overview

The next chapter will highlight the history and operation of PBG structures and
HIGP’s. In chapter two, the applications of I-IIGP’s to planar antennas will be presented,
and their advantages to the operation of these antennas will be discussed. Chapter two
will also explain work that has been done to make the HIGP more broadband. Chapter
three will present results from computational armlysis of some hybrid antenna/HIGP
structures that have previously been built and tested at the Air Force Institute of
Technology. In chapter four, a new design concept is presented in order to improve the
bandwidth of a HIGP/antenna combination. This concept uses electric-type antennas
separated from a HIGP surface by a thin layer of dielectric material. It is the goal of this
thesis to present and analyze this new design concept for planar antenna/HIGP structures.
Because the design equations for these structures treat the surface as a lumped surface
impedance made of periodic elements, implicit in the design is that the periodicity of the
surface is much smaller than the wavelength of operation, i.e., that many more than one
HIGP element exist per wavelength This places a large burden on computational design
and the subsequent analysis, which requires that the mesh which represents the structures
consist of triangular elements that are at least M15 — N20 in spacing, or smaller.
Therefore, a high number of HIGP elements translate into a high number of surface
triangles that are used to represent those elements, leading to huge memory requirements
and even more extreme computation and solution time. Some of the meshes used for this
work took up to ﬁve weeks for a medium-resolution frequency sweep. Therefore, a

secondary goal of this work is to determine how few HIGP elements can be used to create

the surface and yet still behave well as a high-impedance ground plane. This knowledge,
coupled with the design concept presented in chapter four, can lead to streamlined HIGP
structures that are low-proﬁle in both volume and surface area, are easy to build due to
the low number of elements, and yet still yield surface-mounted electric-type antennas
that are well matched to a 50 0 transmission line. Therefore, though the new structures
and design concepts presented here are certainly not optimized and complete, they open
the door to a new way of designing and building HIGP/planar antenna combinations.

In chapter ﬁve, some grounds for future work are presented. This involves several
concepts to aid or even enhance the design process and the computational analysis used

to predict the performance of HIGP surfaces.

CHAPTER 2
HISTORY OF HIGH IMPEDANCE GROUND PLANES

2.1 Problems With Conventional Conformal Antennas

The patch antenna is a versatile, lightweight antenna used in many applications, from
handheld GPS receivers to electronic warfare (EW) systems and radars on aircraft
surfaces. The patch can radiate energy in almost any direction in a half-space. This
antenna requires a ground plane to concentrate energy under the patch and out to the
edges where it is radiated (e.g., the cavity model). The normal AC image currents on the
ground plane created from the radiating element can have negative effects on the antenna
itself or on other surrounding devices. If the ground plane or cavity is placed too close to
the antenna, surface waves traveling on the dielectric substrate will partially reﬂect ﬁ'om
the ground plane and travel back to the antenna, thus drastically changing the input
impedance of the antenna. If the perimeter of the ground plane is truncated too quickly,
the normal AC image currents coupled to the ground plane ﬁ'om the antenna will have
enough energy to radiate into space when they encounter a discontinuity, such as the edge
of the ground plane. This radiation can alter the pattern and gain signiﬁcantly. If enough
power is input to the antenna, surface currents can couple to surrounding objects, such as
wingtips or discontinuities in an aircraft skin, and radiate. The common solution to this
problem is to make the ground plane bigger, so that surface currents will attenuate in the
imperfect metal before they reach an edge. This generally requires a ground plane that

extends several wavelengths out from the antenna at the lowest operating ﬁ'equency,

which can substantially increase the amount of real estate required for the antenna to
operate efﬁciently.

A known problem with the patch is that it is very narrowband and has relatively low
gain, even at resonance. Electric type antennas, such as bowtie dipoles, spirals, or log-
periodics can have tremendous broadband behavior with equally impressive gain and
suitable patterns. However, these real-source antennas do not lend themselves well to
surface-mount environments. These antennas rely on an electric ﬁeld that is parallel-
polarized to the plane in which the antenna lies. They radiate out in both directions

parallel to the antenna, as in Figure 2-1.

Printed dipole

 

Dielectric Substrate

Figure 2-1: Printed probe-fed bowtie dipole on dielectric substrate

In a surface-mount environment, the radiation extending through the substrate and to the
back side can interfere with other devices, such as electronics or radars, or can couple to
other radiating elements and increase the radar cross section of the vehicle tremendously.
The solution to this problem is to place a shield behind the antenna to protect these
devices, typically in the form of a quarter-wave cavity at the center ﬁ'equency. This
conﬁguration is shown in Figure 2-2. The cavity-backed antenna, however, can be

extremely narrowband, signiﬁcantly reducing the bandwidth of a normally broadband

antenna, as in the bowtie. The ﬁelds reﬂected by the bottom of the cavity interact with the
ﬁeld at the feed and make the antenna appear as a short circuit at frequencies other than

where the cavity depth is a quarter-wavelength.

/Pn'nted Type | Antenna

#1

 

Dielectric Substrate or Airer .
N4 metal cawty

 

 

 

 

Microwave Absorber Coaxial Feed Line

Figure 2-2: Cavity-Backed Printed Type I Antenna Conﬁguration

The bandwidth can be extended by adding layers of absorbing material at the bottom of
the cavity, attenuating the ﬁeld transmitted down to the cavity bottom, and again after the
wave has been reﬂected. However, the absorber reduces the total available power for
radiation. The most obvious problem with the quarter wave cavity is that it requires
signiﬁcant real-estate in the backward half-space, precluding its use in surface mount
environments. Finally, the ﬁelds tend to concentrate in the dielectric region of a printed
electric-type antenna, instead of radiating into free space. For a higher dielectric material,
the ﬁelds become more coupled to surface waves in the dielectric substrate than to plane
waves in free space. Figure 2-3 shows the E-plane pattern of a printed dipole antenna
over a non-grounded dielectric substrate. It is clear that most of the radiation extends out

through the substrate and then into space, instead of into space directly.

 

 

 

Figure 2-3: E-plane pattern of a printed dipole over dielectric slab (from [7])

The problems presented here in the design of planar antennas can be alleviated by the
use of photonic band gap (PBG) technology and high-impedance ground planes (HIGP).
The discovery of photonic band gaps in 1989 has allowed for many developments in
microwave and antenna engineering. The high-impedance ground plane is an extension of
the study of PBG’s, in that the HIGP is treated as a lumped surface impedance in a

macroscopic sense. The history of these two ﬁelds will be presented next.

2.2 Photonic Band Gaps

A photonic band gap (PBG) structure, also called a high-impedance ground plane
(HIGP) when used in the RF-rnicrowave range, is a device that suppresses tangentially
traveling electromagnetic energy (surface waves) and reﬂects incident energy with no
phase reversal in the tangential electric ﬁeld when the frequency of the energy is within
the photonic band gap of the structure. When the reﬂected electric ﬁeld has no phase
reversal, the surface acts as a magnetic conductor, complementary to the phase reversal

of the electric ﬁeld in an electric conductor.

 

 

Electric Electra: Magnetic Magnetic Actual
Sources
T 1 _. 1 _.
2h Perfect Electric Conduztor
__L I 4— i Imaged
—. Sources
Electric Electric Magnetic Magnetic Actual
Sources
T 1 _, 1 _.
2h Perfect Memoir: Conductor
_1_ 1 —e I imaged
‘— Sources

Figure 2-4: Actual and Imaged Sources Above Perfect Electric (PEC) and Perfect
Magnetic (PMC) Conductors (from [6])

The real electric current ﬂowing along the surface of an electric conductor is replaced by
a ﬁctitious magnetic current when the analogy is extended to magnetic conductors. This
is summarized in Figure 2-4.

In the early analysis of PBG’s, much attention was devoted to formulating analogies
between the PBG structure and a crystal or molecule, and to understanding the
interactions between an electromagnetic wave and the entities comprising the crystal. By
using band theory of photons, a structure can be designed which forbids the ﬂow of light
through the structure. The ﬁrst PBG structure, developed by Yablonovitch, was a small
cube of dielectric material with spherical pockets of air embedded in it in a grid fashion.
Yablonovitch found that this structure forbids the ﬂow of electromagnetic waves over a
signiﬁcant bandwidth (14%) [2].

Since this original study, many researchers have incorporated PBG structures into the
design of planar antennas [7,8,9,10,11]. Figure 2-5 shows a patch antenna surrounded by,

and a printed dipole on top of, a PBG substrate.

Impedance Transition Planar Dipole

   

Figure 2-5: Patch antenna (left, from [10]) and printed dipole (right, from [7]) over
PBG substrates

 

Figure 2-6: Radiation pattern of a bowtie-dipole over PBG substrate (from [7])

Gonzalo and others found that the patch surrounded by PBG substrate was effective at
suppressing surface waves and improving the gain compared to a normal patch with
dielectric border [11]. Brown found that the dipole, when operated over the PBG
substrate, exhibited far better performance than when operated over the high-dielectric
substrate. Figure 2-6 shows the radiation pattern of the dipole over a PBG substrate.
Comparing to Figure 23, it is clear that the radiation now extends into space instead of
through the dielectric.

Figure 2-7 shows a typical microstrip-fed patch surrounded by grounded dielectric
substrate. Figure 2-8 shows a surface ﬁeld plot of the electric ﬁelds for this structure
when operated at a frequency of 2.14 GHz. The bright areas indicate high ﬁeld intensity,
while the dark areas indicate low ﬁeld intensity. Notice the areas of high ﬁeld intensity
around the transmission line and the center of the patch, but also at points away from the

patch. Figure 2-9 is the same patch but with a PBG structure border.

11

 

 

 

 

Figure 2-7: Microstrip-fed Patch

 

Figure 2-8: Surface Fields for Microstrip-fed Patch

 

 

 

 

 

Figure 2-9: Microstrip—fed Patch with PBG Border

3
3

 

‘32
a
a
1‘
2.
3';
‘11

Figure 2-10: Surface ﬁelds for Microstrip-fed Patch with PBG Border

*Figures Figure 2-7, Figure 2-8, Figure 2-9, and Figure 2-10 are from [11]

The PBG structure consists of air columns embedded in a dielectric material (a, = 10) in a
lattice-like fashion. Figure 2-10 shows the surface ﬁelds for this structure when operated
at the same frequency as the normal patch, 2.14 GHz. The intensity of the surface ﬁelds
has clearly been reduced at points other than in the immediate vicinity of the patch.
Looking forward to later chapters, the design shown in Figure 2-9 is one on which the
novel designs in this thesis are based, in that the air columns that comprise the surface are
spaced roughly a distance apart similar to the size of the patch, indicating that the
periodicity is on the order of the wavelength of the radiated ﬁelds.

Sievenpiper found that a PBG structure could be described in a macroscopic sense,
using surface impedance models to predict the behavior of the structure. This progression
of research has formed a new topic and new method of analysis in PBG structures: the

high impedance ground plane.

14

 

2.3

The cc
found
be am
much :
LC cir
imagir

3.121885

P101331
Sie
the Shl

0f the

2.3 High-Impedance Ground Planes

The concept of a high-impedance ground plane was ﬁrst presented by Sievenpiper [3]. He
found that photonic band-gap structures consisting of periodic elements of some sort can
be analyzed using a surface impedance model as long as the periodicity of the structure is
much smaller than a wavelength. This analysis treats the entire PBG surface as a resonant
LC circuit, with an appropriate center frequency and bandwidth. At some frequency, the
imaginary part of the surface impedance goes to infinity. At this frequency, the surface
acts as a magnetic conductor, in that the reﬂected tangential electric ﬁeld is in phase with
the incident ﬁeld. In some band around this center ﬁ'equency, neither TM nor TE modes
propagate along the surface as waves.

Sievenpiper found that in a high impedance surface comprised of periodic elements,
the sheet capacitance and inductance can be described in terms of the physical parameters

of the sheet. Figure 2-11 is an example of a periodic hexagonal based HIGP surface.

15

 

 

 

 

Figure 2-11: Hexagonal-based HIGP surface

The capacitance of the surface comes from the charge separation on adjacent metal pads
across the dielectric substrate. The black circles in the middle of each pad represent metal
Vias connecting the pads to a continuous copper conducting ground plane on the back
side of the surface, with some dielectric substrate in between. The sheet inductance
comes ﬁ'om currents traveling from the pads on the top layer down through these vias,
across the bottom ground plane and looping around to the via of an adjacent pad.

The capacitance of an individual element is found ﬁom conformal mapping to be

C _ W60 (gal + ng)

element _

Cosh'l (SXFarads / square) (2.1)

where w is the edge length of an element, 8,, I is the relative permittivity of the ambient
media (usually free space, but can be dielectric for multi-layer applications as will be
seen later), an; is the permittivity of the dielectric substrate immediately beneath the

metal pads, a is the center to center spacing of elements and g is the gap that exists

between adjacent elements. The geometry of the structures Sievenpiper used is shown

below in Figure 2-12.

 

 

 

 

 

 

Figure 2-12: HIGP Geometry

The capacitance of an individual element is multiplied by a geometrical correction factor
to obtain the sheet capacitance, which accounts for the grid-like nature of the elements. In
the case of hexagonal elements, the geometrical correction factor is 1/\/3 . The sheet
inductance, in Henrys/ square, is found by integrating the magnetic ﬁeld around a
solenoidal loop. It is given by
L3,”, = pop,t(Henrys/ square) (2.2)

where ,u., is the permeability of free space, ,u, is taken to be 1.0 for non-magnetic
substrates, and t is the thickness of the dielectric.

The result of a measurement of the phase of the reﬂected ﬁelds from the HIGP surface
is shown in Figure 2-13. The phase of the reﬂected wave from the HIGP surface,

referenced to the phase of the incoming wave, travels from TI radians, through 0 and to -1r

17

radians. This measurement consisted of performing a mono-static reﬂection measurement
of a large metal sheet in an anechoic chamber for calibration purposes, and then of a
HIGP. The HIGP data was divided by that of the metal sheet to calibrate, and a phase
shift of n was added back in to account for the phase of the metal sheet. An inﬁnite
perfect metal conductor would have a phase shift of 1: or -1r radians when referenced to

the phase of the incoming wave across the entire RF band.

 

 

1r/2

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed

 
  

 

Resonant

   

 

e

i

o 5 1o 15 23 25 30
Frequency (GI-Iz)

Figure 2-13: Reflection Phase of a Wave from a Resonant HIGP (from [3])

18

The surface wave measurements were performed by inducing TM and TE surface waves
on both a ﬂat metal sheet and then across a HIGP surface. The measurement had to be
performed at ﬁequencies at which surface waves could be coupled to the lossy metal
sheet, starting at roughly 2 GHz. Two small monopole probes (Tx and R) were placed
vertically on both sides of the ﬂat metal sheet or the hexagonal-based HIGP. The vertical
electric ﬁeld launched by the probe couples to the vertical electric ﬁeld of a TM surface
wave. The experiment was repeated with the probes oriented parallel to the surfaces in
order to couple to the parallel electric ﬁeld of a TE surface wave. The results of the TM
measurements are shown in Figure 2-14. The PBG for this high-impedance surface exists

between 12 and roughly 17 GHz.

19

 

 

 

 

 

 

 

 

 

 

“'10 I I I I I I I I I
a - d
32.
5 -20 -
“a ..
a -
E
'a '40 '
a -
E
2' -50 h
a:
l- _

.50

0 6 12 18 24 30
Frequency [GHz]
(8)

H '10 I I I l I I I I I
m _ ..
2- <—->
g -20 - Band -
‘5’ " Gap "1
5 -30 - ..
C
lg i v
i. I "
5 -50 . -
'— -

_60 l 1 l 1 L J l L

O 6 12 18 24 30
Frequency [GI-12]
(b)

Figure 2-14: TM Surface Wave Measurements of a Flat Copper Sheet (a) and a
HIGP Surface (b) (from [3])

20

2.4 Electric Source Antennas (Type 1) and High Impedance Ground Planes

High impedance ground planes can be used in conjunction with planar antennas to
produce some useful antenna characteristics. It was found that monopole antennas could
be placed parallel at a very small distance (< M4) from a HIGP and still operate well.
This means that electric type antennas can be placed very near a reﬂecting ground plane,
allowing for efﬁcient radiation into one half-space without consuming too much volume.
Golla tested several electric type antennas, in the form of zigzag dipoles and copper-tape
monopoles placed directly above a HIGP structure [4]. These structures are shown in

Figure 2-15 and Figure 2-16.

21

 

 

 

 

 

 

 

- 1,1' , .

Figure 2-15: Wideband Zigzag Dipole Over a Wideband HIGP structure

Copper Tape

HIGP

 

Coax Feed

Figure 2-16: Probered Monopole Over HIGP surface

‘Figure 2-15 and Figure 2-16 are ﬁ'om [4]

22

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CODSIB.

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seen i
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ante
thel

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The zigzag dipole is a Wideband antenna whose input impedance is known to stay fairly
constant over a broad range of ﬁequencies. A wave traveling on the antenna will launch
at points where the distance from one side of the zigzag to the other is a half-wavelength,
making the antenna to appear as a half-wave dipole over a broad range. This antenna,
made of copper tape, was placed directly on top of a Wideband HIGP surface. As can be
seen in the ﬁgure, the surface is comprised of hexagonal elements of varying sizes. These
elements scale ﬁom the high-ﬁequency end of the dipole (closer to the center) to the
lower frequency end, towards the outer edges. It was thought that the different frequency
ranges of the HIGP elements would roughly overlap to form a broad frequency band of
operation in which surface waves are suppressed and incident waves are reﬂected with no
phase reversal. This band of frequencies should fall within the operating range of the
dipole to form a well tuned antenm/HIGP structure. However, Golla found that this
antenna did not perform well. Figure 2-17 is the broadside fi'equency response (821)
measurement of this antenna. These measurements are standard 821 transmission
measurements performed in an anechoic chamber with a vector network analyzer. A
standard gain horn is connected to one port of the network analyzer and the antenna
under test is connected to the second port. An $21 measurement is performed on both the
antenna-under-test, and then a second standard gain born. The antenna-under-test data is
then divided by that of the standard gain horn data in order to calibrate. The antenna
performs worse than an isotropic radiator over nearly the whole measurement range.
There is a band around 15 GHz however that does perform better than an isotropic
radiator. Golla attributes the poor performance to the HIGP surface suppressing the

traveling wave on the dipole in all bands but the high-frequency band that is radiated

23

from the small region close to the feed. The desirable surface wave suppression that is
usually associated with HIGP appears to hinder the performance of a broad band,
traveling wave antenna. However, the experiment was performed by placing the zigzag
antenna directly over the HIGP surface, with only a negligible ﬁhn of adhesive that is
found on the back of copper tape separating the antenna from the HIGP surface. It is
quite possible that the extremely small separation distance between the antenna and the
HIGP surface causes the antenna to short directly to the HIGP elements themselves. In
Chapter 4, an antenna is presented that uses the same design principle, a broadband
electric-type antenna over a HIGP surface. However, the separation between the antenna
and the HIGP surface is more signiﬁcant, .059 mils (1 mil = .001”) or 1.5 mm. This
design has the desired qualities of a broadband antenna yet requires less volume and

surface area than the current design methodology would require for this type of antenna.

24

 

 

 

 

 

 

m T I I I I I I
8" -I
a.
4_
s 21
3
0
3 Di- ------------------------------------------------------- -4
E . .
< 2
.4 .
-8- .
-8b .
.n' l L L 4L l 1 l
2 4 6 8 1O 12 14 16 18
Frequency(Gl-lz)

Figure 2-17: Broadside Transmission Measurement of a Wideband Zigzag Antenna
over Wideband HIGP surface (from [4])

25

 

The copper tape monopole was also placed directly adjacent to the HIGP surface. In
this experiment, the goal was to actually create an antenna from the HIGP elements
themselves. The copper tape stretches from the coaxial probe feed across the HIGP
surface and connects one or more HIGP hexagonal pads together. Because the conducting
vias in a typical HIGP surface provide a shorting path to ground, they were removed for
this experiment. It was found that a monopole connecting together 4 of the HIGP pads
performed reasormbly well over a small band. The experiment was then repeated with the
conducting vias in place, except for the vias in the elements directly below the antenna
(leaving these vias intact would have shorted the antenna directly to the ground plane
underneath). Figure 2-18 is the broadside ﬁ'equency response (321) of the copper tape
monopole linking together 4 of the elements. Both antenna structures have bands in
which they perform better than an isotropic radiator. These bands are fairly narrow, and
the maximum received signal even at best is only 2 dbi. This experiment did prove,
however, that the HIGP elements could be used as antennas. This led to the development
of integrated antennas that married together the HIGP elements and the antenna itself, so
that one or more HIGP elements were probe-fed as patches in the same plane as the HIGP

surface, creating an extremely low proﬁle surface mounted antenna.

26

w I I I I I

—- monopole tidbits
3 . — monopoleulhnouia J

 

 

 

Amplludealal)

 

 

 

 

 

 

 

10
Frequency (GHz)

Figure 2-18: Broadside Frequency Response of Copper Tape Monopoles Connecting
4 HIGP Elements, with and without Vias (from [4])

27

2.5 Magnetic Source (Type 2) Antennas and High Impedance Ground Planes

ItwasfoundthatpatchantennascouldbeplacedintheplaneoftheI-IIGPsm'faceand
radiate well, without the surface waves that are normally a byproduct ofa patch antenna.
This was seen in Figure 2-5 where the patch is adjacent to the HIGP elements. Golla did
work in trying to increase the bandwidth of a HIGP/patch antenna hybrid design. He
fabricated the antenna itselfout of the same elements that make up the HIGP, using a
superposition of different sizes of hexagonal pads. The antenna by itselfis shown below,

in Figure 2-19.

 

Figure 2-19: Wideband Hexagonal-Based Patch Antenna

The antenna consists of hexagonal pads of different sizes, with the design philosophy tint

the diﬁ‘erent sizes will radiate at different ﬁ'equencies. There are four different sizes of

28

metal pads shown here, with the dimensions of each unique pad size increasing linearly
by a factor of two. The base hexagonal unit is 120 mils in diameter. From equation 2.1,
the element-to-elements spacing (a) is 114 mils, the gap width (g) is 10 mils, the edge-
length (w) ofanelement is60 mils, andthe substrateonwhichthe structure isprinted is
FR4 of thickness 59 mils with a dielectric constant of 4.9. The aperture size (large square
of dielectric surrounding the patch) is 2.5” x 2.5”. The goal of his work was to then build
an appropriately sized HIGP that would ﬁt around this antenna and suppress surface
waves, reduce the aperture size and yet still allow the antenna to radiate well over a large

band of ﬁ'equencies. The antenna with the HIGP border is shown below in Figure 2-20.

 

Figure 2-20: Wideband Patch with HIGP Border

29

The HIGP elements wrap around the antenna, so that the entire aperture size now shows a
signiﬁcant reduction compared to that of the dielectric border. The dark lines surrounding
the metal pads and the antenna represent dielectric substrate. The HIGP surface for this
antenna scales in size linearly with the sizes of the metal antenna elements create
theoretical wideband HIGP surface. The third antenna tested in this series was an
extreme-case scenario: the dielectric border of Figure 2-19 border was shrunk so that
there was only a small 10 mil gap separating the antenna ﬁom the surrounding PEC
surface, shown in Figure 2-21. This structure has the smallest aperture size possible, in
that the metal surrounding the antenrm, which could, in a surface mount environment,
represent the fuselage of an aircraft or the nosecone of a missile, is now nearly directly
adjacent to the antenna leaving little room for radiation ﬁelds to escape from beneath the

patch.

30

 

Figure 2-21: Wideband Patch with PEC border

Golla performed broadside transmission measurements of these three antennas. The
results of these measurements are shown in Figure 2-22. He found that the antennas with
the dielectric border and the HIGP border radiated better than an isotropic radiator over a
very signiﬁcant bandwidth. In fact, the antenna with the HIGP border outperformed the
antenna with dielectric border at certain ﬁ'equencies. This indicates that a patch antenna
with a small aperture can still perform well over certain bands. The signiﬁcance of this is
that the surrounding mdia of a surface mounted antenna can be shrunk down reasonably
close to the antenna. In the case of the antenna with HIGP border here, the surrounding
metalsm'ﬁtce is separated fromthe antenna byat mostthe diameter ofthe largest

hexagonal patch that comprises the HIGP, 480 mils or 0.48 inches. This is a marked

31

improvement over the normal one to two wavelengths of dielectric that are required for a
typical patch in a surface mounted environment.

The antenna with a PEC border did not radiate well at all. This is because the
proximity of the surrounding metal border tended to short out the signal from the feed,
instead of radiating. It was found, though, that the antenna with the PEC border did
radiate slightly better than an isotropic radiator over several small bands. This seems
counterintuitive, since, at the frequency range of operation (2—14 GHz) the gap between
the antenna and the surrounding metal border would have appeared as continuous metal,
making the antenna appear as a large metal plate separated from a ground plane by a
layer of dielectric. It is possible that the antenna with PEC border and even the antenna
with HIGP border are acting as leaky parallel plate waveguides over certain bands. A 10
mil gap is no more than .0085)» at ﬁequencies as high as 10 GHz. It is not likely that most
of the radiation comes from the gaps between the antenna and the PEC border, or even
from the gaps between the antenna and the HIGP structure. It is possible that these two
structures radiate parallel plate modes that are excited from the probe-feed at the center
and travel outward to the edges of the dielectric/metal plates. In the next chapter, the
computational analysis that was performed provides insight as to how these structures

radiate.

32

 

 

 

Amplitude (dBl)

   
 

l

— HIGP border

 

 

 

 

 

'9 ' —~— PEC border
I — - dielectric border
.ﬂ - 1 1 1 L I 7y I 4 -
2 4 O 8 1O 12 14 16 18

F requency (GI-12)

Figure 2-22: Broadside Transmission Measurement of Hexagonal Based Wideband
antennas with three diﬂ‘erent borders (from [4])

33

 

2.6 Summary

This chapter has provided the background work on photonic band gap structures and high
impedance ground planes. In summary, the work in this ﬁeld started with extremely small
structures with antennas that radiate at small wavelengths. Sievenpiper used an effective
medium model to analyze structures that are small compared to a wavelength and
therefore developed the surface impedance analysis of photonic band gap structures,
leading to the development of high impedance ground planes. Golla, amongst others,
created antenna/HIGP hybrid structures in an attempt to make surface mounted antennas
smaller in surface area and in depth. Golla primarily used patch (aperture) antennas for
the work he performed in this ﬁeld. However, it was demonstrated in this chapter how
both aperture and real source antennas can be placed very near the HIGP surface and still
radiate well. The large bandwidths and relatively high gain of electric-type (real-source)
antennas make them suitable for many applications, but generally not for low-proﬁle
surface mounted environments, where the depth and surface area of the antenna are a
premium. That is why patch antennas are generally used, and much effort has been
devoted to creating more broadband and high gain patch antennas. It would be extremely
useful if the low proﬁle of a patch could be married to the performance of electric-type
antennas, a dipole for example.

The purpose of the next chapter is to provide computational analysis for the patch
antennas with the three different borders that were built by Go 11a: the patch with
dielectric, HIGP and metal borders. Because these antennas are narrow-band by nature,

the results of the proceeding analysis underscore the need to use a wider-band antenna if

34

 

wide-band performance is required of the antenna/HI GP structure. This impetus leads to
chapter four, where a wideband antenna is used integrally with a HIGP substrate in a
four-layer design concept. This concept both improves the performance of low-proﬁle
surface-mounted antennas and permits the operation of electric-type antennas, which are
known'to have broader operational bandwidths, close to the ground plane that shields

them.

35

 

CHAPTER 3

COMPUTATIONAL RESULTS OF PREVIOUSLY BUILT STRUCTURES

3.1 Method of analysis

The ﬁnite element method was used to simulate all structures. The particular code
used herein is a Fortran77 program called Prism [5]. It is an edge-based FEM code with
extruded triangles as the basic elements. A two dimensional structure meshed with
triangular sub-elements is input into the program, and when the triangles on the two-
dimensional surface are extruded three-dimensionally down multiple layers, they become
prisms. The user inputs the two dimensional surface to the program, and then speciﬁes
how the surface varies layer by layer in the z-direction. A z-directed edge is then selected
to be the feed edge, and a reference source ﬁeld is placed upon that edge. The program
then iteratively solves a Finite Element-Boundary Integral (FE - BI) matrix for the
electric ﬁeld coefficients on each unknown edge (non-metal edges), and then applies a
near-to-far-ﬁeld transformation in the form of the dyadic Green’s function to obtain the
far zone ﬁelds. The program can output the antenna pattern, input impedance and S-
parameters at the feed, amongst other characteristics. For this analysis, the input
impedance and far-ﬁeld gain of the antenna were used as the main criteria as to whether a
structure operates efficiently or not. In general, an antenna with an input impedance
whose real part is large and imaginary part is small is a resonant structure. Matching the
antenna to a typical 50 (2 transmission was not a concern, since this work focuses only on

creating theoretical resonant radiating structures.

36

The process by which a structure is drawn in a standard drawing package and then
converted into an acceptable format for the analysis code is quite lengthy and involved.
For brevity’s sake, this process will not be discussed here; however, the reader is referred
to Appendix A for details. Figure 3-1 shows a sample square patch that has been meshed
using triangular sub—elements. The model is drawn in two dimensions, with separate
polygons drawn for all distinct regions of the antenna: dielectric border, antenna, and
feed region. A meshing program entitled Skymesh is then used to produce the triangular
mesh, given the coordinates of the distinct regions. The mesh is then input to Prism
where the user speciﬁes the number of layers and what material the triangles of each
layer are made of: dielectric, metal or absorber. For this example, the sub-elements of the
outer region would consist of horizontal edges made of dielectric on the top layer, and the
vertical edges would be also be made of dielectric, representing the dielectric substrate
surrounding and lying beneath the antenna. The metal regions, regions 2 and 3, would
have horizontal edges made of metal on the top layer, and have vertical edges made of
dielectric, representing the dielectric substrate. Region 3 is meshed heavily in order to
have more control over which vertical edge to feed. It is important to remember that the
mesh does not vary in cross section layer by layer. This can be a constraint in some cases,
especially in the case of the HIGP analysis. The only parameter that changes layer by
layer is the material code for each closed region and the material code for each layer, and
thus for the sub-elements that comprise that region. Therefore, a square patch antenna
could not be simulated over a hexagonal I-HGP substrate, unless the spatial resolution of

HIGP elements was high enough to where multiple elements could be ﬂagged as antenna

37

“Mi“!
1.: I

elements on the top, including the dielectric space between elements, and then as HIGP

elements on the next layer.

 

 

 

 

 

 

 

 

 

Figure 3-1: A sample ﬁnite element model of a square patch

In general, all meshes must satisfy the requirement that no edge-length is greater than
M15 to 71/20 at the highest frequency. This requirement subsequently leads to very large
meshes for structures that are electrically large (greater than 2’» on a side). For some of
the structures analyzed in this work, the mesh consisted of as many as 8700 unknowns,
which in a square matrix results in around 76"‘106 complex double precision memory

locations. The computers used are two Linux workstations, each with four 512 MHz

38

parallel processors and 2 gigabytes of RAM. The most complex structures took up to
eight to ten hours per ﬁequency point using a single processor, and in order to get
sufficient resolution, the structures were all tested at frequency increments of 20 MHz.
Because of the available multiple processors, the frequency sweeps were divided into
multiple ranges so that more than one frequency sweep could be run at a time on each
machine. The structures simulated at each ﬁequency range were meshed according to the
highest ﬁ'equency of that range. For example, a structure that required a frequency sweep
of2-l4 GHz would have been run in 6 sweeps: 24 GHz, 4-6, 6-8, 8-10, 10—12, and 12-14
GHz with the mesh of each sweep range becoming progressively ﬁner in edge-size
resolution as the ﬁ‘equency increases. Even with this ability, some full frequency sweeps
took as long as four weeks. The structures built and tested by Golla were swept from 2-18
GHz. The computers used to analyze them simply did not have enough memory to
feasibly simulate this whole range. Therefore, all simulations are truncated at '14 GHz,
and some to 8 GHZ.

The Prism program is a versatile and robust code, and has shown good agreement
between computational results and experimental data for virtually any ﬁnite planar
electromagnetic surface. For a more detailed discussion of the Prism program, the reader

is referred to Chapter 3 of [12].

39

 

3.2 Wideband Hexagonal Patch with Normal Dielectric Border

The ﬁrst patch simulated, shown in Figure 2-19, is the wideband hexagonal-based patch
antenna tint Golla designed, built and measured. The actual mesh used to represent the
structure ﬁom 2-4 GHz is shown in Figure 3-2. This antenna was simulated from 2-14
GHz in increments of 20 MHz. The input impedance is shown in Figure 3-3. From the
computational analysis, it appears that the patch is very narrowband. The antenna was
then simulated at 4.4186 GHz in order to obtain information about the surface ﬁelds at
this particular frequency. From Figure 3-3 , 4.4186 GHz is the ﬁrst frequency at which
the real part of the input impedance is non-zero and the imaginary part goes through zero.
There are other ﬁequencies at which the reactive input impedance goes through zero.
However, the real part equals zero at my of these points. The data collected at the
single resonant point is in the form of electric ﬁeld coefﬁcients for each ﬁnite-element
edge of the mesh. The data was then imported and plotted in Matlab. The results of this
single-ﬁequency simulation are shown in Figure 3-4. The total tangential surface ﬁelds
are shown in (a) and the z-directed surface ﬁelds are shown in (b). The highest intensity
of ﬁeld strength is located near the feed point for both ﬁeld polarizations. The tangential
ﬁelds are necessarily zero under the metal patch to satisfy the boundary conditions. Upon
ﬁirther inspection, it can be seen that the z-directed ﬁelds have large magnitudes out
away ﬁom the patch, only roughly 1 to 2 db down from the maximum value at the feed,
indicating the presence of traveling surface waves.

The input impedance, from Figure 3-3, goes through second much smaller resonance

at 6.2685 GHz. The surface ﬁelds of the antenna were collected at this frequency as well,

40

in order to determine whether different parts of the antenna were indeed radiating at

different ﬁequencies. The results of this simulation are shown in Figure 3-5.

 

 

 

 

 

Figure 3-2: Sample Mesh for Wideband Patch used from 2-4 6111

41

 

15500r

R,X (0)

 

‘ \

T
L._._'— -*—-_- ._ _._ -..—. —._ _._-"-“a.".“--_«_—

 

 

 

 

.. .. "mm

 

 

 

 

 

Figure 3—3: Input Impedance of Wideband Hexagonal-based Patch with simple

Dielectric Border

42

12

14

NormalizedField Strum, db

 

Normalized Field Strength, db

   

(b)
Figure 3—4: Normalized tangential (a) and Zodirected (b) substrate-level E-ﬁeld
strength for hex-based wideband patch antenna at 4.4186 GHz

43

 

 

Normalized Field Strength, db

   

(a)

 

Normalized Field Strength, db

   

(b)
Figure 3-5: Normalized tangential (a) and z-directed (b) substrate-level E-field
strength for hex-based wideband patch antenna at 6.2685 GHz

It can be seen, upon comparing the normal z-directed surface ﬁelds at 4.4186 and 6.2685
GHz that the antenna certainly does radiate more at different places for different
frequencies. On the two largest hexagonal pads on the right side of the antenna, at 4.4186
GHz there is a clear null running from the top of the upper pad to the bottom of the lower
pad in a wide arc. At 6.2685 GHz, there are now two nulls in this vicinity, perpendicular
to each other, indicating the presence of a different radiating mode. There is clearly more
relative energy at this location on the antenna than at the lower resonance.

The design principle behind this antenna is that if a wideband patch antenna can be
created, then it would be useful to create a wideband HIGP surface to ﬁt around it. The
next section discusses computational results ﬁom the wideband patch and the wideband

HIGP border.

45

3.3 Wideband Patch with HIGP Border

The wideband hexagonal-based patch with a high-impedance ground plane border
(Figure 2-20) that was built and tested by Golla was also simulated and analyzed
computationally. The actual mesh used for this structure is shown in Figure 3-6. Because
of the extremely small air gaps (10 mils) separating the antenna ﬁ'om the HIGP elements,
and the HIGP elements themselves, the meshing program, SkyMesh, must create triangles
with extremely small edge-lengths in order to accurately represent the structure. At 14
GHz, the number of triangular sub-elements in the mesh that represents the antenna with
the HIGP border is seven times that of the mesh that represents only the patch, (Figure
3-2). Because of the extremely high number of unknowns, and the huge matrices that are
created when the FEM program solves for the ﬁelds, it was necessary to truncate the
frequency sweep at 8 GHz. Meshing at higher frequencies simply required too much
memory and computation time. In order to sweep to 8 GHz, the computers ran four sub-
sweeps in 2 GHz increments for a total raw computation time of about ﬁve weeks.
Further simulations would have taken even longer because of the increased resolution in
mesh size at the higher frequencies. The mesh was therefore swept from 2-8 GHz in

increments of .02 GHz. The input impedance is shown in Figure 3-7.

46

 

 

 

 

 

Figure 3-6: Mesh used for Wideband Patch with HIGP border from 2-4 GHz

47

RX (0)

 

 

 

 

 

 

 

 

 

 

 

-— Real
" -‘ "mg
1500 - -
1W - 1 -
i
‘ 1
i I
500 ’ '1 J. ‘
’l '
l . .
o [it g I .(A ’ “A J I :l" b ' - nnnnnn Ag -
i I. l ./ l‘ '1']
I? : '1
-500 h :i H -1
,1 I!
'1“ '- fl : -‘
3 1
,1
4500 ~ 3 ~
1
l
-2000 _ i _
|
_m 1 1 1 1
2 3 4 5 7 8
F(GHZ)

Figure 3-7: Input Impedance for Wideband Patch with HIGP border

48

Above 5 GHz, the antenna is a short circuit. It is likely that truncating the ﬁ'equency
sweeps at 8 GHz caused no loss in useful data. There appears to be only one resonant
frequency for this structure, at 4.32645 GHz. From the computational analysis, the
antennawith HIGP is as narrow band as the antenna by itself. The antenna was simulated
at the resonant frequency and the surface ﬁelds were again collected and plotted. The
normalized tangential and z—directed ﬁelds are shown in Figure 3-8 (a) and (b)
respectively. Because the border is mostly PEC, the tangential surface ﬁelds are zero
throughout most of the structure except for inside the air gaps. It can also be seen that the
tangential ﬁelds in the gaps are higher in intensity in the gaps that are closer to the feed
region, and much lower in intensity in the gaps that are away from the feed region. The
normal surface ﬁelds, however, are intense even away from the feed region. It is possible
that these ﬁelds move outward radially toward the edges of the structure, as in a parallel

plate waveguide, and radiate ﬁ'om the edges.

49

 

 

Normalized Field Strength, db

   

(a)

 

Normalized Field Strength, db

   

(b)

Figure 3-8: Normalized Tangential (a) and Z-directed (b) Substrate-Level E-field
Strength for Wideband Patch with HIGP Border at 4.32645 GHz

50

3.4 Wideband Patch with PEC border

The ﬁnal structure simulated is the wideband patch with the PEC border that runs directly
up to the edge of the antenm, with only a 10 mil gap separating the antenna from the
PEC border. The input impedance for this antenna is shown in Figure 3-9. This antenna
was simulated ﬁ'om 2-14 GHz in .02 GHz increments. The real part of the input
impedance is zero or very near zero across the entire frequency range. This is not
surprising, since across the entire frequency range, the antenna most certainly appears to
be a large metal plate above a ground plane separated by a layer of dielectric with a
vertical probe feed in between. Surface ﬁelds were not collected and plotted for this

structure since the antenna does not resonate in this band.

51

14

 

 

 

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800b

Input Impedance for the Wideband Patch with PEC Border

Figure 3-9

52

3.5 Conclusions

The structures simulated here have one problem in common: they are very narrow band.
Even the patch by itself only resonates at two distinct ﬁ'equencies, and away ﬁ'om those
ﬁequencies, the real part of the input impedance goes to zero. Consequently, the antenna
with the I-HGP border does not perform much better, since it is based on the same
antenna.

The new design work at MSU focused on starting with a known broadband antenna
and building a HIGP surface to ﬁt to it. This antenna takes the form of the printed bowtie
dipole. The next chapter discusses the design principles used for this antenna and the

HIGP surface for it, as well as computational results.

53

CHAPTER 4

PROPOSED FOUR LAYER ANTENNA/HIGP DESIGN METHOD

4.] Introduction

Part of Golla’s work involved taking copper-tape monopoles and placing them ﬂat
against a HIGP surface. His theory was that since the HIGP is known to reﬂect incident
electric ﬁelds in the PBG of the surface in phase, if a monopole antenna was placed
directly adjacent (touching) a HIGP surface, the surface should reﬂect the incident wave
in phase and will thereby allow the antenna to radiate as a monopole. Golla found that
this structure did not work well. However, placing the antenna directly on the HIGP
surface most likely shorted the antenna to ground through the vias. This structure may
operate quite a bit more efﬁciently if a small gap is placed between the antenna and the
HIGP surface. The design work done at MSU focused on extending Golla’s work with
electric source antennas to multi-layer antenna/HIGP combinations that make use of the
zero-reﬂected-phase property of the HIGP.

The designs presented in this chapter all use a dipole separated from the HIGP surface
or the ground plane underneath with a thin layer of substrate. A bowtie dipole is the
antenna chosen, because of its known broadband characteristics. When a printed bowtie
dipole is placed parallel in close proximity to a ground plane, it behaves like a two-
element array of triangular patches. However, when the same antenna is placed parallel in
close proximity to a HIGP surface with a thin slab of dielectric separating the two, the

antenna starts to behave like a normal dipole. It must be reiterated that the designs in this

54

section are not completely optimized. They do, however, underscore two important
points. First, a wideband dipole antenna can be placed very close to the ground plane that
shields it in the backward half-space and still exhibit characteristics that are typical of a
dipole: strong radiation in the plane parallel to the dipole axis and decent impedance
matching over a signiﬁcant bandwidth compared to a patch antenna. Second, this section
shows that the periodicity of HIGP elements does not necessarily have to be much
smaller than the wavelength of operation, i.e., the ratio of HIGP elements to the
wavelength of operation does not have to be in the vicinity of 20:] or thereabouts, as
previously thought. The new structures proposed here and the design concept introduced
permit decent operation from a bowtie dipole with a periodicity as low as 4:1, four HIGP
elements per wavelength of operation. Though not optimized and perfectly matched to 50

9 transmission lines, this work opens a new door in HIGP/antenna hybrid structures.

55

4.2 Bowtie Dipole over HIGP Substrate

Figure 4—1 shows the top view of a bowtie dipole with a HIGP substrate.

Baﬂtlecbdeelemertsmthetoplayer

      

HIGP elemerts wlh vies fr”
it the center ~""

 

 

 

 

 

 

 

 

Figure 4-1: A Bowtie Antenna with HIGP Substrate

56

A cress-sectional view of this structure is seen in Figure 4-2. These ﬁgures represent the

four-layer design method for combining dipole antennas with HIGP substrates.

 

Dipole antenna
elements
Low dielectric HIGP elements (nag
b str at not shown)
5" 9 \ﬂ 1 1 JJ

 

Dielectnc Substrate mm mm Plane

Coaxial Prom Feed

Figure 4-2: Cross Section of Proposed F our-Layer Design for a Dipole over a HIGP
Substrate

The dipole is printed on a layer of low-permittivity substrate. The substrate is then placed
directly on top of the HIGP elements, which have been printed on a layer of grounded
dielectric substrate. This design concept takes advantage of the zero-reﬂection phase
property of the HIGP, in that a real-source antenna is placed above the HIGP and can still
operate regardless of its proximity to the metal HIGP elements. The antenna feed is
simulated via a probe that exists on one of the vertical dielectric edges immediately under
the antenna. In reality, this feed could be accomplished by aligning the vias of the HIGP
elements with the antenna and running the center conductor of a coax up though one of

the vias, and attaching the outer conductor to the ground plane underneath. The two

57

simulated probe feeds have unity voltage strength with 180° of phase shift between the
two probes, the so-called “push-pull” feed arrangement. The HIGP was designed using
the equations for sheet capacitance and inductance found in chapter two. The gap
between elements (g) is 2.0 mm. The center-to-center spacing between vias (a) is 2.13
cm., and the edge—length of an element (w) is 3.21 cm. The substrate separating the
antenna from the HIGP has a dielectric constant of 2.0 with a thickness of 59 mils (1.5
mm), and the HIGP substrate has a dielectric constant of 4.9 with a thickness of 59 mils.
Each antenna half shown in Figure 4-1 is exactly the same size as the HIGP elements
underneath. This is because of the restraint that was explained in chapter three, that only
the materials that make up the sub-elements can vary from layer to layer, not the cross-
section of the mesh. The antenna consists of prisms whose tangential edges on top are
metal, and vertical edges (edges of the prism) are dielectric. All surrounding regions on
the top layer consist of prisms whose tangential edges on the top layer and whose vertical
edges are all dielectric. The HIGP elements, on the second layer, have metal tangential
prism edges on top and vertical dielectric prism edges below to represent the layer of
substrate below the HIGP elements. The small triangles in the middle of the HIGP
elements represent vertical vias, whose tangential prism edges are also metal on top but
whose vertical prism edges are metal instead of dielectric, connecting the HIGP to
ground. The bottom tangential edges of the prisms on the second layer are metal to
account for the ground plane underneath the entire structure. The HIGP substrate shown
in Figure 4-1, according to the design equations of chapter 2, has a resonant frequency of
3.5 GHz. The antenna was simulated from 1 to 6 GHz in 20 MHz increments. Figure 4-3

is a plot of measured resistance and reactance curves for a triangular monopole (bowtie

58

monopole) of 60° ﬂare angle over a ground plane. The antennas in this chapter all have a
ﬂare angle of 60°. According to Figure 4-3, this antenna lms an electrical length of 47° at
1 GHz and 283° at 6 GHz. Electrical degrees are deﬁned as the product of the physical
length of each monopole and 360°0tg, where kg is the applied (guided) wavelength. Since
this antenna is simulated over a substrate with permittivity of 2.0, the guided wavelength
is the freespace wavelength divided by 12.0. According to Figure 4-3, at 120 electrical
degrees, a bowtie dipole with 60° ﬂare angle will encounter its ﬁrst resonance. This
corresponds to 8.3334 cm of guided wavelength, or 2.57 GHz. The antenna is not
designed exactly to ﬁt with the PBG of the substrate, but these are some design tradeoﬂs
that are encountered when optimizing computation time. At the resonant frequency of the
HIGP, the antenna is 165 electrical degrees in length. However, there are many design
parameters to consider when performing computational analysis on these structures: the
resonant ﬁequency of the HIGP, the resonant frequency of the antenna, the periodicity of
the surface vs. the guided wavelength, and the overall frequency range of operation.

The ﬁrst criterion was that the structure be operated at low frequencies to reduce the
number of sub-elements used to represent the structure, thus reducing the overall
computation time. It was found, however, that this structure still required around ﬁve
weeks of computation time, even when dividing the ﬁequency sweep into multiple
ranges. A second criterion for this design is that the dielectric substrates be of commonly
found materials in industry, such as FR4 or other substrates. This requirement is relaxed

in other designs in order to better ﬁt the antenna to the HIGP.

59

The periodicity of the HIGP elements vs. the guided wavelength is 4: 1, or four HIGP

elements per guided wavelength.

6O

 

500 TTI 1111‘ T'l—T ﬁrl—IT 111r 1‘11—1

l

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200

 

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109
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0 , 50 100 150 200 250 300
AmamaLenghDeg’ees
(a)
20011111111111F 11111111111
100

 

 

o
l l l T
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Ramona!
Illl

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.300 1 L l 1 1 l l l 1 1 I l 1 1 1 L 1 l 1 1 1 1 1 1
0 50 100 150 200 250 300
Antamalsngth.Degeee
(b)

Figure 4-3: Measured Resistance (a) and Reactance (b) vs. Electrical Length for
Triangular Dipole with 60" Flare Angle (from [13])

61

The computed input impedance of this antenna is shown in Figure 4-4. The antenna
appears to resonate at around 3.95 GHz, off from the expected resonant value. This is
perhaps due to the fact that the antenna and HIGP are not optimized together. However,
an expanded view of the input impedance is shown in Figure 4-5. While not perfectly
matched to a 50 (2 transmission line, the real part is certainly non-zero over a signiﬁcant
portion of the measurement band. If the center ﬁ-equency is taken to be 3.95 GHz, then
the plot of Figure 4-5 represents a fairly matched antenna over a 20% bandwidth of the
center frequency. With some simple tuning methods, such as changing the location of the
probe feed, the real part of the input impedance can be perfectly matched to a 50 (1

transmission line.

62

 

 

 

R.X (0)

 

 

 

 

.m - 5
. /
1‘ I
_1m 1 1_ 1 1 1 1 \ I 1
1.5 2 2.5 3 3.5 4 4.5 5
F (GI-k)

Figure 44: Computed Input Impedance for the Bowtie Antenna with HIGP
substrate

63

 

 

 

 

 

 

 

— Real
— - minty
60 ..
40 - e
20 P ..
§
X.
a: 0 F g“ _ _ -7
-20 _ / ‘ / / , ’ ’ q
/ \ \ - / " /
40 r- / r
/,
£0 '- / / 'J
1' 1 l l 1 1 l 1
4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
F(GHz)

Figure 4-5: Expanded view of Input Impedance of Bowtie Dipole over HIGP
substrate from 4.2 - SGHz

One of the goals of this thesis is to determine the fewest number of elements possible
to achieve HIGP performance. Even without changing the periodicity of the structure, the
structure analyzed in this section can be reduced in size (and therefore matrix entry
unknowns) simply by removing one ring of HIGP elements from the outside of the
surface. This structure is shown in Figure 4-6. This structure now has only one ring of
HIGP elements surrounding the antenna instead of two. This resulted in a reduction of
computation time by a factor of one-ﬁfth, because of the lower number of FEM elements I
used to represent the structure. It was found that reducing the structure did not have an

effect on the input impedance, as shown in Figure 4-7. Though it is not shown here, in, an

 

expanded view of the antenna with the HIGP substrate, the input resistance settles to
around 20 0 just like the substrate with one extra layer of elements. Since the extra ring
of elements surrounding the HIGP surface did not affect the performance of the antenna,
higher frequencies (and thus more sub-elements) could feasibly be simulated, allowing

for the antenna and HIGP to be designed to resonate closely together.

65

 

 

 

 

 

><><>
><><><>
<><><><

/.>.>.\
D D .m
w

m

m

 

 

 

 

 

RX (0)

 

 

 

 

_1m 1 1 1 l
1 1.5 2 2.5 3 3.5 4 4.5 5
F (GHz)

Figure 4-7: Input Impedance of Bowtie Dipole with Reduced-Size HIGP Substrate

67

4.3 Bowtie Dipole over Grounded Dielectric Substrate

The bowtie dipole was also simulated over a grounded dielectric substrate, as

demonstrated in Figure 4-8.

Primed antenna elements

Dielectric Substrate

  

Ground Plane ._.-—9

Coaxial Probe Feed with 180° phase shiﬁ in between

Figure 4-8: Diagram of a Printed Bowtie over Grounded Dielectric Substrate

It is expected that the antenna, when operated in this conﬁguration, will behave as a two-
element array of patches, probe-fed with a 180° phase shift between the feeds. The
computed input impedance of this antenna is shown in Figure 4-9. The real part of the
input impedance becomes very large at resonance. The input impedance moves quickly
oﬁ' resonance, however, indicating that the antenna is acting like a two-element array of
patches. Figure 4-10 shows an expanded view of the input resistance of the antenna over
the HIGP and grounded dielectric substrates. The input resistance of the antenna over the
grounded dielectric substrate quickly moves ﬁ'om resonance back down to 0 Q, as is

expected for a patch antenna. The input resistance of the antenna over the HIGP

68

substrate, though, hovers around 20 0 over a signiﬁcant band. This plot reiterates the
non-patch-like behavior of the antenna over the HIGP substrate, even when the antenna
and HIGP surface are not optimized together. This plot also suggests that the bandwidth
of operation of the HIGP spans several GHz. Since the antennas with the two different
substrates both appear to resonate at the same frequency, it can be inferred that the
antenna with HIGP substrate acts as a patch at the resonance shown here. But away from
the patch resonance, the dipole radiation mode takes over, still within the PBG of the
HIGP sibstrate. The next section presents several other designs, based on the four layer

concept, that optimize the antenna with the resonant ﬁequency of the HIGP.

69

 

T 1 1
—Red

 

 

gage

EX (0)
8

 

 

 

 

 

450 l 1 1 1 1 1 1
1 .
F (GHZ)

Figure 4-9: Input Impedance of a Probe-fed Bowtie Antenna over Grounded
Dielectric Substrate

70

 

 

mq—HIGPM ..
—- Grundeleelectrlcalbstrate

 

 

 

Resistance (0)

 

 

 

 

0L 1 1 1 1 L l 1 F
43 44 4.5 4.3 47 48 49
F(GHZ)

Figure 4-10: Expanded Input Resistance of the Bowtie over HIGP and Grounded
Dielectric Substrate from 4.2 - 5.0 GHz

71

4.4 Optimized Bowtie Dipole/HIGP Design

A design for a HIGP/Bowtie antenna combination that brings the resonant ﬁ'equency of
the antenna closer to the resonant frequency of the HIGP is now presented. A ﬁlrther
criterion for this optimized design is that the periodicity of the HIGP surface be increased
to 5:1, or ﬁve HIGP elements per guided wavelength at resonance. This required tailoring
the size and spacing of the elements as well as the materials on which the structure is
built. The basic shape of the structure is relatively identical to the one analyzed in the
previous section, simply the size of the elements and their spacing has changed. For this
reason, a picture of the optimized design is not provided.

The optimized design has elements spaced 1.0 mm ﬁom each other, with an edge
length of 1.675 cm. and a center-to-center via spacing of 1.1 cm. The dielectric substrate
underneath the elements is 59 mils in thickness with a dielectric constant of 4.9.
However, the substrate separating the antenna ﬁ'om the HIGP layer is a ‘custom
designed’ mateth with a dielectric constant of 1.23 and a thickness of 59 mils. This
makes the resonant frequency of the HIGP 5.1 GHz. The antenna is now roughly 100
degrees in electrical length at the resonant frequency of the HIGP. Furthermore, the
element periodicity is now 5:] at resonance, or 5 HIGP elements per wavelength. This
structure was simulated from 4 GHz to 6 GHz. The antenna was then simulated over a
grounded dielectric substrate, to compare the operation of the two substrates. The input
resistance of the antenna with these two substrates is shown in Figure 4-11. The ﬁrst
noticeable characteristic about this plot is that the input resistance (R5,) of the antenna

over HIGP substrate is higher than the R1,. of the antenna over grounded dielectric

72

substrate over almost a 1.4 GHz band. While the actual value of resistance is not high, the
R5,. can be timed to 50 Q by moving the probe feed around on the antenna. It is left for
future investigation to perform this investigation. Furthermore, the spacing of the two
dipole halves is 5 mm‘This parameter is not ﬂexible, based on the drawing of the HIGP
structure underneath and the constraint nmntioned previously about the cross-section of
the layers not changing ﬁ'om layer to layer. The dipole feed gap could play a large part in
the value of the input impedance. If the dipole halves are spaced too far apart, the input
resistance of the antenna drops.

There are two distinct peaks in the input resistance, indicating that either the antenna
or the HIGP operates in a multi-mode fashion. Also of interest is the clear lack of a
distinct resonant peak, as was found in the ﬁrst design presented. It is believed that the
ﬁrst design operated more like a resonant patch over HIGP substrate because the antenna
and HIGP were not optimized together. However, it is believed that this antenna is
operating as a pure dipole, albeit not a well matched one, but still utilizing the zero-‘
reﬂection phase property of the HIGP nonetheless. Furthermore, this behavior is seen
even when the periodicity of the HIGP is as low as 5:1. Were the periodicity increased to
10:1 or greater, perhaps distinct dipole resonant behavior would be observed. The huge
number of sub-elements required to simulate such a structure renders this task unfeasible
with the analysis method used here. However, use of a mixed-element (hexahedral/prism)
FEM code offers the promise of accomplishing this analysis due to the reduced number
of aperture unknowns using that method. Such a tool is currently being developed at

Michigan State University.

73

 

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- — WMcame
16- -
14— a
12* 4

lnputReslstanoe
3
I
1

 

 

 

a- \ _
i“
'1
i l f
6b , ' \ T
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. I -
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4’— “ VA‘ { i ’
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\ ‘1
r /‘\. ~I \v'/ ‘,P \v
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o l I l I l l l L l
4 42 44 46 4.8 5 52 54 56 58 6
F(GHZ)

Figure 4-11: Input Resistance for Bowtie Antenna over HIGP and Grounded
Dielectric Substrates

74

Figure 4-12 and Figure 4-13 show the broadside normalized E-plane and H-plane gain vs.
incident angle for the bowtie over the two substrates. In the E-plane pattern cut, the
dipole halves are oriented along the y-axis, and the measurement is taken with (p = 90°,
aligned with the y-axis and 0 is swept ﬁom -90 to 90°. The ﬁelds plotted are 0-directed
ﬁelds. The H-plane pattern cut is taken with the same orientation but with (p = 0°, aligned
with the x-axis. The ﬁ'equency is 5.58 GHz, corresponding to the largest value of
resistive input impedance from Figure 4-11. The gain of the antenna over the HIGP
substrate in the E-plane is a full 10 db greater than that of the dielectric substrate over
120° of the coverage area. The offset null at 30° is most likely attributable to either under-
meshing (under-sampling) or having an asymmetry near the feed region in the mesh that
is used to simulate the structure, or by the large gap separation in the dipole halves.
Furthermore, an ideal dipole has an expected null at grazing angles of incidence, here
towards 0 = -90° and 90°. However, the pattern is still strong at these angles. This
suggests that the HIGP substrate is not suppressing surface ﬁelds as it is expected to do.
Figure 4-14 and Figure 4-15 show the normalized tangential and z-directed electric ﬁelds
for the antenna over the two substrates. While the electric ﬁeld intensity is certainly
lower for both ﬁeld polarizations towards the edges with the HIGP substrate compared to
the dielectric substrate, there is most likely enough energy to contribute to signiﬁcant
gain at grazing angles of incidence or transmission.

A nearly omni-directional pattern is expected in the H-plane pattern of the antenna over
HIGP substrate, since the H-plane ﬁelds of a dipole do not vary when the measurement is
broadside. Again, this is most likely attributable to imperfections in the mesh. The

antenna over the dielectric substrate simply behaves like a patch off resonance. A distinct

75

nearly omni-directional pattern is observed in both principal plane cuts for the antenna

over grounded substrate.

76

 

 

— HIGP Substrate
-.--- Gromded Diebetric Substrate

 

 

330

 

 

270 r ‘ 3’ L? 3 '9 o m
240 120
210 150

180

Figure 4-12: Broadside Normalized E-plane Pattern (gain, db) of the Bowtie
Antenna with HIGP Substrate and Grounded Dielectric Substrate, F=5.58

GHz

77

 

— HIGP Substrate

— - Grounded Dielectric Substrate

 

 

D
an

\

P

/

“/

 

I

\

'p

I

93

 

I
\

m e

 

1&1

}
¢(

‘0 .

On
17 I

\
an
'2'

m
r.

15]

Figure 4-13: Broadside Normalized H-plane Pattern (gain, db) of the Bowtie
Antenna with HIGP Substrate and Grounded Dielectric Substrate, F=5.58
GHz

78

 

 

Normalized Field Strength, db

   

(a)

     

Normalized Field Strength, db

 

(b)
Figure 4-14: Normalized Tangential (a) and z-Directed E-ﬁelds for Antenna over
HIGP Substrate

79

 

(b)

Figure 4-15: Normalized Tangential (a) and z-Directed E-ﬁelds for Antenna over
Grounded Dielectric Substrate

80

4.5 Proposed Design not Computationally Tested

A ﬁnal HIGP/antenna combination was designed at MSU, but was not computationally
analyzed because of limitations in the program used to generate the FEM mesh of the

structure. This design is shown in Figure 4-16.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4-16: Untested Antenna/HIGP Four Layer Design

81

The shaded areas in the middle represent the two halves of the bowtie dipole on the top
layer, continuous metal along with the dark triangles in the middle. The dielectric
between the metal triangles is also speciﬁed as continuous metal in this region. The
vertical prism edges for this layer are all dielectric, representing the dielectric substrate
underneath On the second layer, the antenna elements (gray triangles) as well as the
other larger triangles are all speciﬁed as metal with vertical dielectric edges, representing
the l-HGP elements over top of dielectric substrate, and the dark smaller triangles, as well
as all the other smaller triangles, are metal on the surface with metal vertical edges,
representing vias. The antenna on the top layer is realized by creating a closed region in
the meshing program that would enclose the antenna triangles and the dielectric in
between (see Appendix A). This is a way of working around the constraint in the FEM
code that all layers have identical cross-section, only different materials characteristics.
However, because of an apparent bug in the meshing program, this structtu‘e could not be
created in this fashion. Skymesh would not allow the creation of the region that encloses
the HIGP elements and dielectric that make up the antenna on the top layer. Time would
not allow for ﬁnding a new meshing program and tailoring the FEM code for reading in
the output ﬁles generated by it.

This design would be the most optimized design thus far. The gap-width between
HIGP elements is 0.5 mm, the HIGP element edge length is .84 cm, and the center-to-
center spacing between vias is .54 cm. The HIGP is printed over a dielectric .762 cm
(0.3“) in thickness with a dielectric constant of 4.9, a thick version of FR4. The substrate
separating the antenna ﬁ'om the HIGP layer is 59 mils in thickness, with a permittivity of

2.0. Each dipole half shown in Figure 4-16 is 2.3 cm in length The resonant ﬁequency of

82

the HIGP is 3.03 GHz, and the antenna is 118 electrical degrees at this frequency, from
the input impedance plot of the bowtie dipole in Figure 4-3. Therefore, the antenna and
the HIGP are now optimized together nearly perfectly. Furthermore, the guided
wavelength at 3.03 GHz is 7 cm, making the ratio of HIGP elements-to-wavelength
13.2:1. The overall thickness of this design is .359” or .9 cm, slightly larger than N8. The
distinct shape of the HIGP substrate is a product of removing as many HIGP elements as
possible, thus streamlining the design and reducing unknowns. The border of the HIGP is
only roughly 2.0 cm away from the low-ﬁ'equency end of the antenna, or 7113.5. Due to its
low proﬁle, small aperture area and high HIGP element periodicity, computational
analysis should verify that this is the most streamlined yet operationally sound structure

that could be designed with the proposed four-layer method.

83

CHAPTER 5

CONCLUSIONS AND GROUNDS FOR FUTURE WORK

This work has served several purposes. First, computational analysis of designs that have
already been built and tested has been provided. Secondly, a new method of integrating
dipole antennas with the ground plane that shields them from the backward lmlf-space
has been introduced, and in doing so, the commonly held notion that the periodicity of
HIGP elements that form the substrate must be much be much smaller than the
wavelength has been challenged. The four-layer design method allows for an electric-
source antenna, with an electric ﬁeld polarization vector parallel to the ground plane, to
be placed near the ground plane (> U4) and still operate well. Decent, albeit not
optimized performance is exhibited from these structures.

Several research questions exist for the structures presented here: ﬁrst, can the input
impedance of the dipoles be optimized simply by moving around the location of the
probe feed. This would allow for better performance from the structures presented here
without changing much about the structure itself. Second, computational analysis is
needed of the ﬁnal HIGP/antenna design ﬁ'om Section 4.5. This structure, based on the
design equations and on the performance of less-optimized designs, could exhibit the best
performance yet ﬁ'om a dipole antenna placed near a HIGP substrate. Finally, this thesis
provides analysis of a wideband antenna with a single-band HIGP structure. It is possible
that a HIGP design exists itself that operates in a wideband fashion. Such a structure

would account for the different wavelengths that are radiated ﬁ'om a wideband antenna.

84

This substrate could be used in conjunction with simple spiral antennas or log-periodics
to obtain good performance form surface mounted, low proﬁle wideband antennas.

One of the hindrances to the design of HIGP/antenna structures using the ﬁnite
element method is the enormous computation time required to accurately characterize the
performance of the design. In this work, the antenna and HIGP substrate are always
simulated together. It would be useful if the HIGP and antenna could be designed
separately and then brought together in the ﬁnal design, which would eliminate the time
consuming process of ‘tweaking’ a design. It is suggested that the planar electromagnetic
code PMM (Periodic Method of Moments) be used to determine the performance of the
HIGP substrate. PMM simulates two dimensional inﬁnite periodic surfaces, and has the
capability of multiple-layer analysis, extending its usefulness to three dimensions. This
code is generally used in the design of frequency selective surfaces (F88) and radomes,
in that the reﬂection ﬁ'om and transmission through the surface of plane waves at
different frequencies and different polarizations can be analyzed. This code can be
extended to HIGP substrates by examining the reﬂection phase of a plane wave at
different frequencies from the surface. Furthermore, the design of dipole antennas by
themselves is not easily done with the FEM code used in this work, in that this code
assumes the antenna is surrounded by a cavity. Though good for patch antennas, the
program is not easy to use for dipole and electric type antennas. It is suggested that a
code that is conducive to printed dipoles be used here. The Numerical Electromagnetics
Code (N.E.C.) would be a suitable means to this end. N.E.C. simulates wire antennas in
free space. If enough wire elements are used, a continuous metallic triangle can be

simulated. The resonant frequency of the antenna would then simply have to be scaled to

85

account for the dielectric substrate. Then, the FEM code Prism could be used to perform
a high resolution ﬁequency sweep of the ﬁnal, optimized design of the antenna and HIGP

together.

86

APPENDICES

87

APPENDIX A
CREATING INPUT FILES FOR PRISM
A.l Methodology

One of the true challenges to this work was devising a way by which structures can be
drawn in a standard drawing package, and then converted to the type of data that the
FEM analysis program requires. The process by which a drawing becomes an input ﬁle to
the Prism program is a lengthy one.

First, a model is drawn two-dimensionally in any CAD program. The one used for the
structures presented here is called CadStd, and it is available on the Internet for free
download. The structure is ﬁrst drawn in discrete, closed sections using only polylines in
CAD. For example, in the sample patch of Figure A-l the outer square represents a
dielectric border, and all space interior to that but exterior to the next rectangle is
dielectric. The middle square represents the patch, and the smallest square represents the

feed region.

88

 

 

 

 

 

 

 

 

Figure A-l: Square Patch Drawn in CAD

All polylines are drawn counter-clockwise, a convention used by the meshing program,
Skymesh. A counter-clockwise element is considered to be ﬁlled with some material,
metal or dielectric, and a clockwise element is considered to be a hole. The CAD ﬁle is
then exported to a DXF ﬁle, using the built in converter available with the package. A
program called DXF2XYZ, also available for ﬁee on the Internet, is then used to convert
the DXF ﬁle to an ordered set of points, with the vertices of each polygon grouped
together and ﬂagged uniquely. The result is a group of points that contains the start and
stop point of each polyline drawn in CAD, representing the edges of each closed region.
Edges from the same region are given a unique identiﬁer (an incremented counter). A
typical output ﬁle ﬁ'om DXF2XYZ is listed below, in Table A-1 , the second and third
column are x and y values of the vertices of each line, and the ﬁrst column is a unique
identiﬁer indicating that points with that same number belong to the same identiﬁer. In
this case, all points with the ID number 1 are vertices of the outer square, ID number 2

are vertices of the inner square, and ID 3 are vertices of the smallest, inner-most square.

89

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 0.0787 2.4409
1 0.0787 0.0787
1 2.8346 0.0787
1 2.8346 2.4409
1 0.0787 2.4409
2 0.8661 1 .6535
2 0.8661 0.8661
2 2.0472 0.8661
2 2.0472 1.6535
2 0.8661 1 .6535
3 1.8897 1 .2992
3 1.7716 1.2992
3 1.7716 1 .2204
3 1.8897 1.2204
3 1 .8897 1 .2992

 

 

Table A-1: Sample Output from DXF2XYZ

There are ﬁve points listed for the vertices of each square, yet a square has only four
vertices. This is because when a polyline is drawn in CAD, the user must specify the start
and stop points of each line. Therefore, the start vertex is listed twice, since the polyline
goes around counterclockwise until it gets back to the start point. It is important to note
tlmt DXF2XYZ converts all dimensions to inches automatically. Then, the author wrote a
Fortran code, called ReadXY Z, to read the output of DXF2XYZ and create the ﬁles
necessary for SkyMesh to read. This program parses the output of DXF2XYZ for the
unique identiﬁers and throws away the last point of each region, since nodes in Skymesh
may only be listed once. It is recommended that each separate entity be drawn in a
different layer in CadStd, because DXF2XYZ has the ability to parse out different layer
from the DXF ﬁle and save them to different ﬁles. Since Skymesh relies on its input

being listed from outermost entities to innermost, it is a good idea to draw similar entities

90

on different layers and use this feature of DXF2XYZ. An example of this would be
something similar to Figure 4-1, where there are dielectric regions, metal pads, antennas
and vias. The outer border would be drawn in one layer in CAD, the metal pads on a
different layer, the vias on a third layer, the antenna elements on a fourth layer, and the
two feed vias on a ﬁnal layer. In DXF2XYZ, then, all these layers can be parsed out one
at a time and saved to different ﬁles. The ReadXY Z program then takes these ﬁles and
assembles them in a format acceptable to Skymesh.

The Skymesh program requires several different ﬁles in order to read in a geometry
and create a mesh that has triangle edges of a user-deﬁned length. These ﬁle include a
.pts ﬁle, a .edg ﬁle, a .ref ﬁle, a .prj ﬁle, and a .geo ﬁle. The .pts ﬁle contains an ordered

list of nodes (node number, x-coordinate, y-coordinate), as shown in Table A-2.

91

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 0.0787 2.4409
2 0.0787 0.0787
3 2.8346 0.0787
4 2.8346 2.4409
5 0.8661 1 .6535
6 0.8661 0.8661
7 2.0472 0.8661
8 2.0472 1 .6535
9 1 .8897 1 .2992
10 1 .7716 1 .2992
1 1 1 .7716 1 .2204
12 1 .8897 1 .2204

 

Table A-2: Sample Skymesh .pts File

These nodes contain the vertices of the squares/polylines that make up the closed regions
of Figure A-l. Note that the .pts ﬁle does not contain the extraneous endpoint that was
found in the .xyz ﬁle. The .edg ﬁle, listed in Table A-3, contains an ordered list of edges

that specify which nodes in the .pts ﬁle are connected together to make an edge (edge

number, node 1, node 2).

92

 

@normal 001
1 1 2
2 2 3
3 3 4
4 4 1
@normal 0 01
5 5 6
6 6 7
7 7 8
8 8 5
@normal 001
9 9 10
1O 10 11
11 11 12
12 12 9

Table A-3: Sample Skymesh .edg File

This says that edge 1 connects nodes 1 and 2, edge 2 connects nodes 2 and 3, and so on.
The ‘@normal 0 0 1’ line deﬁnes coefﬁcients of a three-dimensional rectangular-
coordinate unit vector that is normal to the drawing: 05% + 05’ +12 , which means that the
drawing lies purely in the x-y plane. There are three sections of edges, corresponding to
three closed regions in the drawing.

The .ref ﬁle in Skymesh speciﬁes the maximum edge length for any element. In this
case, the edge length corresponds to the length of the edge of each triangle. A standard
I practice is to always use edge lengths that are 2/15 - xi / 20 at the highest ﬁ'equency.
Coarser meshing can cause incorrect ﬁeld values to be calculated on the surface of the
mesh. An example of a .ref ﬁle is found in Table A-4. The word g-face speciﬁes that the
following data corresponds to a closed region. The regions are in the same order as they

are found in the .pts ﬁle, so g_face 1 corresponds to the dielectric region of the square

93

patch of Figure A- 1 , g_face 2 corresponds to the metal patch, and g_face three
corresponds to the feed region. The ﬁrst number is the normal edge length (which has no
meaning in a two—dimensional surface mesh!) and the second number is the tangential

edge length, the important one in this case.

 

 

 

 

 

 

 

 

 

 

 

auto
114806
1 0.12 0.12
_g_face
2 0.12 0.12
14am
3 0.02 0.02

 

Table A-4: Sample Skymesh .ref File

The .prj ﬁle simply speciﬁes in what ﬁles to look for all of this information and where

to store the resulting output. The data in this ﬁle is similar to that of Table A-5.

 

Project File F :\square\Patch_only\patchOnly.prj - Saved on 6-Jun-02 at 21 :12
GEOMETRY Patchonly.geo
REFINEMENTS patch0n1y.ref

 

DENSITY Patchonly.den
ESH Patchonly.fem
GRID Patchonlyqrd

 

Table A-5: Sample Skymesh .prj File

94

The geometry ﬁle speciﬁes where to ﬁnd the points (.pts ﬁle) and the edges (.edg ﬁle),
and its contains only the following line:
@2d_style "Patchonlypts" "Patchonly.edg"

where @2d_style speciﬁes a two-dimensional drawing. The reﬁnements ﬁle, as discussed
above, contains information about the maximum edge lengths. The DENSITY, MESH
AND GRID ﬁles are all outputs of Skymesh. The particular format of these ﬁles is
immaterial, but it is important to note that prism uses the GRID ﬁle (.grd) as its input.

The program ReadXYZ must be modiﬁed every time a new antenna is drawn to
ensure that the outer regions are input into the Skymesh ﬁles in the correct order. This
information is speciﬁed in the .pts, .edg, and .ref ﬁles, where the nodes, edges and edge
lengths of the outer regions are speciﬁed ﬁrst, and then any inner regions are speciﬁed.
This is made easy by drawing regions in CAD in different layers, and then parsing out
each individual layer in DXF2XYZ and saving it in a separate ﬁle. ReadXYZ then reads
the ﬁles speciﬁed (in order ﬁ'om outer to inner) by the user. The code that is found in the
next section is that which was used to generate the mesh of Figure 4-1. The subroutine
getPts actually writes the data to the ﬁle. This subroutine is ﬁrst called for the outer
border, then the HIGP metallic pads, and then the vias that lie inside the pad. Then the
code is called for the antenna (the two middle triangles in the ﬁgure) and the for the feed
regions for those triangles. These were drawn separately so that a different edge length
could be speciﬁed for these two regions. The details of other Prism input ﬁles are
immaterial, but a good grasp of the .grd process is vital to creating accurate meshes. This

entire process is summarized in Table A-6.

95

 

 

-Draw structure in CAD
Use only polylines
Draw different types of closed regions in different layers

11

-Export structure to .dxf format using built-in CAD converter

1

~Use DXF2XYZ to parse out different layers to separate ﬁles

1

-Use ReadXYZ to create the ﬁles necessary for Skymesh
Call subroutine getPts for outer regime ﬁrst, then any
interior regions
If regions occur in multiple internal levels, outer regions
are speciﬁed ﬁrst

-Run Skymesh, and use .grd ﬁle as input to Prism

 

Table A—6: Flowchart for Creating the Prism Input Files

96

 

A.2 ReadXYZ Fortran Code for Reading DXFZXY Z Ouptut

Cttttttttttttttttl¥t¥i¥******##*********#*****¢***********tIt

****** Order of Skymesh input file creation:

******
******
******
******
******
******
******

1.
2.

3.

4.

Create drawing in CAD (.cad file)

Export .cad file to .dxf file using 'Export'
option in CAD program ‘
Use DXF2XYZ.exe program to convert .dxf file
to x,y,z, triplet

This program converts .xyz file to .pts and
edg files used by Skymesh

program readXYZ
use dfport
implicit none

character*70 directory,infile,the_date
integer totPts,totSecs,totEdges
real*8 edgeSize

infile='bow_higp'
directory='f:\bowtie\bow_higp\'

open(unit=12,file=trim(directory)//trim(infile)//'_outerBo
+rder.xyz',status='old')

open(unit=13,file=trim(directory)//trim(infile)//'_element
+s.xyz',status='old')

open(unit=14,file=trim(directory)//trim(infile)//'_vias.xy
+z',status='old')

open(unit=15,file=trim(directory)//trim(infile)//'_antenna
+.xyz',status='old')

Open(unit=16,file=trim(directory)//trim(infile)//'_feed.xy
+z',status='old')

97

open(unit=7,file=trim(directory)//trim(infile)//'.pts',sta
+tus='unknown')

open(unit=8,file=trim(directory)//trim(infile)//'.edg',sta
+tus='unknown')

open(unit=9,file=trim(directory)//trim(infile)//'.ref',sta
+tus='unknown')

open(unit=10,file=trim(directory)//trim(infile)//'.prj',st
+atus='unknown')

open(unit=ll,file=trim(directory)//trim(infile)//'.geo',st
+atus='unknown')

1 format(a,2x,a)
write(9,'("aut0")')

call fdate(the_date)
write(10,'(a,a,a,a)') '# Project file - ',trim(infile)
+,'.prj,Modified on ',trim(the_date)
write(10,1) 'GEOMETRY',trim(infile)//'.geo'
write(10,1) 'REFINEMENTS',trim(infile)//'.ref'
write(10,1) 'DENSITY',trim(infile)//'.den'
write(10,1) 'MESH',trim(infile)//'.fem'
write(10,1) 'GRID',trim(infile)//'.grd'
2 format('@2d_style "',a,'"',2x,'"',a,'"')
write(11,2) trim(infile)//'.pts',trim(infile)//'.edg'

totEdges=O

totPts=O

totSecs=O

edgeSize=O.105

call getPts(totPts,totSecs,totEdges,edgeSize,12)

edgeSize=0.157
call getPts(totPts,totSecs,totEdges,edgeSize,13)

edgeSize=.O8
call getPts(totPts,totSecs,totEdges,edgeSize,l4)

98

edgeSize=1.0
call getPts(totPts,totSecs,totEdges,edgeSize,15)

edgeSize=.03
call getPts(totPts,totSecs,totEdges,edgeSize,l6)

end
C*****~k**********~k*****~k******~k************~k~k*******~k~k~k***~k

*

c*****THIS SUBROUTINE PERFORMS THE ACTUAL DATA PARSING
subroutine getPts(totPts,totSecs,totEdges,edgeSize,
+file_read)
implicit none

integer totPts,totSecs,totEdges

integer
marker(1000),i,j,ioerr,numPts,start_edg,stop_edg

integer secLoc(IOO),ptsPerSec(lOO),numRegions

integer file_read,region

real*8 xTemp(1000),yTemp(lOOO),edgeSize

region=totSecs
numPts=O
numRegions=1
totSecs=totSecs+1
marker=0

ioerr=0

do while(ioerr .eq. 0)
numPts=numPts+l
read(file_read,*,iostat=ioerr)marker(numPts),
+xTemp(numPts),yTemp(numPts)
enddo
numPts=numPts-l

C******FIND LOCATIONS OF DIFFERENT CLOSED REGIONS IN THE
XYZ C******FILE,BASED ON IDENTIFIER FLAG IN DXF2XYZ
secLoc(1)=1
do i=1,numPts-l
if(marker(i) .ne. marker (i+1)) then
ptsPerSec(numRegions)=i-secLoc(numRegions)
totSecs=totSecs+1
numRegions=numRegions+l
secLoc(numRegions)=i+1
endif

99

15
20
25
30

enddo
ptsPerSec(numRegions)=numPts-secLoc(numRegions)

do i=1,numRegions
do j=secLoc(i),secLoc(i)+ptsPerSec(i)-1
totPts=totPts+l
write(7,15) totPts,xTemp(j),yTemp(j)
enddo
write(7,*)

start_edg=totEdges+l

stop_edg=totEdges+ptsPerSec(i)

write(8,25)

do j=start_edg,stop_edg-1
totEdges=totEdges+1
write(8,20) j,j,j+1

enddo

totEdges=totEdges+1

write(8,20) j,j,start_edg

write(8,*)

write(9,30) region+i,edgeSize,edgeSize

enddo

format(2x,I4,4x,F12.6,4x,F12.6)
format(2x,I4,4x,I4,4x,I4)
format(2x,'@normal O 0 1')
format(2x,'g_face',/,6x,13,5x,F6.3,F6.3)
return

end

100

REFERENCES

 

[1] RS. Elliott, “Antenna Theory and Design,” Prentice Hall, New Jersey, 1982, pp. 27
38

[2] E. Yablonovitch, T.J. Gmitter, “Photonic band structure: the face-centered-cubic
case,” J. Opt. Soc. Am. A, vol. 7, no. 9, Sep. 1990

[3] DR Sievenpiper, High-Impedance Electromagnetic Surfaces, Ph.D. dissertation,
University of California at Los Angeles, Los Angeles, CA, 1999

[4] KJ. Golla, Broadband Applications of High Impedance Ground Planes, M.S. Thesis,
Air Force Institute of Technology, Dayton, OH, March 2001

[5] LC. Kempel, “Anisotropic Right Prism Finite Element-Boundary Integral Theory,”
unpublished, April 2002

[6] CA. Balanis, “Antenna Theory,” 2"d Ed., John Wiley and Sons, 1996

[7] ER. Brown, C.D. Parker, E. Yablonovitch, “Radiation properties of a planar antenna
on a photonic-crystal substrate,” J. Opt. Soc. Am. B, vol. 10, no. 2, Feb. 1993

[8] SD. Cheng et a1, “Optimized dipole antennas on photonic band gap crystals,” Appl.
Phys. Lett., vol 67, no. 23, Dec. 1995

[9] M. Thévenot, C. Cheype, A. Reineix, B. Jecko, “Directive Photonic-Bandgap
Antennas,” IEEE Trans. Microwave Theory T ech., vol. 47. no. 11, Nov. 1999

[10] R. Coccioli et al, “Aperture-Coupled Patch Antenna on a UC-PBG Substrate,” IEEE
Trans. Microwave Theory Tech., vol. 47, no. 11, Nov. 1999

[11] R. Gonzalo, P. de Maagt, M. Sorolla, “Enhanced Patch-Antenna Performance by
Suppressing Surface Waves Using Photonic-Bandgap Substrates,” IEEE Trans.
Microwave Theory Tech., vol. 47, no. 11, Nov. 1999

101

 

[12] L. Hunt, “Analysis of Microstrip Antennas on Substrates with High Permeability,”
M.S. Thesis, Michigan State University, East Lansing, MI 2002

[13] G.H. Brown, O.M. Woodward, “Experimentally Determined Radiation
Characteristics of Conical and Triangular Antennas,” RCA Rev., Dec. 1952

102

 

  

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