The Radiation Quality Factor Of Vertically Polarized Spherical Antennas Above A Conducting

97 Pages·2017·1.59 MB·English

by  Hsieh-chi Chang

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Masters Theses 1911 - February 2014
2012
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Hsieh-chi Chang
University of Massachusetts Amherst
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THE RADIATION QUALITY FACTOR OF VERTICALLY
POLARIZED SPHERICAL ANTENNAS ABOVE A CONDUCTING
GROUND PLANE

A Thesis Presented
by
HSIEH-CHI CHANG

Submitted to the Graduate School of the University of Massachusetts Amherst in
partial fulfillment of the requirements for master of

MASTER OF SCIENCE IN ELECTRICAL AND COMPUTER ENGINEERING

September 2012

Electrical and Computer Engineering
© Copyright by Hsieh-Chi Chang 2012
All Rights Reserved
THE RADIATION QUALITY FACTOR OF VERTICALLY
POLARIZED SPHERICAL ANTENNAS ABOVE A CONDUCTING
GROUND PLANE

A Thesis Presented
by
HSIEH-CHI CHANG

Approved as to style and content by

Do-Hoon Kwon, Chair

Ramakrishna Janaswamy, Member

David M. Pozar, Member

Christopher V. Hollot, Department Head
Electrical and Computer Engineering
ACKNOWLEDGMENTS

I’d like to express my gratitude to Prof. Yong Heui Cho of Mokwon University,
Korea for his guidance in the initial stage of this research. I also want to thank my
advisor Prof. Do-Hoon Kwon. I would not have been able to finish the thesis work
without his guidance. He always points me in the right direction. I also want to thank
Mary McKay for her encouragement to finish the thesis. I am grateful to Prof. Pozar
and Prof. Janaswamy, my thesis committee members. Their constructive comments
improved the quality of the thesis. Finally, I appreciate the support from my family
and friends.
This thesis work was supported in part by The SI Organization, Inc.

iv
ABSTRACT

THE RADIATION QUALITY FACTOR OF VERTICALLY POLARIZED
SPHERICAL ANTENNAS ABOVE A CONDUCTING GROUND PLANE
SEPTEMBER 2012
HSIEH-CHI CHANG
B.Sc., NATIONAL CHIAYI UNIVERISTY
M.S.E.C.E. UNIVERSITY OF MASSACHUSETTS AMHERST
Directed by: Professor Do-Hoon Kwon

The radiation quality factor of small vertically polarized antennas above a ground
plane is investigated. Although the quality factor of small antennas in free space has
been investigated extensively in the past, the exact effect of a conducting ground
plane on the antenna bandwidth is not clearly understood. In this thesis, quality
factors of vertically polarized antennas above a ground plane are computed and
compared with their free-space counterparts. The theoretical results on quality factors
are validated with simulations of electrically small spherical helix antennas.
v
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS..........................................................................................iv
ABSTRACT..................................................................................................................v
LIST OF TABLES.......................................................................................................vi
LIST OF FIGURES..................................................................................................viii
CHAPTER
1. INTRODUCTION................................................................................................1
2. REVIEW OF ANTENNA QUALITY FACTOR IN FREE SPACE.................4
2.1 Spherical Wave Function...............................................................................4
2.2 Radiation Quality Factor of a TM -Mode Spherical Current........................9
01

3. RADIATION QUALITY FACTOR OF A CONDUCTOR-BACKED
SMALL ANTENNA...........................................................................................12

3.1 A Conductor-Backed Small Antenna...........................................................12
3.2 Vector Addition Theorem.............................................................................15
3.3 Non-Propagating Stored Energy..................................................................22

3.3.1 Division of Space and Q-Computation Approach................................22
3.3.2 Region I................................................................................................27
3.3.3 Region II...............................................................................................29
3.3.4 Region III..............................................................................................31
3.3.5 Region IV..............................................................................................33
3.3.6 Region V...............................................................................................34
3.3.7 Radiated Power.....................................................................................36

4. THEORETICAL RESULTS..............................................................................37

vi
5. VALIDATION WITH ANTENNA SIMULATION..........................................50

6. CONCLUSION....................................................................................................57

APPENDIX: ANTENNA SIMULATIONS..............................................................59

BIBLIOGRAPHY......................................................................................................84

vii
LIST OF TABLES
Table Page
1. The resonant antenna's properties in free space....................................................50

2. The resonant antenna's properties above a PEC ground plane with different
separation..............................................................................................................55

3. The resonant 5-arm helix antenna's properties above a PEC ground plane..........59

4. The resonant 3-arm helix antenna's properties above a PEC ground plane..........61

5. The resonant 4-arm helix antenna's properties above a PEC ground plane..........64

6. The resonant 4-arm helix antenna's properties above a PEC ground plane..........66

7. The resonant 4-arm helix antenna's properties above a PEC ground plane..........69

8. The resonant 4-arm helix antenna's properties above a PEC ground plane..........71

9. The resonant 2-arm helix antenna's properties above a PEC ground plane..........74

10. The resonant 2-arm helix antenna's properties above a PEC ground plane..........76

11. The resonant 2-arm helix antenna's properties above a PEC ground plane..........79

12. The resonant 2-arm helix antenna's properties above a PEC ground plane..........81

viii
LIST OF FIGURES
Figure Page
1. Coordinate system definition for an electric surface current over a sphere of
radius a center at O.................................................................................................4

2. Comparison of three quality factors for a spherical antenna in free space...........11

3. (a) Spherical antenna above PEC ground plane. (b) After applying image
theorem to replace the PEC ground plane............................................................12

4. Translation of the coordinate origin from O and O'.............................................16

5. Translation of the coordinate system along the z axis..........................................18

6. Fields expanded by O' inside the boundary..........................................................19

7. Fields expanded by O' outside the boundary........................................................21

8. Boundaries for the addition theorem and volume integrations............................24

9. Two different coordinate system (x,y,z) and (x ,y ,z )...........................................29
1 1 1

10. Two different coordinate system (x,y,z) and (x ,y ,z )...........................................30
2 2 2

11. The translation coordinate from O to O ............................................................34
1 2

12. Comparison of quality factors of antennas. (a) Quality factors of antennas in
free space and those above a ground with a separation kh=0.6. (b) The
comparison of quality factors of free-space antennas and grounded antennas with
a fixed ratio kh=2ka. In both cases, the quality factor from [10] is also shown for
comparison...........................................................................................................38

13. Comparison of effective volume. (a) A spherical antenna is placed in free space.
(b) Two spherical antennas are placed in free space............................................40

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