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Tunable frequency selective surfaces and true-time-delay lenses for high-power-microwave (HPM) applications

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TUNABLE FREQUENCY SELECTIVE SURFACES AND TRUE-TIME-DELAY LENSES
FOR HIGH-POWER-MICROWAVE (HPM) APPLICATIONS
by
Meng Li
A dissertation submitted in partial fulfillment of
the requirements for the degree of
Doctor of Philosophy
(Electrical and Computer Engineering)
at the
UNIVERSITY OF WISCONSIN–MADISON
2013
Date of final oral examination: 05/03/13
The dissertation is approved by the following members of the Final Oral Committe:
Nader Behdad, Assistant Professor, Electrical and Computer Engineering
Susan C. Hagness, Professor, Electrical and Computer Engineering
Hongrui Jiang, Professor, Electrical and Computer Engineering
Zhenqiang Ma, Professor, Electrical and Computer Engineering
Robert D. Lorenz, Professor, Mechanical Engineering
UMI Number: 3589392
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
UMI 3589392
Published by ProQuest LLC (2013). Copyright in the Dissertation held by the Author.
Microform Edition © ProQuest LLC.
All rights reserved. This work is protected against
unauthorized copying under Title 17, United States Code
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346
c Copyright by Meng Li 2013
⃝
All Rights Reserved
i
To my wonderful parents XiaoLing and BaoLai
To my lovely wife Jing Huang
ii
ACKNOWLEDGMENTS
It is definitely a rewarding journey for me for the past four years at madison. It all started
when I first met my advisor, Prof. Nader Behdad. I would like to thank him for giving me the
opportunity to work with him and continue my graduate studies. I am deeply grateful to him for
his mentorship, support, and advise that I wont soon forget. As an advisor, he guided me through
quite a lot of difficulties that I encountered in my research. And more importantly, I learned many
important life lessons which I believe will benefit me for the rest of my life.
I would also like to thank the members of my doctoral committee: Professors Susan C. Hagness, Zhenqiang (Jack) Ma, Hongrui Jiang, and Robert D. Lorenz. Their valuable suggestions are
extremely beneficial in improving the overall quality of my research and thesis.
I would like to thank my colleagues and friends at Madison. Special thanks and appreciations
go out to Mudar Al-Joumayly, Bin Yu, and Chien-Hao Liu for always being there in tough times
and for their personal friendship outside the lab. In particular, I would like to thank my wife Jing
Huang for her support and love during the days of our marriage.
Last but not least, I would like to thank my parents BaoLai Li and XiaoLing Meng. It is your
constant love and endless support, great sacrifices, and guidance that made this accomplishment
possible.
iii
TABLE OF CONTENTS
Page
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1
1.2
1.3
1.4
2
Motivation . . . . . . . . . . . . . . .
Proposed Approach . . . . . . . . . .
Literature review . . . . . . . . . . .
1.3.1 Frequency Selective Surfaces
1.3.2 Microwave Lenses . . . . . .
1.3.3 Tuning Mechanism . . . . . .
1.3.4 Power handling capability . .
Thesis overview . . . . . . . . . . . .
1.4.1 Chapter 2 . . . . . . . . . . .
1.4.2 Chapter 3 . . . . . . . . . . .
1.4.3 Chapter 4 . . . . . . . . . . .
1.4.4 Chapter 5 . . . . . . . . . . .
1.4.5 Chapter 6 . . . . . . . . . . .
1.4.6 Chapter 7 . . . . . . . . . . .
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1
1
4
7
8
12
14
16
17
18
18
19
19
20
20
A Third-Order Bandpass Frequency Selective Surface with a Tunable Transmission Null . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1
2.2
2.3
Introduction . . . . . . . . . . . . . . .
FSS Design and Principles of Operation
2.2.1 FSS Topology . . . . . . . . . .
2.2.2 Synthesis Procedure . . . . . .
Experimental Verification . . . . . . . .
2.3.1 Free-Space Demonstration . . .
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22
25
25
26
28
28
iv
Page
2.4
3
Fluidically Tunable Frequency Selective/Phase Shifting Surfaces for High-Power
Microwave Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1
3.2
3.3
3.4
4
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fluidically Tunable MEFSSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Principles of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 The Fluidic Varactor Concept . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Approximate Closed Form Formula For Liquid Varactor . . . . . . . . . .
3.2.4 Fluidically Tunable MEFSSs . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Linearity and Transient Power Handling Capability of Electronically Tunable MEFSSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental Verification and Measurement Results . . . . . . . . . . . . . . . . .
3.3.1 Experimental Demonstration of Second-Order Fluidically Tunable MEFSSs
3.3.2 Experimental Demonstration of Third-Order Fluidically Tunable MEFSSs .
3.3.3 Experimental Demonstration of a Fluidically Tunable SPS with a 0◦ -360◦
Phase Shift Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
39
39
42
44
46
52
56
56
59
64
66
Frequency Selective Surfaces for Pulsed High-Power Microwave (HPM) Applications 71
4.1
4.2
4.3
4.4
5
2.3.2 Experimental Demonstration of an FSS with a Tunable Transmission Null . 31
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Optimization of The Power Handling Capability of MEFSSs . . . . . . . . . . .
4.2.1 Comparison of the Transient Power Handling Capabilities of a 2nd-Order
MEFSS and a 2nd-Order Jerusalem Cross FSS . . . . . . . . . . . . . .
4.2.2 Analysis of the Transient Power Handling Capability of MEFSSs . . . .
4.2.3 MEFSSs Optimized for High Transient Power Operation . . . . . . . . .
Experimental Verification and HPM Measurements . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 71
. 73
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74
78
82
88
95
Broadband True-Time-Delay Microwave Lenses Based on Miniaturized Element
Frequency Selective Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.1
5.2
5.3
Introduction . . . . . . . . . . . . . . . . . . . . .
TTD Lens Design and Principles of Operation . . .
5.2.1 Sub-wavelength Spatial Time Delay Units .
5.2.2 TTD Lens Design Procedure . . . . . . . .
Experimental Verification and Measurement Results
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98
102
103
107
122
v
Appendix
Page
5.4
6
Wideband True-Time-Delay Microwave Lenses Based on Metallo-Dielectric and
All-Dielectric Lowpass Frequency Selective Surfaces . . . . . . . . . . . . . . . . . . 133
6.1
6.2
6.3
6.4
7
5.3.1 TTDs Lens Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.3.2 Transient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .
TTD Lens Design and Principles of Operation . . . . . . . .
6.2.1 Sub-wavelength Lowpass Spatial Time-Delay Units .
6.2.2 Lowpass FSS-Based TTD Lens Design Procedure .
Experimental Verification and Measurement Results . . . . .
6.3.1 TTDs Lens Characterization . . . . . . . . . . . . .
6.3.2 Time-Domain Analysis . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . .
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133
136
137
140
150
151
157
161
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.1
7.2
7.3
Enable tuning mechanism in large scale . . . . . . . . . . . . . . . . . . . . . . . 162
Compact true-time-delay lenses for high gain antenna application . . . . . . . . . . 163
Design of harmonic-suppressed frequency selective surfaces for low-observable
applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
APPENDICES
Appendix A:
List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
vi
LIST OF TABLES
Table
Page
2.1
Physical and electrical parameters of the first FSS prototype discussed in Section2.3.1.
All dimensions are in mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2
Physical and electrical parameters of the second FSS prototype discussed in Section2.3.1.
All dimensions are in mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3
Physical dimensions of the waveguide version of the FSS with a tunable transmission
null studied in Section 2.3.2. All dimensions are in mm. . . . . . . . . . . . . . . . . 33
2.4
Measured -10db transmission null BW and insertion loss of the waveguide prototype
b-d shown in Fig.2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1
Physical and geometrical parameters of the fifth-order tunable MEFSS discussed in
Section 4.2.3 for different tuning states. Physical units are in mm. . . . . . . . . . . . 48
3.2
Parameters of the equivalent circuit model of the fifth-order tunable MEFSS discussed
in Section 4.2.3 for different tuning states. Capacitance units are in pF . . . . . . . . . 49
3.3
Physical and geometrical parameters of the first tunable MEFSS prototype discussed
in Section 3.3.2 for different tuning states. All physical dimensions are in mm. . . . . 64
3.4
Physical and geometrical parameters of the second tunable MEFSS prototype discussed in Section 3.3.2 for different tuning states. All physical dimensions are in mm.
66
3.5
Physical and geometrical parameters of the third tunable MEFSS prototype discussed
in Section 3.3.3 for different tuning states. All physical dimensions are in mm . . . . 67
4.1
Physical parameters of a 2nd -order MEFSS and a 2nd -order JC slot FSS shown in Fig.
4.1. The dielectric substrates in both FSSs are air. All dimensions are in mm. . . . . . 74
vii
Table
Page
4.2
Different implementations of wire grid patterns in the MEFSS shown in Fig. 4.6(a)
for the same desired frequency response described in Section 4.2.3. All dimensions
are in mm. h = 0.38 mm, h1 = 0.47 mm. The high-εr layers have a dielectric
constant of εr = 85 and the dielectric spacers have a dielectric constant of εr = 3.4. . . 80
4.3
Comparison between the predicted breakdown power level and the measured ones
for FSSs shown in Fig. 4.12. The predicted values are obtained using the MFEF
values presented in Fig. 4.14 assuming that air breakdown occurs for an electric field
intensity of 3 × 106 V/m. The measured breakdown levels are obtained from the
high-power measurements shown in Fig. 4.15. Power level units are in kW. . . . . . . 95
5.1
Distances between the center of each zone and the center of the lens aperture for the
two lens prototypes discussed in Section 6.2.2. All values are in mm. . . . . . . . . . 110
5.2
Physical and electrical properties of the time delay units that populate each zone of the
TTD lens with a desired frequency range of 8−10.5 GHz and f /D ≈ 1.6. Time delay
values in the desired frequency range are in psec. Maximum insertion loss values
within the desired frequency range are in dB and all physical dimensions are in mm.
For all of these TDUs, Dx = Dy = 6 mm, h1,2 = h2,3 = h5,6 = h6,7 = 0.813 mm,
h3,4 = h4,5 = 0.508 mm. The dielectric substrate used is Rogers 4003C with a
dielectric constant of 3.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.3
Physical and electrical properties of the time delay units that populate each zone of
the TTD lens with a desired frequency range of 8.5 − 10.5 GHz and f /D ≈ 1. Time
delay values within the desired frequency range are in psec. Insertion loss values
within the desired frequency range are in dB and all physical dimensions are in mm.
For all of these TDUs, Dx = Dy = 6 mm, h1,2 = h2,3 = h5,6 = h6,7 = 0.813 mm,
h3,4 = h4,5 = 0.508 mm. The dielectric substrate used is Rogers 4003C with a
dielectric constant of 3.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.1
Distances between the center of each zone and the center of the lens aperture for the
three lens prototypes discussed in Section 6.2.2. Lenses 1 and 2 are the first and the
second metallo-dielectric TTD lenses in Section 6.2.2.1, and lens 3 is the all-dielectric
TTD lens in Section 6.2.2.2. All values are in mm. . . . . . . . . . . . . . . . . . . . 141
viii
Appendix
Table
Page
6.2
Physical and electrical properties of the time-delay units that populate each zone of
the first metallo-dielectric TTD lens with a desired frequency range of 6.5 − 10.5 GHz
and f /D ≈ 1.5. Time delay values in the desired frequency range are in psec. All
physical dimensions are in mm. For all of these TDUs, Dx = Dy = 6 mm, h2 =
h4 = h6 = 3.175 mm. The dielectric substrate used is Rogers 5880 with a dielectric
constant of 2.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
6.3
Physical and electrical properties of the time-delay units that populate each zone of the
second metallo-dielectric TTD lens with a desired frequency range of 6.5 − 8.5 GHz
and f /D ≈ 1. Time delay values within the desired frequency range are in psec.
All physical dimensions are in mm. For all of these TDUs, Dx = Dy = 6 mm,
h2 = h4 = h6 = 3.175 mm. The dielectric substrate used is Rogers 5880 with a
dielectric constant of 2.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.4
Physical and electrical properties of the time-delay units that populate each zone of the
all-dielectric TTD lens with a desired frequency range of 7.5 − 11.5 GHz and f /D ≈
1.3. Time delay values within the desired frequency range are in psec. All physical
dimensions are in mm. For all of these TDUs, Dx = Dy = 6 mm, h1 = h3 = h5 =
h7 = 1.27 mm, h2 = h4 = h6 = 1.575 mm. The high-εr dielectric substrate used
is Rogers 6010 with a dielectric constant of 10.2, and the low-εr dielectric substrate
used is Rogers 5880 with a dielectric constant of 2.2. CU T from zone 9 to zone
12 indicates the corresponding high-εr layer is completely removed. All the low-εr
substrates of zone 11 have substrate through-holes with diameter of 3.7 mm, and all
the low-εr substrates of zone 12 have substrate through-holes with diameter of 5.7 mm 148
ix
LIST OF FIGURES
Figure
Page
2.1
Topology of the proposed bandpass FSS. The unit cells of the capacitive and hybridresonator layers are shown on the right hand side of the figure. . . . . . . . . . . . . . 24
2.2
Equivalent circuit model of the FSS discussed in Section 2.2.1. . . . . . . . . . . . . . 26
2.3
(a) Measured and calculated transmission coefficients of the first FSS prototype discussed in Section 2.3.1 for normal incidence. The device has an out-of-band transmission null. (b)-(c) Measured transmission coefficient of the FSS for oblique incidence
angles for the TE (b) and TM (c) polarizations of incidence. . . . . . . . . . . . . . . 30
2.4
(a) Measured and calculated transmission coefficients of the second FSS prototype
discussed in Section 2.3.1 for normal incidence. The device has an in-band transmission null. (b)-(c) Measured transmission coefficient of the FSS for oblique incidence
angles for the TE (b) and TM (c) polarizations of incidence. . . . . . . . . . . . . . . 32
2.5
Topology of the waveguide version of the FSS presented in Fig. 2.1 with a tunable
transmission null. (a) Top view of a capacitive iris. (b) Top view of the hybridresonator iris. (c) Topology of the loaded resonator used in the hybrid-resonator iris.
(d) Perspective view of the whole device. . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6
Measured and simulated transmission coefficients of the FSS with a tunable transmission null discussed in Section 2.3.2. The results are shown for four tuning stages
corresponding to different values of CL . (a) 0.15 pF (b) 0.3 pF (c) 0.5 pF (d) 2.0 pF. . 35
3.1
(a) Topology of a fluidically tunable miniaturized-element frequency selective surface. The structure is composed of successive capacitive and inductive layers separated from one another by thin dielectric substrates. Columns of Teflon tubes, containing discontinuous Galinstan droplets, are embedded within the dielectric substrates to
dynamically tune the surface impedances of the capacitive layers. (b) Top view of
four unit cells of the structure located on the x − y plane. (c) Side view of the FSS in
the x − z plane. (d) Side view of the structure in the y − z plane. (e) Top views of the
unit cell of a capacitive patch and an inductive wire grid. . . . . . . . . . . . . . . . . 37
x
Figure
Page
3.2
Top view of a column of capacitive patch layers with the Teflon tube underneath it.
(a) Maximum capacitance value is obtained as the liquid metal droplets are placed
directly underneath the gap between two adjacent capacitive patches. (b) Minimum
capacitance value is achieved when the liquid metal droplets are moved entirely away
from the gap region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3
(a) Equivalent circuit model of the general tunable FSS shown in Fig. 3.1(a) for
normal angle of incidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4
(a) Unit cell of a liquid varactor composed of a sub-wavelength capacitive patch integrated with a liquid metal droplet. The horizontal and vertical offsets of the liquid
metal droplet with respect to the center of the gap between the two adjacent capacitive
patches are referred to as O1 and O2 respectively. (b) The equivalent circuit model
of the liquid varactor. (c) The extracted effective capacitances of a tunable capacitive
surface. The structure has unit cell dimensions of 6.5 mm × 6.5 mm. Four different
cases are shown. Case i: l = 1 mm, Case ii: l = 2 mm, Case iii: l = 3 mm, Case iv:
l = 4 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5
(a) A unit cell of the fifth-order fluidically tunable FSS discussed in Section 4.2.3
is placed inside a waveguide with periodic boundary conditions to simulate the frequency response of the infinitely large FSS. (b) The side view of unit cell of the fifthorder MEFSS showing all the dimensions and various capacitive and inductive layers.
45
3.6
(a) A fluidic varactor of the type discussed in Section 6.2.2 is composed of three
different capacitors of Cu , Cl , and Ci as depicted. (b) The equivalent circuit model of
the fluidic varactor showing the relative arrangement of Cu , Cl , and Ci . . . . . . . . . 46
3.7
Comparison between the capacitance values predicted using the analytical method
and those extracted from full-wave EM simulations. The results are shown for the
four liquid varactors considered in Section 6.2.2. . . . . . . . . . . . . . . . . . . . . 47
3.8
(a) Transmission coefficient of the fifth-order FSS of Section 4.2.3 calculated using
both full wave EM simulations and the equivalent circuit model presented in Fig. 3.3.
Different tuning states are described in Table 4.1 and the values of the equivalent circuit elements are presented in Table 4.2. (b) The phase of the transmission coefficient
of the fifth-order FSS of Section 4.2.3 calculated using full wave EM simulations for
different tuning states described in Table 4.1. . . . . . . . . . . . . . . . . . . . . . . 50
xi
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Figure
3.9
Page
Magnitude (a) and phase (b) of the transmission coefficient of the tunable MEFSS
discussed in Section 4.2.3 as a function of angle of incidence. The results are obtained using full-wave EM simulations for the transverse electric (TE) polarization of
incidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.10 Magnitude (a) and phase (b) of the transmission coefficient of the tunable MEFSS
discussed in Section 4.2.3 as a function of angle of incidence. The results are obtained using full-wave EM simulations for the transverse magnetic (TM) polarization
of incidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.11 (a) Magnitude of the transmission coefficient of the tunable MEFSS, discussed in
Section 3.2.5, which utilizes GaAs varactors to achieve tuning. (b) The change of
the phase of the transmission coefficient of the GaAs-tunable MEFSS discussed in
Section 3.2.5 when the instantaneous electric field intensity is increased from 1 V/m
to 1000V/m. (c) Magnitude of the transmission coefficient of the tunable MEFSS,
discussed in Section 3.2.5, which utilizes BST varactors to achieve tuning. (d) The
change of the phase of the transmission coefficient of the BST-tunable MEFSS discussed in Section 3.2.5 when the instantaneous electric field intensity is increased
from 1 V/m to 1000V/m. Description of all tuning states are provided in Table 4.2. . . 55
3.12 Topology of the FSS pieces that are used in the measurement process. The dimensions of these pieces are equal to the inner dimensions of the WR-90 waveguide. The
topology of each piece is derived from the topology of the unit cell show in Fig. ?? . . 57
3.13 Measured and simulated transmission coefficient for (i), (ii), (iii)
. . . . . . . . . . . 58
3.14 Measured and Simulated results of the operating center frequency and fraction bandwidth (BW) as a function of the offset . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.15 Topology of the waveguide version of the third-order tunable FSS discussed in Section
3.3.2. Top view of a capacitive and inductive iris, the side view of the structure, and
the photograph of a fabricated section are shown. . . . . . . . . . . . . . . . . . . . . 60
3.16 (a) The assembly of the waveguide version of the third-order tunable MEFSS discussed in Section 3.3.2 (waveguide shims acting as spacers are not shown here). (b)
The photograph of the experimental setup used to characterize the response of this
structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
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Figure
Page
3.17 (a) Simulated and measured magnitudes of the transmission coefficient of MEFSS
Prototype 1 (discussed in Section 3.3.2). Simulations are conducted in CST Studio.
(b) The simulated and measured phase of the transmission coefficient of this prototype. The description of all tuning states is provided in Table 4.3. . . . . . . . . . . . 63
3.18 Simulated and measured magnitude (a) and phase (b) of the transmission coefficient
of MEFSS prototype 2 (described in Section 3.3.2). (c) The insertion loss and transmission phase of the structure, at 10 GHz, for a number of different tuning states.
Description of the tuning states is provided in Table 3.4. . . . . . . . . . . . . . . . . 65
3.19 Simulated and measured magnitude (a) and phase (b) of the transmission coefficient
of MEFSS prototype 3 (described in Section 3.3.3). (c) The insertion loss and transmission phase of the structure, at 10 GHz, for a number of different tuning states.
Description of the tuning states is provided in Table 3.5. . . . . . . . . . . . . . . . . 68
4.1
(a) 3-D topology of a 2nd -order MEFSS composed of capacitive and inductive impedance
layers cascaded sequentially. (b) 3-D topology of a 2nd -order JC slot FSS. . . . . . . . 75
4.2
Calculated transmission and reflection coefficients for the 2nd -order MEFSS and 2nd order JC slot FSS using the physical parameters provided in Table 4.1. . . . . . . . . . 76
4.3
MFEF for a 2nd -order MEFSS and a 2nd -order JC slot FSS as a function of frequency.
Each FSS has a bandpass Butterworth frequency response centered at 10 GHz with a
fractional bandwidth of 20%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4
Frequency-dependent MFEF values for MEFSSs with different fractional bandwidths
and response types. (a) 3rd -order Butterworth response, (b) 3rd -order Chebyshev
(0.1 dB ripple) response, (c) 5th -order Butterworth response, and (d) 5th -order Chebyshev response (0.1 dB ripple). All frequency responses are centered at 10 GHz and all
MEFSSs are designed to have the same unit cell sizes of 5.8 mm ×5.8 mm. . . . . . . 78
4.5
Frequency-dependent MFEF values for MEFSSs with different unit cell sizes. (a)
3rd -order Butterworth response, (b) 3rd -order Chebyshev response (0.1 dB ripple), (c)
5th -order Butterworth response, (d) 5th -order Chebyshev response (0.1 dB ripple). All
frequency responses are centered at 10 GHz with 20% fractional bandwidth. . . . . . . 80
4.6
(a) 3-D topology of a 2nd -order MEFSS using thin high-εr substrate layers rather than
capacitive layers composed of rectangular patches. (b) Top view of one unit cell of
the inductive layer. (c) Equivalent circuit model for the 2nd -order MEFSS using thin
high-εr substrate layers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
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Figure
Page
4.7
Transmission coefficients of the MEFSS shown in Fig. 4.6(a) for different wire grid
dimensions, which results in the same effective inductance. The results for cases A,
C, E, G, and H listed in Table 4.2 are shown. . . . . . . . . . . . . . . . . . . . . . . 82
4.8
(a) A unit cell of the wire grid is placed inside a waveguide with PBC conditions to
compute its frequency response for different grid parameters that are listed in Table
4.2. (b) Equivalent circuit model of the wire grid shown in part (a). (c) The transmission coefficients of different wire grids whose dimensions are listed in Table 4.2. The
transmission coefficient of the ideal inductor needed for this MEFSS is also presented
for comparison. The value of the desired indictor is calculated using the procedure
described in [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.9
Electric field distribution in the inductive layer MEFSSs optimized for HPM operation
using different wire grid patterns with dimensions listed in Table 4.2. All MEFSSs
have essentially the same 2nd -order bandpass response centered at 10 GHz with a
fractional bandwidth of 20% as shown in Fig. 4.7. . . . . . . . . . . . . . . . . . . . 85
4.10 MFEF values of the MEFSS shown in Fig. 4.6(a) implemented with wire grid patterns
A, C, E, G, and H listed in Table 4.2. All MEFSSs have the same 2nd -order bandpass
Butterworth response centered at 10 GHz with 20% fractional bandwidth. . . . . . . . 86
4.11 Experimental setup for measuring the transient power handling capability of an FSS
in a waveguide environment using a high-power magnetron. The magnetron generates
a single-frequency pulse at 9.382 GHz with a peak power of 25 kW and a pulse width
of 1µs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.12 Waveguide prototypes equivalent to one unit cell of different types of FSSs with different expected transient power handling capabilities. (a) Case A: 2nd -order MEFSS
with 10% fractional bandwidth. (b) Case B: 2nd -order JC slot FSS with 20% fractional
bandwidth. (c) Case C: 2nd -order MEFSS with 20% fractional bandwidth. (d) Case D:
2nd -order MEFSS optimized for HPM operation with 20% fractional bandwidth implemented with thin high-εr substrate and rectangular shape inductive wire grids. (e)
Case E: 2nd -order MEFSS optimized for HPM operation with 20% fractional bandwidth implemented with thin high-εr substrate and circular shape inductive wire grids.
All waveguide prototypes are designed to have a Butterworth bandpass response centered at 9.382 GHz. WR-90 waveguide shims with inner dimensions of 0.9” × 0.4”
are used for all the prototypes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.13 Measured and calculated transmission coefficients of different waveguide FSS prototypes, cases A-E, shown in Fig. 4.12. . . . . . . . . . . . . . . . . . . . . . . . . . . 90
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Figure
Page
4.14 Full-wave simulated MFEFs for all the waveguide prototypes, cases A-E, shown in
Fig. 4.12. MFEF values are extracted by normalizing the maximum electric field
intensity within the waveguide version of the FSS to the maximum electric field intensity of the dominant T E10 mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.15 Time domain transmission and reflection coefficients for the waveguide prototypes,
cases A-E, shown in Fig. 4.12 under different incident peak power levels. (a) Case A
under 1.17 kW peak power level. (b) Case A under 1.20 kW power level. (c) Case
B under 3.37 kW power level. (d) Case B under 3.43 kW power level. (e) Case C
under 5.43 kW power level. (f) Case C under 5.57 kW power level. (g) Case D under
25 kW power level. (h) Case E under 25 kW power level. The magnetron generates a
single-frequency pulse at 9.382 GHz with a peak power of 25 kW and a pulse width
of 1µs. The different incident power levels are achieved by adjusting the E-H tuner
shown in Fig. 4.11. Each measurements has been repeated many times over the span
of a few days. All measurements were found to be highly reproducible. . . . . . . . . 97
5.1
(a) Topology of a conventional double-convex dielectric lens. (b) Topology of the
planar true-time-delay lens populated with spatial TDUs. (c) Relative time delay that
different rays of a spherical wave experience at the input of the lens aperture and the
time delay profile provided by the lens to achieve a planar wavefront at the output
aperture of the lens. Note that the time delay is referenced to the time it takes from the
focal point to the center of the lens aperture. The results are calculated for two circular
aperture lens. A lens with aperture diameter of D = 18.6 cm and focal distance of
f = 30 cm (f /D ≈ 1.6) and another one with aperture diameter of D = 18.6 cm and
focal distance of f = 19 cm (f /D ≈ 1). . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2
(a) Topology of the proposed TTD lens populated with spatial TDUs. (b) Top view of
both the capacitive and inductive layer of each TDU. (c) Equivalent circuit model of
each TDU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3
Calculated frequency responses of three MEFSSs having second-, third-, and fourthorder bandpass responses. (a) Magnitudes and phases of the transmission coefficients.
(b) Magnitudes of the transmission coefficients and the corresponding group delays.
As the order of the MEFSS response increases, the transmission phase shift within
the highlighted region increases and a correspondingly larger group delay can be
achieved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
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5.4
Calculated frequency responses of three MEFSSs with fourth-order bandpass responses
and different fractional bandwidths. (a) Magnitudes and phases of the transmission
coefficients. (b) Magnitudes of transmission coefficients and the corresponding group
delays. As the fractional bandwidth increases, the transmission phase shift within the
highlighted region decreases and the group delay is reduced. . . . . . . . . . . . . . . 107
5.5
(a) Top view of the proposed TTD planar lens. A spherical wave is launched from
a point source located at the focal point of the lens, (x = 0, y = 0, z = −f ). To
transform this input spherical wavefront to an output planar one irrespective of the
frequency, T (x, y) + T D(x, y) must be constant for every point on the aperture of
the lens. T D(x, y) is the time delay provided by the lens. T (x, y) is the time it takes
for the wave to travel from the focal point of the lens, (x = 0, y = 0, z = −f ),
to a point at the lens aperture, (x, y, z = 0). (b) Topology of the proposed TTD
lens prototype with a circular aperture. The lens aperture is divided into M concentric
zones populated with identical spatial TDUs within each zone. d1 , d2 , ...... dM are
the distances between the center of each zone and the center of the lens aperture. Two
lens prototypes with M = 12 and M = 16 are discussed in Section 6.2.2. . . . . . . . 108
5.6
Topology of the unit cell of a fourth-order MEFSS which is used as the time delay
units of the TTD lenses discussed in Section 6.2.2. . . . . . . . . . . . . . . . . . . . 111
5.7
(a) The comparison between the full-wave simulated transmission phases and the ideal
linear transmission phases for different zones of the first lens prototype with 12 concentric zones and f /D ≈ 1.6. Zi : ideal represents an ideal desired linear transmission phase with the desired time delay for Zone i as listed in Table 6.2. (b) The
simulated transmission and reflection coefficients of the TDUs occupying each zone
of the second lens prototype. The highlight region (8 − 10.5 GHz) in both figures
indicates the area where an approximate linear transmission phase close to the required ideal linear phase can be obtained. This region is considered to be the desired
frequency range of operation for the TTD lens. . . . . . . . . . . . . . . . . . . . . . 114
5.8
(a) The comparison between the full-wave simulated transmission phases and the ideal
linear transmission phases for different zones of the second lens prototype with 16
concentric zones and f /D ≈ 1. Zi : ideal represents an ideal desired linear transmission phase with the desired time delay for Zone i as listed in Table 6.3. (b) The
simulated transmission and reflection coefficients of the TDUs occupying each zone of
the first lens prototype. The highlight region (8.5−10.5 GHz) in both figures indicates
the area where an approximate linear transmission phase close to the required ideal
linear phase can be obtained. This region is considered to be the desired frequency
range of operation for the TTD lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
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Figure
5.9
Page
(a) Photograph of the fabricated lens prototype with 12 zones and a f /D = 1.6. (b)
Photograph of the fabricated lens prototype with 16 zones and a f /D = 1. In both
of these two figures, the only visible metallic layer is the first capacitive layer within
which the size of the capacitive patches decrease from the center of the lens to the
edges. Note here the same trend exists for all the other capacitive layers located in the
interior layers of the structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.10 (a) Calculated and measured focusing gains of the first TTD lens prototype with
f /D ≈ 1.6 at its expected focal point (x = 0 cm, y = 0 cm, z = −30 cm). The
measured 3 dB gain bandwidth is 43%. (b) Calculated and measured focusing gains
of the second TTD lens prototype with f /D ≈ 1 at its expected focal point (x = 0 cm,
y = 0 cm, z = −19 cm). The measured 3 dB gain bandwidth is 38%. . . . . . . . . . 119
5.11 Measured normalized received field intensity of the fabricated TTD lens with f /D ≈
1.6 in a rectangular grid in the vicinity of the expected focal point. The “x” symbol
shows the actual focal point of the lens determined by the measurement and the color
bar values are in dB. In all of the figures, the horizontal axis is the x axis with units of
[cm] and the vertical axis is the z axis with units of [cm]. (a) 8.0 GHz. (b) 8.5 GHz.
(c) 9.0 GHz. (d) 9.5 GHz. (e) 10.0 GHz. (f) 10.5 GHz. . . . . . . . . . . . . . . . . . 120
5.12 Measured normalized received field intensity of the fabricated TTD lens with f /D ≈
1 in a rectangular grid in the vicinity of the expected focal point. The “x” symbol
shows the actual focal point of the lens determined by the measurement and the color
bar values are in dB. In all of the figures, the horizontal axis is the x axis with units of
[cm] and the vertical axis is the z axis with units of [cm]. (a) 8.5 GHz. (b) 9.0 GHz.
(c) 9.5 GHz. (d) 10.0 GHz. (e) 10.5 GHz. (f) 11.0 GHz. . . . . . . . . . . . . . . . . 121
5.13 The measured focal lengths of the two fabricated TTD lens prototypes discussed in
Section 6.2.2 as a function of frequency. As a reference for comparison, the measured
focal lengths of the two non-TTD MEFSS-based prototypes presented in [46] are also
reported in this figure. Observe that the effects of chromatic aberrations in non-TTD
lenses are manifested in the form of significant focal point movements vs. frequency.
These effects are conspicuously absent in the TTD lenses reported in this chapter. . . . 123
5.14 Measured scanning performance of the fabricated TTD lens with f /D ≈ 1.6. The
power pattern is measured over the focal arc of the lens for plane waves arriving at
various incidence angles. (a) 8.0 GHz. (b) 8.5 GHz. (c) 9.0 GHz. (d) 9.5 GHz. (e)
10.0 GHz. (f) 10.5 GHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
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Page
5.15 Measured scanning performance of the fabricated TTD lens with f /D ≈ 1. The
power pattern is measured over the focal arc of the lens for plane waves arriving at
various incidence angles. (a) 8.5 GHz. (b) 9.0 GHz. (c) 9.5 GHz. (d) 10.0 GHz. (e)
10.5 GHz. (f) 11.0 GHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.16 Time-domain responses and fidelity factors of three different lens prototypes for various excitation signals. (a)-(c) The incident and transmitted pulses of the TTD lens with
f /D ≈ 1.6 for the modulated Guassian pulses centered at 9.25 GHz with fractional
bandwidths of (a) 10%, (b) 20%, and (c) 30%. (d)-(f) The incident and transmitted
pulses of the TTD lens with f /D ≈ 1 for the modulated Guassian pulses centered at
9.5 GHz with fractional bandwidths of (d) 10%, (e) 20%, and (f) 30%. (g)-(i) The incident and transmitted pulses of the spatial phase shifter (SPS) based lens reported in
[46] (with five zones) for the modulated Guassian pulses centered at 10 GHz with fractional bandwidths of (g) 10%, (h) 20%, and (i) 30%. In all cases, the center frequency
of operation of the Gaussian pulse is matched to the center frequency of operation of
the respective lens. In all of the figures, the horizontal axis is the time axis with units
of [ns] and the vertical axis is the normalized magnitude for the time-domain signals. . 130
6.1
(a) Topology of the proposed TTD lens populated with lowpass FSS-based spatial
TDUs. The inset shows the composition of each TDU. (b) The equivalent circuit
model of each lowpass type TDU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.2
Calculated frequency responses of three lowpass FSSs with N = 5, having three different cutoff frequencies (fcutof f = ∞, 16, and 11 GHz for states A, B, and C). State
A has no capacitive patches. (a) Magnitudes (solid) and phases (dashed) of the transmission coefficients. (b) Group delays. As fcutof f decreases, the transmission phase
shifts within the highlighted region increases and a correspondingly larger group delay
can be achieved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.3
Calculated frequency responses of three lowpass FSSs with N = 7, having three
different cutoff frequencies (fcutof f = ∞, 30, and 11 GHz for states D, E, and F. State
D has no capacitive patches. (a) Magnitudes (solid line) and phases (dashed line) of
the transmission coefficients. (b) Group delays. As the N increases, the maximum
delay variation within the highlighted region increases. . . . . . . . . . . . . . . . . . 139
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Figure
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6.4
(a) The comparison between the full-wave simulated transmission phases and the ideal
linear transmission phases for different zones of the first metallo-dielectric TTD lens
prototype with 16 concentric zones and f /D ≈ 1.5. Zi : ideal represents an ideal
desired linear transmission phase with the desired time delay for Zone i as listed in
Table 6.2. (b) The simulated transmission and reflection coefficients of the TDUs occupying each zone of the first metallo-dielectric TTD lens prototype. The highlighted
region (6.5 − 10.5 GHz) in both figures indicates the area where an approximate linear transmission phase close to the required ideal linear phase can be obtained. This
region is considered to be the desired frequency range of operation for the TTD lens. . 143
6.5
(a) The simulated transmission and reflection coefficients of the TDUs occupying
each zone of the second metallo-dielectric lens prototype. The highlighted region
(6.5 − 8.5 GHz) in both figures indicates the area where an approximate linear transmission phase close to the required ideal linear phase can be obtained. This region is
considered to be the desired frequency range of operation for the TTD lens. (b) The
comparison between the full-wave simulated transmission phases and the ideal linear
transmission phases for different zones of the second metallo-dielectric lens prototype
with 17 concentric zones and f /D ≈ 1. Zi : ideal represents an ideal desired linear
transmission phase with the desired time delay for Zone i as listed in Table 6.3. . . . 147
6.6
The effective dielectric constant of the high-εr substrate that is periodically loaded
with cylindrical through-substrate holes as a function of the diameter of the throughsubstrate holes. The high-εr substrate is Rogers 6010 with dielectric constant of 10.2
and a thickness of 1.27 mm. The periodicity of the substrate through-holes is 6 mm. . 149
6.7
(a) The simulated transmission and reflection coefficients of the TDUs occupying each
zone of the all-dielectric TTD lens prototype. The highlight region (7.5−11.5 GHz) in
both figures indicates the area where an approximate linear transmission phase close
to the required ideal linear phase can be obtained. This region is considered to be the
desired frequency range of operation for the TTD lens. (b) The comparison between
the full-wave simulated transmission phases and the ideal linear transmission phases
for different zones of the all-dielectric TTD lens prototype with 12 concentric zones
and f /D ≈ 1.3. Zi : ideal represents an ideal desired linear transmission phase with
the desired time delay for Zone i as listed in Table 6.3. . . . . . . . . . . . . . . . . . 151
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6.8
(a) Top view of the fabricated metallo-dielectric TTD lens prototype with 17 zones
and a f /D ≈ 1. (b) Side view of the metallo-dielectric TTD lens prototype with
17 zones and a f /D ≈ 1. (c) The detailed zoom in view of one corner of the only
visible metallic layer, the first capacitive patch layer. The size of the capacitive patches
decrease from the center of the lens to the edges. Note here the same trend exists for
all the other capacitive layers located in the interior layers of the structure. . . . . . . . 152
6.9
(a) Top view of the fabricated all-dielectric TTD lens prototype with 12 zones and a
f /D ≈ 1.3. (b) Side view of the all-dielectric TTD lens prototype with 12 zones and
a f /D ≈ 1.3. (c) The detailed zoom in view of one corner of the only visible high-εr
layer. The size of the substrate through-hole increase from the center of the lens to the
edges. Note here the same trend exists for all the other high-εr layers located in the
interior layers of the structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.10 (a) Calculated and measured focusing gains of the first metallo-dielectric TTD lens
prototype with f /D ≈ 1.5 at its expected focal point (x = 0 cm, y = 0 cm, z =
−24 cm). (b) Calculated and measured focusing gains of the second metallo-dielectric
TTD lens prototype with f /D ≈ 1 at its expected focal point (x = 0 cm, y = 0 cm,
z = −19 cm). (b) Calculated and measured focusing gains of the all-dielectric TTD
lens prototype with f /D ≈ 1.3 at its expected focal point (x = 0 cm, y = 0 cm,
z = −21 cm). All of the focusing gains are measured using the same setup shown in
Fig. 10(a) of [46]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.11 Measured normalized received field intensity of the fabricated TTD lens prototypes
in a rectangular grid in the vicinity of their expected focal points. The normalized
field pattern of the first metallo-dielectric TTD lens with f /D ≈ 1.5 is shown at (a)
6.5 GHz, (b) 8.0 GHz, and (c) 10 GHz. The normalized field pattern of the second
metallo-dielectric TTD lens with f /D ≈ 1 is shown at (d) 7 GHz, (e) 8.0 GHz, and
(f) 9 GHz. The normalized field pattern of the all-dielectric TTD lens with f /D ≈ 1.3
is shown at (g) 8.0 GHz, (h) 9.5 GHz, and (i) 11.5 GHz. The “x” symbol shows the
actual focal point of the lens determined by the measurement and the color bar values
are in dB. In all of the figures, the horizontal axis is the x axis with units of [cm] and
the vertical axis is the z axis with units of [cm]. The measurement is conducted using
the same setup shown in Fig. 10(b) in [46]. . . . . . . . . . . . . . . . . . . . . . . . 155
6.12 Measured focal length of all the fabricated lens prototypes. . . . . . . . . . . . . . . . 156
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Page
6.13 Measured scanning performance of the fabricated metallo-dielectric TTD lens with
f /D ≈ 1.5 at (a) 6.5 GHz, (b) 9GHz, and (c) 10.5 GHz. Measured scanning performance of the fabricated metallo-dielectric TTD lens with f /D ≈ 1 at (d) 7 GHz, (e) 8
GHz, and (f) 9 GHz. Measured scanning performance of the fabricated all-dielectric
TTD lens with f /D ≈ 1.3 at (g) 8.5 GHz, (h) 9.5 GHz, and (i) 10.5 GHz. The power
pattern is measured over the focal arc of each lens for plane waves arriving at various
incidence angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.14 Time-domain responses and fidelity factors of all proposed TTD lens prototypes for
various excitation signals. (a)-(c) The incident and transmitted pulses of the proposed
metallo-dielectric lowpass FSS-based TTD lens with f /D ≈ 1.5 for the modulated
Guassian pulses centered at 8.5 GHz with fractional bandwidths of (a) 10%, (b) 30%,
(c) 50%. (d)-(f) The incident and transmitted pulses of the proposed metallo-dielectric
lowpass FSS based TTD lens with f /D ≈ 1 for the modulated Guassian pulses centered at 7.5 GHz with fractional bandwidths of (d) 10%, (e) 20%, (f) 30%. (g)-(i)
The incident and transmitted pulses of the proposed all-dielectric lowpass FSS based
TTD lens with f /D ≈ 1.3 for the modulated Guassian pulses centered at 8.5 GHz
with fractional bandwidths of (g) 10%, (h) 30%, (i) 40%. The incident and transmitted pulses of the previously proposed bandpass FSS-based TTD lens in [63] with
f /D ≈ 1.5 for the modulated Guassian pulses centered at 9.25 GHz with fractional
bandwidths of (j) 30% and (k) 50%. In all cases, the center frequency of operation of
the Gaussian pulse is matched to the center frequency of operation of the respective
lens. In all of the figures, the horizontal axis is the time axis with units of [ns] and the
vertical axis is the normalized magnitude for the time-domain signals. . . . . . . . . . 158
6.15 Measured fidelity factors under oblique angle of incidences for all the TTD lenses. . . 160
xxi
ABSTRACT
Phased array antennas and agile antenna apertures can potentially play a significant role in the
future wireless system, and benefit several strategic areas such as ultra-fast data rate wireless
transmission and economically viable solar power transmissions. Despite the conventional use
of phased array antennas in many military sectors such as airborne and ground based radar systems, the complexity of the array structures as well as the excessive cost of phase shifters and T/R
modules prohibits the phased arrays from being deployed in many strategic and commercial systems. A significant amount of this thesis is dedicated to providing innovative and interdisciplinary
solutions that could potentially enable the widespread use of high-power-capable and affordable
phased-array technology in the future wireless systems.
In this thesis, the concept of tunable space-fed microwave lens is proposed as a promising approach
of realizing affordable agile antenna apertures. Using this approach, the entire system is expected
to have wideband operation, a strong capability of handling high RF power levels, and negligible
losses with greatly simplified architecture. The proposed planar microwave lenses are composed
of numerous true-time-delay (TTD) units, and are extremely suitable in broadband pulsed applications. A linear tuning technique that dose not rely on solid-state devices is also proposed as a
potential way of making these lenses tunable.
Each true-time-delay unit in the proposed microwave lenses is in the form of one unit cell of an
appropriately designed frequency selective surfaces (FSSs). In this thesis, the FSSs of choice are
composed of multiple impedance sheets separated from each other by thin dielectrics. It is first
demonstrated that these FSSs can be made tunable by using a fluidically tuning technique that
xxii
dose not rely on solid state devices. The resulting tunable FSSs have a wide tuning range and
can maintain linearity in high power applications. Subsequently, the power handling capability of
these FSSs are studied extensively, and the guidelines of designing extremely high-power capable
FSSs are provided. Finally, the design of true-time-delay microwave lenses composed of these
FSSs are demonstrated. In particularly, the true-time-delay units of these lenses can be composed
of bandpass, lowpass and all-dielectric type FSSs, depending on the specific application.
1
Chapter 1
Introduction
1.1
Motivation
Recently, there has been a growing interest in phased array antennas due to their wide appli-
cations in collision avoidance radar [1], military radar [2], space communication [3], imaging [4],
and smart antenna systems [5]. A phased array is an array of antennas in which the relative phases
of the respective signals feeding the antennas are varied in such a way that the effective radiation
pattern of the array is reinforced in a desired direction and suppressed in undesired directions. The
phased array antenna has been around for more than half a century. During the second world war,
the development of phased array antennas took a quantum leap, due to the fast growing demand
of steerable radar systems in military sectors. While traditional radars achieve beam steering by
physically moving their antenna apertures, a phased-array radar uses electronic beam steering and
does not necessarily rely on movement of the aperture. The tracking of multiple targets in a phased
array radar system can be achieved by scanning the main beam very quickly. A typical example of
the application of phased array radar in military sectors is its usage in many modern warships. The
agile beam scanning characteristics of the phased array radar allow the warships to track both surface targets and air targets simultaneously. It is not exaggerating to state the fact that the initiative
in a modern warfare is heavily dependent on the performance level of a phased array system.
While it is fair to say that the rapid growth of phased array technology is mainly due to its wide
deployment in military sectors, phased array antennas have great potentials in many other areas
as well. The agile beam forming capability of phased array antennas can be a great asset for next
generation wireless communication standards. Over the past several decades, we have witnessed
2
a dramatic growth in the wireless communication area, especially on smart phone and tablets.
From 2G to 3G and 4G, each generation of wireless standard is dedicated to offer higher and
higher data rates. This rapid increase in datarates cannot continue without developing technologies
that can be used to enhance access to the radiowave spectrum. An example of a technology that
can be used to enhance the capacity of a communication system is the multiple-input-multipleoutput (MIMO) approach. One important key in the future MIMO technology is beam forming
technology which takes the advantage of spatial diversity to achieve higher channel capacity. In
the latest release of LTE, which stands for long-term evolution and is developed by the 3GPP
(3rd Generation Partnership Project) as a standard for wireless communication of high-speed data
for mobile phones and data terminals, MIMO technology in conjunction with beam forming has
already been adopted as the next step of boosting the wireless channel capacity. The phased array
antennas, in this sense, can potentially play a major role in these latest wireless standards due to
their agile beam forming capabilities.
Enhancing the wireless channel capacity is just one possible potential application of phased
array antennas in civilian systems. More application areas such as imaging and space communication can also benefit from phased array antennas too. In general, with an agile beam forming
capability, the phased array antennas can benefit many applications that require dynamic beam
forming. Judging from the above discussion, it all seems really tempting to apply the phased array
antenna technology beyond its original deployment in military applications. However, this trend
has not been going as smooth as was expected during the past decades. Up to know, any complex
phased array system can still only be seen in military sectors, where the cost is of less concern.
The efforts of pushing phased array technology towards commercial applications have never been
stopped. However, the major setback in these efforts is the extremely high cost of the phased-array
antenna technology. The state-of-art phased array systems are very costly and hence, cannot be
widely used in commercial applications. In addition to this major cost issue, other problems exist
as well that need to be addressed for the phased array antennas. These problems include enlarging the operation bandwidth of the system, enhancing the power handling capability, reducing the
system loss, as well as introducing minimum distortion to the incident signal. All these issues are
3
critical in determining the performance level of a phased array system. In order to find effective
solutions for these problems, one has to gain a deep understanding of the current phased array
antenna systems first.
Traditional phased array antennas can be categorized into either active or passive arrays, depending on the specific system architecture. Passive electronically steered arrays (PESAs) have a
central transmitter and receiver, with phase shifters located at each radiating element or sub-array.
The passive array is the least expensive phased array because of its low number and cost of components. Active electronically steered arrays (AESAs), on the other hand, use a Transmitter/Reciver
(T/R) module for each radiating element. Each T/R module is a fully fledged transceiver that can
not only amplify the transmitted and received signal, but also control the phase and amplitude of
these signals to achieve beam steering.
Both PESAs and AESAs have been widely used, and each of these two types has its own pros
and cons. PESAs have less complicated implementations, in which only a single source is used
to feed the array. The radiated power from the feeding source is then distributed over the array
aperture. In this case, the system loss of the array becomes an important issue that cannot be neglected [7]-[25]. The loss considered in PESAs mainly falls into two parts, feeding network loss
and loss brought by the phase shifters. In order to reduce the loss in the feeding network, low loss
transmission lines such as waveguide have been used to reduce the loss associated with the feeding
network. However, this increases the overall profile of the array tremendously while increasing
the complexity of the feeding network. In order to reduce the phase shifter losses, various types of
phase shifters, featuring different insertion loss, switching time, and power handling capabilities
have been extensively investigated. Unfortunately, few of the phase shifters investigated can provide the desired properties of low profile, low bias power, and high power handling capabilities at
the same time [7]-[25].
As opposed to PESAs, where a single source with high input power must be used, AESAs have
an individual RF source for each of its many T/R modules. One of the advantages of doing so
is that in the event of the failure in certain transmitting array elements, the overall performance
of the array will not be severely deteriorated. Another advantage of the AESAs is that the T/R
4
module of each array element can provide a solid state power amplification for the transmitted
signal. Such distributed amplification mechanism can lead to a considerably smaller system loss
compared to the case of PESAs, where a single T/R module with a single power amplification
is used. Furthermore, the distributed T/R modules of the AESAs offer more degrees of freedom
in choosing the relative phase and amplitude at each array element and hence, more flexible beam
scanning and synthesizing can be achieved in AESAs systems. Despite all these desired advantages
offered by the AESAs, the extremely high cost of the T/R modules has proven to be an obstacle to
the development of AESAs. Various attempts have been made in the past to reduce the cost and
increase the output power of AESAs. Gallium Arsenide (GaAs) monolithic microwave integrated
circuits (MMICs) have been one of the most successful ways of designing T/R modules [26].
GaAs can achieve high power amplification as well as wideband, low-noise amplification at higher
frequencies than silicon. However, the most crucial bottleneck for the GaAs MMIC T/R modules is
the production cost per module unit. This is mainly due to the large number of modules required for
each phased array system. At the moment, the T/R module costs are still high for many commercial
wireless systems.
In summary, despite the significant developments that have been made over the past decades,
neither the PESA nor the AESA architectures has resulted in the development of low-cost and
high-power phased-array system. A compromise has always to be made amongst system’s losses,
power handling capability, cost, and architecture complexity. In this thesis, I will present a new
approach that has the potential for developing affordable, efficient, high-power, wideband phasedarray antenna systems.
1.2
Proposed Approach
As stated above, high-power, wide band, and affordable phased arrays have still not been ma-
terialized. In this thesis, I propose to use a tunable space-fed microwave lenses as a promising
candidate for designing a low-cost, high-power phased array antennas. There are several main
features of this proposed approach. These include the use of a linear electronic-free tuning mechanism, wide bandwidth operation, a system with reduced loss, the capability of handling extremely
5
high RF power, and non-dispersive operation within a broadband frequency range. The proposed
tunable microwave lenses in this approach can be considered as a passive phased array system,
where only a single high power vacuum electronic device (VED) feed source is used. Such a simple spatial feeding mechanism eliminates feed network losses of a traditional corporate-fed PESA.
The proposed lenses are composed of numerous pixels, each of which can be properly designed to
act as either a spatial phase shifter or a time-delay unit. When used as a time-delay unit, each pixel
is designed to provide a certain time delay within a broad frequency range and create a constant
time delay profile over the output aperture of the lens. When designed in a true-time-delay fashion,
the proposed microwave lens dose not introduce any distortion to the incident signal and hence,
would be extremely suitable for applications where broadband pulsed signals are used. The constituting elements of the proposed lenses can be carefully optimized in a way such that the resulting
microwave lenses can handle extremely high pulsed RF power levels. Ultimately, beam forming in
the proposed tunable lens will be achieved by dynamically tuning time delay profile over the lens’
aperture. The tuning mechanisms in the proposed approach have a wide band tuning range and can
maintain the linearity under high power applications.
Several key strategies exist in the proposed approach. These include implementing a tuning
mechanism suitable for high power applications, designing wide band true time delay lenses, as
well as optimizing the power handling capability of the proposed lenses. With regards to the lens
design strategy presented in this thesis, each time-delay unit of the lens is one unit cell of a class
of non-resonant sub-wavelength periodic structures. Such a multi-layer structure is composed of
multiple impedance surfaces separated from each other using ultra-thin dielectric substrates. These
impedance sheets can either have capacitive or inductive surface impedances. The capacitive surfaces are implemented using a two-dimensional (2D) periodic arrangement of sub-wavelength and
non-resonant rectangular patches. The inductive surfaces are implemented using two-dimensional
(2D) periodic arrangements of inductive wire grids. A detailed synthesis procedure is developed
in this thesis to obtain the required time delay for each time-delay unit, as well as the way to
synthesize the geometrical properties of each time-delay unit. Thanks to the sub-wavelength feature of each time-delay unit as well as its small overall thickness, the resulting high resolution
6
lenses demonstrate excellent scanning performance up to 60◦ . One of the most desired features
of this proposed lens is that when operating as TTD lens, the transmitted signal through the system remains undistorted. This is highly desirable in situations where broadband pulse signals are
of interest. In sharp contrast to this, traditional microwave lenses composed of resonant building
blocks are typically highly dispersive, and can cause sever distortion even to a very narrow band
modulated incident signal.
As far as the tuning strategy is concerned, over decades, electronic tuning has long been used
as a tuning mechanism of choice that provides a fast tuning speed. Such tuning can be achieved by
utilizing solid state varactor diodes [27] and MEMS switches [24] for example. However, there are
several challenges that need to be addressed with this type of tuning technique. Prominent among
these are the need for biasing individual electronic devices and ensuring that RF/DC isolation is
maintained at the unit cell level. Satisfying these requirements is rather challenging in large panels. Another important but often overlooked issue in using electronic tuning devices is the power
handling capability and the linearity issues. Electronically controllable varactors are inherently
nonlinear devices and their use in a tunable microwave lens results in a nonlinear frequency response. In many applications (e.g. radar systems), microwave lenses are placed in close proximity
to antennas radiating microwave signals with very high peak power levels. In such situations, the
linearity (or lack thereof) of the response of a tunable microwave lens is an important factor that
can fundamentally limit its power handling capability. In order to overcome the above shortcomings brought by the electronic tuning, an alternative tuning mechanism called fluidic tuning, is
used in this thesis. This novel tuning mechanism does not rely on any nonlinear electronic devices
and hence, the corresponding frequency response of a tunable microwave lens using this tuning
technique is expected to remain linear under pulsed high-power excitation conditions. In this thesis, the proposed fluidic tuning mechanism is applied to different types of time-delay units, and
a wide tuning range can be observed from all of these tunable time-delay units. The preliminary
examinations of the proposed fluidic tuning strategy presented in this thesis turns out to prove its
advantage in high power RF applications, compared to its counterpart of electronic tuning technique. However, challenges do exist for the proposed tuning strategy, and need to be addressed in
7
the future before its wide deployment. In this thesis, both advantages and disadvantages of this the
proposed fluidic tuning strategy will be discussed in detail.
Another important strategy in the proposed approach is the design of extremely high power
capable microwave lenses. The sub-wavelength time-delay units in the proposed true time delay
lenses belong to a type of miniaturized-element frequency selective surfaces (MEFSSs). Therefore,
the key to design high power microwave lenses is to enhance the power handling capability of such
frequency selective surfaces. In this thesis, only pulsed power handling capability is investigated.
The failure mechanism under such a scenario is the breakdown event caused by the high electric
field intensity developed within the structure. The effect of various design parameters on the
peak power handling capability of these frequency selective surfaces are investigated throughout
the thesis and methods for increasing their peak power handling capability are proposed. Using
the design guidelines provided in this thesis, extremely high-power capable frequency selective
surfaces are demonstrated. Such high power frequency selective surfaces are highly desired as the
constituting elements of a high power microwave lens, and can also be used as various counterhigh-power-microwave (HPM) devices.
1.3
Literature review
As was mentioned in the previous section, the main goal of this thesis is to examine key
strategies that are indispensable in designing tunable and high-power-capable true-time-delay microwave lenses. Before describing each key strategy in great details, it is necessary to conduct a
sufficient literature review with respect to the historical development of these strategies. Firstly, the
time-delay units used through out this thesis are composed of various types of frequency selective
surfaces. Therefore, the literature review of frequency selective surfaces designs are conducted
first, with an emphasis on the recently proposed miniaturized-element frequency selective surfaces. Secondly, the literature review of traditional microwave lenses will be provided. With a
brief picture of the microwave lens evolvement, one can have a better understanding of the planar
true-time-delay microwave lenses proposed in this thesis. Thirdly, the traditional tuning techniques
such as electronic varactor tuning will be briefly reviewed. This will help us understand the pros
8
and cons of the proposed fluidic tuning strategy in contrast to the traditional electronic tuning techniques. Finally, the review of power handling capability of metamaterials and periodic structures
are conducted.
1.3.1
Frequency Selective Surfaces
Frequency selective surfaces (FSSs) are any surface constructions that are designed as a filter for the incoming electromagnetic waves. They are typically in the form of two dimensional
periodic structures, and can provide low-pass, high-pass, band-pass, and band-stop frequency responses depending on the specific geometrical characteristics of the constituting elements. Ever
since the early 1960s, FSSs have been extensively studied, and were successfully used in many
application areas such as metallic radomes [28], reflectors [29], phase screens for beam steering
[30], and electromagnetic shielding [31]. Similar to a guided-wave microwave filter, an FSS can be
considered as a microwave filter with its overall performance evaluated by several factors such as
the bandwidth, center frequency, response type, and the order of the response. In addition to these
parameters shared in common with guided-wave filters, the response of an FSS is also sensitive
to the angle and polarization of the incident electromagnetic waves. This is an important factor
that distinguishes a spatial filter from a guided-wave filter. The aforementioned performances of
an FSS are determined largely by the choice of the its element types, periodicity, as well as the
overall thickness. In general, depending on the type of the element used in each unit cell, the
FSS can be categorized into both non-resonant and resonant types. A non-resonant type FSS is
typically a two-dimensional periodic arrangements of sub-wavelength patches or wire grids. The
periodic rectangular patches can be considered as a capacitive surface impedance sheet, and the
corresponding non-resonant FSS behaves as a low-pass spatial filter. Similarly, the periodic wire
grids can be regarded as a inductive surface impedance sheet, and the corresponding non-resonant
FSS behaves as a high-pass spatial filter.
The resonant type FSS, as its name indicates, is composed of resonant type element within each
unit cell. Over past several decades, a significant body of research has been focused on choosing
different types of resonant elements to shape the frequency response of an FSS. Despite the various
9
shapes of elements proposed, they can generally be categorized into two types, namely dipole-type
and slot-type elements. The dipole-type FSSs always exhibit band-stop frequency responses at
their first resonances, while the slot-type elements exhibit band-pass frequency responses. The
earliest and simplest dipole-type FSS used is just simple linear dipole arrays. From the well known
antenna theory of dipole antennas, such dipole elements can be modeled as a series LC circuits,
thus providing a band-stop response [32]. Later on, more resonant type FSSs have been proposed
that fall into the category of the dipole-type FSSs. These include cross dipole FSSs [33] that can
provide dual polarization for the incident wave as well as single, double and triple square loop FSSs
[34]-[36] that can provide multi-band band-stop responses. Another category of resonant type
FSSs is slot-type FSSs. The simplest form of slot-type FSS is just linear slot arrays. According
to Babinet principles, the equivalent circuit model of a linear slot antenna can be represented as a
shunt LC circuit, thus providing a band-pass response for the FSS. Other examples of FSSs that
fall into slot-type FSS category include ring-slot FSSs[37] and Jerusalem-cross-slot FSSs [38].
Irrespective of the type of resonant elements used, the desired center frequency of a resonant
type FSS is always the resonant frequency of the resonant element within each unit cell. Since the
resonant length of either a dipole or a slot-type element is around λ/2, where λ is the desired wavelength of interest, the unit cell size of the corresponding resonant type FSS structure is typically
on the order of λ/2 × λ/2. In applications where sharp frequency responses are required, FSSs
with high-order responses are needed. A resonant type high-order FSS typically requires several
first-order resonant FSS panels cascaded together with a quarter-wavelength spacer between the
adjacent panels. While these quarter-wavelength spacers act as impedance transformers and are
required in a high-order resonant FSS, they greatly increase the overall thickness of the resonant
FSSs and further prohibit them from being deployed in low frequency applications. In addition,
another consequence of such a bulky FSS is that the corresponding frequency response is expected
to be quite sensitive with respect to the oblique angle of incidence [39]. In general, the drawbacks
of these resonant type FSSs include both a relatively large unit cell size comparable to half of the
wavelength of interest and a bulky overall structure when high-order filtering response is desired.
10
More recently, a class of bandpass FSSs referred to as miniaturized-element frequency selective surfaces (MEFSSs) has been studied by various research groups [40]-[46], [47]-[50]. MEFSSs are periodic structures with sub-wavelength periods1 and most MEFSS implementations use
non-resonant constituting elements (unit cells). Therefore, MEFSS belongs to the category of nonresonant element based FSSs. Compared to the resonant type FSSs, the main advantage MEFSS
offers is a much smaller unit cell size and a significantly reduced overall thickness. These advantages will in turn contribute to a much more stable frequency response with respect to the incident
angle for the MEFSSs. Firstly proposed in [40], first-order MEFSS is composed of both a capacitive layer and an inductive layer. Each layer is printed on one side of the substrate. Capacitive
layer is in the form of a 2D periodic arrangements of the capacitive patches and the inductive layer
is in the form of a 2D periodic arrangement of the inductive wire grids. Therefore, the overall FSS
structure can be considered as a parallel LC circuit that provided a bandpass filtering response for
the incident electromagnetic waves. The unit cell size of MEFSS is around 0.15λ × 0.15λ, with
λ being the desired wavelength of the MEFSS. Such unit cell size is considerably smaller than
that of the traditional resonant type FSS. Later on, MEFSSs with high-order filtering purposes are
also reported. In [41], MEFSS with second-order bandpass response is presented, along with a detailed synthesis procedure. Such a second-order MEFSS is composed of two capacitive layers and
one inductive layer cascaded subsequently by using a very thin substrate in between. The overall MEFSS topology can be characterized by a second-order coupled resonator filter circuit. To
synthesis this type of MEFSS, one has to first determine the circuit values from the desired center
frequency of operation, fractional bandwidth (BW) and response type of the MEFSS. After that,
the geometrical values of each capacitive layer and inductive layer can be determined by mapping
the obtained circuit values to the sizes of the capacitive patches and the widths of the inductive
grids, using the procedures provided in [41]. In addition to the benefit of having a sub-wavelength
unit cell, the proposed second-order MEFSS has a very low profile with the overall thickness of
1
In this proposal, we consider a periodic structure to be a sub-wavelength periodic structure if the dimensions of
its unit cell are less than λ0 /4 × λ0 /4.
11
only λ/30, where λ is the wavelength of interest. This is in sharp contrast to the case of a secondorder resonant type FSS with a quarter-wavelength spacer. The second-order MEFSS corresponds
to a 10 times reduction in the overall thickness compared to the traditional second-order resonant
type FSS. A generalized method for synthesizing MEFSSs with transfer functions of any arbitrary
order has also been proposed in [42], where it was shown that an MEFSS of N metallic layers acts
as an ( N2+1 )th order bandpass spatial filter, where N is always an odd number (i.e., N = 3, 5, 7, ...).
The development of MEFSS has demonstrated superior performances that can be offered by the
non-resonant element based FSSs. In the mean time, a new category of FSSs that combines both
non-resonant and resonant type elements have emerged, and quickly become an attractive approach
in designing low profile FSSs with high frequency selectivity. In [44], a technique for designing a
low-profile, third-order bandpass FSS using a combination of resonant and non-resonant elements
was proposed. The FSS consists of three metal layers and two dielectric substrates where the first
and the third metal layers are in the form of two-dimensional (2-D) periodic arrangement of subwavelength capacitive patches, while the middle metal layer is a periodic structure composed of
miniaturized slot resonators. It is demonstrated in [44] that such FSSs with combined non-resonant
and resonant elements can exhibit a third-order bandpass responses with an ultra-thin overall thickness (only 0.04λ). The successful design presented in [44] can be further extended to FSSs with
arbitrary odd-order bandpass responses. Later on in [45], a generalized synthesis procedure for designing low-profile FSSs with bandpass responses of odd-order is provided. Using this technique,
an FSS with N th -order bandpass responses is composed of N metallic layers, of which (N − 1)/2
of the metallic layers are composed of resonant elements and (N +1)/2 of the layers are composed
of sub-wavelength non-resonant elements. The main advantage of this type of FSS is the extremely
thin overall thickness, however challenges do exist for this technique. One important drawback is
that such FSS requires miniaturized slot resonators with relatively high quality factors (Q) [45]. As
demonstrated in [45], this high-Q operation is achieved by decreasing the physical dimensions of
the miniaturized slot resonators while maintaining their resonant frequencies. For a given resonant
frequency and fabrication technology (which determines the minimum feature sizes that can be
reliably fabricated), the highest achievable Q of the miniaturized slot resonator is limited. Thus,
12
designing FSSs with combined non-resonant and resonant elements may require using fabrication
techniques that are relatively costly and not readily available, especially at higher frequency bands
(e.g., X-band).
It is worthwhile to briefly mention other technologies of designing FSSs that do not fall into
the aforementioned categories. One example is all-dielectric frequency selective surface, which
can serve as an alternative to its metallic counterpart when high power and low loss applications
are desired. Firstly proposed in [51], it is shown that quite a number of modes can be supported
within the all-dielectric FSS structure. Another example is resonant cavity-based FSSs [52] that
can achieve sharp frequency selectivity. Such FSS is based on the recently developed substrate
integrated waveguide concept [53], and its response is determined by both the resonance of the
periodicity and the resonance of the cavity. The advantage of this type of FSS is that the high
quality factor of the cavity can result in a sharp frequency response for the corresponding FSS.
1.3.2
Microwave Lenses
Lenses operating at different wavelengths across the electromagnetic (EM) wave spectrum are
widely used in our daily lives. Optical lenses used for imaging are nowadays ubiquitous partly
due to the widespread use of multi-functional wireless devices that include miniaturized cameras.
Similarly lenses operating within the microwave and millimeter-wave frequency bands are used for
a variety of applications ranging from imaging for biomedical [54], [55] and security [56] applications to high-gain antennas [57], phased-arrays [58], and radar systems [59]. Chromatic aberration
is an important phenomenon observed in most lenses whether operating at optical wavelengths or
microwave frequencies. In optical lenses, chromatic aberration is due to the change of refraction
index of the lens material as a function of frequency. Because of this change of refraction index,
the focal length of the lens is different for different wavelengths. This phenomenon can result in
the deterioration of the image quality when such lenses are used as part of an imaging system. In
modern optical imaging systems, extra-low dispersion lenses are employed to reduce the adverse
effects of chromatic aberration [60]. Many microwave lenses also suffer from chromatic aberration [61]-[62]. When used as part of a wireless system (e.g., a high-gain antenna) these lenses
13
tend to significantly distort the temporal characteristics of broadband pulses [63]. Therefore, in
applications where signals with instantaneously broad bandwidths are used, microwave lenses free
of chromatic aberration must be employed.
Over the past several decades, various types of microwave lenses and collimating structures
have been reported in the literature. Dielectric lenses are among the most well-known types of
microwave lenses [64]-[65]. This type of lens is indeed designed in a true-time-delay fashion and
satisfies Fermat’s principle over a broad frequency band provided that the dielectric constant of
the material constituting the lens does not change as a function of frequency. However, dielectric lenses suffer from the internal reflection losses and are typically heavy, bulky, and expensive
to manufacture, especially at low microwave frequencies. Planar microwave lenses address these
shortcomings of dielectric lenses and have widely been used as the primary method of designing microwave lenses at low RF/microwave frequencies [66], [67]-[69], [70]-[72], [73]. Planar
microwave lenses are typically composed of an array of transmitting and receiving antennas connected together using either a phase shifting or a time delay mechanism. A number of different
techniques have been used to achieve the desired phase shift or time delay between the transmitting and receiving antennas. These include using coupled apertures [73], resonant slots [66],
filters [74], or transmission lines with variable lengths [75] between the transmitting and receiving
antennas. The time delays between the transmitting and receiving antenna elements can also be
tuned by loading the true-time-delay transmission lines with varactor diodes [76]-[77] or micro
electro-mechanical system (MEMS) switches [78]. However, the inter-element spacings between
the antennas used in these planar lenses are relatively large, since the transmitting and receiving
antenna elements have dimensions in the order of a half-wavelength. Such a large element spacing
generally deteriorates the lens’ scanning performance.
More recently, with the progress in the design and synthesis of artificially engineered materials,
the controllable material properties of metamaterials have been exploited to design various types
of microwave lenses [79]-[82]. In [81], a bi-planar gradient metamaterial lens with an index refraction ranging from −2.67 to −0.97 was designed at 10.3 GHz. Microwave lenses designed based
14
on transformation optics concepts have also been examined [82]. Transmission line type metamaterials such as negative-refractive-index transmission lines [83] have also been used to design
three-dimensional microwave lenses operating at microwave frequencies. Despite the design flexibility offered by the use of metamaterials, most metamaterial-based microwave lenses use high-Q
resonant constituting elements and hence, they tend to be narrowband and dispersive [84]. In addition to being narrowband, many metamaterial lenses that exploit the negative refraction index
concept tend to be highly dispersive even for narrowband modulated signals. In such lenses, even
a narrowband modulated signal can experience a significant temporal distortion when transmitted
through the lens (e.g., see discussions in [84] regarding time-domain behavior of a double-negative
lens). Frequency selective surfaces (FSSs) have also been used to design planar microwave lenses
[85]-[86]. In FSS-based microwave lenses, each pixel of the lens acts as a spatial-phase-shifter
(SPS) that provides a desired phase shift at the frequency of interest. In such lenses, the spatial
phase shifters of the lens must generally provide phase shifts in the range of 0◦ − 360◦ . Since a
simple first-order FSS does not provide such large phase shift values, higher-order FSSs are generally used. Recently, a planar microwave lens that uses the unit cells of miniaturized element
frequency selective surfaces (MEFSSs) as its spatial phase shifters was reported in [46]. It was
demonstrated that using MEFSSs, low-profile, broadband planar microwave lenses could be designed. While this lens demonstrates a wideband response, it suffers from significant chromatic
aberrations within this frequency band [46]. Thus, such a lens is not suitable for broadband pulsed
applications.
1.3.3 Tuning Mechanism
Different tuning mechanisms have been used in the past to tune the responses of periodic structures such as frequency selective surfaces and microwave lenses. In [87], by using varactor diodes
that provide a continuous variable capacitance, the phase of individual array elements can be accurately tuned without the degradation in directivity and side-lobe levels associated with phase
quantization. However, due to distortion, varactor diodes are only suitable for low-power operation. Furthermore, the resistive loss in the varactor diodes can degrade the overall efficiency of a
15
periodic structure that uses them to achieve tunability. In order to support high-power applications
with lower losses, MEMS technology could be used in place of the varactor diodes in designing
tunable microwave lenses [88]-[89]. In [88], the tunable MEMS capacitors have demonstrated the
ability to eliminate intermodulation distortion and losses competitive with those of varactor diodes.
The complicated fabrication process is the main drawback for the MEMS based tunable lens. Tunable lenses that use ferroelectric dielectrics to achieve tuning have also been proposed to reduce
the number of phase shifters needed to achieve the beamforming [90]. Such tunable lens made of
ferroelectric dielectrics can potentially lead to low-cost and high power phase arrays. However, DC
biasing is still required for the ferroelectric material along each column of the lens. A microwave
lens with magnetic field controlled index of refraction and focal length has also been designed in
[91]. The magnetic field tunability is achieved through the variation in the permeability of a cube
of yttrium aluminum iron garnet (YAIG). The liquid crystal tuning has also been proposed in reflectarray design in [92]. Dynamic phase control is achieved by filling the gap between the patch
array and the ground plane with nematic state liquid crystal (LC). The permittivity of the LC substrate and hence, the electrical size of the individual patches can be controlled by applying a DC, or
a low frequency AC, bias voltage. The most significant impact of this new active control strategy
is likely to be in the sub-millimetre waveband. Since, in addition to overcoming the performance
limitations of conventional semiconductor phase shifters, a broadband reflectarray performance
and very fast switching speeds can be obtained from physically thin liquid crystal films, which
exhibit lower loss tangents at these frequencies than at X-band. Optical tuning technique in a
periodic structure has also been recently proposed in [93]. In [93], the feasibility of a new optically controlled approach which exploits variable dielectric property of organic semiconductor
under the optical illumination is investigated. The mechanism lies in the fact that illuminated organic dielectric will have a complex permittivity different from that of the complex permittivity
of non-illuminated material. The optically controlling device provides several advantages such as
dynamic control, fast response, immunity from electromagnetic interference, and good isolation
between the controlling and controlled devices. This method enables us to take advantage of the
availability and easy fabrication of polymer semiconductors.
16
1.3.4
Power handling capability
As have been shown, a significant body of research has been devoted to investigating techniques
used to optimize the frequency responses of FSSs, yet few studies have examined the power handling capability of these structures in any detail. Similarly, very few studies have examined the
development of FSSs that can be used for high-power microwave (HPM) applications [94]. In
such applications, FSSs are located next to sources of high-power RF/microwave radiation. Under these circumstances, the power handling capability of the FSS becomes an important factor in
determining whether or not it can be used as part of the system. The importance of high power
capable FSSs can be best felt in military sectors. With the recent advances in the area of high
power microwave weapons, there is a growing concern around the world with regards to the liability of the integration of technology. This is especially true for U.S military sectors. Despite of the
significant technological advantages possessed by the U.S military in information battlefield, there
are still possible threats posed by the potential enemies through asymmetric attack. One of the possible way of achieving asymmetric attack is through high power microwave attack. As have been
shown by Boeing in its Counter-electronics High-powered Microwave Advanced Missile Project,
the high power microwave radiation launched by the missile can easily disable PCs and any other
electronic devices as it soars through the skies. Thus, one can imagine the potential catastrophic
result due to the lack of protection against high power microwave weapons in a future battle field.
The maximum power level that an FSS can handle depends on the nature of the excitation
signal. One can imagine either a transient or a continuous wave (CW) excitation for an FSS.
The CW power handling capability is of primary concern when the FSS is under a sustained high
average-power illumination. Under these conditions, if the average power level is high enough,
the lossy materials within the FSS will heat up and the structure will eventually melt or burn. The
transient power handling capability, on the other hand, becomes important when short duration
pulses with extremely high peak power levels are applied to the FSS. Similarly to a microwave
filter [95]-[96], the failure mechanism in this mode is the dielectric or air breakdown within the
structure. The breakdown event short circuits the metallic elements of the periodic structure and
renders it useless. The arcing within the structure can also permanently damage the dielectric
17
material. This breakdown is a major factor that limits the application of FSSs in high-power
microwave systems (e.g. systems used for electronic attack applications). In such systems, FSSs
capable of handling extremely high power levels (e.g. 0.5-1.0 MW/cm2 ) for short duration pulses
are required. Since the duty cycles of such systems are rather low, the thermal issues are expected
to be of secondary concern in these structures. Most conventional FSSs reported in literature,
however, are not capable of handling such high peak power levels. As a result of this, the benefits
offered by FSSs (e.g. electromagnetic interference mitigation or radar cross section reduction) are
not exploited in many HPM systems.
1.4 Thesis overview
The goal of this thesis is to seek promising solutions of designing tunable and high-powercapable true-time-delay lenses as an alternative way to substitute current phased array antennas.
To accomplish this, three main tasks need to be carried out. These include finding a suitable tuning
strategy, optimizing the power handling capability of the FSS, as well as designing true-time-delay
lenses. Revolved around these key tasks, this thesis is divided into the following chapters. In Chapter 2, a third-order bandpass frequency selective surface with a transmission null is proposed. This
type of FSS is composed of non-resonant elements combined with resonant elements together. The
advantage of such design is that sharp frequency response with agile transmission null tuning can
be achieved without using higher-order topologies. In Chapter 3, a novel fluidic tuning mechanism
is extensively studied. Such tuning technique is proven to be suitable in high power microwave
applications, and can be potentially used for tunable lens applications. In Chapter 4, the effect of
various design parameters on the power handling capability of an FSS is thoroughly studied, and
the guidelines of increasing the power handling capability are provided. Using these guidelines,
FSSs capable of handling extremely high pulsed RF power are demonstrated. Chapter 5 and 6
focus on the various techniques of designing planar true-time-delay lenses. The time delay units
used in a TTD lens can be either a band-pass type FSS in Chapter 6 or a low-pass type FSS in
Chapter 5. The detailed overview of each chapter is provided as below.
18
1.4.1
Chapter 2
In this chapter, the design and analysis of a frequency selective surface (FSS) capable of providing a third-order bandpass response are provided. The transfer function of the proposed FSS
has a transmission null, the frequency of which can be tuned to suppress strong interference signals
with frequencies close to or within the main transmission band. The principles of operation of the
device are presented along with an approximate analytical procedure for synthesizing the desired
FSS response. Two prototypes are fabricated and characterized using a free-space measurement
setup and the FSS’s different modes of operation are experimentally demonstrated. Finally, the
tuning performance of the FSS’s transmission null is experimentally demonstrated in a WR-90
waveguide environment.
1.4.2
Chapter 3
In this chapter, fluidically tunable periodic structures acting as highly-selective frequency selective surfaces (FSSs) or spatial phase shifters (SPSs) capable of providing phase shifts in the
range of 0◦ − 360◦ is investigated. These devices are multi-layer periodic structures composed of
non-resonant unit cells. The tuning mechanism is based on integrating small, movable liquid metal
droplets with the unit cells of the periodic structure. By moving these liquid metal droplets by
small distances within the unit cell, the structure is frequency response can be tuned continuously.
Using this technique, a fluidically tunable FSS with a fifth-order bandpass response is designed
and its tuning performance is examined for various incidence angles and polarizations of the incident EM wave. Additionally, electronically tunable counterparts of the same structure are also
designed and their tuning performances are examined under short-duration high-power excitation
conditions. It is demonstrated that such electronically tunable FSSs/PSSs demonstrate extremely
nonlinear responses. Since the fluidically tunable structure examined in this work does not use
any nonlinear devices, its response is expected to remain linear for such short-duration high-power
excitation conditions. The tuning performances of these fluidically tunable periodic structures are
also experimentally demonstrated by fabricating three prototype and characterizing their responses
in a waveguide environment.
19
1.4.3
Chapter 4
In this chapter, the peak power handling capability of a class of miniaturized-element frequency
selective surfaces composed entirely of non-resonant constituting elements is investigated. The
effects of various design parameters on the peak power handling capability of these structures
are investigated using electromagnetic simulations and methods for increasing their peak power
handling capability are proposed. These methods are used to design a high-power microwave
(HPM) frequency selective surface (FSS), which is expected to be capable of handling extremely
high peak power levels. The power handling capabilities of these devices are also experimentally
investigated using an HPM source with a frequency of 9.382 GHz, a peak power of 25 kW, and
a pulse length of 1 µs. Unit cells of various FSSs under investigation are placed in a waveguide
and excited with pulses with variable power levels. The time-domain reflection and transmission
coefficients of each device is measured at various power levels and the power level at which the
device breaks down is determined. The results of these experimental investigations follow the same
trend observed in the simulations. Additionally, the experiments demonstrate that the HPM FSSs
developed in this work are indeed capable of handling extremely high peak power levels.
1.4.4
Chapter 5
In this chapter, a new technique for designing low-profile, ultra-wideband, true-time-delay
(TTD) equivalent microwave lenses is proposed. Such a lens is composed of numerous spatial
time delay units (TDUs) distributed over a planar surface. Each spatial TDU is the unit cell of
an appropriately-designed miniaturized-element frequency selective surface composed entirely of
non-resonant constituting elements. Each TDU is designed to provide a frequency-independent
time delay within the frequency bands of interest. Two TTD lens prototypes with different focal
length to aperture dimension (f /D) ratios are designed, fabricated, and experimentally characterized at X band. The first TTD lens has a f /D ratio of 1.6, and the second one has a f /D ratio of 1.
Each fabricated lens is a low-profile structure with an overall thickness of 4.76 mm, or equivalently
0.146λ0 (0.150λ0 ) for the first (second) lens prototype 2 , and uses spatial TDUs with dimensions
2
λ0 is the free space wavelength at the desired center frequency of operation of each fabricated lens
20
of 6 mm × 6 mm, or equivalently 0.185λ0 × 0.185λ0 (0.19λ0 × 0.19λ0 ) for the first (second)
lens prototype. The frequency range within which the focusing gain does not vary by more than
3 dB is 7.5 − 11.6 GHz for the first lens, and 7.8 − 11.5 GHz for the second lens. Both of the
lenses have a system fidelity factor close to 1, when excited with a broadband pulse. Furthermore,
due to their true-time-delay equivalent behavior, the fabricated lenses do not suffer from chromatic
aberration within their operational bands. When used in a beam-scanning antenna system, each
lens demonstrates an excellent scanning performance in a field of view of ±60◦ .
1.4.5 Chapter 6
Based on the studies in Chapter 5, this chapter continues the efforts of designing true-timedelay lenses with wider bandwidths. The lenses examined in this work are still planar structures
with circular apertures populated with numerous spatial time-delay units (TDUs). Each TDU is
the unit cell of an appropriately designed lowpass frequency selective surface (FSS) that provides
a desired time delay over a wide frequency range. The lowpass FSSs used in this paper are either
metallo-dielectric or all-dielectric type multi-layer structures. A metallo-dielectric lowpass FSS
is composed of a number of capacitive patch layers separated from each other by thin dielectric
substrates. An all-dielectric lowpass FSS, on the other hand, is composed of high-εr and low-εr
dielectric substrates cascaded sequentially. Two metallo-dielectric lowpass FSS-based true-timedelay (TTD) lens prototypes and one all-dielectric lowpass FSS-based TTD lens prototype with
focal length to aperture diameter ratios (f /D) of 1, 1.5 and 1.3 are designed, fabricated, and
experimentally characterized. They respectively operate over a bandwidth of 30%, 50% and 40%
without any chromatic aberrations. This is demonstrated experimentally by characterizing the
responses of these lenses both in frequency domain and in time domain. Moreover, all of these
lenses demonstrates excellent scanning performances with fields of views of ±60◦ .
1.4.6 Chapter 7
In this future work session, some insights are provided with respect to the future work of this
thesis. From Chapter 2 to Chapter 6, several critical techniques in designing tunable microwave
21
lenses have been carefully studied. These include implementing a suitable fluidic tuning technique
for high power microwave applications, designing extremely high power capable frequency selective surfaces, as well as implementing various types of low profile and wideband true-time-delay
microwave lenses. These studies are indeed essential in our goal of designing tunable space-fed
microwave lenses for next generation high power phased array systems. Several future works will
be presented in this chapter to extend this thesis towards practical implementations.
22
Chapter 2
A Third-Order Bandpass Frequency Selective Surface with a Tunable Transmission Null
2.1
Introduction
A frequency selective surface (FSS) is a device that acts as an analog spatial filter for elec-
tromagnetic waves propagating through space. FSSs are used in a wide range of applications
including radar cross section (RCS) reduction of military targets [39], interference reduction in
indoor wireless environments [97]-[98], shielding sensitive electronics from unwanted interference or jamming signals, design of artificial magnetic conductors [99]-[100], microwave absorbers
[101], and reflectarrays and lenses [102]-[103] among others. The selectivity of the frequency
response of an FSS is an important factor that determines its suitability for a given application.
Similar to microwave filters, the selectivity of an FSS response is determined by the order of its
transfer function and its response type [39]. To achieve highly selective transfer functions, FSSs
with higher-order responses are generally employed. The traditional techniques used to design
FSSs with higher-order bandpass or band-stop responses often require cascading multiple firstorder FSS panels a quarter wavelength apart from each other (e.g. see pp. 253 - 255 of [39]). This
approach, however, results in relatively thick structures that are heavy and bulky, especially at low
frequencies (e.g., see Chap. 7 of [39]). Narrow bandpass selective FSS design based on aperture
coupled microstrip patches has also been proposed in [104], where relatively large periodicity on
the order of half a wavelength is used.
Recently, the application of non-resonant, sub-wavelength periodic structures in the design of
frequency selective surfaces has been extensively studied by various research groups [47]-[50].
23
Using such periodic structures, new FSS topologies are presented that allow for the design of
low-profile frequency selective surfaces with higher-order bandpass responses [42]. Additionally,
modified versions of such FSSs that use a combination of both resonant and non-resonant elements
to achieve highly selective responses have also been studied. In particular, we recently reported a
technique for designing low-profile FSSs with odd-order bandpass responses using a combination
of resonant and non-resonant elements [44]-[45]. These FSSs are composed of multiple metallic
layers separated from one another by thin dielectric substrates. Each metallic layer is either in the
form of a two-dimensional (2D) periodic arrangement of sub-wavelength capacitive patches or a
2D periodic arrangement of miniaturized slot resonators. Using this FSS topology, generalized
bandpass transfer functions of odd order (N = 3, 5, ...) can be synthesized. One advantage of this
type of FSS is its extremely thin overall thickness. An N th order FSS of this type has a typical
overall thickness of ∼ (N − 1)λ0 /50 which is significantly smaller than the overall thickness of a
traditionally designed N th order FSS ∼ (N − 1)λ0 /4, where λ0 is the free space wavelength. One
important drawback of this type of FSS, however, is that it requires miniaturized slot resonators
with a relatively high quality factor (Q)[45]. As demonstrated in [45], this high-Q operation is
achieved by decreasing the physical dimensions of the miniaturized slot resonators while maintaining their resonant frequencies. For a given resonant frequency and fabrication technology (which
determines the minimum feature sizes that can be reliably fabricated), the highest achievable Q
of the miniaturized slot resonator is limited. Thus, achieving certain response types from FSSs of
the type reported in [44]-[45] requires using fabrication techniques that are relatively costly and
not readily available. Moreover, while these FSSs are low-profile structures, achieving extremely
selective frequency responses from them still requires using many different closely spaced metallic
layers. This could complicate the design of the device and increase its overall fabrication cost. In
many scenarios, however, highly selective responses are needed only when strong interference or
jamming signals are present at frequencies close to the main operating band. In such situations,
introducing a transmission null into the transfer function of a moderately selective FSS could be
used as an effective means of mitigating the undesirable effects of interfering signals.
24
TM Plane
of Incidence z
TE Plane
of Incidence
Sub-wavelength
Capacitive Patch
Dx
x
y
Dy
s/2
h
Hybrid Resonator
Dx
h
g4
g2
ws
Dy
g3
g1
Sub-wavelength
Capacitive Patches
w
Hybrid Resonator
Layer
Spiral Inductive
Resonator Wire
Figure 2.1 Topology of the proposed bandpass FSS. The unit cells of the capacitive and
hybrid-resonator layers are shown on the right hand side of the figure.
In this communication, we demonstrate how the topology of the FSSs presented in [44]-[45]
can be modified to address the aforementioned issues. In particular, by converting the miniaturized
slot resonators used in the FSSs of the types reported in [45] to a hybrid resonator that consists of a
dipole type spiral resonator and a wire grid structure, the requirement for using high-Q miniaturized
slot resonators is alleviated. Moreover, the hybrid resonator topology introduces a transmission
null into the FSS’s transfer function that can be controlled conveniently. The frequency of this
transmission null can be placed in the vicinity of the FSS’s pass band or even within its pass
band. An approximate procedure for synthesizing this type of FSS is presented and two FSS
prototypes that show these two different modes of operation are designed, fabricated, and tested
using a free-space measurement setup. Finally, the continuous tuning of the FSS’s transmission
null is experimentally demonstrated in a waveguide environment. It is worthwhile to mention that
25
the proposed design technique can be applied to the design of highly selective FSS with multiple
transmission nulls by increasing the layer of the FSS similarly as [45].
2.2
FSS Design and Principles of Operation
2.2.1
FSS Topology
Figure 2.1 shows the three-dimensional (3D) topology of the proposed FSS. The structure is
composed of three different metal layers separated from one another by two thin dielectric substrates. The top and bottom metal layers consist of two-dimensional periodic arrangements of
sub-wavelength capacitive patches. The center metal layer consists of a two-dimensional periodic arrangement of a hybrid resonator. The hybrid resonator layer is formed by juxtaposing a
one-dimensional (1D) wire grid and a two-dimensional periodic arrangement of balanced spiral
resonators. The spiral resonator has already been proposed as the constituent element of a FSS in
[105]. The top views of one unit cell of the capacitive patch layer and the hybrid resonator are
also shown in the inset of Fig. 2.1. At the unit cell level, the spiral resonator is embedded between
two adjacent wire strips as shown in Fig. 2.1. The dimensions of each unit cell are Dx and Dy
respectively along the x and y directions. The capacitive patch is in the form of a square metallic
patch with side length of Dx,y − s, where s is the separation between the two adjacent capacitive
patches. The hybrid resonator is composed of both non-resonant (wire strips) and resonant (spiral
resonator) elements. In the arrangement depicted in Fig. 2.1, the hybrid resonator layer and the
FSS are polarization dependent and respond to linearly-polarized plane waves with electric fields
oriented along the ŷ direction.
This FSS can be modeled with the simplified equivalent circuit shown in Fig. 2.2, which is
valid for a normally incident plane wave. In this circuit model, the hybrid resonator layer of the
FSS is modeled with the series L2 C2 resonator in parallel with the inductor L1 . The series combination of L2 and C2 represents the miniaturized spiral resonator portion of the hybrid resonator
and L1 represents the wire grid portion of the hybrid resonator. The two capacitive patch layers
are modeled with two parallel capacitors C1 and the dielectric substrates that separate different
layers of the structure from one another are modeled with transmission lines with the characteristic
26
Z1 ,h
Z1 ,h
Z0
C2
C1
L2
Capacitive Patches Spiral Resonator
L1
C1
Z0
Inductive Strip Capacitive Patches
Hybrid Resonator
Figure 2.2 Equivalent circuit model of the FSS discussed in Section 2.2.1.
√
impedances of Z1 and lengths of h. Z1 = Z0 / ϵr , where Z0 = 377 Ω is the free space impedance
and ϵr is the dielectric constant of the substrate. Following an analysis procedure similar to the one
presented in [45], it can be shown that this circuit can be approximated with a third-order coupled
resonator bandpass filter. It can also be shown that the filter exhibits a transmission null contributed
by the series resonance of the hybrid resonator.
2.2.2
Synthesis Procedure
The design procedure of the proposed device is based on synthesizing the desired filter response
from the equivalent circuit model presented in Fig. 2.2 and mapping these equivalent circuit parameter values to the physical and geometrical parameters of the proposed FSS. In the procedure,
we assume that the proposed FSS has a center frequency of operation of f0 , fractional bandwidth
of δ = BW/f0 and a transmission null frequency at fnull . The values of the equivalent circuit
model of Fig. 2.2 can be determined by analyzing this circuit as a coupled-resonator filter with
inductive coupling [106]. Doing this, the values of the elements of the equivalent circuit model
can be calculated using the following procedure. First, we calculate the value of C1′ , which is an
intermediate variable, from:
C1′ =
q
ω0 Z0 δ
(2.1)
where Z0 = 377 Ω and q is the normalized qualify factor of the first or third resonator of a coupledresonator filter. q values are tabulated for different response types in filter design handbooks (e.g.
27
pp. 341-379 of [106]). The next step is to calculate the value of an effective capacitor Cef f , using:
Cef f =
C1′
2
k1,2
δ2
(2.2)
where k1,2 is the normalized coupling coefficient between the first and second resonators of an
inductively coupled, coupled resonator filter (e.g. see pp. 341-379 [106]). By determining the
value of Cef f , L1 can be determined from:
L1 =
ω02 (Cef f
1
√
− 2k1,2 δ C1′ Cef f )
(2.3)
The substrate thickness can be calculated as:
h=
1
√
ω02 µr µ0 k1,2 δ C1′ Cef f
(2.4)
where µr is the relative permeability of the substrate. The values of L2 and C2 can be determined
from:
ω02
)
2
ωnull
(2.5)
1
2
− ϵ0 ϵr h)(ωnull
− ω02 )
(2.6)
C2 = (Cef f − ϵ0 ϵr h)(1 −
L2 =
(Cef f
Finally, the values of the first and third capacitor can be determined from:
C1 = C1′ − ϵ0 ϵr h/2
(2.7)
where ϵr is the relative permittivity of the dielectric substrates used to implement the FSS. Note
here these calculated circuit element values are solely determined by the desired system level
parameters and are only approximations that provides a good starting point for the following optimization process. In the optimization process, the commercially available substrate as well as
the bonding layer need to be taken into account as the constraints for the optimization. The final optimized values of the equivalent circuit model of the FSS can then be mapped to the exact
geometrical and physical parameters of the unit cell shown in Fig. 2.1. This can be done using
procedures similar to those described in [44]-[45] and will not be repeated here.
28
2.3
Experimental Verification
2.3.1
Free-Space Demonstration
The design procedure described in Section 2.2 is carried out for an FSS with a third-order
bandpass response having a center frequency of 10.4 GHz, a fractional bandwidth of δ = 24%, a
transmission null frequency of 11.5 GHz, and k1,2 and q values of 0.8 and 1.5 respectively. Using
(1)-(7) and assuming the substrate material has a permittivity of ϵr = 3.5 (Rogers 4003C), the
circuit parameters are calculated as C1 =0.25 pF, L1 =36.7 pH, C2 =1.25 pF, L2 =0.15 nH, h=0.73
mm. These formula calculated circuit values are just approximations that provides a good starting
point for the following optimization step. The response of the equivalent circuit model shown in
Fig. 2.2 was then optimized in the circuit simulation software, Agilent Advanced Design System
(ADS). This optimization step is carried out under the constraints of the commercially available
substrate thickness h=0.51 mm as well as the bonding layer. Since the synthesis procedure provided in Section 2.2.2 is an approximate one, this fine tuning and optimization stage is expected to
be necessary even if substrates with exact desired values of h are available. The optimized equivalent circuit parameter values are then mapped to the geometrical parameters of the FSS shown in
Fig. 2.1 using a procedure similar to the one described in [45]. These optimized geometrical and
electrical values are shown in Table 4.2. The FSS prototype is then simulated using full-wave EM
simulations in CST Studio and it was fabricated using standard lithography and substrate bonding
techniques [44]. The bonding material used is the Rogers 4550B prepreg with dielectric constant
of 3.3 and the thickness 0.091 mm. The introduction of the bonding material creates an asymmetry
in the FSS structure, which is compensated by tuning the dimensions of the two capacitive patch
layers as described in [41]. This is reflected in the data shown in Table 4.2, where s1 corresponds
to gaps between the capacitive patches located on the FSS side without bonding layer while s3
corresponds to the capacitive layer on the side with bonding layer. The dimensions of the fabricated prototype are 25 cm × 19 cm and it was characterized using the free-space measurement
setup described in [41]. The simulated frequency response obtained from CST Studio as well as
the measured results and the results predicted by the equivalent circuit model are presented in Fig.
29
Table 2.1 Physical and electrical parameters of the first FSS prototype discussed in Section2.3.1.
All dimensions are in mm.
Dx
Dy
w
s1
s3
h
Physical
6.50
6.50
2.10
0.385
0.5
0.51
Parameter
ws
g1
g2
g3
g4
ϵr
0.15
0.25
2.32
0.15
0.15
3.4
Electrical
C1 /C3
h
C2
L1
L2
Z1
Parameter
0.28/0.25pF
0.51
0.82pF 0.05nH 0.20nH
205Ω
2.3(a). A relatively good agreement is observed between the calculated and measured results. The
maximum measured insertion loss within the passband is -0.93dB, and the measured fractional 3dB fractional BW is 23%. The response of this FSS for oblique incidence angles is also measured
for both the transverse electric (TE) and the transverse magnetic (TM) polarizations of incidence
and the results are shown in Fig. 2.3(b) and 2.3(c). As shown in Fig. 2.1, for both TE and TM
incidence, the incident electric field will always have a ŷ component such that the hybrid resonator
can be excited. As can be seen, the structure demonstrates a relatively stable frequency response as
a function of incidence angle for both the TE and TM polarizations. This stability can be attributed
in part to the extremely small overall thickness of the structure (1.11 mm or equivalently λ0 /26,
where λ0 is the free space wavelength at 10 GHz) and its small unit cell dimensions.
Using the hybrid resonator in this FSS topology offers a convenient method for tuning the
frequency of its transmission null. The frequency of this transmission null can be controlled conveniently by changing the resonant frequency of the miniaturized spiral resonator (L2 C2 in Fig.
2.2) that constitutes part of the middle hybrid-resonator layer. By changing the resonant frequency
of this resonator the frequency of the transmission null can be changed and it can even be placed
within the main band of the FSS to provide a sharp in-band transmission null. To demonstrate this
flexibility, the equivalent circuit model described in Section 2.2.1 is used to design a bandpass FSS
operating in the 8.5-12.5 GHz range with an in-band transmission null at 9.6 GHz. The analytical
formulas presented in Section 2.2.2 can be used for filter synthesis only if fnull is outside of the
30
(a)
(b)
(c)
Figure 2.3 (a) Measured and calculated transmission coefficients of the first FSS prototype
discussed in Section 2.3.1 for normal incidence. The device has an out-of-band transmission null.
(b)-(c) Measured transmission coefficient of the FSS for oblique incidence angles for the TE (b)
and TM (c) polarizations of incidence.
main operation band of the FSS and fnull > f0 . The synthesis procedure for this type of FSS with
in-band transmission null can be simplified into two steps: First, the formulas provided in Section
II-B can be used to design a band-pass FSS with the transmission null very close to the passband;
Second, the resonant frequency of the spiral resonator can be tuned so that the transmission null
can be shifted down to the middle of the passband. The final values were optimized in ADS under
the constraints of the commercially available substrate thickness as well as the bonding layer. The
geometrical and electrical parameters of this FSS prototype are provided in Table 4.3. A prototype
of this FSS panel, with finite dimensions of 25 cm × 18.6 cm, is fabricated and tested using a
free-space measurement setup. Figure 2.4(a) shows the simulated and measured transmission coefficients of this FSS prototype. As is observed, a sharp transmission null occurs in the pass band
31
Table 2.2 Physical and electrical parameters of the second FSS prototype discussed in
Section2.3.1. All dimensions are in mm.
Dx
Dy
w
s1
s3
h
Physical
5.50
5.50
1.44
0.22
0.28
0.51
Parameter
ws
g1
g2
g3
g4
ϵr
0.15
0.2
0.15
0.15
0.15
3.4
Electrical
C1 /C3
h
C2
L1
L2
Z1
Parameter
0.25/0.23pF
0.51 0.1pF
0.19nH 2.77nH
205Ω
of the structure as expected. The measured -10dB fractional BW of this transmission zero is 3.5%,
while the maximum insertion loss at the lower and upper band are -1 dB and -0.5 dB respectively.
The response of this FSS, under oblique incidence angles, is also measured for both the TE and
the TM polarizations of incidence and the results are shown in Figs. 2.4(b) and 2.4(c). As can
be observed, the frequency responses of the structure do not vary significantly as a function of
angle and polarization of incidence of the electromagnetic wave. More importantly, the frequency
and the bandwidth of the transmission null are very stable as a function of both the angle and the
polarization of the incidence of the EM wave for incidence angles in the ±50◦ range.
2.3.2
Experimental Demonstration of an FSS with a Tunable Transmission
Null
As demonstrated in Section 2.3.1, the proposed FSS architecture offers a third-order bandpass
frequency response with a highly-controllable transmission null. In some applications, it may be
desirable to dynamically change the frequency of this transmission null (e.g. to suppress a strong
interfering or jamming signal). In these situations, a tunable version of this structure can be employed. This can be accomplished by loading the miniaturized spiral resonator shown in Fig. 2.1
with a varactor at its center. Doing this allows for electronically tuning the resonant frequency of
the series L2 C2 resonator shown in Fig. 2.2, which results in continuous tuning of fnull . In designing such FSSs the procedure described in Section 2.2 may be used as a starting point. By choosing
32
(a)
(b)
(c)
Figure 2.4 (a) Measured and calculated transmission coefficients of the second FSS prototype
discussed in Section 2.3.1 for normal incidence. The device has an in-band transmission null.
(b)-(c) Measured transmission coefficient of the FSS for oblique incidence angles for the TE (b)
and TM (c) polarizations of incidence.
fnull to be outside the main band, the FSS can be synthesized using the procedure described in
Section 2.2.2. When implementing the hybrid resonator layer, the spiral resonator loaded with the
variable capacitor, CL , at its center must be designed to provide the desired L2 and C2 values. By
dynamically changing CL , the frequency of the device’s transmission null can then be changed
dynamically.
This procedure is carried out for a third-order FSS operating at X-band. To simplify the experimental characterization, a waveguide version of the FSS shown in Fig. 2.1 is used. Similar
approach can be found in [40]. Figure 3.15 shows the waveguide setup used for these experiments.
A waveguide version of the FSS, which is equivalent to one unit cell of the structure is placed
inside a WR-90 waveguide and its calibrated transmission coefficient is measured. In this device,
33
Table 2.3 Physical dimensions of the waveguide version of the FSS with a tunable transmission
null studied in Section 2.3.2. All dimensions are in mm.
w1
w2
w3
l1
l2
s
Dx
Dy
8.00
3.40
0.35 8.16
1.25
0.35 22.86
10.16
Table 2.4 Measured -10db transmission null BW and insertion loss of the waveguide prototype
b-d shown in Fig.2.6
stage b
stage c
stage d
-10dB Trans. null BW
2.75%
2.60%
3.20%
Max. IL(lower/upper band)
0.4/1.2 dB
1.2/0.7 dB
1.04/0.64 dB
two capacitive irises mimic the capacitive layers of the FSS as shown in Fig. 3.15(a). The hybrid resonator layer is modeled with an iris composed of two inductive strips at the edges and a
dipole type resonator loaded with a lumped capacitor at its center as shown in Fig. 3.15(b). A
magnified view of the loaded dipole resonator, which clearly shows its dimensions and topology,
is shown in Fig. 3.15(c). All irises are fabricated out of 0.005”-thick brass sheets using chemical
etching. Two WR-90 waveguide shims with thicknesses of 1.58 mm are machined out of a 1/16
inch thick brass sheet and are used as spacers separating the three layers of the structure. These
spacers are equivalent to the dielectric substrates of the FSS shown in Fig. 2.1. The physical and
geometrical parameters of the waveguide filter are provided in Table 4.1. Figure 3.15(d) shows
a three-dimensional perspective view of different layers of the waveguide structure, in which two
capacitive irises, two waveguide shims, one hybrid iris with the lumped capacitor are assembled to
form the waveguide equivalent version of the the proposed FSS with a tunable transmission null.
The frequency response of the fabricated prototype is measured using a calibrated vector network analyzer. To simplify the fabrication of the device and its measurement, several lumped
capacitors with different capacitance values are used instead of a single varactor. Figure 2.6 shows
the simulated and measured transmission coefficients of the fabricated prototype for four different capacitance values. As can be observed, for CL =0.15 pF, the transmission null is just slightly
higher than the main transmission band. As CL is increased to 0.3 pF, 0.5 pF, and 2.0 pF, fnull
34
Alignment Hole
s
Waveguide Cross
Section
w3
0.4”
w1
0.9”
(a)
w2
Lumped
Capacitor CL
(b)
1.58 mm
CL
l2 l
1
(c)
1.58 mm
(d)
Figure 2.5 Topology of the waveguide version of the FSS presented in Fig. 2.1 with a tunable
transmission null. (a) Top view of a capacitive iris. (b) Top view of the hybrid-resonator iris. (c)
Topology of the loaded resonator used in the hybrid-resonator iris. (d) Perspective view of the
whole device.
continuously decreases as seen from Figs. 2.6(b), 2.6(c), and 2.6(d) respectively. In all cases,
the transmission null provides a sharp in-band attenuation with a depth of at least 20 dB as its
frequency is tuned.
2.4 Conclusion
A highly selective bandpass FSS with a tunable transmission null was presented and discussed
in this chapter. An approximate method for synthesizing the desired transfer functions from such
35
(a)
(b)
(c)
(d)
Figure 2.6 Measured and simulated transmission coefficients of the FSS with a tunable
transmission null discussed in Section 2.3.2. The results are shown for four tuning stages
corresponding to different values of CL . (a) 0.15 pF (b) 0.3 pF (c) 0.5 pF (d) 2.0 pF.
low-profile FSSs was also presented and experimentally verified. The flexibility of controlling the
frequency of the FSS’s transmission null was demonstrated experimentally in a free-space measurement setup as well as a waveguide environment. Simple design method, reduced fabrication
complexity, and a possession of a conveniently tunable transmission null are among the advantages
of this class of frequency selective surfaces.
36
Chapter 3
Fluidically Tunable Frequency Selective/Phase Shifting Surfaces
for High-Power Microwave Applications
3.1
Introduction
A frequency selective surface (FSS) is a device which acts as a distributed spatial filter for elec-
tromagnetic waves propagating in space. FSSs have found numerous applications at RF/microwave
[39], infrared [108]-[109], and optical [110] frequency bands. In the RF/microwave range, they
have been used to design various types of spatial filters [39], artificial magnetic conductors [100],[111],
radar absorbing materials [101],[112], planar reflect-arrays [102] and lenses [103] to name a few.
With the proliferation of multifunctional systems in both the commercial and the military sectors,
the need for reconfigurable FSSs having agile frequency responses is on the rise. Reconfigurable
FSSs have been investigated by various research groups in the past [49], [113]-[118]. Many tunable FSSs are designed by incorporating electronically tunable elements into the unit cells of the
periodic structures that constitute an FSS. Examples of this include embedding solid-state varactor
diodes [27], [49] and MEMS switches [117] in traditional FSSs. By changing the state of these
varactors (switches), the frequency response of the FSS can be tuned (switched) electronically.
In designing an electronically tunable FSS, several important challenges must be addressed.
Prominent among these are the need for biasing individual electronic devices and ensuring that
RF/DC isolation is maintained at the unit cell level. Satisfying these requirements is rather challenging in large FSS panels and generally requires using several tunable elements (switches and
37
Sub-wavelength
Capacitive Patches
TM plane
of incidence
y
TE plane Liquid Metal
of incidence Droplet
Teflon Tube Filled
with Discontinuous
Galinstan Droplets
x
Sub-wavelength
Inductive Grid
Sub-λ
Capacitive
Patches
Liquid
Teflon
Solution
y
x
Cvariable
Fluid
Channel
Offset
z
z
Capacitive
Layer
Inductive
Layer
y
Liquid Metal
Liquid
Teflon Solution Droplet
Liquid-Varactor
Capillary Tubes
(b)
(d)
Capillary Tubes Capacitive
Layer
Inductive
Layer
Dy
z
Dielectric
Substrate
Dx
s
Dy
w
x
Inductive
Layer
(a)
Dx
Two Adjacent
(half) Capacitive Patches
(c)
Inductive
Grid
(e)
Figure 3.1 (a) Topology of a fluidically tunable miniaturized-element frequency selective surface.
The structure is composed of successive capacitive and inductive layers separated from one
another by thin dielectric substrates. Columns of Teflon tubes, containing discontinuous Galinstan
droplets, are embedded within the dielectric substrates to dynamically tune the surface
impedances of the capacitive layers. (b) Top view of four unit cells of the structure located on the
x − y plane. (c) Side view of the FSS in the x − z plane. (d) Side view of the structure in the
y − z plane. (e) Top views of the unit cell of a capacitive patch and an inductive wire grid.
varactors) and fixed elements (capacitors for RF/DC isolation) per unit cell of the FSS. This becomes even more challenging where tunable FSSs with higher-order responses are required. Another important but often overlooked issue in designing such tunable FSSs is the power handling
capability and the linearity of the FSS response. Electronically controllable varactors are inherently nonlinear devices and their use in tunable FSSs results in a nonlinear frequency response. In
many applications (e.g. radar systems), FSSs are placed in close proximity to high-power sources
of RF/microwave radiation. In such situations, the linearity of the response of a tunable FSS is an
important factor that can fundamentally limit its power handling capability.
Over the past several years, a class of bandpass FSSs referred to as miniaturized-element
frequency selective surfaces (MEFSSs) has been studied by various research groups [40]-[46],
38
[47]-[50]. MEFSSs are periodic structures with sub-wavelength periods1 and most MEFSS implementations use non-resonant constituting elements (unit cells). Several studies show that such
sub-wavelength periodic structures have stable frequency responses with respect to the angle and
polarization of incidence of the EM wave [41]-[45]. Recently, we demonstrated that MEFSSs can
be used to design wideband planar microwave lenses [46]. In such lenses, MEFSS unit cells are
used as spatial phase shifters (SPSs) (as opposed to a spatial filter) that populate the aperture of
the lens. When illuminated with an appropriately designed feed antenna, the combination of the
feed antenna and the lens acts as a high gain aperture antenna. Tunable versions of these lenses
can be used to develop high-gain beam-steerable aperture antennas. Such tunable lenses can be
developed if tunable spatial phase shifters - capable of providing a wide range of phase shifts - are
used. In this chapter, we examine one method of designing such tunable spatial phase shifters. In
particular, we examine the application of using a fluidic tuning technique in designing a tunable
MEFSS capable of providing a broadband, fifth-order bandpass response. The principles of this
liquid tuning technique were first reported in [118] for a second-order bandpass FSS. We demonstrate that, within a given frequency range, this tunable MEFSS acts as a phase shifting surface
(PSS) capable of providing a tunable 0◦ -360◦ phase shift range with minimal insertion loss.
In what follows, we will first discuss the principles of operation of the proposed structure in
Section 6.2.1 and examine the fluidic varactor concept in Section 6.2.2. Then, we present the design
of a wideband fluidically tunable MEFSS that can act as a spatial phase shifter capable of providing
0◦ − 360◦ phase shift values in Section 4.2.3. In Section 3.2.5, we examine electronically-tunable
versions of this PSS that offer the same tuning capability. We demonstrate that these electronically
tunable PSSs show extremely nonlinear responses under short-duration high-power excitation conditions. In contrast, the proposed fluidically tunable PSS does not use any nonlinear devices and
its response is expected to remain linear under short-duration high-power excitation conditions.
The stability of the phase response of these PSSs is of particular interest when they are used in
constructing lenses of the type reported in [46]. In Section 6.3, we present measurement results
1
In this proposal, we consider a periodic structure to be a sub-wavelength periodic structure if the dimensions of
its unit cell are less than λ0 /4 × λ0 /4.
39
of three fluidically tunable MEFSS prototypes with third- and fifth-order bandpass responses. In
these experiments, both the frequency selectivity and the phase responses of these tunable MEFSSs
are examined. The former is important in spatial filtering applications and the latter is important in
the design of tunable microwave lenses similar to those described in [46]. In particular, we experimentally demonstrate that tunable phase shifts in the range of 0◦ -360◦ can be achieved from these
structures. In Section 6.4, we briefly discuss the tuning speed of these devices, discuss challenges
involved in large-scale implementation of these structures, and present a few concluding remarks.
3.2
Fluidically Tunable MEFSSs
3.2.1
Principles of Operation
Figure 3.1(a) shows the three-dimensional (3-D) topology of the proposed fluidically tunable
frequency selective surface. The top view of a section of this FSS comprised of four unit cells and
two side view cuts are shown respectively in Figs. 3.1(b), 3.1(c), and 3.1(d). The structure consists
of multiple metal layers separated from one another by thin dielectric substrates. Each metallic
layer is either in the form of a two-dimensional (2-D) periodic arrangement of sub-wavelength
capacitive patches or a 2-D wire grid with sub-wavelength periodicity. This arrangement can be
clearly seen from Fig. 3.1(c) and 3.1(d). In this particular FSS topology, the top and bottom
metal layers are composed of sub-wavelength capacitive patches while the layers in between are
composed of sub-wavelength inductive grids and capacitive patches repeated sequentially. Figure
3.1(e) depicts the top view of a unit cell of a capacitive patch array and the inductive wire grid.
The different capacitive patch layers (or wire grids) are not necessarily identical to one another.
Additionally, this structure is composed of an odd number of metal layers and an even number of
dielectric spacers. An FSS of this topology, which is composed of N metallic layers acts as an
( N 2+1 )th order bandpass spatial filter, where N is always an odd number (i.e., N = 3, 5, 7, ...). The
principles of operation of this type of FSS along with its comprehensive synthesis procedure are
provided in [42] and will not be repeated here.
The response of an FSS of the type shown in Fig. 3.1 is a function of the surface impedances
of its various inductive and capacitive layers as well as the dielectric constant and thicknesses of
40
the thin dielectric layers separating them [42]. Examination of the synthesis procedure discussed
in [42] reveals that a simple method for tuning the frequency response of this FSS is to change
the surface impedances of the capacitive layers without changing the surface impedances of the
inductive layers. The surface impedance of a two-dimensional arrangement of sub-wavelength
capacitive patches of the type shown in Fig. 3.1 can be calculated from (3.1) [119]:
Zc =
−jZ0 π
2k0 ϵef f D ln( sin1 s )
[Ω]
(3.1)
2D
As can be seen from (3.1), the surface impedance of such capacitive layers can be tuned dynamically by changing the effective dielectric constant of the medium immediately surrounding it. To
do this, we propose the “liquid varactor” concept. Figure 3.1(d) shows the cross section of the
proposed FSS that can be tuned using this technique. In this example, a single narrow capillary
tube is placed underneath (or above) each capacitive patch column. Each capillary tube, which
extends along the height of a column of capacitive patches, is filled with discontinuous chunks of
liquid metal droplets immersed in a liquid Teflon solution. The teflon solution used here is Teflon
AF 400S2-100-1, 1% teflon powdered resin dissolved in 3M FC-40 from DuPont. The separation
between the droplets is the same as the period of the structure and the length of each droplet is
less than the length of each capacitive patch as shown in Fig. 3.2. When a liquid metal droplet
is moved to a location directly underneath the gap between two adjacent capacitive patches, the
capacitance between them increases and attains its maximum value. On the other hand, when
the liquid metal droplets are completely moved away from the gap and are placed underneath the
patches, the capacitance between them reaches its minimum value. However, the transition between these two states is not abrupt and the capacitance value continuously changes as the liquid
metal droplets are moved away from the gap region. This way, by varying the location of the
liquid metal droplet within the material’s unit cell, continuous tuning of the structure’s frequency
response can be achieved in a manner similar to what is done using a varactor. The combination
of the capacitive patches and the liquid metal filled capillary tube acts as a fluidic varactor that can
dynamically change the surface impedances of the capacitive layers of the structure shown in Fig.
3.1. While in this chapter we focus on the use of liquids in implementing the structure shown in
41
Fig. 3.1, other mechanically driven systems can also be envisioned that accomplish the same task.
For example, in the structure shown in Fig. 3.1(b), solid metallic pellets separated from each other
by an incompressible (liquid or solid) medium can be used instead of liquid metal droplets and the
Teflon solution. In this regards, the implementation technique examined in this chapter is a special
case of a more general mechanically tunable structure that may or may not use liquids.
Galinstan
Droplets
Teflon
Solution
(a)
Capillary
Tubes
(b)
Figure 3.2 Top view of a column of capacitive patch layers with the Teflon tube underneath it. (a)
Maximum capacitance value is obtained as the liquid metal droplets are placed directly
underneath the gap between two adjacent capacitive patches. (b) Minimum capacitance value is
achieved when the liquid metal droplets are moved entirely away from the gap region.
With this clarification in mind, we use the liquid metal Galinstan in this study. Galinstan is a
eutectic alloy of gallium, indium, and tin and it is liquid at room temperature. It has a conductivity
of 3.46 × 106 S/m and has freezing and boiling points of -19◦ C and 1300◦ C respectively [120].
Galinstan is a non toxic fluid that has a low viscosity (approximately twice the viscosity of water
([121]) at room temperature and possesses a thin oxide skin. This thin skin provides mechanical
stability for the liquid metal droplets ensuring that they maintain their shapes and will not mix
with the liquid Teflon solution within the microfluidic channels [122]. The Teflon solution acts
as a lubricant and facilitates the movement of the liquid metal droplets within the channels [122]
while ensuring that Galinstan does not stick to the inner walls of the tubes.
The equivalent circuit of the proposed tunable FSS, valid for a normally incident ŷ polarized
wave, is shown in Fig 3.3. This equivalent circuit model, represents an ( N 2+1 )th -order bandpass
filter [42]. Here, the capacitive patch layers and the liquid-filled capillary tubes are modeled
42
Z2
Z1
Z0
C1
h1
L2
ZN-2
C3
CN-1
h2
ZN-1
LN-1
hN-2
CN Z 0
hN-1
Figure 3.3 (a) Equivalent circuit model of the general tunable FSS shown in Fig. 3.1(a) for
normal angle of incidence.
with variables capacitors, C1 , C3 , ..., CN . The sub-wavelength inductive wire grids are modeled
using parallel inductors (L2 , L4 , ..., LN −1 ) and the dielectric substrates separating the layers are
modeled with transmission lines with lengths of h1 , h2 , ..., hN −1 and characteristic impedances of
Z1 , Z2 , ..., ZN −1 . Free space on each side of the FSS is modeled with semi-infinite transmission
lines with characteristic impedances of Z0 = 377Ω. The MEFSS response is tuned by changing
the values of the variable capacitors C1 , C2 , ..., CN , whose values are determined by the relative
position of the Galinstan droplets with respect to the open gap in the capacitive layer. This way,
by varying the location of the liquid metal droplet, a continuous capacitance change is achieved.
Thus, a continuous variation of the capacitance values C1 , C3 , ..., CN is expected when the Galinstan droplets flow smoothly within the Teflon tubes. In practice, the actuation of liquid metal
droplets can be done using small micro-pumps to exert pressure at the input or output of the microchannels and achieve the necessary fluid movement.
3.2.2 The Fluidic Varactor Concept
In addition to the physical dimensions of the capacitive patches, D and s, the capacitance
values and tuning ranges of the liquid varactors, C1 , C3 , ..., CN , depend on the dimensions of the
liquid metal droplets and their relative positions within the MEFSS unit cell. To demonstrate
these effects, we conducted a case study for a fluidically tunable varactor composed of a periodic
arrangement of capacitive patches with unit cell dimensions of Dx × Dy = 6.5 mm ×6.5 mm
and spacing of s = 0.5 mm. The capacitive patches are located in free space. A single Teflon
capillary tube is placed underneath each capacitive patch column. The tubes have circular cross
43
sections with an inner diameter of 0.025” and an outer diameter of 0.033”. Each tube is filled
with discontinuous sections of Galinstan droplets as shown in Fig. 3.2. The length of each droplet
within the capillary tube is l. This structure is simulated using full-wave EM simulations in CST
Studio to compute its effective capacitance as a function of dimensions and the location of the
liquid metal droplets within the MEFSS unit cell. To do this, the unit cell of the structure, shown in
Fig. 3.4(a), is simulated in CST Studio using the periodic boundary conditions [42]. The reflection
and transmission coefficients of this structure for a normally incident, vertically polarized (ŷ) plane
wave are calculated. Subsequently, the simplified equivalent circuit model of the structure, shown
in Fig. 3.4(b), is simulated using the circuit simulation software Agilent Advanced Design System
(ADS) and its transmission and reflection coefficients are also calculated. The value of Ceq in Fig.
3.4(b) is varied to match the magnitude and phase of the transmission and reflection coefficient
obtained from the equivalent circuit model to those predicted by the full-wave EM simulation.
This way, the effective capacitance of the structure is extracted.
Figure 3.4(c) shows the results obtained from these case studies for the aforementioned capacitive structure. Each graph corresponds to the capacitance extracted for a different length of liquid
metal droplet, l = 1, 2, 3, or 4 mm. For each l value, the capacitance is calculated as a function of
the relative position of the liquid metal droplet within the MEFSS unit cell. Offset 1 (O1 ) refers to
the horizontal displacement of the capillary tube away from the center of the unit cell and offset 2
(O2 ) refers to the vertical displacement of the center of the liquid metal droplet with respect to
the center of the gap. As can be observed, the relative position of the liquid metal droplets with
respect to the gap region between the capacitive patches, O2 , has the most significant effect on the
capacitance values while the horizontal location, O1 , only affects it negligibly. Additionally, the
capacitance values continuously change by changing the values of O2 . Furthermore, by increasing the length of the Galinstan droplets, l, the capacitance values and the achievable tuning range
increase. For this structure, the maximum capacitance value of 0.21 pF occurs for l = 4 mm and
O2 = 0 mm. The minimum capacitance values of 0.129 pF is obtained for the four cases shown in
Fig. 3.4(c) when the Galinstan droplets are completely moved away from the capacitive gap.
0.142
0.14
0.138
0.136
0.134
0.132
0.13
0.14
0.135
O1
0.13
0
0.125
0
2
3 2
Capacitance (pF)
Ceq
0.13
0.12
0
0
0.22
0.17
0.2
0.16
0.18
0.15
0.16
0.14
0.14
0
0.12
0
1
1
2
O2 (mm)
32
1
2
32
1
m)
(m
O2 (mm)
O1
ii: l=2mm
0.13
m)
(m
0.22
0.2
0.18
0.16
0.14
0
0.12
0
1
0.2
0.19
0.18
0.17
0.16
0.15
0.14
0.13
m)
(m
1
2
O2 (mm) 3 2 O 1
iv: l=4mm
O1
iii: l=3mm
(b)
0.14
m)
(m
0.18
Port 2
0.15
O2 (mm)
O1
i: l=1mm
(a)
Port 1
0.16
1
1
0.16
0.155
0.15
0.145
0.14
0.135
0.13
0.17
Capacitance (pF)
s
l
O2
Capacitance (pF)
0.145
Capacitance (pF)
44
(c)
Figure 3.4 (a) Unit cell of a liquid varactor composed of a sub-wavelength capacitive patch
integrated with a liquid metal droplet. The horizontal and vertical offsets of the liquid metal
droplet with respect to the center of the gap between the two adjacent capacitive patches are
referred to as O1 and O2 respectively. (b) The equivalent circuit model of the liquid varactor. (c)
The extracted effective capacitances of a tunable capacitive surface. The structure has unit cell
dimensions of 6.5 mm × 6.5 mm. Four different cases are shown. Case i: l = 1 mm, Case ii:
l = 2 mm, Case iii: l = 3 mm, Case iv: l = 4 mm.
3.2.3 Approximate Closed Form Formula For Liquid Varactor
To better understand the fluidic varactor concept, an analytical formula has also been developed
that can be used to determine the effective capacitance of a liquid varactor, to a first-order approximation. Figure 3.6(a) shows one unit cell of the proposed liquid varactor. It can be observed that
the upper side of the liquid metal droplet, with the length of l/2 + O2 , forms an effective capacitance Cu with the upper half of the capacitive patch. Similarly, the lower side of the liquid metal
droplet, with the length of l/2 − O2 , forms another effective capacitance Cl with the lower half of
the capacitive patch. Clearly, both Cu and Cl are a function of O2 , and can be approximated by
using parallel plate formula:
ϵ0 ϵef f ( 2l + O2 )d
Cu =
h
(3.2)
45
s1
O2,1
FC: Fluidic Channel
PBC Walls
FC1
C1
l1
FC2
FC3
L2
O2,3
s3
l3
l5
FC4
L6=L4
s7
O2,7
C7=C3
l7
l9
FC5
s9
(a)
L4
C5
O2,5
s5
C3
O2,9
L8=L2
C9=C1
(b)
Figure 3.5 (a) A unit cell of the fifth-order fluidically tunable FSS discussed in Section 4.2.3 is
placed inside a waveguide with periodic boundary conditions to simulate the frequency response
of the infinitely large FSS. (b) The side view of unit cell of the fifth-order MEFSS showing all the
dimensions and various capacitive and inductive layers.
ϵ0 ϵef f ( 2l − O2 )d
Cl =
h
(3.3)
where d is the diameter of the liquid metal droplet, h is the wall thickness of the Teflon tube,
and ϵef f represents the effective dielectric constant of the region between the liquid metal and
capacitive patch. As can be observed from Fig. 3.6(a), this region is a combination of both teflon
tube and air. Therefore, a simple first order approximation of ϵef f =
1+ϵT ef lon
2
can be used (here
ϵT ef lon = 2.2 is used).
As shown in the equivalent circuit model of Fig. 3.6(b), Cu and Cl are in series with each other.
Taking into account of the intrinsic capacitance brought by the capacitive gap, the total effective
capacitance can be modeled as shunt capacitance Ci in parallel with a series combination of Cu
46
O2
Ceq
Cl
Cu
Ci
Cu
Cl
Ci
(a)
(b)
Figure 3.6 (a) A fluidic varactor of the type discussed in Section 6.2.2 is composed of three
different capacitors of Cu , Cl , and Ci as depicted. (b) The equivalent circuit model of the fluidic
varactor showing the relative arrangement of Cu , Cl , and Ci .
and Cl , shown in Fig 3.6(b). Therefore, the analytical approximation for the effective capacitance
can be represented as:
Cu Cl
Cu + Cl
(3.4)
2D
1
ln(
πs )
)
π
sin( 2D
(3.5)
Cef f = Ci +
where
Ci = ϵ0 ϵef f
The analytical formulas of (3.2)-(3.5) are used to calculate the effective capacitance of one of the
liquid varactors examined in Section 6.2.2 (D = 6.5 mm, s = 0.5 mm, O1 =0 mm, and l = 1,2,3,4
mm). Figure 3.7 shows the capacitance values calculated using these closed form formulas and
compares the results with the capacitance values extracted from full-wave EM simulations. As can
be seen, equations (3.2)-(3.5) can be used to predict the capacitance of the proposed liquid varactor
to a first order approximation.
3.2.4 Fluidically Tunable MEFSSs
To demonstrate the capabilities of the proposed tuning mechanism, we have designed a fluidically tunable MEFSS of the type shown in Fig. 3.1. The FSS has a fifth-order bandpass response
and it is composed of nine metal layers (five capacitive and four inductive) separated from each
other by eight thin dielectric substrates. Following the procedure described in [45], the structure
47
Figure 3.7 Comparison between the capacitance values predicted using the analytical method and
those extracted from full-wave EM simulations. The results are shown for the four liquid
varactors considered in Section 6.2.2.
is designed to ensure that it is symmetric with respect to the fifth metal layer (i.e., the metallic
patterns on layers m and N − m + 1, m = 1, 2, ..., N 2+1 , are identical). The frequency response of
this structure can be tuned by dynamically changing the capacitance values of the five capacitive
layers.Therefore, in this fifth-order MEFSS,the first and the fifth capacitive layers are identical to
each other as well as the second and the fourth capacitive layers. Similarly, the first and the fourth
inductive layers are also identical while the second and the third inductive layers are the same.
To dynamically change these effective capacitances, five Teflon capillary tubes filled with liquid metal droplets immersed in a Teflon solution are embedded within the unit cell of the structure.
Figure 3.5 shows the top and side views of one unit cell of this structure. Since the structure is symmetric, the movements of the liquid metal droplets in fluidic channels 1 and 2 can be synchronized
with the movements in channels 5 and 4 respectively (i.e., O2,1 = O2,9 and O2,3 = O2,7 in Fig.
3.5(b)). Therefore, the frequency response of this fifth-order MEFSS can be continuously tuned by
48
Table 3.1 Physical and geometrical parameters of the fifth-order tunable MEFSS discussed in
Section 4.2.3 for different tuning states. Physical units are in mm.
tuning state
A
B
C
D
E
O2,1 = O2,9
0
1.20
2.00 2.60
3.20
O2,3 = O2,7
0
1.60
1.90 2.30
3.20
O2,5
0
1.60
1.90 2.30
3.20
s1 = s9 = 1.40, s3 = s7 = 1.30
F ixed values
w2 = w8 = 1.4, w4 = w6 = 1.25
s5 = 1.2, D = 6.5, l1 = l9 = 4.0
l3 = l7 = 5.4, l5 = 5.2, ϵr = 3.4
h1 , ..., hN −1 = 1mm
three control variables of O2,1 , O2,3 , and O2,5 . Table 4.1 shows the geometrical parameters of the
proposed structure for five different tuning states with different offset values O2,1 , O2,3 , and O2,5 .
Table 4.2 shows the values of the equivalent circuit elements at each of these five different tuning
states.
This MEFSS is simulated using full-wave EM simulations in CST Studio. A unit cell of this
structure is placed inside a waveguide with periodic boundary condition walls as shown in Fig.
3.5(a) and the transmission and reflection coefficients of the infinite periodic structure are calculated. The side view of one unit cell of the fifth order tunable FSS is shown in Fig. 3.5(b). With
regards to the Fig. 3.3, O1 determines the effective capacitance values of the two varactors C1 and
C9 , O2 affects the capacitance value of the varactors C3 and C7 , and O3 controls the varactor C5 .
Figure 3.8(a) shows the simulated transmission coefficients of the tunable MEFSS for the five different tuning states described in Table 4.1. As can be seen, the frequency response of this FSS is
continuously tuned over a relatively broad bandwidth. Increasing O2,1 , O2,3 and O2,5 values causes
C1 , C3 , and C5 to decrease and hence, the center frequency of operation of the filter to increase.
The center frequency of the lowest band of this tunable MEFSS occurs for O2,1 = O2,3 = O2,5 = 0
49
Table 3.2 Parameters of the equivalent circuit model of the fifth-order tunable MEFSS discussed
in Section 4.2.3 for different tuning states. Capacitance units are in pF .
tuning state
A
B
C
D
E
C1 = C9
0.202 0.166
0.148 0.130
0.118
C3 = C7
0.382 0.306
0.274 0.242
0.220
C5
0.385 0.308
0.280 0.246
0.222
F ixed values
L2 = L8 = 0.580nH, L4 = L6 = 0.602nH
Z1 , ..., ZN −1 = 205Ω, h1 , ..., hN −1 = 1mm
and the highest center frequency of operation is achieved when the liquid metal droplets are entirely removed from the gap region. As observed from Fig. 3.8, changing the center frequency of
operation of the filter also changes its fractional bandwidth. To explain this bandwidth change, one
must notice that frequency tuning in this structure is achieved by only changing the capacitance
values while maintaining the inductance values. Therefore, as frequency increases, the loaded
quality factor of the equivalent resonators of this coupled-resonator filter decreases causing the
fractional bandwidth to increase [42]. This phenomenon is not unique to the proposed design and
is also observed in other tunable filters that achieve tuning using variable capacitors [123].
Figure 3.8(a) also shows the magnitude of the transmission coefficient of this structure calculated from the equivalent circuit model shown in Fig. 3.3 using the element values provided in
Table 4.2. As can be observed, there is a good agreement between the results obtained from the
circuit simulation and those obtained from the full-wave EM simulations. Figure 3.8(b) shows
the transmission phase of the proposed structure calculated using full-wave EM simulations. This
tunable MEFSS is designed to have a very wideband transmission response. Consequently, when
the response of the structure is tuned, an overlap frequency band exists that remains in the pass
band of all of these tuned responses. Within this overlap region, which is highlighted in Fig. 3.8,
the frequency selective surface acts as a phase shifting surface with a tunable phase response. The
range of phase shift values that can be achieved from such a PSS depends on the order of the filter
response with higher-order responses providing grater phase variations [46]. At the center of the
50
Overlap
Region
(a)
Overlap
Region
(b)
Figure 3.8 (a) Transmission coefficient of the fifth-order FSS of Section 4.2.3 calculated using
both full wave EM simulations and the equivalent circuit model presented in Fig. 3.3. Different
tuning states are described in Table 4.1 and the values of the equivalent circuit elements are
presented in Table 4.2. (b) The phase of the transmission coefficient of the fifth-order FSS of
Section 4.2.3 calculated using full wave EM simulations for different tuning states described in
Table 4.1.
overlap region highlighted in Fig. 3.8, this fifth-order MEFSS can provide a relative phase delay
in the range of 0◦ to 360◦ as seen from Fig. 3.8(b). Therefore, this type of tunable PSS may be
useful in designing tunable lenses of the type discussed in [46].
The sensitivity of the frequency response (both magnitude and phase) of this tunable MEFSS to
the angle and polarization of incidence of the EM wave is also examined using full wave simulation
51
(a)
(b)
Figure 3.9 Magnitude (a) and phase (b) of the transmission coefficient of the tunable MEFSS
discussed in Section 4.2.3 as a function of angle of incidence. The results are obtained using
full-wave EM simulations for the transverse electric (TE) polarization of incidence.
in CST Studio. Figures 3.9(a) and 3.9(b) show the magnitude and phase of the MEFSS’s transfer
function for the transverse electric (TE) polarization and various incidence angles. The results
are shown for tuning states “A” and “E” (see Table 4.1). Similar results are presented for the
transverse magnetic (TM) polarization in Figs. 3.10(a) and 3.10(b). In the arrangement depicted in
Fig. 3.1(a), the proposed tunable MEFSS has a polarization sensitive response, since the tubes are
only placed along one dimension. Thus, with reference to Fig. 3.1(a), the TE plane of incidence is
the x − z plane and the TM plane of incidence is the y − z plane. In general, as the order of the
filter response of an FSS is increased, its frequency response tends to become more sensitive to the
polarization and the angle of incidence of the EM wave [39]. However, as can been seen from Figs.
3.9 and 3.10, this fifth-order tunable MEFSS demonstrates a relatively stable frequency response
as a function of angle and polarization of incidence of the EM wave. This is mostly attributed to
the relatively thin overall thickness of the structure as well as the compactness of its unit cells [42].
The overall thickness of this structure is 8 mm, which corresponds to 0.21λ0,A for tuning state “A”
52
(a)
(b)
Figure 3.10 Magnitude (a) and phase (b) of the transmission coefficient of the tunable MEFSS
discussed in Section 4.2.3 as a function of angle of incidence. The results are obtained using
full-wave EM simulations for the transverse magnetic (TM) polarization of incidence.
and 0.29λ0,E for tuning state “E” (λ0,A(E) is the free space wavelength at the center frequency of
operation for tuning state “A” (“E”)).
3.2.5
Linearity and Transient Power Handling Capability of Electronically
Tunable MEFSSs
The power handling capability of a tunable FSS is limited by three main factors; these include
heat dissipation, dielectric and air breakdown, and the linearity of the FSS’s response. The heat
dissipation mechanism of failure occurs under sustained high-average-power illumination where
lossy materials will heat and the FSS will eventually melt or burn. This mechanism is not very
significant in situations where high peak power but short duration pulses are used. Under high
peak power excitation, very high electric fields may develop in the metallic inclusions used within
the FSS and arcing can occur. This arcing will effectively short circuit the metallic elements of the
FSS and can also permanently damage it. Another important limiting factor is the linearity of the
53
FSS response under high-power excitation. Traditionally, the majority of tunable frequency selective surfaces reported in the literature achieve tunability by using an electronically tunable device
such as a semiconductor varactor [27]-[49]. The inherently nonlinear nature of such varactors is
an important and often overlooked factor that can limit their power handling capability. In such
tunable FSSs, the incident RF energy can significantly change the DC bias voltage of the FSS’s
varactors and change its frequency response. The extent of this nonlinear behavior is mainly determined by the instantaneous intensity of the incident electric field and the peak envelope power
of the transmitted signal.
To demonstrate the effect of this nonlinear behavior in electronically tunable MEFSSs, we designed two electronically tunable versions of the MEFSS discussed in Section 4.2.3. In doing this,
we examined achieving the desired tuning range by using either a typical Gallium Arsenide (GaAs)
semiconductor varactor [124] or a typical Barium-Strontium-Titanate (BST) ferroelectric varactor
[125]. For consistency, we maintained all the physical dimensions of the MEFSS described in
Section 4.2.3. Tuning is achieved by placing varactors between each adjacent capacitive patches in
a manner similar to what is done in [49]. The parameters of the varactors are chosen to achieve the
same exact tuning range as the one obtained using the fluidic-tuning technique (shown in Fig. 3.8).
To do this, GaAs and BST varactors with the following capacitance-voltage (C-V) characteristics
are used [124]-[125]:
CGaAs =
CBST =
0.2
V 2
(1 + 3.5
)
0.2
V 2 1/3
))
(1 + ( 0.35
[pF]
[pF]
(3.6)
(3.7)
where C is the varactor’s capacitance and V is the potential difference between its two terminals.
The varactors are placed across the center of each capacitive gap and the biasing voltage value
of each varactor is carefully chosen to match the same capacitive tuning effects achieved from its
Galinstan counterpart. The five tuning states (“State A” to “State E”) shown in Fig. 3.8(a) can be
reproduced using either the GaAs or the BST varactors specified by (3.6) and (3.7). The nonlinear equivalent circuit models of the electronically tunable MEFSSs are simulated in ADS using
the harmonic balance method. Using this, the power dependent frequency responses of the two
54
electronically tunable MEFSSs are calculated. Figure 3.11(a) shows the transmission coefficients
of the GaAs-tunable MEFSS for the tuning states “A”, “C”, and “E” calculated for an incident
power density of approximately 1300 W/m2 (electric field intensity of 1000 V/m). As can be
seen, the response of the GaAs-tunable MEFSS is significantly degraded under a moderately high
incident power density. As the incident power density is increased beyond 1300 W/m2 , the performance of the GaAs-tunable MEFSS further deteriorates. Figure 3.11(b) shows the difference
between the transmission phase of this tunable MEFSS when it is illuminated by an EM wave
with an incident power density of 1300 W/m2 and the transmission phase calculated under small
signal illumination (a power density of 1.3 mW/m2 or an electric field intensity of 1.0 V/m) for
each tuning state. As can be observed, the transmission phase of this structure changes considerably under high-power excitation levels. A similar behavior is also observed for the BST-tunable
MEFSS. Figure 3.11(c) shows the magnitude of the transmission coefficient for the BST-tunable
MEFSS for an incident power density of 1300 W/m2 and Fig. 3.11(d) shows the change in the
transmission phase of the structure when the incident power density is increased from 1.3 mW/m2
to 1300 W/m2 . Similar to the previous case both the magnitude and the phase of the transmission
coefficient of this structure change significantly compared to their small signal values. The results
shown in Figs. 3.11(a)-3.11(d) suggest that the power handling capability of these electronically
tunable surfaces, whether used as FSSs or PSSs, is primarily limited by their nonlinear responses.
Unlike these electronically tunable MEFSSs, the proposed fluidically tunable MEFSS does not use
any nonlinear materials or devices. Therefore, its frequency response is expected to remain linear
for short-duration high-peak-power excitations.
While the transient power handling capability of an electronically-tunable MEFSS can be examined using computer simulations, determining its continuous-wave (CW) power handling capability is a more challenging task. When electronically tunable MEFSSs are used under sustained
high-average-power excitation conditions, the temperature dependency of their varactors and the
lumped element components used in their biasing network must also be taken into account in addition to the nonlinearity of the varactors. Additionally, the maximum temperature within the lumped
element devices (e.g. junction temperature of a semiconductor varactor) must also be determined
55
(a)
(b)
(c)
(d)
Figure 3.11 (a) Magnitude of the transmission coefficient of the tunable MEFSS, discussed in
Section 3.2.5, which utilizes GaAs varactors to achieve tuning. (b) The change of the phase of the
transmission coefficient of the GaAs-tunable MEFSS discussed in Section 3.2.5 when the
instantaneous electric field intensity is increased from 1 V/m to 1000V/m. (c) Magnitude of the
transmission coefficient of the tunable MEFSS, discussed in Section 3.2.5, which utilizes BST
varactors to achieve tuning. (d) The change of the phase of the transmission coefficient of the
BST-tunable MEFSS discussed in Section 3.2.5 when the instantaneous electric field intensity is
increased from 1 V/m to 1000V/m. Description of all tuning states are provided in Table 4.2.
to ensure that it will not exceed a level that causes device failure. In a fluidically tunable MEFSS,
thermal effects can also impact the response of the structure. In particular, under high-averagepower excitation levels, thermal heating gradually expands the physical dimensions of the structure
(including those of the liquid metal droplets, the Teflon solution, and the Teflon tubes). In principle, this gradual expansion can alter the the effective capacitance of the liquid varactors and hence,
affect the frequency response of the structure. Due to the aforementioned modeling challenges, we
56
believe that accurate characterization of the response of an electronically- or a fluidically-tunable
MEFSS, under high-average-power excitation conditions, can best be performed using high-power
microwave measurements in a controlled environment. Since conducting such high-power measurements is beyond the scope of the current chapter, we will defer the examination of the CW
power handling capability of these structures to a future publication.
3.3
Experimental Verification and Measurement Results
To experimentally demonstrate the proposed tuning concept, four different fluidically tunable
MEFSS prototypes are designed, fabricated, and characterized using a waveguide measurement
setup. In these experiments, a multi-layer structure equivalent to one unit cell of the proposed
fluidically tunable MEFSS is placed inside a rectangular waveguide and its calibrated frequency
response is measured. One of these prototypes is tunable MEFSS with second-order bandpass
responses presented in Section 3.3.1, two of these prototypes are tunable MEFSSs with third-order
bandpass responses and are presented in Section 3.3.2. The other prototype, which is presented
in Section 3.3.3 is a fifth-order tunable bandpass MEFSS with a wideband response, which could
be used as a tunable spatial phase shifters for the design of tunable microwave lenses of the type
described in [46].
3.3.1
Experimental Demonstration of Second-Order Fluidically Tunable MEFSSs
In order to characterize the behavior of the FSSs without concerning the construction of a
planar phase front and edge diffraction, the standard approach is to use a metallic waveguide at the
desired band. Following the same approach, a section equivalent to one unit cell of the proposed
FSS is placed along the cross section of the Rectangular waveguide. The arrangement of the FSS
unit cell inside the waveguide is shown in Fig. 3.12, where the standard WR-90 waveguide with
inner dimension of 0.9” × 0.4” is used. Two waveguide shims with the thicknessh = 1.58mm are
used here as spacing substrate. The capacitive patch with the open gap g = 1mm is attached to
the outer surface of both of the two waveguide shims. The metallic strip with the width w = 6mm
57
22. 86mm (0.9’’)
g
Top and Bottom View
w
10.16mm (0.4’’)
10.16mm (0.4’’))
22. 86mm (0.9’’)
Offset
Center View
Waveguide
Shim
Top View of the Galinstan tube
Teflon tube
with Galinstan
h
Inductor
Galinstan in the tube
Capacitor
Side View
Figure 3.12 Topology of the FSS pieces that are used in the measurement process. The
dimensions of these pieces are equal to the inner dimensions of the WR-90 waveguide. The
topology of each piece is derived from the topology of the unit cell show in Fig. ??
is sandwiched between the two waveguide shims. A trench is drilled on the outer surface of the
waveguide shim to accommodate the Teflon tube with inside diameter of 0.032” and wall thickness
of 0.01”. The top view of the Galinstan is shown in Fig. 3.12, where the ”offset” indicates the
distance between the center of capacitor gap and the center of the Galinstan slug.
The transmission response is first measured in the absence of the FSS unit cell and this result is
used for calibration purposes. Then the two capacitive patches, two waveguide shims, two Teflon
tubes with Galinstan, and one inductive strip are assembled together to form the FSS unit cell for
testing. The transmission response is measured again with the assembled unit cell sandwiched
between the two sections of the WR-90 waveguide; the response the FSS is then obtained using
these two measured results.
58
Figure 3.13 Measured and simulated transmission coefficient for (i), (ii), (iii)
The comparison between the measured and simulated transmission response is shown in Fig.
3.13, where (i) is the situation when the center of the Galinstan slug falls into the center of the
capacitor gap; (ii) is the situation when there is no tube embedded in the waveguide shims; (iii) is
the situation when the Teflon tube is filled everywhere with the Galinstan. Clearly observed, the
lowest center frequency occurs at (i) at 7.65 GHz, when the maximum varactor value is obtained.
The highest center frequency occurs at (iii) at 12.10 GHz, when an effective parallel inductor is
added. The insertion loss at (iii) is larger compared to (i) and (ii). That is due to the decreased
inductive coupling brought by the extra inductor, which results in an under-coupled second order
band-pass performance. Both the measured and simulated results agree well with each other, and
demonstrate a possible flexible tuning over nearly the entire X band (from 7.65 GHz to 12.10 GHz).
In Fig. 3.14, a gradually changed center frequency and fractional BW is observed. With the
increment of the offset, the center frequency increases from 7.65 GHz (offset=1mm) to 10.05 GHz
59
Figure 3.14 Measured and Simulated results of the operating center frequency and fraction
bandwidth (BW) as a function of the offset
(offset=15mm), which is due to a decreasing varactor value as shown in Fig. 2. In the mean time,
the fractional BW increases from 14.38% (offset=1mm) to 24% (offset=15mm). According to
[41], the fractional BW is inversely proportional to the capacitor value in the second-order coupled
resonator band-pass filter model. Note here that when the Galinstan slug moves far away from the
capacitor gap, the frequency response becomes more and more similar to the circumstances when
there is no tube in the testing FSS unit cell (as (ii) in Fig. 3.13).
3.3.2
Experimental Demonstration of Third-Order Fluidically Tunable MEFSSs
The MEFSS prototypes (Prototype 1 and 2) have third-order bandpass responses with minimum fractional bandwidths of 10% and 24% respectively. Both prototypes are designed to operate
at X-band in a standard WR-90 waveguide with inner dimensions of 0.9” × 0.4”. Waveguide irises
that represent the capacitive and inductive layers of the MEFSS are fabricated out of 0.005”-thick
0.9”
41.4 mm
si
wi
0.4”
41.4 mm
60
0.9”
Capacitive Iris
Inductive Iris
O1,i
Waveguide
Shim
li
Teflon Tube
Alignment
Hole
Liquid Varactor
Galinstan
Capacitive
Irises
Inductive
Irises
h
Waveguide
Shims
Figure 3.15 Topology of the waveguide version of the third-order tunable FSS discussed in
Section 3.3.2. Top view of a capacitive and inductive iris, the side view of the structure, and the
photograph of a fabricated section are shown.
brass sheets using chemical etching. Figure 3.15 shows the top view of a typical inductive and
capacitive iris used in these measurements. WR-90 waveguide shims with the fixed thickness of
1.58 mm are machined out of a 1/16 inch thick brass sheet using a computer controlled milling
machine. These waveguide shims, which are equivalent to the dielectric substrates used in the
MEFSS of Fig. 3.1(a), are used as spacers between the capacitive and inductive irises. Narrow
61
trenches with the width of 1.25 mm and depth of 1 mm are milled in the waveguide shims that are
placed adjacent to the capacitive irises to accommodate the capillary tubes. Figure 3.15 shows the
side view of the waveguide assembly for the two third-order filter prototypes. The main difference
between Prototypes 1 and 2 is in their bandwidths. An MEFSS of the type shown in Fig. 3.1 is
equivalent to a coupled-resonator filter and its fractional bandwidth is determined by the quality
factor (Q) of its effective resonators [42]. With reference to the equivalent circuit model shown
in Fig. 3.3, achieving a narrow-band operation requires having large capacitance and small inductance values. In the waveguide implementations, the capacitance of the capacitive irises can be
increased (decreased) by decreasing (increasing) the width of the horizontal gap, si in Fig. 3.15.
The inductance of the inductive iris can be decreased (increased) by increasing (decreasing) the
width of the vertical metallic strip, wi in Fig. 3.15.
Tables 4.3 and 3.4 show the physical and geometrical parameters of these fabricated prototypes.
For each prototype, the three capacitive irises, four waveguide shims, three Teflon capillary tubes
filled with Galinstan and liquid Teflon solutions, and two inductive irises are assembled to form
the waveguide equivalent version of the fluidically tunable MEFSS. Figure 3.16 shows a threedimensional perspective view of different layers of the waveguide structure and a photograph of a
prototype during the assembly process.
The calibrated transmission responses of both MEFSS prototypes are measured using the setup
shown in Fig. 3.16(b). In these experiments, the liquid metal droplets are moved within the
capillary tubes by applying air pressure to the slugs within the tubes using identical syringes.
Figure 3.17(a) shows the simulated and measured transmission coefficients of Prototype 1. The
physical and geometrical dimensions of this prototype, for different tuning states, are provided
in Table 4.3. The measurement agrees well with the simulation and they both demonstrated a
wide range of frequency tuning covering the frequency range of 8.00 GHz to 11.20 GHz. As
expected, the lowest center frequency occurs for O2,1 = O2,3 = O2,5 = 0 mm, which corresponds
to the maximum C1 = C5 and C3 values. The highest center frequency occurs when there are no
Galinstan droplets under any capacitive gap, which indicates a minimum C1 = C5 and C3 value.
Also, as the offset values are changed continuously, the frequency response of the structure is
62
Alignment hole Inductive Irises
Teflon tube
l
5
l
l
3
1
o2,1
o2,3
o2,5
Capacitive Irises
(a)
(b)
Figure 3.16 (a) The assembly of the waveguide version of the third-order tunable MEFSS
discussed in Section 3.3.2 (waveguide shims acting as spacers are not shown here). (b) The
photograph of the experimental setup used to characterize the response of this structure.
continuously tuned. The measurement results shown in Fig. 3.17(a) also demonstrates a relatively
low insertion loss. The insertion loss can mostly be attributed to the Ohmic losses in the capacitive
and inductive irises as well as the Galinstan droplets. Figure 3.17(b) shows the simulated and
measured transmission phases of this MEFSS prototype. As can be observed, a good agreement
between the simulation and measurement is achieved. Additionally, the transmission phase of the
structure is also tuned continuously using the proposed liquid varactor concept.
63
(a)
(b)
Figure 3.17 (a) Simulated and measured magnitudes of the transmission coefficient of MEFSS
Prototype 1 (discussed in Section 3.3.2). Simulations are conducted in CST Studio. (b) The
simulated and measured phase of the transmission coefficient of this prototype. The description of
all tuning states is provided in Table 4.3.
The response of the second MEFSS prototype is also measured using a similar procedure. The
physical and geometrical dimensions of this prototype, for different tuning states, are provided in
Table 3.4. Figure 3.18(a) shows the simulated and measured transmission coefficients of Prototype
2. This structure has a considerably larger bandwidth compared to the previous one. In principle,
the MEFSS topology shown in Fig. 3.1 can be used to synthesize narrow-band, wideband, or
ultra-wideband filter responses. In these demonstrations, however, the measurements are carried
out within a WR-90 waveguide, which is inherently band limited (maximum usable range is 7
- 13 GHz). Therefore, Prototype 2 has only a moderately wideband frequency response. In the
frequency band that falls within the overlap region of all the magnitude responses, this wideband
MEFSS acts as a spatial phase shifter. Figure 3.18(b) shows the measured and simulated phase
responses of this prototype. For Prototype 2, a narrow-band frequency range centered around 10
GHz always remains in the pass band as the frequency response of the structure is tuned. Thus,
64
Table 3.3 Physical and geometrical parameters of the first tunable MEFSS prototype discussed in
Section 3.3.2 for different tuning states. All physical dimensions are in mm.
tuning state
A
B
O2,1 = O2,5
0
1.6
1.70 2.40
2.70
2.90 5.00
O2,3
0
2.10
2.15 2.90
3.30
3.80 5.00
F ixed values
C
D
E
F
G
s1 = s5 = 1.50, s3 = 0.35, l1 = l5 = 7.10
l3 = 8.50, w2 = w4 = 6.50
within this frequency band, the MEFSS acts as a fluidically tunable phase shifter. Figure 3.18(c)
shows the insertion loss and the phase response of this phase shifter for various tuning states (tuning
state parameters are defined in Table 3.4). The structure’s insertion loss remains better than 1 dB
for all tuning states and it can provide a relative phase shift in the range of 0◦ − 200◦ .
3.3.3 Experimental Demonstration of a Fluidically Tunable SPS with a 0◦ -360◦
Phase Shift Range
As demonstrated in Section 3.3.2, a wideband tunable MEFSS can act as a spatial phase shifter.
To increase the range of phase shift values that can be achieved from such a device, an MEFSS with
a higher-order bandpass response may be used. To experimentally demonstrate this, an MEFSS
with a fifth-order bandpass response is designed, fabricated, and tested in a WR-90 waveguide
environment. The topology of this prototype (Prototype 3) is similar to the one shown in Fig.
3.15 with the exception that the number of its capacitive and inductive irises are increased. The
physical and geometrical parameters of this structure, for each tuning state, are provided in Table
3.5. The structure is fabricated and its frequency response is measured using the methods described
in Section 3.3.2. Figure 3.19(a) shows the simulated and measured transmission coefficients of
Prototype 3 for three different tuning states. The description of each tuning state is provided in
Table 3.5. Figure 3.19(b) shows the simulated and measured transmission phases of the device.
Within the highlighted overlap region, the structure is equivalent to a spatial phase shifter with a
tunable phase response. The transmission phase and insertion loss of this device, at 10 GHz, are
65
(a)
(b)
A
B
C
D
E
F
G
H
I
J
K
(c)
Figure 3.18 Simulated and measured magnitude (a) and phase (b) of the transmission coefficient
of MEFSS prototype 2 (described in Section 3.3.2). (c) The insertion loss and transmission phase
of the structure, at 10 GHz, for a number of different tuning states. Description of the tuning
states is provided in Table 3.4.
66
Table 3.4 Physical and geometrical parameters of the second tunable MEFSS prototype discussed
in Section 3.3.2 for different tuning states. All physical dimensions are in mm.
tuning state
A
B
C
D
E
F
O2,1 = O2,5
0
0.2
0.5
0.8
0.9
1.0
O2,3
0
0.6
1.0
1.2
1.3
1.5
tuning state
G
H
I
J
K
O2,1 = O2,5
1.2
1.4
1.8
2.0
2.3
O2,3
1.7
1.8
2.3
2.5
2.8
F ixed values
s1 = s5 = 2.55, s3 = 1.25, l1 = 5.50
l5 = 5.50, l3 = 6.50, w2 = w4 = 3.00
shown in Fig. 3.19(c) for different tuning states. As observed, a relative phase shift of 0◦ -360◦ can
be achieved with an insertion loss better than 1 dB.
3.4 Discussion
In this chapter, we examined the potential applications of a fluidic tuning mechanism in the
design of tunable periodic structures that act as either highly-selective spatial filters or spatial
phase shifters capable of providing a wide range of phase shift values. We demonstrated that electronically tunable MEFSSs that use semiconductor or ferroelectric varactors are not suitable for
high-power applications due to their inherently nonlinear nature. In contrast, the proposed fluidically tunable structures do not use any nonlinear devices. Consequently, the proposed tunable
surfaces are expected to be capable of handling significantly higher transient power levels than
their electronically tunable counterparts. Since examining the CW power handling capability of
both electronically- and fluidically-tunable structures can best be accomplished using high-power
microwave measurements, which is beyond the scope of the current chapter, that topic will be
67
Table 3.5 Physical and geometrical parameters of the third tunable MEFSS prototype discussed
in Section 3.3.3 for different tuning states. All physical dimensions are in mm
tuning state
A
B
O2,1 = O2,9
0
0.80
O2,3 = O2,7
0
O2,5
0
C
D
E
F
1.00 1.20
1.20
5.00
0.60
1.50 1.70
2.10
5.00
0.60
1.50 1.80
1.90
5.00
s1 = s9 = 2.35, s3 = s7 = s5 = 0.60
F ixed values
w2 = w8 = 2.75, w4 = w6 = 2.50
l1 = l9 = 5.00, l3 = l7 = 6.00, l5 = 6.00
68
(a)
(b)
A
B
C
D
E
F
(c)
Figure 3.19 Simulated and measured magnitude (a) and phase (b) of the transmission coefficient
of MEFSS prototype 3 (described in Section 3.3.3). (c) The insertion loss and transmission phase
of the structure, at 10 GHz, for a number of different tuning states. Description of the tuning
states is provided in Table 3.5.
treated in a future publication. Proof-of-concept experiments were carried out in a WR-90 waveguide environment to demonstrate the tuning performance of these spatial filters and phase shifters.
In all cases, good agreements between the measurements and theory were observed.
69
While this tuning technique is expected to have considerable advantages in terms of linearity
and power handling capability over its electronic tuning counterparts, its tuning speed is quite
slower. This fluidic-tuning mechanism relies on small movements of liquid metal droplets within
the unit cell of a periodic structure. For example, the entire tuning range shown in Fig. 3.8 is
covered by moving the liquid metal droplets by a distance of 3.2 mm from their resting position
(the unit cell size is 6.5 mm × 6.5 mm). Therefore, the tuning speed of this device is determined
by how fast this movement can be accomplished. Galinstan is a low-viscosity liquid metal with a
viscosity approximately twice that of water [121]. The viscosity of the liquid Teflon’s solution is
also similar to water [126]. In a practical application, the liquids are expected to be moved in the
fluidic channels using a micropump. Typical flow rates of miniature micropumps are in the order
of 10 millilitters per second (mL/sec) to 15 mL/sec [127]. The volume of a typical liquid metal
droplet required for this application ranges from 0.5 to 2 micro-litters (typical channel diameter
0.635 mm and liquid metal lengths of 3 mm results in 1µL). Therefore, using such micropumps
the response of this type of an MEFSS could potentially be tuned over its entire tuning range in 33
micro-seconds (µs) to 200 µs.
The control mechanism of large number of unit cells is also an important practical issue that
needs to be considered for lens applications. Details of the implementation strategy for large fluidic
arrays are beyond the scope of this chapter, but nonetheless, we are exploring several different
implementation methods that can address this issue. One of these implementation methods is
based on integrating microfluidic channels in Polydimethylsiloxane (PDMS) and utilizing a single
micropump to move the liquids in each parallel column synchronously. This technique is expected
to enable the controlling of a large number of unit cells over a large FSS aperture. The control
accuracy of the droplet is largely determined by the type of the pump used and the characteristics
of the droplet. Studies have already shown that Galinstan behaves like a true liquid with good
air and liquid interface as shown in [128]. Meanwhile, the accuracy of a typical syringe pump is
better than 1% of the dispense rate and volume [129]. This 1% variation of the droplet location
is not expected to have any meaningful change on the frequency response of the structure. The
control accuracy of a electronic varactor, on the other hand, is mainly determined by the accuracy
70
of the biasing voltage control as well as the repeatability of the varactor C-V characteristics. For
a varactor working in a highly nonlinear region in the C-V chart, even slight change in the biasing
voltage could result in a large variance in the varactor capacitance.
It is also worthwhile to mention that in theory, the proposed tuning technique can work in
the same fashion by using a purely mechanical approach. One does not necessarily require liquid metals to achieve the desired tuning. In principle, any small metallic piece (whether liquid
or solid), which can be mechanically moved within the unit cell of the structure can be used to
achieve similar results. However, a potential advantage of using a liquid-based system over a rigid
mechanical tuning (e.g. a piston driven system) is in the relative ease of pressure transfer in the
liquid system. One can imagine that moving long rigid columns in a large FSS panel is not as
easy as moving a liquid in a channel. Additionally, movement of fluids in curved channels (e.g. in
conformal structure) is easier than moving solid pistons. Overall, in examining the suitability of
this technique for a given application, a wide range of issues including the required power handling
capability, linearity, electromagnetic interference issues, tuning speed, and the complexity of the
required control mechanisms (extensive biasing network in electronic device vs. micropumps in
this technique) must be all be taken into account.
71
Chapter 4
Frequency Selective Surfaces for Pulsed High-Power Microwave
(HPM) Applications
4.1
Introduction
Frequency selective surfaces (FSSs) are used as spatial filters across the entire electromagnetic
spectrum. At microwave and millimeter-wave frequencies, FSSs serve important functions such
as reducing electromagnetic interference and radar cross section of antennas in many military
systems. Similar to conventional analog filters, FSSs can be designed to offer a wide range of
filter responses. FSSs with bandpass spectral responses have found applications in solar power
generation [130], radio astronomy [131], millimeter/sub-millimeter wave transceivers [132]-[133],
energy saving [134] and microwave lenses [46]. FSSs with bandstop response types have been used
in cellular systems [135], millimeter wave imaging [136], indoor wireless propagation [137], and
electromagnetic interference (EMI) reduction [138]. With the widespread use of multi-functional
wireless communication systems, more complicated FSS designs, that are either highly selective
[45] or capable of covering multiple frequency bands[139]-[141], have also been proposed. While
a significant body of research has been devoted to investigating techniques used to optimize the
frequency responses of FSSs, few studies have examined the power handling capability of these
structures in any detail (e.g. see Chapter 10 of [39]). Similarly, very few studies have examined
the development of FSSs that can be used for high-power microwave (HPM) applications [94]. In
such applications, FSSs are located next to sources of high-power RF/microwave radiation. Under
these circumstances, the power handling capability of the FSS becomes an important factor in
determining whether or not it can be used as part of the system.
72
The maximum power level that an FSS can handle depends on the nature of the excitation
signal. One can imagine either a transient or a continuous wave (CW) excitation for an FSS.
The CW power handling capability is of primary concern when the FSS is under a sustained high
average-power illumination. Under these conditions, if the average power level is high enough,
the lossy materials within the FSS will heat up and the structure will eventually melt or burn. The
transient power handling capability, on the other hand, becomes important when short duration
pulses with extremely high peak power levels are applied to the FSS. Similarly to a microwave
filter [95]-[96], the failure mechanism in this mode is the dielectric or air breakdown within the
structure. The breakdown event short circuits the metallic elements of the periodic structure and
renders it useless. The arcing within the structure can also permanently damage the dielectric
material. This breakdown is a major factor that limits the application of FSSs in high-power
microwave systems (e.g. systems used for electronic attack applications). In such systems, FSSs
capable of handling extremely high power levels (e.g. 0.5-1.0 MW/cm2 ) for short duration pulses
are required. Since the duty cycles of such systems are rather low, the thermal issues are expected
to be of secondary concern in these structures. Most conventional FSSs reported in literature,
however, are not capable of handling such high peak power levels. As a result of this, the benefits
offered by FSSs (e.g. electromagnetic interference mitigation or radar cross section reduction) are
not exploited in many HPM systems.
Recently, we reported a class of bandpass miniaturized-element frequency selective surfaces
(MEFSSs) [41]. These MEFSSs are composed of capacitive and inductive surface impedance
sheets cascaded sequentially. Unlike most conventional resonant type FSSs, each impedance sheet
of the MEFSS is entirely composed of non-resonant constituting elements. In [41]-[42], we demonstrated that the separated capacitive and inductive layers of these structures form distributed resonators that result in their bandpass filtering behavior. In this chapter, we exploit this trait to
optimize the power handling capability of these devices1 . In particular, we will demonstrate that
1
The investigations reported in this chapter focus only on transient power handling capability of these devices.
Examination of CW power handling capability of MEFSSs is left for a future study.
73
the separation between the capacitive and inductive layers of these MEFSSs can be exploited to reduce the localized electric field intensity in these structures and thereby, reduce their susceptibility
to breakdown under high-power excitation. In this chapter, first we examine the power handling
capability of an MEFSS of the type reported in [41] and compare it with that of a conventional
Jerusalem cross FSS. Subsequently, we identify the factors that limit the power handling capability of an MEFSS and offer techniques for enhancing it. Using these techniques, we propose an
MEFSS design that is expected to be capable of handling extremely high power levels. We also
examine the power handling capabilities of these devices experimentally by placing unit cells of
these MEFSSs in a waveguide environment and measuring their responses at high-power levels.
A high-power source operating at 9.382 GHz with peak output power level of 25 kW and a pulse
width of 1 µs is used for this purpose. We experimentally demonstrate that the HPM FSSs developed in this work are capable of handling extremely high power levels while the conventional
Jerusalem cross FSS and non-HPM MEFSSs break down at significantly lower power levels.
4.2
Optimization of The Power Handling Capability of MEFSSs
Most FSSs exploit various metallic patterns in multi-layer structures. Due to the presence of
metals, the local electric field intensity within an FSS can be significantly enhanced compared to
the electric field intensity of the incident EM wave. Thus, a relatively low incident EM power level
can cause local electric field intensities within the FSS structure that exceed the breakdown level.
To quantify the level by which the electric field intensity inside the FSS is enhanced compared
to that of the incident EM wave, we define a factor called maximum field enhancement factor
(MFEF). MFEF is defined as the ratio of the maximum electric field intensity inside the FSS to the
electric field intensity of the incident EM wave. MFEF can be used as a means to compare the relative power handling capabilities of different FSS designs to one another. A lower MFEF indicates
a higher breakdown level for the FSS and hence, a higher transient power handling capability2 .
2
Here we assume that the dielectric media surrounding the different FSS designs are the same. This assumption is
necessary since different dielectric materials have different breakdown field levels.
74
Table 4.1 Physical parameters of a 2nd -order MEFSS and a 2nd -order JC slot FSS shown in Fig.
4.1. The dielectric substrates in both FSSs are air. All dimensions are in mm.
MEFSS
D h1
s
w
εr
values
10
0.5
0.145
5
1
JC slot FSS
D
h2
g1
g2
g3
εr
values
10
6
3.5
1
0.145 0.28
For a given FSS, MFEF can be extracted using full-wave EM simulations. In this work, CST Microwave Studio is used to carry out full-wave simulations. In the remainder of this section, we
will first study the transient power handling capability of a second-order bandpass MEFSS of the
type reported in [41] and compare that to a Jerusalem cross second-order bandpass FSS. We will
then examine factors that impact the power handling capability of MEFSSs of the type reported in
[41] and [42]. Finally, we examine a method that can be used to considerably enhance the power
handling capability of a generalized MEFSS.
4.2.1
Comparison of the Transient Power Handling Capabilities of a 2ndOrder MEFSS and a 2nd-Order Jerusalem Cross FSS
In [45], it was demonstrated that MEFSSs have certain advantages over conventional FSSs in
terms of their lower overall profiles and stability of their frequency responses with respect to the
angle and polarization of incidence of the EM wave. However, it is not clear whether or not an
MEFSS has any advantages over a conventional FSS in terms of its transient power handling capability. In this sub-section, we attempt to address this question by examining the power handling
capability of a second-order bandpass MEFSS [41] and a conventional Jerusalem cross FSS having the same frequency response. Figs. 4.1(a) and 4.1(b) show the topologies of the two FSSs
examined here. As shown in Fig. 4.1(a), the 2nd -order MEFSS is composed of three impedance
sheets. The top and bottom capacitive impedance sheets are in the form of two-dimensional (2-D)
periodic arrangements of sub-wavelength rectangular patches, and the center inductive impedance
sheet is a 2-D wire grid with sub-wavelength periodicity. The detailed synthesis procedure of this
75
Dielectric Substrates Capacitive Layer
D
s
D
Sub-wavelength
Capacitive Patches
Inductive Layer
h1
w
D
w
Sub-wavelength
Inductive Grids
D
(a)
Dielectric Spacer
Jerusalem Cross Slot layers
D
h2
g2
D
g1
g1
g3
g1
(b)
Figure 4.1 (a) 3-D topology of a 2nd -order MEFSS composed of capacitive and inductive
impedance layers cascaded sequentially. (b) 3-D topology of a 2nd -order JC slot FSS.
type of 2nd -order MEFSS has already been reported in [41] and will not be repeated here. Fig.
4.1(b) shows the 3-D topology of a 2nd -order Jerusalem cross (JC) slot FSS that is composed of
two JC slot layers separated by a quarter-wavelength spacer. The detailed design instructions for
multi-layer JC slot FSSs can be found in [39] (Chapter 7). In order to make a fair comparison, both
of these two types of FSSs are designed to have a 2nd -order bandpass response centered at 10 GHz
76
C
C
Figure 4.2 Calculated transmission and reflection coefficients for the 2nd -order MEFSS and
2nd -order JC slot FSS using the physical parameters provided in Table 4.1.
with a 20% fractional bandwidth and a butterworth response type. In addition, both FSSs are designed to have the same unit cell size as well as the same minimum feature sizes3 . Table I shows
the physical parameters of the two FSSs. Fig. 4.2 shows the full-wave simulated transmission and
reflection coefficients of the two FSSs.
Based on the design parameters provided in Table 4.1, the power handling capability of the
MEFSS and that of the JC FSS can be compared by examining their MFEF as a function of frequency. MFEF is obtained from full-wave EM simulations, in which one unit cell of the FSS is
placed inside a waveguide with periodic boundary conditions (PBCs). The maximum electric field
value within the FSS unit cell is obtained from the full-wave simulation results and the MFEF value
is calculated by normalizing the maximum electric field intensity to the electric field intensity of
the incident wave. Fig. 4.3 shows the MFEF values calculated for the JC FSS and that of the
MEFSS as a function of frequency. As can be seen, the MFEF of both structures are very close to
each other indicating that this MEFSS does not have a significant advantage over the conventional
3
The minimum feature size in a 2nd -order MEFSS is the width of the capacitive gap, and the minimum feature size
in a 2nd -order JC slot FSS is the narrowest width within a JC slot.
77
100
90
MFEF
80
70
60
50
Jerusalem Cross FSS
40
30
MEFSS
7
8
9
10
11
12
13
Frequency [GHz]
Figure 4.3 MFEF for a 2nd -order MEFSS and a 2nd -order JC slot FSS as a function of frequency.
Each FSS has a bandpass Butterworth frequency response centered at 10 GHz with a fractional
bandwidth of 20%.
JC FSS. Assuming an air breakdown level of 3 × 106 V/m, a rough estimate of the incident power
level that results in breakdown within the FSS may be obtained4 . Based on the extracted MFEF
values shown in Fig. 4.3, the MEFSS (JC FSS) is estimated to be capable of handling a peak power
level of 490 W/cm2 (425 W/cm2 ). Thus, when the response type, minimum feature size, and the
unit cell size of the two FSSs are similar, an MEFSS does not show any significant advantage over
a conventional FSS in terms of its power handling capability. The maximum electric field in the
MEFSS unit cell occurs at the corners of the capacitive patches. For the JC FSS, the maximum
electric field occurs at the center of the slot. Under high peak power excitation levels, these high
intensity field locations are expected to be the locations where field breakdown occurs. The results
presented in this section seem to demonstrate that an MEFSS of the type shown in Fig. 4.1(a) does
not have an inherent advantage over a conventional FSS in terms of its power handling capability.
However, as is shown later in this chapter, the fact that the capacitive and inductive layers of an
4
Since the exact field levels that cause breakdown depend on the microscopic features of the surface as well as the
environmental conditions, this estimate is only a rough approximation and is not expected to be very accurate.
78
(a)
(c)
(b)
(d)
Figure 4.4 Frequency-dependent MFEF values for MEFSSs with different fractional bandwidths
and response types. (a) 3rd -order Butterworth response, (b) 3rd -order Chebyshev (0.1 dB ripple)
response, (c) 5th -order Butterworth response, and (d) 5th -order Chebyshev response (0.1 dB
ripple). All frequency responses are centered at 10 GHz and all MEFSSs are designed to have the
same unit cell sizes of 5.8 mm ×5.8 mm.
MEFSS are separated from each other provides a degree of flexibility in optimizing its power handling capability, which is not available in conventional FSSs. This is exploited to the maximum
extent in this work, as is demonstrated in Sections 4.2.3 and 4.3.
4.2.2
Analysis of the Transient Power Handling Capability of MEFSSs
In this section, we study the factors that can impact the power handling capability of an MEFSS.
Specifically, we take into account the effect of the MEFSS’s response type, fractional bandwidth,
order of the response, and the unit cell size on its power handling capability. To reasonably assess
the effect of each design parameter on the power handling capability, a systematic investigation
is carried out by varying the design parameter of interest, while fixing all the other parameters.
The design procedure presented in [42] is used to design different MEFSSs with desired frequency
responses. In all of the designs, dielectric substrates with εr = 3.4 and µr = 1 (RO4003 from
Rogers Corp.) are used to separate the different capacitive and inductive layers from one another.
79
First, we examine the effect of the fractional bandwidth on the power handling capability of
an MEFSS. For this purpose, MEFSSs with two different response types and two different orders
are investigated. These include MEFSSs having a 3rd -order Butterworth, a 3rd -order Chebyshev
(0.1 dB ripple), a 5th -order Butterworth, and a 5th -order Chebyshev (0.1 dB ripple) response. The
3rd -order (5th -order) MEFSSs are composed of three (five) capacitive layers and two (four) inductive layers separated from each other by four (eight) dielectric substrates. For each of these four
response types, all MEFSSs are designed to have a center frequency of 10 GHz and a unit cell size
of 5.8 mm ×5.8 mm. The MFEF for each design is obtained following the same procedure described in Section 6.2.1. The physical and geometrical parameters of all these designs are obtained
using the detailed synthesis procedure provided in [42]. For brevity these values are not reported
here. Fig. 7 shows the MFEF of the aforementioned MEFSS prototypes as a function of frequency
for different fractional bandwidths. Observe that, irrespective of the MEFSS response type and
order, as the fractional bandwidth of the structure decreases, its MFEF increases. This is due to
the fact that achieving a small fractional bandwidth requires using coupled resonators having high
loaded quality factors [42]. As shown in [42], achieving a higher quality factor requires employing a larger shunt capacitance value for each capacitive layer of the MEFSS. This is achieved by
reducing the gap size between two adjacent capacitive patches, which will naturally increase the
field intensity in the capacitive layers. The results shown in Fig. 4.4 demonstrate that wideband
MEFSSs are expected to have a higher transient power handling capability.
We also investigated the effect of unit cell size on the power handling capability of an MEFSS.
For this study, similar to the previous case, MEFSSs with two response types and two different
orders are used. For each MEFSS, different unit cell sizes are used to obtain the same frequency
response with a center frequency of 10 GHz and a fractional bandwidth of 20%. The MFEF for
each design is calculated and the results are presented in Fig. 4.5. As can be seen, in all these
MEFSSs, the MFEF value decreases as the unit cell size increases. This is attributed to the fact
that as unit cell sizes increase, the gaps between two adjacent capacitive patches must be increased
to maintain the desired capacitance. The results shown in Fig. 4.5 demonstrate that, for a given
response type, increasing the unit cell size is expected to improve the power handling capability of
80
(a)
(b)
(c)
(d)
Figure 4.5 Frequency-dependent MFEF values for MEFSSs with different unit cell sizes. (a)
3 -order Butterworth response, (b) 3rd -order Chebyshev response (0.1 dB ripple), (c) 5th -order
Butterworth response, (d) 5th -order Chebyshev response (0.1 dB ripple). All frequency responses
are centered at 10 GHz with 20% fractional bandwidth.
rd
Table 4.2 Different implementations of wire grid patterns in the MEFSS shown in Fig. 4.6(a) for
the same desired frequency response described in Section 4.2.3. All dimensions are in mm.
h = 0.38 mm, h1 = 0.47 mm. The high-εr layers have a dielectric constant of εr = 85 and the
dielectric spacers have a dielectric constant of εr = 3.4.
A
B
C
D
E
D
0.50
1.00
2.00
3.00
4.00
w
0.08
0.30
0.86
1.50
2.24
w/D
0.16
0.30
0.43
0.50
0.56
F
G
H
I
D
5.00
6.00
8.00 10.00
w
3.00
3.78
5.52
7.30
w/D
0.60
0.63
0.69
0.73
the MEFSS. The results shown in Fig. 4.4 and Fig. 4.5 do not demonstrate a significant difference
between the power handling capabilities of MEFSSs with Butterworth and Chebyshev responses.
81
h <<λ
D
D
w
h1 <<λ
RO4003
Inductive
Grid
Inductive Layer
High-εr Substrate Layer
(a)
Lh
Z0
Ch
(b)
Z1
Z1
L1
Lh
Ch
Z0
h1
h1
High-εr Substrate Layer
(c)
Figure 4.6 (a) 3-D topology of a 2nd -order MEFSS using thin high-εr substrate layers rather than
capacitive layers composed of rectangular patches. (b) Top view of one unit cell of the inductive
layer. (c) Equivalent circuit model for the 2nd -order MEFSS using thin high-εr substrate layers.
Moreover, the aforementioned discussions demonstrate that the power handling capability of an
MEFSS of the type reported in [42] is primarily limited by the gaps between the adjacent capacitive
patches in the structure’s capacitive impedance layers. Thus, the power handling capability of the
structure can be enhanced significantly if the sizes of the capacitive patches are reduced (for a fixed
unit cell size) or if the metallic capacitive patches are removed altogether.
82
Figure 4.7 Transmission coefficients of the MEFSS shown in Fig. 4.6(a) for different wire grid
dimensions, which results in the same effective inductance. The results for cases A, C, E, G, and
H listed in Table 4.2 are shown.
4.2.3
MEFSSs Optimized for High Transient Power Operation
In the previous section, we demonstrated that the main factor limiting the power handling capability of an MEFSS is the electric field enhancement factor within its metallic capacitive layers.
This problem can be circumvented by eliminating the metallic patches within an MEFSS and substituting each capacitive patch layer with a thin dielectric substrate with a high dielectric constant
value. A thin dielectric substrate with a thickness of h << λ and infinite lateral dimensions can
be modeled with a series inductor and a shunt capacitor with inductance and capacitance values
of5 µ0 h and ε0 εr h. In the special case where the dielectric constant of this substrate is high, the
effect of the shunt capacitance will be dominant and the structure effectively acts as a capacitive
impedance sheet. Therefore, a thin high-εr substrate layer can essentially be used as a capacitive
surface impedance sheet in an MEFSS.
In general, the substitution of the capacitive layers with thin high-εr layers can be applied to
any MEFSS described in [42]. In this work, we apply this to a 2nd -order MEFSS as shown in Fig.
5
Assuming that the dielectric substrate is non magnetic.
83
4.6(a), where two thin high-εr substrates are used to implement the capacitive impedance sheets of
a second-order MEFSS. The inductive impedance sheet is implemented using the same wire grid
described before [42] and the capacitive and inductive impedance sheets are separated from each
other by RO4003 dielectric substrates as before. Fig. 4.6(c) shows the corresponding equivalent
circuit model of this structure, which is valid for a normally incident wave. In this circuit model,
the shunt capacitance Ch and series inductance Lh are contributed from the two thin high-εr layers.
Given the condition that the thickness of each high-εr layer is very small, the series inductance Lh
can be neglected in the design procedure. In the MEFSS shown in Fig. 4.6, the only metallic layer
used is the inductive impedance sheets. Full-wave EM simulation results reveal that the maximum
electric field intensity within a unit cell of the MEFSS shown in Fig. 4.6(a) happens in the inductive
layer. Therefore, the power handling capability of this structure can be enhanced by optimizing the
topology of this inductive layer. To accomplish this, we examined the effect of the inductive wire
grid on the MFEF of the MEFSS shown in Fig. 4.6(a). As can be seen from the top view of one
unit cell of the inductive layer shown in Fig. 4.6(b), the wire grid pattern is determined by both
the periodicity, D, and the width of the inductive strip, w. For a fixed effective inductance value
L, different values of w and D can be chosen to achieve the same desired inductance value. To
maintain the same inductance value, when D is reduced, the ratio of strip width to the periodicity,
w/D, must be reduced as well.
To examine the effect of the inductive wire grid on the power handling capability of the MEFSS
shown in Fig. 4.6(a), an MEFSS with a 2nd -order maximally flat bandpass response centered at
10 GHz with 20% fractional bandwidth is examined. Different wire grid patterns are implemented
while maintaining the desired frequency response of the MEFSS. The physical dimensions of these
different wire grids are given in Table 4.2. The frequency responses of MEFSSs of the type shown
in Fig. 4.6(a), which use these inductive wire grids, are shown in Fig. 4.7. For all these implementations, the thin high-εr substrates have a thickness of h1 = 0.381 mm and a dielectric constant
of 85 (K85 ceramic material from TCI Ceramics, Inc) while the RO4003 substrates used have a
thickness of h2 = 0.47 mm. Fig. 4.7 shows the transmission coefficients of the MEFSSs shown
in Fig. 4.6(a) implemented with different wire grid patterns (cases A, C, E, G, and H in Table
84
Periodic Boundary
Conditions
Port 2
Port 1
Port 2
Leq
Port 1
Unit Cell of Wire Grid
Hy
kz
Ex
PBC
(b)
(a)
(c)
Figure 4.8 (a) A unit cell of the wire grid is placed inside a waveguide with PBC conditions to
compute its frequency response for different grid parameters that are listed in Table 4.2. (b)
Equivalent circuit model of the wire grid shown in part (a). (c) The transmission coefficients of
different wire grids whose dimensions are listed in Table 4.2. The transmission coefficient of the
ideal inductor needed for this MEFSS is also presented for comparison. The value of the desired
indictor is calculated using the procedure described in [42].
4.2). Clearly seen, when the periodicity of the wire grid is relatively large (cases G and H), an
unwanted passband located close to the desired passband and slightly above it appears. This undesired passband is brought by the aperture resonances of the wire grids with larger periods. For the
MEFSS shown in Fig. 4.6(a) implemented with the wire grids with a smaller periods (cases A, C,
85
Thin High-εr
Layer
Wire Grid
Pattern
z
x
y
Ex=1000 V/m
RO4003 Substrate
2000
x
1600
y
1200
800
400
0
A: w/D=0.16 (D=0.5 mm)
B: w/D=0.3 (D=1 mm)
C: w/D=0.43 (D=2 mm)
5000
4000
3000
2000
1000
0
D: w/D=0.5 (D=3 mm)
E: w/D=0.56 (D=4 mm)
F: w/D=0.6 (D=5 mm)
10000
8000
6000
4000
2000
0
G: w/D=0.63 (D=6 mm)
H: w/D=0.69 (D=8 mm)
I: w/D=0.73 (D=10 mm)
Figure 4.9 Electric field distribution in the inductive layer MEFSSs optimized for HPM operation
using different wire grid patterns with dimensions listed in Table 4.2. All MEFSSs have
essentially the same 2nd -order bandpass response centered at 10 GHz with a fractional bandwidth
of 20% as shown in Fig. 4.7.
86
Figure 4.10 MFEF values of the MEFSS shown in Fig. 4.6(a) implemented with wire grid
patterns A, C, E, G, and H listed in Table 4.2. All MEFSSs have the same 2nd -order bandpass
Butterworth response centered at 10 GHz with 20% fractional bandwidth.
and E), this unwanted aperture resonance will appear somewhere far away from the desired frequency band and it can be neglected. Despite the effect of the periodicity on the undesired aperture
resonance, all the cases listed in Table 4.2 are still capable of providing the same desired filtering
response within the frequency band of interest as can be observed in Fig. 4.7. To achieve this, the
different wire grid patterns listed in Table 4.2 must provide the same effective inductance. This
is demonstrated using the setup shown in Fig. 4.8(a), where a unit cell of the wire grid is placed
inside a waveguide with PBC boundary conditions and the frequency responses of wire grids with
the dimensions listed in Table 4.2 are computed. Given the desired frequency response, the required inductance value of L1 shown in Fig. 4.6(c) is also calculated from the synthesis procedure
provided in [41]. The frequency response of this inductor is obtained using the circuit set up in Fig.
4.8(b) and is presented in Fig. 4.8(c). Fig. 4.8(c) also shows the simulated responses of the grids
whose parameters are given in Table 4.2. Observe that the different wire grids have essentially the
same frequency response and they are all capable of providing the inductance value, L1 , calculated
87
from the analytical synthesis procedure described in [41]. Notice that the unwanted aperture resonances seen in Fig. 4.7 are not observed in the responses shown in Fig. 4.8(c), since the inductors
in the setup shown in Fig. 4.8(a) are not surrounded with high-εr substrates. Consequently, the
aperture resonances occur at a higher frequency and are not observed in the results shown in Fig.
4.8(c).
Studying the electric field distributions within the inductive layers of MEFSSs whose responses
are shown in Fig. 4.7 reveals an interesting trend. Assuming a peak incident electric field of
1000 V/m, the electric field intensity within one unit cell of these MEFSSs are calculated using
full-wave EM simulations in CST Microwave Studio. Fig. 4.9 shows the magnitude of the electric
field distribution within the inductive layer of these MEFSSs for different inductive grids whose
parameters are listed in Table 4.2. As can be observed from Fig. 4.9(a) to 4.9(i), the peak electric
field intensity is reduced as the unit cell size, D, decreases. This is due to the fact that a smaller
w/D ratio is required for the wire grid pattern with a smaller periodicity to maintain the same
desired surface inductance. For any wire grid pattern, the percentage of the unit cell covered by
metal determines the maximum electrical field enhancement within the unit cell. The smaller this
percentage is, the lower the maximum electric field intensity will be. The MFEF values for the
MEFSSs shown in Fig. 4.6(a) implemented with wire grid patterns A, C, E, G, and H listed in
Table 4.2 are obtained and shown in Fig. 4.10. As expected, the wire grid with a smaller period
and correspondingly smaller w/D ratio has a desirably smaller MFEF. For the wire grid pattern A
(w/D = 0.16, D = 0.5 mm), the MFEF value is approximately 1 over a wide frequency range.
In this case, the local field density within the FSS is not enhanced significantly compared to that
of the incident EM wave. Additionally, since the dielectric strength of the dielectric materials
surrounding the inductive layers are higher than that of air, this type of an MEFSS (with MFEF=1)
is expected to be capable of handling extremely high transient power levels. For such high-power
microwave (HPM) applications, the periodicity of the wire grids in an MEFSS with thin highεr layers should be as small as possible. Our full-wave EM simulation results indicate that this
conclusion can be extended to inductive wire grids of various other shapes as well (e.g. with
circular apertures). The MFEF shown in Fig. 4.10 is also sensitive to the oblique incident angles
88
and the polarization of the incident wave. For TE incidence, the MFEF decreases as the oblique
incident angle increases. For TM incidence, the MFEF increases as the oblique incident angle
increases.
4.3
Experimental Verification and HPM Measurements
E-H Tuner
Reflection Detector Transmission
Detector
DUT
Magnetron
Figure 4.11 Experimental setup for measuring the transient power handling capability of an FSS
in a waveguide environment using a high-power magnetron. The magnetron generates a
single-frequency pulse at 9.382 GHz with a peak power of 25 kW and a pulse width of 1µs.
To experimentally verify the results presented in the previous section, we conducted a series
of high power experiments on the FSS prototypes discussed in the previous section. In doing this,
we used a high power magnetron source operating at 9.382 GHz with a peak power of 25 kW and
a pulse width of 1µs. To ensure that the FSS prototypes are excited with the maximum power
density levels possible, the tests were conducted within a waveguide environment. A unit cell of
each FSS prototype was placed inside a WR-90 waveguide and its responses both at high and low
power levels were characterized. Fig. 4.11 shows the setup used for these experiments. The magnetron generates a single-frequency pulse at 9.382 GHz with a peak power of 25 kW and a pulse
width of 1µs. The device-under-test (DUT) in Fig. 4.11 is the waveguide version of different FSSs
with different expected power handling capabilities. The actual power level delivered to the DUT
89
8.80 mm
9.06 mm
0.37 mm
0.37 mm
0.12 mm
0.37 mm
13.26 mm
1.00 mm
1.00 mm
(a) Case A
high εr substrate (εr=85.4)
(b) Case B
4.77 mm
0.38 mm
6.20 mm
0.37 mm
1.58 mm
high εr substrate (εr=85.4)
1.58 mm
0.38 mm
(c) Case C
0.54 mm
0.54 mm
(d) Case D
0.78 mm
0.15 mm
1.13 mm
1.24 mm
0.96 mm
1 mm
1.52 mm
0.38 mm
0.54 mm
0.54 mm
0.38 mm
Circular Shape
Wire Grids
Rectangular
Shape Wire Grids
(e) Case E
Figure 4.12 Waveguide prototypes equivalent to one unit cell of different types of FSSs with
different expected transient power handling capabilities. (a) Case A: 2nd -order MEFSS with 10%
fractional bandwidth. (b) Case B: 2nd -order JC slot FSS with 20% fractional bandwidth. (c) Case
C: 2nd -order MEFSS with 20% fractional bandwidth. (d) Case D: 2nd -order MEFSS optimized
for HPM operation with 20% fractional bandwidth implemented with thin high-εr substrate and
rectangular shape inductive wire grids. (e) Case E: 2nd -order MEFSS optimized for HPM
operation with 20% fractional bandwidth implemented with thin high-εr substrate and circular
shape inductive wire grids. All waveguide prototypes are designed to have a Butterworth
bandpass response centered at 9.382 GHz. WR-90 waveguide shims with inner dimensions of
0.9” × 0.4” are used for all the prototypes.
can be adjusted by using an E-H tuner. Directional couplers are used to sample the transmitted
and reflected pulses. Crystal detectors connected to the end of each directional coupler detect the
envelope of the reflected and transmitted pulses and are connected to a digitizing oscilloscope that
records the temporal variations of the transmitted and reflected waves. The maximum transient
peak power the DUT can handle is experimentally examined by adjusting the incident power level
through the E-H tuner and monitoring the transmitted and reflected pulses recorded by the crystal
detectors at the same time. When the incident power level is large enough, the maximum local
90
(a)
(b)
(c)
(d)
(e)
Figure 4.13 Measured and calculated transmission coefficients of different waveguide FSS
prototypes, cases A-E, shown in Fig. 4.12.
field density within the DUT exceeds the breakdown level of air and the device fails. This breakdown event manifests itself in the form of a significant increase in the reflected power level and
a significant decrease in the transmitted power level (i.e., the FSS is short circuited). All of the
measurements are conducted at room temperature and atmospheric pressure in the presence of air.
Fig. 4.12 shows the waveguide equivalent versions of five different FSSs similar to the ones
described in Section 6.2. These FSS prototypes have different expected power handling capabilities. All prototypes are designed to operate at X-band in a standard WR-90 waveguide with inner
dimensions of 0.9” × 0.4”. Waveguide irises that represent the capacitive and inductive layers as
well as the JC slot layer are fabricated out of 0.005”-thick stainless steel sheets using chemical
etching. WR-90 waveguide shims with the rectangular opening hole of 0.9” × 0.4” are machined
out of thick brass sheets using computer controlled milling machine. In all cases of Fig. 4.12, the
waveguide shims with different thicknesses are used as spacers between capacitive and inductive
layers equivalent to the dielectric substrates in an FSS. In particular, the WR-90 waveguide shims
with the same thickness as the high-εr substrates (K85 ceramic material from TCI Ceramics Inc.)
91
are also used in the structures shown in Fig. 4.12(d) and 4.12(e) to accommodate the thin high-εr
dielectric blocks. Inductive wire grids with both rectangular and ellipsoidal holes arranged in a
2-D periodic structure with small periods are used in structures shown in Fig. 4.12(d) and 4.12(e)
respectively to implement the inductive layer of the MEFSS. To make a fair comparison between
the power handling capability of one case with another, all FSS prototypes are designed to have a
2nd -order Butterworth bandpass response centered at 9.382 GHz. In addition, the structures shown
in Figs. 4.12(b)-4.12(e) are designed to have a fractional bandwidth of 20% and the one shown in
Fig. 4.12(a) is designed to have a fractional bandwidth of 10%. The frequency responses of these
FSS prototypes are measured at low power levels using a vector network analyzer and the results
are presented in Fig. 4.13 along with the simulation results. A good agreement between measurement and simulation results is obtained for all the cases, which confirms the desired frequency
responses of the devices. The unpredicted measured transmission nulls in Fig. 4.13(d)-4.13(e)
are mainly due to the measurement errors introduced by the misalignment between the adjacent
waveguide assemblies.
Similar to the discussions in Section 6.2, we first examined the MFEFs of all these devices
using full-wave simulation. The extracted MFEF values for all the structures shown in Fig. 4.12
are shown in Fig. 4.14. Several similarities can be found between the results presented in Fig.
4.14 and those presented in Section 6.2. First, for the same minimum feature size6 , the power
handling capability of an MEFSS exploiting metallic capacitive sheets is expected to be very close
to a conventional JC FSS (compare cases B and C in Fig.4.14). This is in accordance with the
conclusion made in Section 6.2.1. Secondly, given the same center frequency, order of the response
and response type, MFEF value of case C is smaller than that in case A due to a larger fractional
bandwidth. As seen from Fig. 4.12(a) and 4.12(c), the 20% fractional bandwidth in case C leads to
a capacitive gap width of 0.37 mm, which is considerably larger than the capacitive gap width of
0.12 mm in case A. This larger capacitive gap will naturally enhance the structure’s power handling
capability. Finally, similar to the conclusions made in Section 4.2.3, both cases D and E have an
6
The minimum feature sizes for case B and case C are the Jerusalem slot width and the capacitive gap width
respectively. Both of them are 0.37 mm as indicated in Fig. 4.12
92
Figure 4.14 Full-wave simulated MFEFs for all the waveguide prototypes, cases A-E, shown in
Fig. 4.12. MFEF values are extracted by normalizing the maximum electric field intensity within
the waveguide version of the FSS to the maximum electric field intensity of the dominant T E10
mode.
MFEF value close to 1 as shown in Fig. 4.14 (notice that the MFEF values for cases D and E
should be read from the right axis in Fig. 4.14). This indicates that the structures shown in Fig.
4.12(d) and 4.12(e) are expected to have an extremely high transient power handling capability.
Additionally, both cases D and E have almost identical MFEF values over the entire frequency
band of interest. This indicates that inductive impedance sheets with rectangular, ellipsoidal, or
circular aperture shapes may all be used in the design of MEFSSs for HPM applications.
Using the setup shown in Fig. 4.11, we measured the time domain transmission and reflection coefficients of these FSSs at 9.382 GHz for different incident power densities. To obtain the
time domain transmission coefficient, the transmitted pulse without the DUT is first measured and
recorded as the baseline. This baseline corresponds to the total transmission case where the entire
incident pulse is transmitted. Then, the transmitted pulse in the presence of the FSS is measured.
The time domain transmission coefficient is then calculated by normalizing the latter recorded
value to the total transmission baseline value over the time range of interest. To obtain the time
domain reflection coefficient, the reflected pulse is first measured and recorded as a baseline when
93
a conducting sheet is used as the DUT. This recorded baseline corresponds to the total reflection
case where the conducting sheet acts as a PEC wall blocking the transmission in the waveguide
completely. Then, the reflected pulse is measured and recorded by using the waveguide prototype
as the DUT. The time domain reflection coefficient is obtained by normalizing the latter recorded
value to the total reflection baseline over the time range of interest. The time domain measured
transmission and reflection coefficients are particularly helpful in characterizing the time domain
behavior of an FSS before and after breakdown. It is expected that for any case in Fig. 4.12, when
no breakdown happens, the majority of the incident pulse will be transmitted through the DUT
and received by the transmission crystal detector. Therefore, the DUT is expected to have a high
time domain transmission coefficient and a low time domain reflection coefficient before breakdown. On the other hand, when breakdown happens inside the DUT, the majority of the incident
pulse is expected to be reflected back and received by the reflection crystal detector. Consequently,
the DUT is expected to have a low time domain transmission coefficient and a high time domain
reflection coefficient when breakdown happens.
Using the procedure described above, the time domain transmission and reflection coefficients
for each case in Fig. 4.12 is experimentally extracted under different incident power levels. Fig.
4.15(a) and 4.15(b) demonstrate the time domain transmission and reflection coefficients of case
A under the incident peak power of 1.17 kW and 1.20 kW. Clearly observed, Fig. 4.15(a) corresponds to the situation when there is no breakdown, as can be verified by a high transmission
coefficient and a low reflection coefficient. Fig. 4.15(b), however, demonstrates the situation when
the structure breaks down. Shortly after the structure is illuminated with the HPM pulse, the transmission coefficient drops to a low value and the reflection coefficient increases indicating that a
short circuit is created within the FSS. Therefore, the maximum peak power that this prototype can
handle is roughly 1.20 kW. Similarly, Figs. 4.15(c) and 4.15(d) show the time domain transmission
and reflection coefficients of case B before and after the breakdown. The maximum peak power
that this structure can handle is around 3.43 kW. Fig. 4.15(e) and 4.15(f) show the time domain
transmission and reflection coefficients of case C before and after the breakdown, with the approximate break down power level of around 5.57 kW. Note from Figs. 4.15(b), 4.15(d) and 4.15(f),
94
the breakdown always happens after a very short period of transmission. The time required for the
breakdown to occur is mainly a function of two factors. These include the time that it takes for an
initial free electron to appear in air to seed the avalanche and the formation time of the avalanche.
The breakdown formation time has been extensively studied in [143]-[145] and its investigation
is beyond the scope of this chapter. Fig. 4.15(g) and 4.15(h) show the time domain transmission
and reflection coefficients of cases D and E under the incident peak power of 25 kW, which is the
maximum output power the magnetron can offer. As seen from Figs. 4.15(g) and 4.15(h), in both
cases D and E, a high time domain transmission coefficient is obtained, which further indicates no
breakdown event happens in both cases under 25 kW peak power incidence. The magnitude of the
transmission coefficient measured using the time-domain system (|T |2 ≈ 0.8) is also consistent
with the measured insertion losses of these two devices (∼ 1 dB) as seen from Fig. 4.13(d) and
Fig. 4.13(e). Since the maximum field enhancement factors in both of these devices is approximately 1 over their entire frequency range of operation, they are expected to be capable of handling
considerably higher power levels without breakdown. However, our current experimental facilities
limit us to measurements at a maximum level of 25 kW.
As observed from Fig. 4.15, FSS prototypes shown in Fig. 4.12(d) and 4.12(e) have the
maximum transient power handling capability, which is expected to be well over 25 kW. This is
followed by the structure shown in Fig. 4.12(c) with 5.57 kW and that shown in Fig. 4.12(b)
with 3.43 kW peak power handling capability. At 1.2 kW, the structure shown in Fig. 4.12(a)
has the lowest peak power handling capability. The maximum transient power handling capability
of these structures can also be predicted by using the MFEF value for each case provided in Fig.
4.14. This is done based on the assumption that the dielectric strength of air is 3 × 106 V/m
and the results are presented in Table 4.3 along with the measured values. It is observed that the
predicted Pbreakdown differs from the measured value. In fact, the predicted values are calculated
to be approximately 2-3 times smaller than the actual values. This discrepancy is attributed to
the difficulties involved in predicting breakdown events. The field levels at which breakdown
occurs depend on a number of parameters including the temperature, air pressure, atmospheric
conditions, humidity as well as the microscopic features of the surfaces under considerations.
95
Table 4.3 Comparison between the predicted breakdown power level and the measured ones for
FSSs shown in Fig. 4.12. The predicted values are obtained using the MFEF values presented in
Fig. 4.14 assuming that air breakdown occurs for an electric field intensity of 3 × 106 V/m. The
measured breakdown levels are obtained from the high-power measurements shown in Fig. 4.15.
Power level units are in kW.
Case
A
B
C
D
E
MFEF
57.78
27.05 20.45
1.02
1.01
Predicted
0.40
1.84
3.22
1285 1343
Measured
1.2
3.43
5.57
>25
>25
Nevertheless, the approximate calculations carried out using the concept of MFEF demonstrate
that the measurements follow the same trend as the simulations. In other words, a structure that
has a lower MFEF value will have a higher power handling capability. Although it seems difficult
to use the full-wave extracted MFEF values to predict the exact breakdown level, MFEF can be
used as an effective means for comparing the relative power handling capabilities of different
structures under the same operational conditions and optimize the power handling capability of a
given FSS.
4.4
Conclusion
In this chapter, a detailed analysis of the transient power handling capability of different types
of miniaturized element frequency selective surfaces are provided and compared with a conventional Jerusalem cross FSS. Maximum field enhancement factor is used throughout this chapter as
a quantitative means to compare the transient power handling capability of one type of FSS with
another. It was demonstrated that the distributed nature of the capacitive and inductive impedance
sheets of an MEFSS is inherently advantageous when it comes to optimizing the structure’s power
handling capability. In an MEFSS which exploits 2D periodic arrangements of metallic patches
to implement the capacitive impedance sheets, the gaps between adjacent capacitive patches are
the main factor that limits the transient power handling capability of the device. We demonstrated
96
that this problem can be circumvented by using high-εr dielectric substrates to replace the capacitive patches in an MEFSS. Additionally, it was found out that in such a structure the power
handling capability increases as the period of the inductive wire grid layer is reduced as much as
possible. A conventional FSS and four different MEFSS prototypes were also fabricated and their
responses were characterized under low and high power conditions. While predicting the exact
transient power handling capability of an FSS is challenging, we demonstrated that by minimizing
the MFEF of a periodic structure, its power handling capability can be enhanced considerably.
This was experimentally demonstrated using high-power measurements reported in this chapter.
Using these guidelines, two HPM FSS prototypes were designed and experimentally characterized
at a power level of 25 kW within a waveguide environment. Despite using metallic structures with
fine features, the MEFSSs did not break down as expected. Theoretical studies point out to the
possibility that these MEFSSs are capable of handling transient power levels that can be as high as
1.0 MW/cm2 , although this remains to be experimentally characterized. It is finally worthwhile to
mention that for freespace FSS applications where large panels of high-εr ceramic substrates are
not readily available, commercially available microwave substrates with a relatively high dielectric constant (≥ 10) can also be used as an alternative way at the cost of an increased substrate
thickness.
97
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 4.15 Time domain transmission and reflection coefficients for the waveguide prototypes,
cases A-E, shown in Fig. 4.12 under different incident peak power levels. (a) Case A under
1.17 kW peak power level. (b) Case A under 1.20 kW power level. (c) Case B under 3.37 kW
power level. (d) Case B under 3.43 kW power level. (e) Case C under 5.43 kW power level. (f)
Case C under 5.57 kW power level. (g) Case D under 25 kW power level. (h) Case E under
25 kW power level. The magnetron generates a single-frequency pulse at 9.382 GHz with a peak
power of 25 kW and a pulse width of 1µs. The different incident power levels are achieved by
adjusting the E-H tuner shown in Fig. 4.11. Each measurements has been repeated many times
over the span of a few days. All measurements were found to be highly reproducible.
98
Chapter 5
Broadband True-Time-Delay Microwave Lenses Based on Miniaturized Element Frequency Selective Surfaces
5.1
Introduction
Microwave and millimeter-wave lenses have been widely used in applications such as imaging
[147], radar systems [148], and high-gain phased arrays [149]. In many collimating systems, microwave lenses are designed to transform the spherical wave fronts of an incident wave emanating
from the focal point of the lens to a plane wave front at the output aperture. When used in broadband, pulsed applications, the lens must preserve the temporal characteristics of the transmitted
pulse and pass it through with minimal distortion. In such applications, microwave lenses that act
in a true-time delay fashion and satisfy Fermat’s principle1 at every point on the aperture are highly
desired.
Over the past several decades, various types of microwave lenses and collimating structures
have been reported in the literature. Dielectric lenses similar to the one shown in Fig. 5.1(a) are
among the most well-known types of microwave lenses [64]-[65]. This type of lens is indeed designed in a true-time-delay fashion and satisfies Fermat’s principle over a broad frequency band
provided that the dielectric constant of the material constituting the lens does not change as a
function of frequency. However, dielectric lenses suffer from the internal reflection losses and are
typically heavy, bulky, and expensive to manufacture, especially at low microwave frequencies.
Planar microwave lenses address these shortcomings of dielectric lenses and have widely been
used as the primary method of designing microwave lenses at low RF/microwave frequencies [66],
1
the principle of least time, which states that the path taken between two points by a ray of light is the path that can
be traversed in the least time
99
[67]-[69], [70]-[72], [73]. Planar microwave lenses are typically composed of an array of transmitting and receiving antennas connected together using either a phase shifting or a time delay
mechanism. A number of different techniques have been used to achieve the desired phase shift
or time delay between the transmitting and receiving antennas. These include using coupled apertures [73], resonant slots [66], filters [74], or transmission lines with variable lengths [75] between
the transmitting and receiving antennas. The time delays between the transmitting and receiving
antenna elements can also be tuned by loading the true-time-delay transmission lines with varactor
diodes [76]-[77] or micro electro-mechanical system (MEMS) switches [78]. However, the interelement spacings between the antennas used in these planar lenses are relatively large, since the
transmitting and receiving antenna elements have dimensions in the order of a half-wavelength.
Such a large element spacing generally deteriorates the lens’ scanning performance.
More recently, with the progress in the design and synthesis of artificially engineered materials,
the controllable material properties of metamaterials have been exploited to design various types
of microwave lenses [79]-[82]. In [81], a bi-planar gradient metamaterial lens with an index refraction ranging from −2.67 to −0.97 was designed at 10.3 GHz. Microwave lenses designed based
on transformation optics concepts have also been examined [82]. Transmission line type metamaterials such as negative-refractive-index transmission lines [83] have also been used to design
three-dimensional microwave lenses operating at microwave frequencies. Despite the design flexibility offered by the use of metamaterials, most metamaterial-based microwave lenses use high-Q
resonant constituting elements and hence, they tend to be narrowband and dispersive [84]. In addition to being narrowband, many metamaterial lenses that exploit the negative refraction index
concept tend to be highly dispersive even for narrowband modulated signals. In such lenses, even
a narrowband modulated signal can experience a significant temporal distortion when transmitted
through the lens (e.g., see discussions in [84] regarding time-domain behavior of a double-negative
lens). Frequency selective surfaces (FSSs) have also been used to design planar microwave lenses
[85]-[86]. In FSS-based microwave lenses, each pixel of the lens acts as a spatial-phase-shifter
(SPS) that provides a desired phase shift at the frequency of interest. In such lenses, the spatial
phase shifters of the lens must generally provide phase shifts in the range of 0◦ − 360◦ . Since a
100
simple first-order FSS does not provide such large phase shift values, higher-order FSSs are generally used. Recently, a planar microwave lens that uses the unit cells of miniaturized element
frequency selective surfaces (MEFSSs) as its spatial phase shifters was reported in [46]. It was
demonstrated that using MEFSSs, low-profile, broadband planar microwave lenses could be designed. While this lens demonstrates a wideband response, it suffers from significant chromatic
aberrations within this frequency band [46]. Thus, such a lens is not suitable for broadband pulsed
applications.
In this chapter, we present a method for designing MEFSS-based true-time-delay equivalent
microwave lenses. The proposed lenses are composed of a number of time delay units (TDUs)
spread over a planar aperture. Each pixel is the unit cell of an appropriately-designed MEFSS.
The proposed TTD lenses in this chapter, although appear similar to the non-TTD lenses in [46]
at the first glance, behave fundamentally differently. The impedance matched pixel in the TTD
lens provides a fixed time delay over the desired frequency band of operation of the lens, while
the impedance matched pixel in the non-TTD lens [46] can only provide a certain phase shift at
the desired single frequency point. Due to the low profile and miniaturized pixel dimensions, the
proposed TTD lens is capable of providing an excellent scanning performance with a field of view
of ±60◦ .
In what follows, we will first present the detailed design procedure for the proposed TTD microwave lenses. Using this design process, we have developed two TTD lens prototypes with
different focal length to aperture dimension, f /D, ratios. The design, modeling, and characterization of these lenses are discussed in the chapter. In particular, the focusing properties and the
scanning performances of these two lens prototypes are theoretically and experimentally examined in Section 6.3. More importantly, the time-domain responses of these TTD lenses as well
as those of a non-TTD MEFSS-based lens reported in [46] are experimentally characterized and
the results are reported in Section 6.3.2. It is experimentally demonstrated that, unlike the structure reported in [46], the TTD lens prototypes demonstrate an excellent time-domain response for
broadband pulsed excitations with fractional bandwidths as high as 30%. The chromatic aberrations in both lenses are also experimentally characterized by examining the frequency dependent
101
Proposed MEFSS-Based
True-Time-Delay Planar Lens
Double-Convex
Dielectric Lens
Time Delay
Time Delay
Radial Distance
Radial Distance
(a)
Sub-wavelenth Spatial
Time Delay Unit
(b)
(c)
Figure 5.1 (a) Topology of a conventional double-convex dielectric lens. (b) Topology of the
planar true-time-delay lens populated with spatial TDUs. (c) Relative time delay that different
rays of a spherical wave experience at the input of the lens aperture and the time delay profile
provided by the lens to achieve a planar wavefront at the output aperture of the lens. Note that the
time delay is referenced to the time it takes from the focal point to the center of the lens aperture.
The results are calculated for two circular aperture lens. A lens with aperture diameter of
D = 18.6 cm and focal distance of f = 30 cm (f /D ≈ 1.6) and another one with aperture
diameter of D = 18.6 cm and focal distance of f = 19 cm (f /D ≈ 1).
focal point movement in all the lenses. It is demonstrated that the TTD lenses demonstrate a fixed
focal length over their entire frequency bands of operation whereas the non-TTD lens reported in
[46] demonstrate significant focal point movement.
102
Non-resonant capacitive patch Pixel
Non-resonant
capacitive Patch
Pixel N
Pixel N-1
Dx
Dy
s/2
Dx
(a)
C1
h1
Dx<< λ
Z2
Z1
Z0
L2
CN-2
h2
(c)
Non-resonant
inductive grid
(b)
ZN-2
C3
w
y
<<
λ
Non-resonant inductive grid
D
Spatial Time Delay Unit
Dy
h << λ
ZN-1
LN-1
hN-2
CN Z0
hN-1
Figure 5.2 (a) Topology of the proposed TTD lens populated with spatial TDUs. (b) Top view of
both the capacitive and inductive layer of each TDU. (c) Equivalent circuit model of each TDU.
5.2
TTD Lens Design and Principles of Operation
Fig. 5.1(a) shows the topology of a conventional double-convex dielectric lens. The smoothly
curved surface of this structure provides a continuous time delay profile for all the rays of the
incident wave that originate on the focal point and end on the input surface of the lens’ aperture.
If the lens is properly designed, such a continuous time delay profile can satisfy the Fermat’s
principle. This way, all the rays that originate on the focal point of the lens and end at the lens’
103
output aperture will have the same optical path length at all frequencies2 . For a double-convex
dielectric lens with a given aperture size and focal distance, the time delay profile that must be
provided by the lens can be easily calculated. Assuming a spherical wavefront is launched from
the focal point of the lens, the time it takes for each ray to arrive at the lens’ input aperture is
determined by the path length and the speed of propagation in the medium in which the lens is
located. The ray that directly connects the focal point of the lens to the center of its aperture
experiences the shortest time delay to arrive at the input aperture of the lens. Using this time delay
as a reference, the excess free-space time delay for a ray arriving at an arbitrary point on the lens’
aperture can be calculated. Fig. 5.1(c) shows the calculated excess time delays for two lenses with
the same circular aperture diameter of D = 18.6 cm and different focal distances of f = 30 cm and
f = 19 cm. The time delay profiles that these two lenses must provide to achieve beam collimation
can be derived from these results. Both delay profiles have a minimum value of zero at the edges
of the lens’ aperture and gradually increase to their maximum values at the center of the aperture.
√
For a circular aperture, this maximum value can be expressed as ( (D/2)2 + f 2 − f )/c, where
D is the diameter of the circular lens, f is the focal length and c is the speed of the light. Fig.
5.1(b) shows the side view of a planar lens that emulates the double-convex lens shown in Fig.
5.1(a). Here, the aperture of the lens is populated with spatial TDUs with finite lateral dimensions.
Therefore, the time delay profile obtained over the aperture of the lens is not continuous. However,
in such structures, it is desirable to reduce the discretization errors as much as possible. This
requires that the spatial TDUs of the planar lens are made as small as possible. This requirement
can by satisfied by using TDUs that are the unit cells of MEFSSs [42].
5.2.1
Sub-wavelength Spatial Time Delay Units
Fig. 6.1(a) shows the three-dimensional (3D) topology of the proposed TTD lens composed of
spatial TDUs. Each TDU is the unit cell of an appropriately-designed MEFSS with an N th -order
2
Provided that the index of refraction of the dielectric material that constitutes the lens does not change with
frequency.
104
bandpass response3 . MEFSSs belong to a class of non-resonant periodic structures composed of
a number of closely spaced metallic layers separated from one another by very thin dielectric
substrates. Each metallic layer is in the form of a two-dimensional (2D) periodic arrangement of
sub-wavelength capacitive patches or a 2D wire grid with sub-wavelength periodicity. The unit
cells of a sub-wavelength capacitive patch and a wire grid are shown in Fig. 6.1(b). An MEFSS
composed of N metallic layers acts as a spatial filter with an ( N 2+1 )th order bandpass response,
where N is always an odd number [42]. The equivalent circuit model of this structure is also
shown in Fig. 6.1(c). A comprehensive analytical design and synthesis procedure for this type of
MEFSS is reported in [42] and will not be repeated here. Using the synthesis procedures provided
in [42], given a specific center frequency of operation, f0 , fractional bandwidth, BW , and response
type and order, all of the element values shown in Fig. 6.1(c) can be determined and further mapped
to the geometrical parameters of the MEFSS depicted in Fig. 6.1(a). In particular, the TDUs of the
proposed TTD lens are designed by synthesizing MEFSSs with linear phase responses across their
frequency bands of operation. Note that the mutual coupling between the TDUs are not taken into
account in Fig. 6.1(c). This is due to the difficulty involved in predicting the mutual coupling in
a non-periodic lens environment. Due to the sub-wavelength nature of the spatial TDUs, a desired
time delay profile over the aperture can be approximated with a good degree of accuracy.
Within its pass band, an MEFSS allows the signal to pass with little attenuation. The transmitted signal, however, experiences a time delay. For a time-harmonic continuous wave (CW) signal,
this time delay can be characterized by the phase of the MEFSS’s transmission coefficient. For
non-CW signals, however, this time delay is characterized by the group delay of the filter’s transfer
function. To obtain a wideband collimating lens, all the frequency components of the incident EM
wave must arrive at the output aperture at the same time. Therefore, each TDU that populates the
lens’ aperture must provide a constant time delay across its entire frequency band of operation4 .
Since the TDUs are unit cells of appropriately-designed MEFSSs, this requires that each TDU is
3
All the discussions regarding both the frequency and transient responses of the time delay units are based on
the assumption that they will operate in an infinite two-dimensional periodic fashion. This assumption will be used
throughout the chapter.
4
Different TDUs in a single lens have different time delay values but each TDU must maintain its time delay as a
function of frequency.
105
designed to provide a constant group delay over the desired frequency band of operation. In filter
theory, the group delay is defined as the rate of change of the transmission phase with respect to
frequency (τg = − dϕ(ω)
, τg is the group delay, ϕ(ω) is the total phase shift, and ω is the angular
dω
frequency.). Therefore, a filter with a linear phase response will have a constant group delay over
the frequency range where its phase response remains linear. Thus, the TDUs of the proposed lens
are synthesized from MEFSSs that provide a linear phase response over their frequency bands of
operation.
To control the time delay provided by each TDU, the slope of the phase of its transmission
coefficient is controlled. The steeper the slope of the transmission phase is, the larger the time
delay it provides will be. The group delay of an MEFSS-based TDU is determined by several
factors including the order of its response and its fractional bandwidth. Fig. 5.3 shows the effect
of the order of the response of the MEFSS on its group delay. For the second-order bandpass filter
whose response is shown in Fig. 5.3, the phase variation within the highlighted region in Fig.
5.3(a) is 92◦ , which corresponds to a group delay of 128 psec (with ∼ ±5% variation around that
value) within the highlighted region in Fig. 5.3(b). As the order of the filter response increases,
the phase shift gradually increases to 140◦ for the third-order filter and 160◦ for the fourth-order
filter whose responses are shown in Fig. 5.3. Meanwhile, the corresponding group delay increases
to 195 psec for the third-order and 220 psec for the fourth-order filter responses. Clearly observed,
the higher the order of the filter is, the larger its group delay will be within the desired frequency
band. Similarly, the effect of the fractional bandwidth on the group delay is also shown in Fig.
5.4. For a fourth-order bandpass filter with a fractional bandwidth of 20%, the group delay and
the transmission phase shift are respectively 340 psec and 125◦ within the highlighted region in
Fig. 5.4. These values decrease to 225 psec and 82◦ when the fractional bandwidth is increased
to 30%, and further drop to 185 psec and 67◦ when the fractional bandwidth is further increased
to 40%. The examples shown in Fig. 5.3 and Fig. 5.4 show the main mechanisms that can be
used to control the group delay of each TDU. As can be observed from these results, the filter’s
group delay changes rapidly as we move closer to the band edges. Therefore, the bandwidth of the
proposed TDUs are expected to be inherently narrower than the 3 dB transmission bandwidth of
106
(a)
(b)
Figure 5.3 Calculated frequency responses of three MEFSSs having second-, third-, and
fourth-order bandpass responses. (a) Magnitudes and phases of the transmission coefficients. (b)
Magnitudes of the transmission coefficients and the corresponding group delays. As the order of
the MEFSS response increases, the transmission phase shift within the highlighted region
increases and a correspondingly larger group delay can be achieved.
the MEFSSs used to implement them. The desired time delay profile of the proposed TTD lens
is determined from its aperture size, D, focal distance, f , and the required bandwidth of the lens.
This will in turn determine the orders and fractional bandwidths of the MEFSS unit cells that need
to be used to synthesize the required TDUs.
107
(a)
(b)
Figure 5.4 Calculated frequency responses of three MEFSSs with fourth-order bandpass
responses and different fractional bandwidths. (a) Magnitudes and phases of the transmission
coefficients. (b) Magnitudes of transmission coefficients and the corresponding group delays. As
the fractional bandwidth increases, the transmission phase shift within the highlighted region
decreases and the group delay is reduced.
5.2.2
TTD Lens Design Procedure
In [46], an MEFSS-based microwave lens was presented. In the lens presented in [46], each
pixel of the lens is treated as a spatial phase shifter providing a desired phase delay at a single
frequency. Thus, a lens designed using this technique will work perfectly only at a single frequency
(the frequency at which the SPSs are designed to operate) [46]. At frequencies above and below
108
x
y
TM
TM+TDM
D = 18.6 cm
z
T2
T1
T2+TD2
T1+TD1
f
D
M
87 654 32 1
y
z=0 z=h
d1d2
dM x
Figure 5.5 (a) Top view of the proposed TTD planar lens. A spherical wave is launched from a
point source located at the focal point of the lens, (x = 0, y = 0, z = −f ). To transform this
input spherical wavefront to an output planar one irrespective of the frequency,
T (x, y) + T D(x, y) must be constant for every point on the aperture of the lens. T D(x, y) is the
time delay provided by the lens. T (x, y) is the time it takes for the wave to travel from the focal
point of the lens, (x = 0, y = 0, z = −f ), to a point at the lens aperture, (x, y, z = 0). (b)
Topology of the proposed TTD lens prototype with a circular aperture. The lens aperture is
divided into M concentric zones populated with identical spatial TDUs within each zone. d1 , d2 ,
...... dM are the distances between the center of each zone and the center of the lens aperture. Two
lens prototypes with M = 12 and M = 16 are discussed in Section 6.2.2.
the design frequency, the phase shift profile over the lens’ aperture changes and this changes the
response of the lens. This frequency dependent change in the phase shift profile creates significant
chromatic aberrations in the lens reported in [46]. As will be demonstrated later in this chapter,
such a lens is not suitable for wideband pulsed applications. To obtain a wideband collimating
lens, a frequency-independent time delay profile within the frequency band of interest must be
considered. With this clarification in mind, we assume the planar microwave lens, shown in Fig.
5.5(a), is located in the x − y plane and has a circular aperture with diameter of D. A point
source located at the lens’ focal point at (x = 0, y = 0, z = −f ) radiates a spherical wavefront
that impinges upon the surface of the lens and is transformed to a planar wavefront at the output
109
aperture. First, we calculate the travel time of the ray that connects the focal point of the lens to an
arbitrary point on its input aperture:
T (x, y, z = 0) =
where 0 <
√
x2 + y 2 + f 2 /c
(5.1)
√
x2 + y 2 < D/2. The time delay profile that needs to be provided by the lens at each
point on its aperture (x, y) can be calculated from:
T D(x, y) = (
where r =
√
(D/2)2 + f 2 − r)/c + t0
(5.2)
√
x2 + y 2 + f 2 and t0 is an arbitrary positive constant. As described earlier, the TDUs
of the proposed lens are implemented with unit cells of a bandpass MEFSS. If the phase response
of the bandpass MEFSS is designed to be linear over the desired frequency range of operation,
it will provide a constant group delay. However, as can be seen from Figs. 5.3 and 5.4, the
MEFSS’ phase response deviates from a linear function at the band edges and outside of the main
transmission band. Therefore, in addition to the condition specified by (5.2), the phase matching
condition specified by (5.3) must also be satisfied simultaneously for all frequencies within the
desired band of operation:
Φ(x, y) = k0 (
√
(D/2)2 + f 2 − r) + Φ0
(5.3)
where Φ0 is a positive constant that represents a constant phase delay added to the response of
every TDU on the aperture of the lens, k0 =
2π
λ0
is the free space wave number, and λ0 is the free
space wavelength. To ensure that the output aperture of the lens represents both an equiphase and
an equi-delay surface, the lens’ TDUs should be designed to satisfy both of the conditions specified
by (5.2) and (5.3). This can be accomplished by satisfying the condition specified by (5.3) at all
frequencies within the desired band of operation of the lens. Since (5.2) is the negative of the
derivative of (5.3) with respect to frequency, satisfying (5.3) for all frequencies ensures that (5.2)
is also satisfied. Alternatively, both of these conditions can be satisfied by ensuring that the lens’
TDUs provide the time-delays specified by (5.2) and they also satisfy (5.3) at a single frequency5 .
5
This is akin to identifying the linear function y = ax + b by specifying its slope, a, and the y-intercept point, b.
110
Table 5.1 Distances between the center of each zone and the center of the lens aperture for the
two lens prototypes discussed in Section 6.2.2. All values are in mm.
d1
d2
d3
d4
d5
d6
Lens 1 (f /D = 1.6)
0
33
42
48
57
60
Lens 2 (f /D = 1)
0
27
36
42
48
54
d7
d8
d9
d10
d11
d12
Lens 1 (f /D = 1.6)
66
72
78
84
86
90
Lens 2 (f /D = 1)
56
60
66
69
72
75
d13
d14
d15
d16
78
84
85
90
Lens 2 (f /D = 1)
Finally, it is important to note that the reason that both conditions (5.2) and (5.3) must be satisfied is
that the time delay units of the proposed lens are not true time delay units (e.g. unlike a single piece
of a TEM transmission line). Rather, these TDUs act as time delay units over a given frequency
band6 . In a lens utilizing true-time-delay units that are not band limited (e.g. one utilizing TEM
transmission lines as time delay units), satisfying (5.2) will automatically satisfy (5.3). However,
in lenses that use TDUs which emulate true-time-delay units over a finite bandwidth, this is not
necessarily the case. Therefore, in the present design, care must be taken to ensure that both of
these conditions are met7 .
As shown in Fig. 5.5(b), the aperture of the lens is divided into M concentric zones. Each zone
is populated with time delay units of the same type. If the coordinates of a point located at the
center of zone m are given by (xm , ym , z = 0), where m = 1, ..., M , then the desired time delay
required from TDUs that populate this zone can be calculated from:
T D(xm , ym ) = (
6
7
√
(D/2)2 + f 2 − rm )/c
Due to the bandpass nature of the MEFSSs that used to implement them.
Thus, strictly speaking, the proposed lens is a true-time-delay equivalent lens.
(5.4)
111
Dx
P1
w4
w2
Dy
P1
P3
w2 P3
y
z
h1,2
w6
h2,3
P5
w4
h3,4
w6
P5
h4,5
P7
h5,6
h6,7
P7
x
Figure 5.6 Topology of the unit cell of a fourth-order MEFSS which is used as the time delay
units of the TTD lenses discussed in Section 6.2.2.
where rm =
√
2 + f 2 . Additionally, the desired transmission phase required from a time
x2m + ym
delay unit can be calculated from:
√
Φ(xm , ym ) = k0 ( (D/2)2 + f 2 − rm ) + Φ0
(5.5)
once the time delay and phase delay for each zone have been determined, the lens can be designed
using the following procedure:
1. Select the desired center frequency of operation, flens , and operational bandwidth, BWlens ,
of the lens.
2. Select the desired size of the lens aperture, D, and the focal distance, f .
3. Divide the lens aperture into M concentric discrete regions or zones, where M is an arbitrary
positive integer. The maximum value of M is limited by the size of the aperture and the
lateral dimensions of the time delay units (Dx and Dy in Fig. 5.6).
4. Determine the lens’ time and phase delay profiles by calculating the time and phase delays, which are required from TDUs populating each zone of the lens using (5.4) and (5.5)
respectively.
5. Depending on the maximum variation of T D(x, y) and Φ(x, y) over the lens’ aperture, determine the order of the bandpass MEFSS that is needed to implement the time delay units.
In doing so, the analytical synthesis procedure presented in [42] can be used.
112
6. Use the synthesis procedure described in [42] to design the TDUs that populate the central
zone of the lens. This TDU should provide a linear transmission phase with the steepest
slope (or largest time delay) over the desired operational bandwidth, BWlens .
7. Use the synthesis procedure described in [42] to design the spatial time delay units that
populate zone m = 2, ..., M . These time delay units should provide the required time delay
T D(xm , ym ) calculated from (5.4) and provide the phase shift Φ(xm , ym ) calculated from
(5.5) at the center frequency of operation flens 8 .
We applied the aforementioned design procedure to two lens prototypes of the type shown in
Fig. 5.5(b). Both prototypes have circular apertures with diameters of D = 18.6 cm. The primary
difference between the two prototypes is in their focal lengths. The first lens prototype is designed
to operate over the frequency range of 8 − 10.5 GHz. It has 12 concentric zones (M = 12 in Fig.
5.5(b)) and a focal length of f = 30 cm. This corresponds to an f /D ≈ 1.6. The distance between
the center of each zone and the center of the lens’ aperture is shown in Table 6.1. The time delays
that must be provided by TDUs occupying each zone of this lens are calculated and provided in
Table I as well. For this combination of f and D values, the maximum time delay variation over
the lens aperture is observed to be 47 psec. Following the design guidelines provided in [42],
it can be shown that this maximum time delay value can be achieved by using a fourth-order
MEFSS designed to have a linear transmission phase across the frequency of interest. The unit
cell of a fourth-order MEFSS is composed of four capacitive layers and three inductive layers
separated from one another by thin dielectric substrates as shown in Fig. 5.6. The total thickness
of such a fourth-order MEFSS is approximately 0.15λ0 , where λ0 is the free space wavelength at
the desired center frequency of operation. As demonstrated in Section 6.2.1, different time delays
can be achieved either by changing the order of the MEFSS response or changing its fractional
bandwidth. Since changing the order of the MEFSS response from one zone to another is rather
difficult to do, we achieve the different time delays by changing the fractional bandwidth of the
MEFSS response for a given order. Therefore, the TDUs that populate each zone of this lens are
8
If the TDUs provide the time delay specified by (5.4) and provide the phase delay specified by (5.5) at flens , they
will provide the desired phase delay at all frequencies of interest within the bandwidth of the lens.
113
Table 5.2 Physical and electrical properties of the time delay units that populate each zone of the
TTD lens with a desired frequency range of 8 − 10.5 GHz and f /D ≈ 1.6. Time delay values in
the desired frequency range are in psec. Maximum insertion loss values within the desired
frequency range are in dB and all physical dimensions are in mm. For all of these TDUs,
Dx = Dy = 6 mm, h1,2 = h2,3 = h5,6 = h6,7 = 0.813 mm, h3,4 = h4,5 = 0.508 mm. The
dielectric substrate used is Rogers 4003C with a dielectric constant of 3.4.
Time
Sim.
P1 =
P3 =
w2 =
Delay
IL
P7
P5
w6
1
202.7
0.84
5.40
5.72
0.70
1.20
2
198.8
0.83
5.36
5.69
0.70
1.20
3
194.7
0.80
5.31
5.66
0.70
1.20
4
190.8
0.80
5.27
5.62
0.70
1.20
5
186.9
0.83
5.22
5.56
0.70
1.20
6
183.0
0.80
5.18
5.53
0.70
1.20
7
178.8
0.89
5.46
5.56
0.70
1.20
8
175.0
1.01
5.07
5.37
0.67
1.17
9
171.1
1.10
5.02
5.29
0.63
1.13
10
166.9
1.02
4.94
5.16
0.55
1.05
11
163.0
1.20
4.82
5.05
0.48
0.98
12
159.1
1.50
4.66
5.03
0.48
0.98
Zone
w4
114
(a)
(b)
Figure 5.7 (a) The comparison between the full-wave simulated transmission phases and the ideal
linear transmission phases for different zones of the first lens prototype with 12 concentric zones
and f /D ≈ 1.6. Zi : ideal represents an ideal desired linear transmission phase with the desired
time delay for Zone i as listed in Table 6.2. (b) The simulated transmission and reflection
coefficients of the TDUs occupying each zone of the second lens prototype. The highlight region
(8 − 10.5 GHz) in both figures indicates the area where an approximate linear transmission phase
close to the required ideal linear phase can be obtained. This region is considered to be the
desired frequency range of operation for the TTD lens.
unit cells of fourth-order bandpass MEFSSs having linear phase responses with different fractional
bandwidths and slightly different center frequencies of operation. The differences in the responses
of these TDUs cause a gradual change in the physical dimensions of different metal layers that
constitute each TDU. In particular, as we move from one zone to another, the dimensions of the
115
capacitive patches and the inductive wire grids that constitute a TDU (see Fig. 5.6) change. The
unit cell size of the TDUs that populate each zone of the first lens prototype are 6 mm×6 mm
(0.185λ0 × 0.185λ0 ). Such small TDU dimensions enhance the agreement between the discrete
phase profile of the proposed lens and the continuous function that represents the desired phase
profile. The predicted frequency response of the TDUs are based on the assumption that they
operate in an infinite 2D periodic structure. This is shown to be a valid assumption because such
structures can be considered to be locally periodic [46].
Following the design procedure described above, the required time delay and phase shift values
are calculated for each zone of the lens. In the first step, the TDUs that populate the center zone of
the lens, Zone 1, are designed. Zone 1 has the largest group delay among all the zones as can be
observed in Fig. 5.5(a). This maximum group delay corresponds to the steepest linear transmission
phase having the largest slope in the desired frequency range. The TDU occupying Zone 1 is
optimized to ensure that its transmission phase closely matches the required linear transmission
phase within the desired frequency band of operation. This optimization is carried out by using fullwave simulations in CST Microwave Studio. To do this, the TDU is placed inside a waveguide with
periodic boundary conditions. The structure is excited by a plane wave and its transmission phase
and magnitude are calculated. The design parameters of the TDU occupying Zone 1 (Z1 -TDU) are
then used as a reference for designing TDUs populating other zones. The TDUs occupying each
zone must have different group delays and different phase shifts. This is achieved by de-tuning the
frequency of operation and the fractional bandwidth of the Z1 -TDU. This way, the desired linear
transmission phase responses with different slopes are achieved. To facilitate the optimization
procedure for each zone, the structure of all the TDUs are assumed to be symmetric with respect to
the center inductive layer (see Fig. 5.6). This requires P1 = P7 , P3 = P5 , and w2 = w6 , as depicted
in Fig. 5.6. This simplification greatly reduces the complexity associated with the optimization
of the TDUs that occupy each zone and still yields satisfactory results as will be demonstrated
in Section 6.3. The magnitude and phase responses of each TDU are functions of angle and the
polarization of incidence of the EM wave. Therefore, when designing TDUs for each zone, these
effects are taken into account.
116
Table 5.3 Physical and electrical properties of the time delay units that populate each zone of the
TTD lens with a desired frequency range of 8.5 − 10.5 GHz and f /D ≈ 1. Time delay values
within the desired frequency range are in psec. Insertion loss values within the desired frequency
range are in dB and all physical dimensions are in mm. For all of these TDUs,
Dx = Dy = 6 mm, h1,2 = h2,3 = h5,6 = h6,7 = 0.813 mm, h3,4 = h4,5 = 0.508 mm. The
dielectric substrate used is Rogers 4003C with a dielectric constant of 3.4.
Time
Sim.
P1 =
P3 =
w2 =
Delay
IL
P7
P5
w6
1
205.5
0.75
5.40
5.72
0.75
1.20
2
201.4
0.67
5.35
5.70
0.75
1.20
3
197.2
0.66
5.29
5.65
0.75
1.20
4
192.7
0.69
5.25
5.60
0.75
1.20
5
188.6
0.61
5.21
5.57
0.75
1.20
6
184.4
0.55
5.15
5.53
0.75
1.20
7
180.3
0.68
5.12
5.45
0.75
1.20
8
175.8
0.57
5.05
5.41
0.75
1.20
9
171.6
0.32
4.95
5.38
0.75
1.20
10
167.5
0.43
4.80
5.36
0.75
1.20
11
163.3
0.52
4.72
4.95
0.45
0.90
12
159.1
1.02
4.67
4.85
0.45
0.90
13
155.0
1.30
4.50
4.85
0.45
0.90
14
150.8
1.90
4.35
4.75
0.45
0.90
15
146.6
2.20
4.20
4.70
0.45
0.90
16
142.2
2.80
4.00
4.60
0.45
0.90
Zone
w4
117
(a)
(b)
Figure 5.8 (a) The comparison between the full-wave simulated transmission phases and the ideal
linear transmission phases for different zones of the second lens prototype with 16 concentric
zones and f /D ≈ 1. Zi : ideal represents an ideal desired linear transmission phase with the
desired time delay for Zone i as listed in Table 6.3. (b) The simulated transmission and reflection
coefficients of the TDUs occupying each zone of the first lens prototype. The highlight region
(8.5 − 10.5 GHz) in both figures indicates the area where an approximate linear transmission
phase close to the required ideal linear phase can be obtained. This region is considered to be the
desired frequency range of operation for the TTD lens.
Table 6.2 shows the electrical and geometrical parameters of the TDUs populating each zone of
the first lens prototype as well as the required time delay for each zone. Fig. 6.4(a) shows the phase
responses of TDUs occupying different zones of this lens. The results are obtained using full-wave
EM simulations in CST Microwave Studio. Additionally, the ideal phase responses desired from
each TDU are also shown for comparison. As can be observed, within the highlighted region
118
Figure 5.9 (a) Photograph of the fabricated lens prototype with 12 zones and a f /D = 1.6. (b)
Photograph of the fabricated lens prototype with 16 zones and a f /D = 1. In both of these two
figures, the only visible metallic layer is the first capacitive layer within which the size of the
capacitive patches decrease from the center of the lens to the edges. Note here the same trend
exists for all the other capacitive layers located in the interior layers of the structure.
(from 8 − 10.5 GHz), the phase responses of the TDUs closely match the desired ideal linear
phase responses with a maximum deviation less than 5◦ . Fig. 6.4(b) shows the magnitude of
the transmission and reflection coefficients of the TDUs whose dimensions are provided in Table
II. As can be seen, the highlighted region of Fig. 6.4(a) falls within the pass band of all TDUs.
Therefore, in addition to providing the desired linear phase response, each TDU has a low insertion
loss within the desired band of operation and is impedance matched. Fig. 6.4(b) shows that the
maximum insertion loss of TDUs remains below 1.5 dB in this design9 .
The second lens prototype studied here has 16 concentric zones (M = 16) and a focal length
of f = 19 cm. This corresponds to an f /D ≈ 1. The distances between the center of each zone
and the lens center for this lens prototype are provided in Table 6.1 as well. This lens is designed
to operate over the frequency range of 8.5 − 10.5 GHz. Since the second prototype has a lower
f /D ratio, it requires a larger maximum time delay compared to that of the first prototype. This
maximum time delay can still be achieved using a fourth-order bandpass MEFSS. However, this
comes at the expense of sacrificing the operational bandwidth of the lens. This is why the second
9
As seen from Fig. 6.4(b), the TDU occupying Zone 12 has a maximum insertion loss of 1.5 dB at the band edge
at 8.0 GHz. This insertion loss is primarily due to the higher reflection coefficient at the band edge for this design.
119
(a)
(b)
Figure 5.10 (a) Calculated and measured focusing gains of the first TTD lens prototype with
f /D ≈ 1.6 at its expected focal point (x = 0 cm, y = 0 cm, z = −30 cm). The measured 3 dB
gain bandwidth is 43%. (b) Calculated and measured focusing gains of the second TTD lens
prototype with f /D ≈ 1 at its expected focal point (x = 0 cm, y = 0 cm, z = −19 cm). The
measured 3 dB gain bandwidth is 38%.
lens prototype has a smaller operational bandwidth. The lens bandwidth for this f /D ratio can be
increased if an MEFSS with a higher-order bandpass response is employed. The second prototype
is also designed using a procedure similar to that of the first one. The physical and electrical
parameters of TDUs that occupy different zones of this lens are provided in Table 6.3. The phase
responses of the TDUs populating the aperture of this lens are also calculated in CST Microwave
Studio and are presented in Fig. 6.5(a) along with the ideal linear phase responses required from
them. As can be seen, the phase responses match the desired linear responses with a good degree
of accuracy. The maximum deviation of 15◦ is observed for the TDU occupying Zone 1 of the lens
at the band edge at 10.5 GHz. The magnitude of the transmission and reflection coefficients of the
120
−30
−25
−20
−15
40
40
35
35
30
30
25
25
20
−10
−5
0
(a)
5
20
10 −10
40
40
35
35
30
30
25
25
20
−10
−5
0
5
20
10 −10
−10
−5
−5
(c)
40
35
35
30
30
25
25
−5
0
(e)
0
5
10
0
5
10
5
10
(b)
(d)
40
20
−10
−5
5
20
10 −10
−5
0
(f)
Figure 5.11 Measured normalized received field intensity of the fabricated TTD lens with
f /D ≈ 1.6 in a rectangular grid in the vicinity of the expected focal point. The “x” symbol shows
the actual focal point of the lens determined by the measurement and the color bar values are in
dB. In all of the figures, the horizontal axis is the x axis with units of [cm] and the vertical axis is
the z axis with units of [cm]. (a) 8.0 GHz. (b) 8.5 GHz. (c) 9.0 GHz. (d) 9.5 GHz. (e) 10.0 GHz.
(f) 10.5 GHz.
121
−35
−30
−25
−20
−15
29
29
25
25
21
21
17
17
13
13
9
−10
−5
0
5
9
10 −10
−10
−5
(a)
29
25
25
21
21
17
17
13
13
−5
0
5
9
10 −10
−5
(c)
29
25
25
21
21
17
17
13
13
−5
0
(e)
5
10
0
5
10
5
10
(d)
29
9
−10
0
(b)
29
9
−10
−5
5
9
10 −10
−5
0
(f)
Figure 5.12 Measured normalized received field intensity of the fabricated TTD lens with
f /D ≈ 1 in a rectangular grid in the vicinity of the expected focal point. The “x” symbol shows
the actual focal point of the lens determined by the measurement and the color bar values are in
dB. In all of the figures, the horizontal axis is the x axis with units of [cm] and the vertical axis is
the z axis with units of [cm]. (a) 8.5 GHz. (b) 9.0 GHz. (c) 9.5 GHz. (d) 10.0 GHz. (e) 10.5 GHz.
(f) 11.0 GHz.
122
TDUs are also calculated and presented in Fig. 6.5(b). Within the highlighted region, a maximum
insertion loss of 4 dB is observed for the TDU that occupies zone 16 of the lens at the band edge
close to 8.5 GHz. This is due to the fact that 8.5 GHz is barely within the transmission window of
the MEFSS that is used to implement Zone 16 TDUs. In the main transmission band, the TDUs
are all well impedance matched and have low insertion loss values.
5.3 Experimental Verification and Measurement Results
The lens prototypes discussed in Section II were fabricated using standard lithography and
substrate bonding techniques. Fig. 6.8 shows the photographs of the fabricated prototypes. Each
lens prototype has six dielectric substrates, of which two have a thickness of 0.508 mm and the
others are 0.813 mm thick as described in the captions of Tables 6.2 and 6.3. Rogers 4003C dielectric substrates (with ϵr = 3.4) are used for all the substrate layers and the adjacent substrates are
bonded together using five 0.1-mm-thick bonding films (RO4450F from Rogers Corporation). The
overall thickness of each lens, including the bonding layers, is 4.76 mm or equivalently 0.146λ0
(0.150λ0 ) for the first (second) lens prototype discussed in Section 6.2.2, where λ0 is the free space
wavelength at the desired center frequency of operation of each lens. Each spatial TDU as shown
in Fig. 6.8 has a dimension of 6 mm × 6 mm or equivalently 0.185λ0 × 0.185λ0 (0.19λ0 × 0.19λ0 )
for the first (second) lens prototype discussed in Section 6.2.2.
5.3.1 TTDs Lens Characterization
To experimentally characterize the focusing properties of the fabricated lenses, the experimental setup depicted in Fig. 10 in [46] is used. The setup consists of a large metallic screen with
dimensions of 1.2 m × 1.0 m, or equivalently 37λ0 × 30.8λ0 (38λ0 × 31.7λ0 ) for the first (second) lens in Section 6.2.2, with an opening with dimensions of 19 cm × 24 cm, or equivalently
5.86λ0 × 7.40λ0 (6.02λ0 × 7.60λ0 ) for the first (second) lens in Section 6.2.2, at its center. This
fixture is used to hold the fabricated prototypes in place. Since the opening in the fixture is rectangular shaped and the lens’ apertures are circular shaped, the area outside the main aperture of
each lens is covered with copper as can be seen from Fig. 6.8. An X-band horn antenna is used
123
to illuminate the lens. The lens and the fixture are placed in the far field of the horn. On the other
side of the fixture, a probe, which is in the form of an open-ended semi-rigid coaxial cable with
the center conductor extended by 10 mm, is used to sample the received electric field.
In the first set of measurements, the focusing gains of the two lenses are measured at their
expected focal points, (x = 0, y = 0, z = −30) cm for the first prototype and (x = 0, y = 0, z =
−19) cm for the second prototype, as a function of the frequency. This type of measurement is
conducted in two steps. First, the transmission coefficient between the transmitting horn antenna
and the receiving probe is measured in the absence of the test fixture and the lens. Then, the
transmission coefficient is measured when both the lens and the fixture are present. By normalizing
the latter measured values to the baseline value measured in the first step, the focusing gain of
each lens is calculated. Fig. 6.10 shows the comparison between the measured and calculated
focusing gains for both lenses. The simulation results are obtained by treating both lenses as two
dimensional antenna arrays composed of Hertzian radiators as described thoroughly in [46]. As
Meas. Focal Length [cm]
can be seen, the focusing gain of the first lens (the one with an f /D ≈ 1.6) dose not vary by
45
TTD Lens (f/D 1.6)
40
TTD Lens (f/D 1)
35
[29] -- Five Zones
[29] -- Ten Zones
30
25
20
15
10
7
8
9
10
11
12
Frequency [GHz]
Figure 5.13 The measured focal lengths of the two fabricated TTD lens prototypes discussed in
Section 6.2.2 as a function of frequency. As a reference for comparison, the measured focal
lengths of the two non-TTD MEFSS-based prototypes presented in [46] are also reported in this
figure. Observe that the effects of chromatic aberrations in non-TTD lenses are manifested in the
form of significant focal point movements vs. frequency. These effects are conspicuously absent
in the TTD lenses reported in this chapter.
124
(a)
(b)
(c)
(d)
(e)
(f)
Figure 5.14 Measured scanning performance of the fabricated TTD lens with f /D ≈ 1.6. The
power pattern is measured over the focal arc of the lens for plane waves arriving at various
incidence angles. (a) 8.0 GHz. (b) 8.5 GHz. (c) 9.0 GHz. (d) 9.5 GHz. (e) 10.0 GHz. (f) 10.5
GHz.
more than 3 dB in the frequency range of 7.5 − 11.6 GHz. This is equivalent to a fractional
bandwidth of 43%. For the second TTD lens (the one with an f /D ≈ 1), this bandwidth shrinks
to 38% (7.8 − 11.5 GHz), which is expected from the discussion in Section 6.2.2. Observe that the
measured focusing gain of the second prototype is higher than that of the first prototype. This is
also expected since a smaller f /D ratio corresponds to a shorter focal length and hence, a better
field focusing effect. The calculated focusing gain values match well with the measured ones over
125
(a)
(b)
(c)
(d)
(e)
(f)
Figure 5.15 Measured scanning performance of the fabricated TTD lens with f /D ≈ 1. The
power pattern is measured over the focal arc of the lens for plane waves arriving at various
incidence angles. (a) 8.5 GHz. (b) 9.0 GHz. (c) 9.5 GHz. (d) 10.0 GHz. (e) 10.5 GHz. (f) 11.0
GHz.
the entire frequency band of operation of both the lenses. The small differences observed between
the calculated and measured results can be attributed to the Ohmic losses of the lens and the errors
introduced by the local periodicity assumption described in Section 6.2.2.
In the second set of measurements, the focusing properties of the two lenses are characterized
in the vicinity of their expected focal points. To do this, the received field intensity is measured in
a rectangular grid in the vicinity of the expected focal point of each lens using the experimental
126
setup shown in Fig. 10(b) in [46]. In this setup, the receiving probe is swept over a measurement
grid with dimensions of 20 cm×20 cm in the x − z plane with 1 cm increments in the x and z
directions. This measurement grid is centered at the expected focal point of each lens. The transmission response for each grid point is measured and the normalized received pattern is obtained
by normalizing all these measured values at each grid to the maximum measured value. Fig. 5.11
shows the normalized field pattern of the fabricated TTD lens with f /D ≈ 1.6 measured in the
frequency range of 8 − 10.5 GHz with 0.5 GHz increments. At each frequency, the location of the
maximum measured value is indicated with a cross (x) symbol. The distance between this 0 dB
location and the lens aperture is considered to be the measured focal distance. The normalized
received field pattern for the second lens (having f /D ≈ 1) is also measured and is shown in Fig.
5.12, where the actual focal point of the lens is observed to be constant in the frequency range of
9 − 11 GHz. The fact that the focal spots of these TTD lenses remain practically unchanged as
frequency is changing indicates low chromatic aberrations in these lenses. This is best illustrated
by comparing the impact of chromatic aberrations in these TTD lenses with those of non-TTD
MEFSS-based microwave lenses reported in [46]. Fig. 5.13 compares the measured focal lengths
of the TTD lenses examined in this work with the two non-TTD lenses reported in [46]. As can
be seen from Fig. 5.13, the focal lengths of the two TTD lenses examined in this work remain
constant with frequency. On the other hand, the focal lengths of the non-TTD lenses examined
in [46] change significantly over their frequency band of operation (both lenses reported in [46]
were designed to have a focal length of 30 cm). This frequency dependent focal point movement
is indicative of significant chromatic aberration in SPS-based lenses. This phenomenon is perhaps
best observed in dielectric lenses that work at optical frequencies. In such lenses, chromatic aberration is due to the change of the lens’ dielectric constant as a function of frequency [150]-[151].
The frequency-independent focal length observed for the two TTD lenses indicates that chromatic
aberration is minimized in these proposed TTD lens. This is due to the true-time-delay equivalent
behavior of these lenses10 . As can be seen from Fig. 5.13, compared to the fabricated lens with
10
One can imagine that within its frequency band of operation, the effective refraction index of this lens does not
change as a function of frequency.
127
f /D ≈ 1.6, the lens prototype with a f /D ≈ 1 has a narrower frequency range within which
the location of the measured focal point remains unchanged. This is also expected since the linear
transmission phase region for all the TTD units of the lens with f /D ≈ 1 (the highlighted region
in Fig. 6.5) is narrower than that of the lens with f /D ≈ 1.6 (the highlighted region in Fig. 6.4).
In the third set of measurements, the performance of the two fabricated prototypes are also
characterized under oblique angles of incidence. To do this, the measurement setup shown in Fig.
10(c) in [46] is used. The lens is illuminated by a plane wave from various incident angles ranging
from normal to 60◦ and the received field intensity over the lens’ focal arc is measured. The
receiving probe, in this type of measurement setup, is mounted on a rotatable arm with its axis of
rotation at the center of the lens. The length of the arm can be adjusted to accommodate different
lens designs with different focal lengths. The receiving probe is swept over the focal arc with an
increment of 1◦ . Each of the two lenses is illuminated with vertically-polarized plane waves under
the incidence angles of 0◦ , 15◦ , 30◦ , 45◦ and 60◦ in the x − z plane and the received power patten is
measured over the focal arc. Figs. 5.14(a)-5.14(f) show the measured normalized received power
pattern for the TTD lens with f /D ≈ 1.6 in the frequency range of 8−10.5 GHz. At each frequency
point, the maximum measured value always happens at the focal point for normal incidence. All
measured power values are then normalized to this maximum value. Therefore, in all of the figures,
0 dB corresponds to the power level received at the focal point under normal incidence. As can be
seen, when the lens is illuminated under an oblique incidence angle of θ, the maximum received
power on the focal arc will always be steered by an angle equal to θ. Additionally, a decrease
in the peak value is also observed. This reduction in the peak gain is expected from antenna
array theory and it is also observed in scanning antenna arrays as the main beam is scanned from
boresight towards the grazing angles. In the transmitting mode, multiple feed antennas can be
located on the focal arc of the lens. In this case, each feed antenna will generate a beam in a
given direction of space. Based on the results presented in Figs. 5.14(a)-5.14(f) and taking into
account the reciprocity theorem, it is expected that a beam scanning antenna system that utilizes
this lens can demonstrate field of views of at least ±60◦ . Figs. 5.14(a)-5.14(f) demonstrate that
the lens maintains a good performance when operated under oblique incidence. This performance
128
is generally better than many beam scanning antenna systems that exploit dielectric lenses [152][153] or planar microwave lenses that use larger pixel sizes [154]. In such designs, the scanning
range is generally limited to ±20◦ to ±30◦ . Similar measurements are also carried out for the
second lens prototype (with f /D ≈ 1) and the results are presented in Figs. 5.15(a)-5.15(f). As
can be seen, this lens demonstrates an excellent scanning performance over the frequency range of
8.5 − 11.0 GHz. It is worth mentioning that the beam scanning performances of the proposed TTD
lenses are similar to those of the non-TTD lenses reported in [46]. This is expected since the unit
cell sizes of both a TTD lens and a non-TTD lens are quite small compared to the wavelength.
5.3.2
Transient Analysis
To demonstrate the true-time-delay behavior of the proposed lenses, we examined the responses
of the two fabricated lens prototypes in time domain. When a microwave lens is illuminated with
a broadband pulse, the lens’ chromatic aberrations can alter the temporal characteristics of the
pulse and cause distortion. In a TTD lens, however, since the chromatic aberrations are either
very small or non-existent, this distortion is expected to be very small. To quantify the signal
distortion introduced by the lens, we calculated the fidelity factor for each prototype under various
pulsed excitations. The fidelity factor is a measure of the correlation between the lens’ input and
the output signals and is generally used to quantify the distortion introduced by various system
components [155]. Since our measurements are performed in frequency domain, the fidelity factor
of the lenses are calculated based on the measured frequency domain data [156]. In doing so, the
frequency domain analysis is conducted first followed by post processing the data to obtain the
required time-domain signals. The detailed procedure used to carry this out is summarized below:
1. First, the transfer function of the lens is measured in the frequency domain. This was done
using the experimental setup shown in Fig. 10(b) in [46]. To do this, the transmission
response of the test fixture without the lens is measured first by placing the receiving probe
at the focal point of the lens. This measured value was recorded and used as the baseline.
Then the transmission response of the structure with the presence of the lens is measured.
129
By normalizing the latter measured value to the baseline value, the transfer function of the
lens in frequency domain (H(w)) was obtained.
2. The input pulse s(t) is defined in Matlab and a fast fourier transform FFT is performed to
obtain its frequency response S(w). The frequency representation of the input pulse is then
multiplied with the transfer function obtained in the previous step to obtain the received signal in frequency domain, R(w). The time domain representation of the received signal, r(t)
was then obtained by applying the inverse fast Fourier transform IFFT to R(w). Calculation
of the r(t) is summarized using the equations below (5.6)-(5.7):
R(w) = F F T (s(t))H(w)
(5.6)
r(t) = IF F T (R(w))
(5.7)
3. To calculate the correlation between the input and output signals, s(t) and r(t), only the
shape of these two time-domain signals need to be considered (rather than the magnitude).
Therefore, the signals are normalized using (5.8)-(5.9):
ˆ = ∫ ∞ s(t)
s(t)
[ −∞ |s(t)|2 dt]1/2
(5.8)
ˆ = ∫ ∞ r(t)
r(t)
[ −∞ |r(t)|2 dt]1/2
(5.9)
The fidelity factor is then calculated by calculating the cross-correlation between these two
signals at every time point as indicated by (5.10):
∫
∞
F = max
τ
ˆ s(t ˆ+ τ ) dt
r(t)
(5.10)
−∞
A fidelity factor of 1 indicates a perfect match between the incident and the transmitted
pulses. This is an ideal system where no distortion is introduced. Generally, a high fidelity
130
Incident
Transmitted
TTD lens
~
(f/D~1.6)
(a)
Fidelity Factor
0.985
(b)
Fidelity Factor
0.968
(c)
Fidelity Factor
0.95
(d)
Fidelity Factor
0.985
(e)
Fidelity Factor
0.972
(f)
Fidelity Factor
0.96
(g)
Fidelity Factor
0.83
(h)
(i)
Fidelity Factor
0.80
TTD lens
~
(f/D~1)
Lens in
[29] -Five zones
Fidelity Factor
0.815
Figure 5.16 Time-domain responses and fidelity factors of three different lens prototypes for
various excitation signals. (a)-(c) The incident and transmitted pulses of the TTD lens with
f /D ≈ 1.6 for the modulated Guassian pulses centered at 9.25 GHz with fractional bandwidths
of (a) 10%, (b) 20%, and (c) 30%. (d)-(f) The incident and transmitted pulses of the TTD lens
with f /D ≈ 1 for the modulated Guassian pulses centered at 9.5 GHz with fractional bandwidths
of (d) 10%, (e) 20%, and (f) 30%. (g)-(i) The incident and transmitted pulses of the spatial phase
shifter (SPS) based lens reported in [46] (with five zones) for the modulated Guassian pulses
centered at 10 GHz with fractional bandwidths of (g) 10%, (h) 20%, and (i) 30%. In all cases, the
center frequency of operation of the Gaussian pulse is matched to the center frequency of
operation of the respective lens. In all of the figures, the horizontal axis is the time axis with units
of [ns] and the vertical axis is the normalized magnitude for the time-domain signals.
factor close to 1 is highly desired for any system that needs to accommodate broadband
modulated signals.
We studied the time-domain responses of the two fabricated lens prototypes described earlier
in this section using the aforementioned procedure. Additionally, to clearly demonstrate the TTD
nature of these lenses, we compared the time-domain responses of these TTD lenses with the timedomain response of a non-TTD lens discussed in [46]. To do that, the responses of all lenses
were measured in frequency domain and the aforementioned procedure was used to calculate their
fidelity factors for various excitation signals. In particular, the time-domain responses of the three
lenses were calculated for modulated Guassian pulses with fractional bandwidths of 10%, 20%, and
30%. In each case, the center frequency of operation of the Gaussian pulse is matched to the center
131
frequency of operation of the lens. Figs. 6.14(a)-6.14(c) show the incident and transmitted pulses
and the fidelity factors for the TTD lens with f /D = 1.6. The results are shown for modulated
Gaussian excitation pulses centered at 9.25 GHz with fractional bandwidths of 10%, 20%, and
30%. As can be seen from Fig. 6.14(a), a high fidelity factor value very close to 1 (0.985) is
achieved when the lens is excited with a broadband pulse with a bandwidth of 10%. This indicates
that the proposed lens does not adversely affect the temporal characteristics of the incident pulse in
this case. Achieving such high fidelity factor value is only possible in TTD systems. The fidelity
factor of the lens decreases to 0.968 when the bandwidth of the excitation pulse increases to 20%,
and it further drops to 0.95 as the fractional bandwidth of the excitation pulse is increased to 30%.
For the modulated Gaussian excitation with a bandwidth of 30%, part of the frequency content of
the input pulse falls beyond the linear phase range of the lens response that is highlighted in Fig.
6.4(a). This leads to the dispersion for the transmitted signal and hence a lower fidelity factor. The
transient performances of the TTD lens with f /D ≈ 1 are also measured and the results are shown
in Figs. 6.14(d)-6.14(f) for the modulated Gaussian excitation signals centered at 9.5 GHz with
10%, 20%, and 30% fractional bandwidths. As can be observed, the second TTD lens prototype
also demonstrates a good time-domain response with relatively high fidelity factors.
The excellent time-domain performance of these lenses can best be observed when they are
compared with a non-TTD planar lens. To make a fair comparison, we used the MEFSS-based
planar microwave lens reported in [46] for this purpose. This lens has aperture dimensions of
23.4 mm×18 mm and an f /D ≈ 1. While in appearance the structure reported in [46] is similar
to the present lenses, it does not behave like a true time delay lens and suffers from significant
chromatic aberrations as seen in Fig. 5.1311 . The time-domain responses of this lens for pulsed
excitations with fractional bandwidths of 10%, 20%, and 30% were calculated from its measured
transfer function and the results are presented in Figs. 6.14(g)-6.14(i). The fidelity factor of the
lens is also calculated for each pulse and the results are shown in the inset of Figs. 6.14(g)-6.14(i).
As can be observed, while this lens has a relatively broad fractional bandwidth of 20% [46], it
demonstrates a very poor time domain response even for a pulse with a fractional bandwidth of
11
Notice that this feature is a characteristic of any non-TTD system and is not limited to the lens reported in [46].
132
10%. As can be seen, the fidelity factor of this non-TTD MEFSS-based lens is rather low, 0.83,
for an excitation bandwidth of 10% and drops down to 0.815 and 0.80 as the bandwidth of the
pulse is increased to respectively to 20% and 30%. Such poor fidelity factor values indicate a high
mismatch between the input and output pulses, which are attributed to the fact that this lens does
not satisfy the Fermat’s principle as discussed in Section 6.2.
5.4 Conclusion
A new technique for designing TTD planar microwave lenses is proposed. Each time delay unit
(TDU) of the proposed lens is the unit cell of a non-resonant type miniaturized-element frequency
selective surface that is impedance matched. These spatial time delay units (TDUs), although look
similar to the spatial phase shifters (SPSs) in [46], behave fundamentally differently. Despite the
fact that both a TDU and a SPS are in the form of a unit cell of an MEFSS, a TDU is designed
to provide a certain time delay over the frequency range of interest, whereas a SPS is designed to
provide a specific phase shift at the desired single frequency point. The time delays of the TDUs
can be achieved by synthesizing MEFSSs that provide linear transmission phases within the desired
frequency range. A detailed procedure for designing such TTD lens is presented in the chapter.
Using this procedure, two TTD lens prototypes with f /D ≈ 1.6 and f /D ≈ 1 are fabricated
and characterized experimentally. Both of these two lenses demonstrate a broadband operation
with factional bandwidths of 43% and 38% respectively. Due to their true time delay nature, both
of these two lenses demonstrate a relatively constant focal point within their bands of operation.
Moreover, they demonstrate an excellent scanning performance in a field of view of ±60◦ . Finally,
the transient analysis for the fabricated TTD lens prototypes, as well as a non-TTD MEFSS-based
lens previously proposed in [46], are performed to examine the response of each lens when excited
with broadband pulsed signals. It was demonstrated that the TTD MEFSS-based lenses do not
considerably distort a broadband incident pulse whereas even a narrowband modulated pulse can
be seriously distorted when transmitting through a non-TTD lens.
133
Chapter 6
Wideband True-Time-Delay Microwave Lenses Based on MetalloDielectric and All-Dielectric Lowpass Frequency Selective Surfaces
6.1
Introduction
Lenses operating at different wavelengths across the electromagnetic (EM) wave spectrum are
widely used in our daily lives. Optical lenses used for imaging are nowadays ubiquitous partly
due to the widespread use of multi-functional wireless devices that include miniaturized cameras.
Similarly lenses operating within the microwave and millimeter-wave frequency bands are used for
a variety of applications ranging from imaging for biomedical [54], [55] and security [56] applications to high-gain antennas [57], phased-arrays [58], and radar systems [59]. Chromatic aberration
is an important phenomenon observed in most lenses whether operating at optical wavelengths or
microwave frequencies. In optical lenses, chromatic aberration is due to the change of refraction
index of the lens material as a function of frequency. Because of this change of refraction index,
the focal length of the lens is different for different wavelengths. This phenomenon can result in
the deterioration of the image quality when such lenses are used as part of an imaging system. In
modern optical imaging systems, extra-low dispersion lenses are employed to reduce the adverse
effects of chromatic aberration [60]. Many microwave lenses also suffer from chromatic aberration [61]-[62]. When used as part of a wireless system (e.g., a high-gain antenna) these lenses
tend to significantly distort the temporal characteristics of broadband pulses [63]. Therefore, in
applications where signals with instantaneously broad bandwidths are used, microwave lenses free
of chromatic aberration must be employed.
134
Planar wave front
at the output
Planar lowpass
FSS-based TTD lens
Focal point
Spherical wave front
at the input
Dx
P1
y
Dy
PN-2
P3
P1
z
x
PN-2
P3
h4
h2
PN
PN
hN-1
Metallo-dielectric lowpass time-delay unit (TDU)
Dx
D1
high-εr
substrate
Dy
h2
h1
h3
DN
DN-2
D3
hN-2
h4
hN-1
low-εr
hN substrate
All-dielectric lowpass time-delay unit (TDU)
Z2
Z0
C1
Z4
(a)
C3
h2
ZN-1
CN Z 0
CN-2
h4
(b)
hN-1
Figure 6.1 (a) Topology of the proposed TTD lens populated with lowpass FSS-based spatial
TDUs. The inset shows the composition of each TDU. (b) The equivalent circuit model of each
lowpass type TDU.
Over the past several decades, a number of studies have examined the design of various types
of planar microwave lenses. Such lenses are typically composed of arrays of transmitting and
135
receiving antennas connected together through a phase-delay or time-delay mechanism [66], [74],
[67], [70], [73]. However, the array element separation in these planar lenses is generally large due
to the relatively large dimensions of the array elements (generally in the order of half a wavelength).
This results in a poor response when these lenses are illuminated at oblique incidence angles. More
recently, metamaterials with artificially engineered material properties have also been exploited to
develop microwave lenses [79]-[82]. However, such lenses tend to be narrow-band and dispersive
[84] and can introduce significant signal distortion even for narrowband modulated incident pulses.
Frequency selective surfaces have also been used to design planar microwave lenses [86], [157],
[46]. In particular, we recently reported a true-time-delay (TTD) planar microwave lens [63] based
on a class of bandpass frequency selective surfaces [42]. Such lenses are demonstrated to be free of
chromatic aberration over relatively broad bandwidths. However, because of the bandpass nature
of the time-delay units employed in such lenses, it is generally difficult to increase their bandwidths
particularly at the lower edge of their operating band. More importantly, however, these lenses need
to use a large number of metallic and dielectric layers to achieve the desired chromatic-aberrationfree response. For example, the structure reported in [63] uses seven metallic, six dielectric, and
five substrate bonding layers. While these structures can be fabricated using standard lithography
and substrate bonding techniques, using fewer metallic and dielectric layers is inherently preferable
and is expected to result in the reduction of cost and design complexity of the lens.
In this chapter, we present two methods for designing true-time-delay, planar microwave lenses
that are based on lowpass frequency selective surfaces. Each time-delay unit of the proposed
lens is the unit cell of an appropriately designed lowpass FSS and provides a desired time delay
over the frequency range of interest. The lowpass FSSs used in the present work can be in the
form of either a metallo-dielectric or an all-dielectric structure with multiple layers. The metallodielectric lowpass FSSs consist of several metallic layers separated from each other by dielectric
substrates. Each metallic layer is in the form of a two-dimensional arrangement of sub-wavelength
capacitive patches. The capacitive metallic layers separated from each other by dielectric substrates
constitute a lowpass filter. Similarly, the all-dielectric lowpass FSSs consist of high-εr and low-εr
dielectric substrates cascaded sequentially. Each high-εr substrate acts as a capacitive layer and its
136
effective dielectric constant can be adjusted by including a metal-free substrate through-hole with
an appropriately chosen diameter within each unit cell. The high-εr dielectric layers separated from
each other by low-εr dielectric layers form a lowpass filter. Compared to the metallo-dielectric
lowpass FSS, the all-dielectric lowpass FSS is expected to have a much higher power handling
capability due to its metal-free nature.
In what follows, we will first present the detailed design procedure for the proposed microwave
lenses in Section 6.2. In Section 6.2.2.1 we discuss the design of two metallo-dielectric TTD lens
prototypes with circular apertures with diameters of 18.6 cm and 16.2 cm and focal lengths of 19
cm and 24 cm corresponding to f /D ≈ 1 and f /D ≈ 1.5 respectively. The two lens prototypes
examined in Section 6.2.2.1 have similar aperture dimensions and focal lengths compared to the
bandpass lenses reported in [63]. However, the present designs use only four metallic layers and
three substrates (as opposed to 7 metallic and 6 substrate layers used in [63]). In Section 6.2.2.2,
we discuss the design of an all-dielectric TTD lens with circular aperture diameter of 16.2 cm and
focal lengths of 21 cm corresponding to f /D ≈ 1.3. The measurement results of all these three
lens prototypes are presented in Section 6.3. For the same f /D, it is demonstrated that the proposed lowpass lenses offer a broader bandwidth compared to the bandpass TTD lenses reported in
[63]. In particular, it is experimentally demonstrated that all these lenses remain free of chromatic
aberration over very wide bandwidths. This is accomplished by experimentally characterizing their
frequency-dependent focal point movements and by measuring their time-domain responses when
illuminated with broadband modulated pulses. The responses of these lenses under illumination
with oblique incidence angles are also measured and presented in Section 6.3.
6.2 TTD Lens Design and Principles of Operation
Fig. 6.1(a) shows the topology of the proposed TTD lens. The aperture of the lens is populated
with numerous sub-wavelength spatial time-delay units (TDUs). Each TDU is the unit cell of an
appropriately designed lowpass type FSS that provides a desired time delay within the frequency
range of interest. This desired time delay is an explicit function of the lens’ aperture dimensions
and its focal distance. A procedure for determining this time delay is reported in [63] and will
137
not be repeated here. As stated by the Fermat’s principle, the time delay profile provided by
the lens must satisfy the following condition: All the rays that originate on the focal point and
end on the lens’ output aperture must experience the same time delay. The lowpass FSS-based
TDU shown in Fig. 6.1(a) can be composed of either a metallo-dielectric structure with subwavelength capacitive patches and dielectric substrates cascaded sequentially, or an all-dielectric
structure with high-εr and low-εr dielectric substrates cascaded sequentially. Both TDU types
have the same equivalent circuit model as shown in Fig. 6.1(b). In the metallo-dielectric lowpass
FSSs, the capacitive patches can be modeled as shunt capacitors and the dielectric substrates can
be modeled as transmission lines for a vertically incident TEM plane wave. Similarly in the alldielectric lowpass FSSs, the high-εr substrates can be modeled as transmission lines with low
characteristic impedances. As is well-known from microwave filter theory, a short section of a lowimpedance transmission line can be modeled with a shunt capacitor [106]. The low-εr substrates
in this type of lowpass FSS are modeled with simple transmission lines as is shown in Fig. 6.1(b).
The transmission lines shown in Fig. 6.1(b) can be further simplified to series inductors, when
their lengths are sufficiently smaller than the wavelength. Therefore, the circuit model shown in
Fig. 6.1(b) is essentially an N th −order lowpass filter with N reactive elements.
6.2.1
Sub-wavelength Lowpass Spatial Time-Delay Units
A maximally-flat group-delay response can be achieved from a classical lowpass filter composed of lumped circuit elements whose values are fixed and are frequency independent [106].
Such a filter can have a truly constant group delay as a function of frequency over its entire bandwidth. This characteristic is highly desired in TDUs used in a TTD lens of the type demonstrated
in Fig. 6.1(a); since, with a constant group delay for each of the lens’ TDUs, the lens will be truly
free of chromatic aberration over an extremely large bandwidth (i.e., from very low frequencies up
to the cutoff frequency of the TDU with the lowest bandwidth). Unfortunately, this ideal situation
dose not occur in the physically-realizable lowpass FSSs shown in Fig. 6.1(a). The circuit model
shown in Fig. 6.1(b) includes transmission lines whose effective inductance values are determined
by their electrical lengths. Such frequency-dependent inductance values makes it impractical to
138
(a)
(b)
Figure 6.2 Calculated frequency responses of three lowpass FSSs with N = 5, having three
different cutoff frequencies (fcutof f = ∞, 16, and 11 GHz for states A, B, and C). State A has no
capacitive patches. (a) Magnitudes (solid) and phases (dashed) of the transmission coefficients.
(b) Group delays. As fcutof f decreases, the transmission phase shifts within the highlighted
region increases and a correspondingly larger group delay can be achieved.
obtain a constant group delay value within the entire pass band of the circuit model shown in Fig.
6.1(b). Nevertheless, using this structure, achieving relatively constant group delays over a wide
frequency range is still possible. A filter with a constant group delay has a linear phase response,
where the slope of the phase versus frequency determins the group delay of the filter [106]. Therefore, the time-delay units of the proposed lenses are synthesized from lowpass FSSs that provide
linear phase responses over the desired frequency range.
139
(a)
(b)
Figure 6.3 Calculated frequency responses of three lowpass FSSs with N = 7, having three
different cutoff frequencies (fcutof f = ∞, 30, and 11 GHz for states D, E, and F. State D has no
capacitive patches. (a) Magnitudes (solid line) and phases (dashed line) of the transmission
coefficients. (b) Group delays. As the N increases, the maximum delay variation within the
highlighted region increases.
To obtain beam collimation over a wide frequency range, different time-delay values are required for different pixels over the lens aperture. The group delay of a lowpass type FSS can be
controlled by several factors including the cutoff frequency (fcutof f ) and the order of the filter response. Fig. 6.2 shows the effect of the cutoff frequency on the group delay of a fifth-order lowpass
FSS. To obtain these results, a characteristic impedance of 377 Ω is assumed for all the transmission line models in Fig. 6.1(b). As can be seen from Fig. 6.2(a)-(b), the lower fcutof f is, the larger
the group delay and the slope of the transmission phase will be. Within the desired frequency
140
range of 7 − 11 GHz (the highlighted region in Fig. 6.2), the maximum group delay difference that
can be achieved from the lowpass FSS with N = 5 is only 13 psec, as shown in Fig. 6.2(b). To
obtain a larger group delay difference, a higher order lowpass FSS is required. Fig. 6.3 shows the
frequency responses of three lowpass FSSs with N = 7 and three different cutoff frequencies. The
maximum group delay difference within the same desired frequency range of 7−11 GHz increases
to 50 psec, as shown in Fig. 6.3(b). In practice, as described in [63], the desired aperture size and
the focal distance of the lens determine the maximum time-delay difference required over the lens’
aperture. This in turn determines the order of the lowpass FSS needed to implement the TTD lens.
Once the order of the lowpass FSS has been chosen, the cutoff frequency will be varied to obtain
different group delays, or equivalently different slopes of phase responses, for each TDU over the
lens’ aperture.
6.2.2
Lowpass FSS-Based TTD Lens Design Procedure
The design procedure of the lowpass FSS-based TTD lens presented in this work is similar to
the design procedure of the bandpass FSS-based TTD lens covered in Section II-B of [63]. For
brevity, the detailed design procedure will not be repeated here and the reader is referred to [63].
The aperture of the lens is divided into M concentric zones, with identical TDUs populating each
zone. The time delay profile required from the TDUs occupying each zone is calculated from the
dimension of the lens’ aperture, D, and its focal length, f , using the procedure reported in [63].
The lowpass FSS-based TDUs shown in Fig. 6.1(a) can then be used to obtain the required time
delay for each zone. In what follows, we first apply the design procedure to two metallo-dielectric
lowpass FSS-based TTD lens prototypes with different aperture sizes, focal distances, and different
frequency ranges of interest. Then, the same procedure will be used to design an all-dielectric TTD
lens.
6.2.2.1 Design Procedure for Metallo-Dielectric FSS-Based TTD Lenses
The first metallo-dielectric lowpass FSS-based TTD lens is designed to work within the frequency range of 6.5 − 10.5 GHz. The lens has an aperture diameter of 16.2 cm and a focal distance
141
Table 6.1 Distances between the center of each zone and the center of the lens aperture for the
three lens prototypes discussed in Section 6.2.2. Lenses 1 and 2 are the first and the second
metallo-dielectric TTD lenses in Section 6.2.2.1, and lens 3 is the all-dielectric TTD lens in
Section 6.2.2.2. All values are in mm.
d1 d2
d3
d4
d5
d6
Lens 1 (f /D ≈ 1.5)
0
24
30
36
42
48
Lens 2 (f /D ≈ 1)
0
27
36
42
44.5
48
Lens 3 (f /D ≈ 1.3)
0
24
36
42
48
54
d7
d8
d9
d10
d11
d12
Lens 1 (f /D ≈ 1.5)
51
54
56
60
62
66
Lens 2 (f /D ≈ 1)
54
60
62.5
66
70
72
Lens 3 (f /D ≈ 1.3)
57
60
66
69
72
78
d13
d14
d15
d16
d17
Lens 1 (f /D ≈ 1.5)
70
72
76
78
Lens 2 (f /D ≈ 1)
78
80
84
85
90
142
Table 6.2 Physical and electrical properties of the time-delay units that populate each zone of the
first metallo-dielectric TTD lens with a desired frequency range of 6.5 − 10.5 GHz and
f /D ≈ 1.5. Time delay values in the desired frequency range are in psec. All physical
dimensions are in mm. For all of these TDUs, Dx = Dy = 6 mm, h2 = h4 = h6 = 3.175 mm.
The dielectric substrate used is Rogers 5880 with a dielectric constant of 2.2.
Zone Time Delay
P1
P3
P5
P7
5.3
4.62
1
86.94
4.65 5.12
2
84.16
4.65 5.05 4.95 4.75
3
81.66
4.6
4.95
4
78.88
4.43
3
5
76.39
4.25 2.55
6
73.61
4
2
7
71.11
3.4
1.5
4.6
5.35
8
68.33
3.3
1.1
4.4
5.25
9
65.83
3.1
0.9
4.15
5.1
10
63.05
2.9
0.9
4.1
4.85
11
60.55
2.65
0.9
3.8
4.55
12
57.77
2.5
0.9
3.75
4.2
13
55.27
2.2
0.75
3.6
3.8
14
52.5
2
0.5
3.2
3.15
15
50
1.6
0.2
2.5
2.5
16
47.2
0
0
0
0
4.9
4.55
4.95 5.22
4.9
5.24
4.70 5.35
143
(a)
(b)
Figure 6.4 (a) The comparison between the full-wave simulated transmission phases and the ideal
linear transmission phases for different zones of the first metallo-dielectric TTD lens prototype
with 16 concentric zones and f /D ≈ 1.5. Zi : ideal represents an ideal desired linear
transmission phase with the desired time delay for Zone i as listed in Table 6.2. (b) The simulated
transmission and reflection coefficients of the TDUs occupying each zone of the first
metallo-dielectric TTD lens prototype. The highlighted region (6.5 − 10.5 GHz) in both figures
indicates the area where an approximate linear transmission phase close to the required ideal
linear phase can be obtained. This region is considered to be the desired frequency range of
operation for the TTD lens.
of 24 cm, which corresponds to f /D ≈ 1.5. The aperture of the first metallo-dielectric lens is
divided into 16 concentric zones and the distance between the center of each zone and the center of
the lens’ aperture is shown in Table 6.1. The time delay required from the TDUs occupying each
144
zone is calculated and presented in Table 6.2 following the procedure outlined in [63]. For this
lens, the maximum time delay difference over the aperture is 39.74 psec. Following the guidelines
provided in Section 6.2.1, this maximum time delay difference can be achieved by using a lowpass
FSS with N = 7 and a linear transmission phase over the frequency range of interest. The unit
cell of such a FSS is composed of four capacitive patch layers separated from one another by three
dielectric layers. The total thickness of each TDU is 9.8 mm or equivalently 0.27λ0 1 . The detailed
physical and electrical parameters of the TDUs that occupy each zone of the lens are provided in
Table 6.2 as well. As can be seen, the group delays provided by the TDUs of the two adjacent
zones are slightly different and a gradual change of the time delay is achieved from one zone to
the other. This slight group delay difference can be achieved by de-tuning the cutoff frequency of
the TDUs in one zone with respect to the TDUs in its neighboring zone. This de-tuning process
is performed by optimizing the dimensions of the capacitive patches used in different layers of a
TDU. Achieving an approximate linear transmission phase with the desired slope is the main goal
of this optimization process. Fig. 6.4 shows the frequency responses of the TDUs occupying each
zone of this lens. These results are obtained by using full-wave EM simulations in CST Microwave
Studio. Fig. 6.4(a) shows the comparison between the full-wave simulated phase responses and the
desired ideal linear phase responses for each TDU. They match each other closely within the highlighted band. Slight discrepancies are observed between the full-wave simulation results and the
ideal desired responses for some of the zones (Zone 1 and Zone 4) at the edges of the highlighted
region. Fig. 6.4(b) shows the amplitude of the transmission coefficients of the TDUs occupying
each zone of the lens. As can be seen from Fig. 6.4(b), the highlighted frequency region of Fig.
6.4(a) falls within the pass band of all TDUs.
The second metallo-dielectric lowpass FSS-based TTD lens studied in this chapter has an aperture diameter of 18.6 cm and a focal distance of 19 cm. This corresponds to f /D ≈ 1. The second
lens is divided into 17 zones and the detailed position of each zone is listed in Table 6.1. Compared
to the first TTD lens discussed above, the maximum time delay difference over the second lens’
aperture is increased to 63.61 psec. This increased group delay difference can still be achieved by
1
λ0 is the free space wavelength at the center frequency of operation of each fabricated lens.
145
using 7th -order lowpass FSS. This, however, comes at the cost of reducing the frequency range
of operation of the FSS, since fcutof f has to be reduced for the TDU that provides the maximum
group delay (e.g., see Fig. 6.3(b)). Therefore, the desired frequency range of operation for the second lens decreases to 6.5 − 8.5 GHz. The detailed electrical and physical parameters of the TDUs
occupying each zone of the lens are listed in Table 6.3. Fig. 6.5(a) demonstrates the comparison
between the full-wave simulated phase responses of the TDUs of the proposed lens and the desired
ideal linear phase responses needed for perfect TTD operation. Fig. 6.5(b) shows the magnitudes
of the transmission coefficients of the TDUs. As can be observed, the linear phase response region
(the highlighted frequency band) falls within the transmission band of all TDUs as expected.
6.2.2.2
Design Procedure For All-Dielectric FSS-Based TTD Lenses
The metallo-dielectric lenses described in Section 6.2.2.1 require capacitive layers with closelyspaced rectangular patches. As shown in [158], the electric field intensity in such structures can
be greatly enhanced within the small capacitive gaps compared to that of the incident EM wave.
This can lead to air or dielectric breakdown at high peak power levels [158]. This limits the power
handling capability of the TTD lenses designed with such metallo-dielectric FSSs. Since the all dielectric lens shown in Fig. 6.1(a) does not use any metallic structures, it is a more suitable candidate
for high-power microwave applications. Similar to the metallo-dielectric TDUs, the all-dielectric
TDUs also have a lowpass filter equivalent circuit model as shown in Fig. 6.1(b), with the shunt
capacitor values determined by the effective dielectric constants of the high-εr substrate layers.
Different effective dielectric constants are needed to obtain different group delay values from the
all-dielectric TDUs. This can be achieved by including periodically arranged metal-free through
holes within the high-εr substrates of the all-dielectric lowpass FSS as shown in Fig. 6.1(a). Assuming the high-εr substrate used in this design has a dielectric constant of 10.2 (Rogers 6010)
and substrate thickness of 1.27 mm, the effective dielectric constant of the high-εr layer with embedded holes can be easily calculated. Fig. 6.6 demonstrates the effective dielectric constant as a
function of the diameter of the substrate through-hole when the period of the hole pattern is 6 mm.
146
Table 6.3 Physical and electrical properties of the time-delay units that populate each zone of the
second metallo-dielectric TTD lens with a desired frequency range of 6.5 − 8.5 GHz and
f /D ≈ 1. Time delay values within the desired frequency range are in psec. All physical
dimensions are in mm. For all of these TDUs, Dx = Dy = 6 mm, h2 = h4 = h6 = 3.175 mm.
The dielectric substrate used is Rogers 5880 with a dielectric constant of 2.2.
Zone Time Delay
P1
P3
P5
5.75 5.73
P7
1
109.58
5.4
2
105.69
5.35 5.71 5.67
5
3
101.53
5.22 5.65 5.61
4.9
4
97.64
5.1
5.60 5.52
4.7
5
93.75
4.8
5.55 5.45
4.5
6
89.86
5.08 5.24 5.25 4.79
7
85.69
5.31 5.29 4.82
8
81.80
4.7
5.07 4.66 4.77
9
77.91
4.6
4.8
4.47 4.65
10
73.75
4.45
4.4
4.2
4.7
11
69.86
4.2
4
4
4.6
12
65.97
3.95
3.7
3.7
4.45
13
62.08
3.8
3.5
3.4
4.3
14
57.91
3.4
3.9
3.6
3.1
15
54.02
3.1
3.5
3.1
3
16
50.14
2.6
2.65 2.55
17
45.97
1
1
1
5.1
4.3
2.5
1
147
(a)
(b)
Figure 6.5 (a) The simulated transmission and reflection coefficients of the TDUs occupying each
zone of the second metallo-dielectric lens prototype. The highlighted region (6.5 − 8.5 GHz) in
both figures indicates the area where an approximate linear transmission phase close to the
required ideal linear phase can be obtained. This region is considered to be the desired frequency
range of operation for the TTD lens. (b) The comparison between the full-wave simulated
transmission phases and the ideal linear transmission phases for different zones of the second
metallo-dielectric lens prototype with 17 concentric zones and f /D ≈ 1. Zi : ideal represents an
ideal desired linear transmission phase with the desired time delay for Zone i as listed in Table
6.3.
The continuous change of the effective dielectric constant shown in Fig. 6.6 indicates that a correspondingly continuous effective capacitance can be obtained. This in turn will be used to obtain
the desired group delays. The aforementioned TTD lens design procedure described in Section
6.2.2.1 is applied here to an all-dielectric lowpass FSS-based TTD lens with an aperture diameter
148
Table 6.4 Physical and electrical properties of the time-delay units that populate each zone of the
all-dielectric TTD lens with a desired frequency range of 7.5 − 11.5 GHz and f /D ≈ 1.3. Time
delay values within the desired frequency range are in psec. All physical dimensions are in mm.
For all of these TDUs, Dx = Dy = 6 mm, h1 = h3 = h5 = h7 = 1.27 mm,
h2 = h4 = h6 = 1.575 mm. The high-εr dielectric substrate used is Rogers 6010 with a dielectric
constant of 10.2, and the low-εr dielectric substrate used is Rogers 5880 with a dielectric constant
of 2.2. CU T from zone 9 to zone 12 indicates the corresponding high-εr layer is completely
removed. All the low-εr substrates of zone 11 have substrate through-holes with diameter of
3.7 mm, and all the low-εr substrates of zone 12 have substrate through-holes with diameter of
5.7 mm
Zone Time Delay D1
D3
D5
D7
1
88.1
0
0
0
0
2
84.2
2.4
1.6
0.6
2.8
3
80
3.3
1.5
3.5
3.2
4
76.1
4.2
1.5
3.4
4.2
5
72.2
4.5
3.0
4.4
4.2
6
68.3
4.6
4.4
5.0
4.4
7
64.2
4.6
5.6
5.5
4.6
8
60.3
5.2
5.7
5.7
5.0
9
56.4
5.2
CU T
CU T
5.0
10
52.2
5.5
CU T
CU T
5.5
11
48.3
5.7
CU T
CU T
5.7
12
44.4
5.7
CU T
CU T
5.7
149
Diameter
Figure 6.6 The effective dielectric constant of the high-εr substrate that is periodically loaded
with cylindrical through-substrate holes as a function of the diameter of the through-substrate
holes. The high-εr substrate is Rogers 6010 with dielectric constant of 10.2 and a thickness of
1.27 mm. The periodicity of the substrate through-holes is 6 mm.
of 16.2 cm and a focal distance of 21 cm. This corresponds to f /D ≈ 1.3. The lens is divided into
12 zones and the detailed position of each zone is listed in Table 6.1. The total thickness of this
lens is 9.8 mm or equivalently 0.3λ0 . The maximum time delay difference over the lens aperture
is 43.7 psec, which can be achieved using a 7th -order lowpass FSS. A 7th -order all-dielectric type
lowpass FSS is composed of four high-εr substrates separated from each other by three low-εr substrates. Each high-εr substrate has periodically arranged through holes. The detailed physical and
electrical parameters of the all-dielectric lowpass FSS-based TDUs populating each zone are listed
in Table 6.4. As can be seen from Table 6.4, the required time delay gradually decreases as the zone
number increases. This in turn indicates that larger through holes are needed for the zones located
far away from the center of the lens aperture. For these zones, the existence of certain high-εr substrate layers appear to be the bottlenecks of obtaining small time delays. Thus, it was necessary to
completely remove certain high-εr substrate layers in these zones. Therefore, as seen from Table
6.4, the high-εr substrate layers 3 and 5 are completely removed from TDUs of zone 9 to 12 (this
is indicated by the word “CU T ” in Table 6.4). This can be done easily in practice by performing a
square cut using a computer-controlled milling machine. Furthermore, for the zones located at the
very edges of the lens (zones 11 and 12), the required time-delay values are so small that merely
removing the high-εr substrate layers 3 and 5 was not enough. In that case, the through holes are
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also included in all the low-εr substrate layers such that the time delays of zone 11 and zone 12
are made small enough to meet the desired requiement. Fig. 6.7(a) demonstrates the comparison
between the full-wave simulated phase responses of the TDUs of the proposed all-dielectric TTD
lens and the desired ideal linear phase responses needed for perfect TTD operation. Fig. 6.7(b)
shows the magnitudes of the transmission coefficients of the TDUs. As can be observed from the
linear phase response region (the highlighted frequency band) highlighted in Fig. 6.7, the TTD
frequency range of this all-dielectric lens is 7.5 − 11.5 GHz.
6.3 Experimental Verification and Measurement Results
The metallo-dielectric and all-dielectric lenses examined in Section 6.2.2 are fabricated using standard lithography and substrate bonding techniques and experimentally characterized. For
each of the metallo-dielectric TTD lenses, four metal layers and three substrate layers are used.
Rogers 5880 dielectric substrates (with ϵr = 2.2) with the thickness of 3.175 mm are used for
each substrate layer and the adjacent substrates are bonded together using a 0.1-mm-thick bonding
film (Rogers 4450F). Both metallo-dielectric lenses have a total thickness of 9.8 mm, which is
equivalent to 0.27λ0 (0.24λ0 ) for the first (second) lens discussed in Section 6.2.2.1. Each metallodielectric TDU, as shown in Fig. 6.8(c), has a dimension of 6 mm × 6 mm, which is equivalent to
0.17λ0 × 0.17λ0 (0.15λ0 × 0.15λ0 ) for the first (second) metallo-dielectric lens prototype. Fig. 6.8
shows the photograph of the fabricated metallo-dielectric TTD lens with f /D ≈ 1 and 17 zones.
For the all-dielectric TTD lens prototype, four high-εr substrates and three low-εr substrates are
used. Rogers 6010 dielectric substrates with ϵr = 10.2 and thickness of 1.27 mm are used for each
high-εr substrate layer. Rogers 5880 dielectric substrates with ϵr = 2.2 and thickness of 1.575 mm
are used for each low-εr substrate layer. The required substrate through holes are machined into the
substrates using a computer controlled milling machine. The high- and low-εr layers are bonded
together using 0.1-mm-thick bonding films. The all-dielectric lens prototype has a total thickness
of 10.14 mm (or equivalently 0.3λ0 ) and an aperture diameter of 16.2 cm (or equivalently 5.12λ0 ).
Several different pictures of the fabricated all-dielectric TTD lens are shown in Fig. 6.9(a)-6.9(c).
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(a)
(b)
Figure 6.7 (a) The simulated transmission and reflection coefficients of the TDUs occupying each
zone of the all-dielectric TTD lens prototype. The highlight region (7.5 − 11.5 GHz) in both
figures indicates the area where an approximate linear transmission phase close to the required
ideal linear phase can be obtained. This region is considered to be the desired frequency range of
operation for the TTD lens. (b) The comparison between the full-wave simulated transmission
phases and the ideal linear transmission phases for different zones of the all-dielectric TTD lens
prototype with 12 concentric zones and f /D ≈ 1.3. Zi : ideal represents an ideal desired linear
transmission phase with the desired time delay for Zone i as listed in Table 6.3.
6.3.1 TTDs Lens Characterization
The characterization of the fabricated lenses are carried out following the procedure described
in Section III-A of [63]. The measurement setup described in [46] is used to conduct a series of
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Figure 6.8 (a) Top view of the fabricated metallo-dielectric TTD lens prototype with 17 zones
and a f /D ≈ 1. (b) Side view of the metallo-dielectric TTD lens prototype with 17 zones and a
f /D ≈ 1. (c) The detailed zoom in view of one corner of the only visible metallic layer, the first
capacitive patch layer. The size of the capacitive patches decrease from the center of the lens to
the edges. Note here the same trend exists for all the other capacitive layers located in the interior
layers of the structure.
measurements for all of the proposed TTD lenses. First, the focusing gain is characterized. The
focusing gain is obtained by normalizing the received field intensity in the presence of the lens
to the received field intensity in the absence of the lens. This normalization is carried out at the
focal point. Fig. 6.10 shows the measured and simulated focusing gains for all the TTD lenses.
Using the procedure described in [46], the focusing gain of each lens is also calculated and the
results are presented in Fig. 6.10 in conjunction with the measurement results. As is observed, the
measurement agrees very well with the theoretical predictions.
The normalized near field focusing pattern is also measured using the setup shown in Fig. 10(b)
of [46]. Basically, a receiving probe is moved in a 2D grid in the vicinity of the expected focal point
and the signal intensity is measured. Using this data, the location where the maximum received
field intensity occurs (i.e., the focal point) is determined. Fig. 6.11 shows the normalized near
field focusing pattern of all three TTD lenses. The location of the maximum received field value is
marked with the cross symbol (x) in Fig. 6.11(a)-6.11(i) from which the measured focal distance
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Figure 6.9 (a) Top view of the fabricated all-dielectric TTD lens prototype with 12 zones and a
f /D ≈ 1.3. (b) Side view of the all-dielectric TTD lens prototype with 12 zones and a
f /D ≈ 1.3. (c) The detailed zoom in view of one corner of the only visible high-εr layer. The
size of the substrate through-hole increase from the center of the lens to the edges. Note here the
same trend exists for all the other high-εr layers located in the interior layers of the structure.
can be read from the y axis. Fig. 6.12 shows the measured focal length of the three lenses as a
function of frequency. As can be seen, the focal distance of the metallo-dielectric TTD lens with
f /D ≈ 1.5 remains constant within the frequency range of 6.5 − 10 GHz (with ±1 cm variation
around the expected focal length 24 cm). Similarly, the measured focal distance of the metallodielectric TTD lens with f /D ≈ 1 remains constant within the frequency range of 7 − 9 GHz (with
±1 cm variation around the expected focal length 19 cm). Finally, the measured focal distance of
the all-dielectric TTD lens remains constant within the frequency range of 8 − 11.5 GHz (with ±1
cm variation around the expected focal length 21 cm). The fact that the focal lengths of the TTD
lenses do not vary as a function of frequency demonstrates that the proposed lenses act in a TTD
fashion without introducing any significant chromatic aberration over the desired frequency range
(TTD frequency range highlighted in Fig. 6.4, Fig. 6.5 and Fig. 6.7).
Given the same f /D ratio, the TTD frequency range of the proposed lowpass FSS-based TTD
lens (6.5 − 10.5 GHz for the first metallo-dielectric lens) is observed to be much wider than that
of the previously reported bandpass FSS-based TTD lens reported in [63] (8 − 10.5 GHz). This is
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(a)
(b)
(c)
Figure 6.10 (a) Calculated and measured focusing gains of the first metallo-dielectric TTD lens
prototype with f /D ≈ 1.5 at its expected focal point (x = 0 cm, y = 0 cm, z = −24 cm). (b)
Calculated and measured focusing gains of the second metallo-dielectric TTD lens prototype with
f /D ≈ 1 at its expected focal point (x = 0 cm, y = 0 cm, z = −19 cm). (b) Calculated and
measured focusing gains of the all-dielectric TTD lens prototype with f /D ≈ 1.3 at its expected
focal point (x = 0 cm, y = 0 cm, z = −21 cm). All of the focusing gains are measured using the
same setup shown in Fig. 10(a) of [46].
due to the fact that the TTD frequency range in a lowpass FSS-based lens is limited by the lowest
cutoff frequency of all TDUs whereas the TTD frequency range in a bandpass FSS-based TTD
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5
10
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10
(c)
−5
0
(f)
−5
0
5
10
(i)
Figure 6.11 Measured normalized received field intensity of the fabricated TTD lens prototypes
in a rectangular grid in the vicinity of their expected focal points. The normalized field pattern of
the first metallo-dielectric TTD lens with f /D ≈ 1.5 is shown at (a) 6.5 GHz, (b) 8.0 GHz, and
(c) 10 GHz. The normalized field pattern of the second metallo-dielectric TTD lens with
f /D ≈ 1 is shown at (d) 7 GHz, (e) 8.0 GHz, and (f) 9 GHz. The normalized field pattern of the
all-dielectric TTD lens with f /D ≈ 1.3 is shown at (g) 8.0 GHz, (h) 9.5 GHz, and (i) 11.5 GHz.
The “x” symbol shows the actual focal point of the lens determined by the measurement and the
color bar values are in dB. In all of the figures, the horizontal axis is the x axis with units of [cm]
and the vertical axis is the z axis with units of [cm]. The measurement is conducted using the
same setup shown in Fig. 10(b) in [46].
lens is limited by the overlap region of the passbands of all TDUs. Therefore, by using the lowpass
FSS-based TDUs, obtaining a wider TTD frequency range of operation is significantly simplified.
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≈
≈
≈
Figure 6.12 Measured focal length of all the fabricated lens prototypes.
Also, as can be observed from Fig. 6.12, the lens with f /D ≈ 1 has a narrower frequency range
within which the focal point remains constant compared to the TTD lens with f /D ≈ 1.5. This is
expected, since the linear phase region of the TTD lens with f /D ≈ 1 (highlighted region in Fig.
6.5(b)) is narrower than that of the TTD lens with f /D ≈ 1.5 (highlighted region in Fig. 6.4(b)).
Finally, when used as part of a multi-beam antenna, the lens is expected to have a wide field
of view (FOV). This impacts the performance of the system when such an antenna is used for
beam scanning applications by switching the feeds located on the lens’ focal arc. The scanning
performances of all lenses are experimentally characterized using the setup shown in Fig. 10(c)
of [46] and the procedure outlined in Section III-A of [46]. Each lens is illuminated by plane
waves with incident angles of 0◦ , 15◦ , 30◦ , 45◦ , 60◦ , and the received power patterns are measured
over the lens’ focal arc for each incident angle over a broad frequency range. Since the system is
reciprocal, the measured power pattern on the lens’ focal arc gives an indication of the performance
of the system when a feed is located at corresponding location on the focal arc and the transmitted
signal is measured in the far field. At each frequency, the maximum received field intensity always
happens at the focal point under normal incidence. Hence, all the measured values are normalized
to this maximum value, and the normalized power patterns for all three TTD lenses are shown in
Fig. 6.13 over a broad frequency band. Fig. 6.13(a)-6.13(f) show that all three lenses maintain a
FOV of ±60◦ with a maximum performance degradation of around 5dB at 60◦ incidence. These
lenses demonstrate excellent scanning performances similar to the FSS-based lenses previously
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reported in [46] and [63]. This is expected since the unit cell sizes in the proposed lowpass FSS
based TTD lenses, as well as in the lenses reported in [46] and [63], are quite small compared to
the desired wavelength of operation.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 6.13 Measured scanning performance of the fabricated metallo-dielectric TTD lens with
f /D ≈ 1.5 at (a) 6.5 GHz, (b) 9GHz, and (c) 10.5 GHz. Measured scanning performance of the
fabricated metallo-dielectric TTD lens with f /D ≈ 1 at (d) 7 GHz, (e) 8 GHz, and (f) 9 GHz.
Measured scanning performance of the fabricated all-dielectric TTD lens with f /D ≈ 1.3 at (g)
8.5 GHz, (h) 9.5 GHz, and (i) 10.5 GHz. The power pattern is measured over the focal arc of each
lens for plane waves arriving at various incidence angles.
6.3.2 Time-Domain Analysis
To fully characterize the true-time-delay behavior of a TTD lens, time-domain measurements
must be carried out. To quantify the distortion level introduced by each lens, the lens’ fidelity
factor is measured for a pulsed excitation. Fidelity factor is a measure of the correlation between
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the lens’ time-domain input and output pulses. In this work, the fidelity factor is calculated by
using the measured frequency-domain transfer function of the lens. The time-domain output of the
lens is then calculated using the measured frequency response of the lens and the mathematicallydefined input pulse following the procedure described in [63]. For a TTD lens that dose not have
chromatic aberration within the desired frequency band, the fidelity factor is expected to be very
close to 12 .
(a)
(e)
Fidelity Factor
0.982
Fidelity Factor
0.960
(i)
(b)
Fidelity Factor
0.970
(c)
(f)
Fidelity Factor
0.95
(g)
Fidelity Factor
0.910
(j)
Fidelity Factor
0.961
Fidelity Factor
0.981
Fidelity Factor
0.95
(k)
Fidelity Factor
0.974
(d)
(h)
Fidelity Factor
0.935
Fidelity Factor
0.91
Figure 6.14 Time-domain responses and fidelity factors of all proposed TTD lens prototypes for
various excitation signals. (a)-(c) The incident and transmitted pulses of the proposed
metallo-dielectric lowpass FSS-based TTD lens with f /D ≈ 1.5 for the modulated Guassian
pulses centered at 8.5 GHz with fractional bandwidths of (a) 10%, (b) 30%, (c) 50%. (d)-(f) The
incident and transmitted pulses of the proposed metallo-dielectric lowpass FSS based TTD lens
with f /D ≈ 1 for the modulated Guassian pulses centered at 7.5 GHz with fractional bandwidths
of (d) 10%, (e) 20%, (f) 30%. (g)-(i) The incident and transmitted pulses of the proposed
all-dielectric lowpass FSS based TTD lens with f /D ≈ 1.3 for the modulated Guassian pulses
centered at 8.5 GHz with fractional bandwidths of (g) 10%, (h) 30%, (i) 40%. The incident and
transmitted pulses of the previously proposed bandpass FSS-based TTD lens in [63] with
f /D ≈ 1.5 for the modulated Guassian pulses centered at 9.25 GHz with fractional bandwidths
of (j) 30% and (k) 50%. In all cases, the center frequency of operation of the Gaussian pulse is
matched to the center frequency of operation of the respective lens. In all of the figures, the
horizontal axis is the time axis with units of [ns] and the vertical axis is the normalized magnitude
for the time-domain signals.
2
The formulas used for this calculation and a the detailed procedure is provided in Section III-B of [63].
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Using this procedure, the time-domain responses of the three lenses are calculated. Fig. 6.14(a)6.14(c) show the incident and transmitted pulses and the fidelity factors for the proposed metallodielectric lens with f /D ≈ 1.5. The results are shown for modulated Gaussian incident pulses
centered at 8.5 GHz with fractional bandwidths of 10%, 30%, 50%. As can be seen from Fig.
6.14(a)-6.14(c), a very high fidelity factor (0.96 < f idelity f actor < 1) can be achieved when
the lens with is excited with pulses having fractional bandwidths as wide as 50%. This is in accordance with the analysis done in Section 6.2.2.1, where the TTD frequency range of the first
metallo-dielectric lens is shown to be 6.5 − 10.5 GHz. This TTD frequency range corresponds
to a 50% fractional bandwidth with respect to the center frequency of operation (8.5 GHz). As a
general rule, in order for the TTD lens to fully preserve the signal integrity, the bandwidths of the
incident pulse should not exceed the TTD frequency range where all TDUs can have linear transmission phases. Similar responses can be observed in Fig. 6.14(d)-6.14(i), where very high fidelity
factors are observed when the metallo-dielectric lens with f /D ≈ 1 is excited with a modulated
Gaussian pulses having fractional bandwidths up to 30% and when the all-dielectric lens is excited
with modulated Gaussian pulses having fractional bandwidths up to 40%. This is, again, in accordance with the discussions of Section 6.2.2. Observed from the highlighted regions in Fig. 6.5 and
Fig. 6.7 that the TTD frequency range is respectively 6.5 − 8.5 GHz (30% fractional BW) for the
metallo-dielectric TTD lens with f /D ≈ 1 and 7.5 − 11.5 GHz (40% fractional BW) for the alldielectric TTD lens with f /D ≈ 1.3. Another factor that impacts the fidelity factors of the lenses
is the angle of incidence of the EM wave. With increasing the incidence angle, the fidelity factor
deteriorates. However, due to the stability of the responses of the TDUs used in this design, this
deterioration is not expected to be significant. The fidelity factors of these lenses were measured
under oblique incidence angles, and the results are shown in Fig. 6.15. It was observed that the
fidelity factors remain above 0.93 for all three lenses when incidence angles are below 45◦ . As the
incidence angle increases to 60◦ , the fidelity factors drop below 0.9. For the metallo-dielectric lens
with an f /D ≈ 1.5 and all-dielectric lens, the worst case fidelity factor of 0.88 is observed at 60◦
when they are excited with Gaussian pulses with bandwidths of respectively 50% and 30%. For the
metallo-dielectric lens with an f /D ≈ 1, the worst case fidelity factor of 0.81 is observed, which
160
happens when the lens is excited with a modulated Gaussian pulse with a fractional bandwidth of
30% at an incidence angle of 60◦ .
Figure 6.15 Measured fidelity factors under oblique angle of incidences for all the TTD lenses.
The benefits of using a lowpass FSS-based TTD lens can also be observed when its timedomain responses are compared with the time-domain responses of the previously proposed bandpass FSS-based TTD lens discussed in [63]. To make a fair comparison, we use one of the TTD
lenses in [63] with the circular diameter of D = 18.6 mm and f /D ≈ 1.5. Due to the inherent
bandpass nature of each TDU used in this TTD lens, the TTD frequency range of this bandpass
TTD lens is only 8.5 − 10.5 GHz, as shown in Fig. 7 in [63]. Therefore, it is not expected that
the bandpass TTD lens can handle ultra-wideband incident pulses with a fractional bandwidths
broader than this TTD frequency range. Fig. 6.14(j)-(k) show the time domain responses of the
bandpass TTD lens with f /D ≈ 1.5 for the modulated Gaussian pulses of 30% and 50% fractional bandwidths. The fidelity factors in both cases (0.95 in Fig. 6.14(j) and 0.91 in Fig. 6.14(k))
are, indeed, lower than the fidelity factors of the metallo-dielectric lowpass FSS-based lens with
f /D ≈ 1.5 for the modulated Gaussian pulses with 30% and 50% fractional bandwidths (0.97 in
Fig. 6.14(b) and 0.961 in Fig. 6.14(c)). Therefore, TTD lens that exploits lowpass type TDUs
is not only less complicated to design and requires fewer dielectric and metallic layers but also
performs better than a TTD lens exploiting bandpass FSS-based time-delay units.
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6.4
Conclusions
In this chapter, we presented a new method for designing planar microwave lenses that operate
in a true-dime-delay fashion and are free of chromatic aberration over a wide frequency band. The
proposed microwave lenses exploit time-delay units that are unit cells of appropriately designed
lowpass frequency selective surfaces. Either a metallo-dielectric or an all-dielectric type multilayer structure can be used to constitute the lowpass FSS. The proposed concept was experimentally verified by examining three fabricated lens prototypes with different focal length to aperture
dimension ratios. It was demonstrated that all of the lenses are indeed free of chromatic aberration
by examining the movement of their measured focal lengths as a function of frequency. Additionally, the time-domain responses of all lenses were examined by characterizing their fidelity factors
for wideband pulsed excitations. The lenses operate with minimal distortion over their respective true time delay operation region. The performance of one of the proposed lenses was also
compared with the performance of a recently reported true-time-delay planar microwave lens that
exploits bandpass FSS-based time-delay units [63]. It was demonstrated that the proposed lowpass
FSS-based lenses perform better than the ones using bandpass FSS-based time-delay units and can
operate over significantly broader bandwidths for the same f /D. Moreover and perhaps more importantly, the proposed lowpass lens architecture is simpler to design, requires fewer metallic and
dielectric layers than the one reported in [63], and its all-dielectric implementation is suitable for
high power applications.
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Chapter 7
Future Work
In the above chapters, several critical techniques in designing tunable microwave lenses have
been carefully studied. These include implementing a suitable fluidic tuning technique for high
power microwave applications, designing extremely high power capable frequency selective surfaces, as well as implementing various types of low profile and wideband true-time-delay microwave lenses. These studies are indeed essential in our goal of designing tunable space-fed
microwave lenses for next generation high power phased array systems. Future work based upon
this thesis are still needed to continue the existing efforts toward our final goal.
7.1
Enable tuning mechanism in large scale
The fluidic tuning mechanism described in Chapter 3 is free of solid-state phase shifters, and
can maintain linearity under high power incidence. However, the main obstacle in advancing this
new technique of tuning is the fabrication challenges associated with large scale implementation.
The experimental verification in Chapter 3 is carried in a waveguide environment with respect
to only one unit cell. In real practice, a tunable lens is composed of hundreds or thousands of
elements. Integrating the fluidic tuning technique into such a large number of unit cells is not an
easy task. Several significant challenge exist in fabricating a large scale fluidically tunable lens
prototype. Firstly, fabricating the dielectric layers of the lens that host the embedded microfluidic
channels is an important step of the entire design process. This can be potentially solved by
taking the advantage of the recently surged 3D printing technology. With the help of 3D printing,
complex microfluidic channels having cross sections with fixed or modulated widths can be directly
163
drilled out of a low-loss plastic material. Secondly, an accurate control of the movement of the
liquid chains are critical as the offset of liquids from their correct positions can greatly impact
the accuracy of the tuning. This is particularly challenging since the difficulty of moving all the
liquid droplets synchronously within the channel increases as the number of unit cells increases.
To address this issue, one way is to design complex fluidic divider network and the movement of
liquids is controlled by using a micropump. Alternatively, according to the studies in Chapter 3,
other mechanically driven systems can also be envisioned to accomplish the same tuning task as
can be done by the liquids. For example, solid metallic pellets separated from each other by an
incompressible (liquid or solid) medium can be used instead of liquid metal droplets and the Teflon
solution. In this regard, the movements of solid medium are expected to be controlled more easily
compared to their liquid counterparts.
7.2
Compact true-time-delay lenses for high gain antenna application
The true-time-delay lenses discussed from Chapter 5-6 can be used as high gain antennas when
a feeding source is located at the focal point. In order to have a compact lens antenna system,
the distance between the feeding source and the microwave lens must be reduced. This further
corresponds to a small f /D (focal length to aperture diameter) ratio. As the f /D decreases, the
maximum phase shift along the lens’ aperture increases correspondingly. This in turn increases the
difficulty in the design of a true-time-delay lens that can meet such requirement. Several solutions
exist that can potentially solve this problem. One possible solution is to have multiple feeding
sources closely located in front of the lens. This way, each feeding source is only responsible for
part of the lens, and the corresponding f /D ratio associated with each feeding source and the part
of the lens it is responsible for is increased. Such distributed feeding scheme greatly alleviate the
difficulty involved in designing lenses with large phase shift profile. One can imagine that in the
extreme cases where numerous multiple sources are placed in front of the lens, the distance between the feeding source and the lens can be made extremely small, and the resulting lens antenna
system can be very low profile and compact. Alternatively, another solution to achieve a compact lens antenna system is to design true-time-delay lenses with relatively large overall thickness.
164
Typically, in order to achieve smaller f /D ratios, lenses with more metal and dielectric layers are
needed. However, tradeoffs between the overall thickness of the lens, operation bandwidth, and
f /D ratio are always need to be made.
7.3 Design of harmonic-suppressed frequency selective surfaces for low-observable
applications
The majority part of this thesis is centered around miniaturized-element frequency selective
surfaces, ranging from their tunable versions in Chapter 3 to their high power versions in Chapter
4, as well as their application as time-delay units in true-time-delay lenses in Chapter 5 and 6.
In all of these FSS designs, no attention has been paid to their harmonics. Although the high
frequency harmonics typically will not impact the in-band performance of these FSSs, they could
become critically important in certain stealth applications. When used as a radome, the FSSs with
high frequency harmonics could potentially lead to a significant large RCS at high frequencies.
Therefore, suppressing the harmonics of an FSS is highly desired in many stealth environments. In
future studies, the cause of the harmonics of an FSS will be carefully examined, and the methods
and designs of suppressing these high frequency harmonics will be proposed and implemented.
165
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Appendix A: List of Acronyms
FSS: Frequency Selective Surface
MEFSS: Miniaturized-Element Frequency Selective Surface
HPM: High Power Microwave
TTD: True-Time-Delay
TDU: Time-Delay Unit
SPS: Spatial Phase Shifter
PSS: Phase Shifting Surface
CW: Continuous-Wave
MFEF: Maximum Field Enhancement Factor
PBC: Periodic Boundary Condition
DUT: Device Under Test
FOV: Field-of-View
f/D ratio: Focal Length to Aperture Diameter Ratio
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